Answers
Answer:
y = -6
Step-by-step explanation:
We know the formula for slope is:
m = ( y2-y1)/(x2-x1)
We are given the two points using a variable and the slope.
-8 = (2-y)/(3-4)
-8 = (2-y)/(-1)
Multiply each side by -1.
8 = 2-y
Subtract 2 from each side.
8-2 = 2-y-2
6 = -y
Multiply by -1.
-6 =y
Answer:
y = -6
Step-by-step explanation:
The formula to find the slope is:
[tex]m = \frac{y_1 - y_2}{x_1-x_2}[/tex]
Given that,
( 4, y ) ⇒ ( x₁ , y₁ )
( 3, 2 ) ⇒ ( x₂ , y₂ )
m ( slope ) = -8
Accordingly, we have to find the value of y₁.
Let us find it now by making y₁ the subject.
[tex]\sf m = \frac{y_1 - y_2}{x_1-x_2} \\\\-8 = \frac{y_1 - 2}{4-3}\\\\-8 = \frac{y_1 - 2}{1}\\\\Multiply\:\:Both\:\:sides\:\:by\:\:1.\\\\-8=y_1-2\\\\Add \:\:2\:\:to\:\:both\:\:sides.\\\\-8+2=y_1\\\\-6=y_1=y[/tex]
Related Questions
The quadrilateral ABCD on the coordinate plane has the following characteristics. Line segment A. D. Can be represented by the equation Y equals minus 3X where -1 is less than or equal to X less than or equal to zero. Line segment BC can be represented by the equation Y equals negative 3X +11 where to is less than or equal to X less than or equal to three. Lines CD has coordinates C(2,5) and D (-1,3). In order for ABC D to be a parallelogram with the following coordinates correspondent line segment AB ?
Answers
The equation of line segment AB is y = 3.5x - 0.5.
Line segment AB starts at point A(-1, -3) and ends at point B(3, 11). The equation for this line can be found by calculating the slope and then using the point slope formula, y-y1=m(x-x1).
The slope of the line is m= (11-(-3)) / (3-(-1)) = 14/4 = 3.5.
Using the point-slope formula, we can find the equation of the line:
y-(-3) = 3.5(x-(-1))
y + 3 = 3.5x + 3.5
y = 3.5x - 0.5
Therefore, the equation of line segment AB is y = 3.5x - 0.5.
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What is the seven-sided shape called?
Answers
A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.
Define polygon?In geometry, a polygon is any closed curve made up of a series of line segments (sides) that are connected in such a way that no two segments cross. Triangles (with three sides), quadrilaterals (with four sides), and pentagons are the simplest polygons (five sides).A polygon is a closed two-dimensional shape with three or more sides. Polygons include triangles, squares, and more complicated shapes such as a twelve-sided dodecagon.A polygon is a plane figure defined by a finite number of straight line segments connected to form a closed polygonal chain in geometry. A polygon is a bounded plane region, a bounding circuit, or the two together. A polygonal circuit's segments are referred to as its edges or sides.To learn more about polygon refer to:
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In the diagram below of triangle IJK, L is the midpoint of IK and M is the
midpoint of JK.If LM = 4x+8, and IJ = 5x + 22, what is the measure of
LM?
Answers
On solving the provided question, we can say that in the triangle LM = 2*(IJ) x = |-6| = 6 and LM = 4x + 8 = 32 units
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given,
LM = 4x + 8 and IJ = 5x +22
in the triangle LM = 2*(IJ)
4x + 8 = 2*(5x + 22)
4x + 8 = 10x + 44
6x + 36
x = |-6| = 6
LM = 4x + 8 = 32 units
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building is 120 meters tall. A scale model of the building uses a scale of 1 entimeter = 6 meters. How tall is the model?
Answers
Answer:
The answer is 20 cm.
Step-by-step explanation:
From the scale, we know that 1 cm in the model represents 6 meters in the actual building.
So, h cm in the model represents 6h meters in the actual building.
The actual building is 120 meters tall, so 6h = 120 meters.
Dividing both sides by 6, we get:
h = 20 cm.
Therefore, the height of the model is 20 cm.
5.what are the valúes of x and y? (1 point)
Answers
Answer:
Below
Step-by-step explanation:
First find the value of the common vertical side
12/v = v/16
v^2 = 192
v = 8 sqrt 3
Now use pyhtag theorem to find x and y
y^2 = 12 ^2 + (8 sqrt3)^2
y = sqrt (336) = 4 sqrt (21)
now find x the same way
x^2 = 16^2 + (8 sqrt(3))^2 = 448
x = sqrt (448 ) = 8 sqrt 7
Which congruence transformation follows the rule (x,y) --> (-x,y)
Answers
Answer:
Congruence D transformation follows the rule (x,y)--> (-x,y)
Which type of triangle is ABC?
A) right
b) scalene
c)isosceles
d) equilateral
Answers
An equilateral triangle is one that has equal angles.
two trains start from towns 495 mi apart and travel toward each other on parallel tracks. they pass each other 4.5 hours later. if one train travels 10 mph faster than the other, find the rate of each train.
Answers
The faster train would be travelling at 120 mph.
Let's give the slower train's speed the designation of x mph. The speed of the speedier train would then be x + 10 mph.
The 4.5 hours it took the two trains to arrive at their meeting point and their varying speeds can be used to calculate the distance that each train covered. The relative speed is equal to the product of the velocities of the two trains,
Therefore (x) + (x + 10) = 2x + 10 mph.
Distance = rate x time gives the distance covered by each train.
The slower train's route can be expressed as follows:
x * 4.5 hours = 495 miles.
Additionally, the quicker train covered 495 miles in (x + 10) * 4.5 hours.
We can now use these two equations to solve for x:
x * 4.5 = 495
x = 110 mph
And, the faster train would be traveling at 110 + 10 = 120 mph.
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What are the multiplication and division properties of equality?
Answers
Multiplication and division properties of equality are stated below.
What is Multiplication and Division?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Multiplication property of equality states that if a real number has been multiplied with the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is, if x = y, then ax = ay, where a is a real number.
Division property of equality states that if a real number has been divided by the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is if x = y, then x/a = y/a.
Hence the multiplication and division property of equality has been stated.
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Given two systems of equations, determine if they have the same solution.
System A System B
−12x+9y=7 −12x+9y=7
9x−12y=6 −9x+5y=9
1. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 3
and adding to the first equation in system A
2. No, they don't have the same solution.
3. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.
4. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3
and subtracting from the first equation in system A.
Answers
No, they don't have the same solution. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
−12x + 9y = 7 ...1
9x − 12y = 6 ...2
From equations 1 and 2, then we have
−36x + 27y = 21 ...3
36x − 48y = 24 ...4
Add both equations, then we have
27y − 48y = 21 + 24
− 21y = 45
y = − 45/21
y = − 15/7
Then the value of the variable 'x' is given as,
9x − 12(−15/7) = 6
9x + 180/7 = 6
9x = −138/7
x = −46/21
No, they don't have the same solution. Then the correct option is B.
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A list of terms follows. For each term: (i) State whether the term is a variable name or a variable value. (ii) State the level of measurement. Example: support for same-sex marriage. (i) variable name. (ii) ordinal.A. ageB. conservativeC. strongly opposeD. regionE. 57 yearsF. strictly enforcedG. CatholicH. gender
Answers
(i) State whether the term is a variable name or a variable value.
(ii) State the level of measurement.
A. age
(i) Variable name.
(ii) Ratio.
Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).
B. conservative
(i) Variable name.
(ii) Nominal.
Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.
C. strongly oppose
(i) Variable value.
(ii) Ordinal.
Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).
D. region
(i) Variable name.
(ii) Nominal.
Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.
E. 57 years
(i) Variable value.
(ii) Ratio.
Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).
F. strictly enforced
(i) Variable value.
(ii) Ordinal.
Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).
G. Catholic
(i) Variable name.
(ii) Nominal.
Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.
H. Gender
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Help me please
Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
Answers
The values of x and y are 15 and 7 respectively.
What are Similar Triangles?Similar triangles are those triangles which has the same shape but different size.
The length of sides are proportional in similar triangles.
Two sails are similar triangles.
So the angles of two sails are equal and the corresponding sides are proportional.
We can write the relation as,
x / 30 = x- 2 / 26 = y + 9 / 5y - 3
Consider x / 30 = x- 2 / 26.
Cross multiplying,
26x = 30(x - 2)
26x = 30x - 60
-4x = -60
x = 15
Consider x / 30 = y + 9 / 5y - 3.
Substituting x = 15,
15 / 30 = y + 9 / 5y - 3
1 / 2 = y + 9 / 5y - 3
Cross multiplying,
5y - 3 = 2y + 18
3y = 21
y = 7
Unknown sides are,
x = 15 feet
x - 2 = 13 feet
y + 9 = 16 feet
5y - 3 = 32 feet
Hence the value of x is 15 and the value of y is 7.
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Suppose that the annual amount of rainfall (in million tons) accumulated in a lake follows a gamma distribution with alpha = 3 and gamma = 5.
a) Find the expected annual rainfall accumulated in this lake.
b) Find the standard deviation of the annual amount of rainfall in this lake.
c) Find P(X < 4), use R.
d) Find P(2 < X < 5), use R
Answers
a) The expected annual rainfall accumulated in this lake is 30 million tons. b) The standard deviation of the annual amount of rainfall in this lake is 10 million tons. c) P(X < 4) = 0.3085. d) P(2 < X < 5) = 0.4293.
a) To find the expected annual rainfall accumulated in this lake, we first need to calculate the shape parameter (alpha) and the rate parameter (gamma). alpha = 3 and gamma = 5. Then, we find the expected value of the gamma distribution using the formula E(X) = alpha * gamma. This gives us E(X) = 3 * 5 = 15. Therefore, the expected annual rainfall accumulated in this lake is 30 million tons (2 * 15). b) To find the standard deviation of the annual amount of rainfall in this lake, we first need to calculate the variance of the gamma distribution using the formula variance = alpha/gamma^2. This gives us variance = 3/25 = 0.12. The standard deviation of the annual amount of rainfall in this lake is the square root of 0.12, which is 0.346. This is equivalent to 10 million tons (2 * 0.346). c) To find P(X < 4), we can use the R programming language. In R, we can use the pgamma() function to calculate the cumulative probability of a gamma distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the value 4. This gives us P(X < 4) = 0.3085. d) To find P(2 < X < 5), we can use the R programming language. In R, we can use the pnorm() function to calculate the cumulative probability of a normal distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the values 2 and 5. This gives us P(2 < X < 5) = 0.4293.
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Yoooo please help meeeeeee tyyyyyyyyy ik its easy but I’m just not smart
Answers
Answer:
Step-by-step explanation:
The answer will be 24 because the LCM ( Lowest common Multiple)
of 3 and 8 is 24.
Answer:
24
Step-by-step explanation:
3 x 8 = 24
what+is+the+value+of+a+bond+with+a+coupon+rate+of+8%,+a+par+value+of+$1,000,+maturing+in+8+years,+making+semi-annual+payments,+if+the+appropriate+discount+rate+is+6%+per+year?
Answers
The value of the bond if the rate of interest currently is 6% the value of the bond is Rs. 1,000 and if it is 8% it is 750
Now, According to the question:
A bond is a sort of financial instrument where the issuer (debtor) owes the holder (creditor) a debt and is required, based on the terms, to pay the creditor cash flow at the bond's maturity date as well as interest over a certain period of time. The interest is often due annually, semi-annually, and on occasion less frequently. Bonds give the borrower access to external capital for momentary investments or, in the case of government bonds, for the financing of ongoing expenses. Despite the fact that both bonds and stocks are securities, bondholders hold a position as a creditor and stockholders hold equity in a firm. The main distinction between the two is this.
Value of the bond= V = 1/I = 60/.08 = 750
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Perform the calculation and round the answer to the correct number of significant figures. 19.948 - 8.57 =
Answers
Answer:
11.4
Step-by-step explanation:
19.948-8.57=11.378
approximately 11.4
The correct number of significant figures is found as 1.1378 x 10⁻¹ .
Define the term significant figures?To demonstrate the accuracy of measurements and calculations in the fields of math, chemistry, and other sciences, significant figures are essential.
The following five rules can be used to assess whether a number is significant.
All non-zero digits, from 1 to 9, have meaning.Between nonzero numbers, all zeros have meaning.Zeros that come before or on the left of a non-zero digit have no meaning. These zeros are only stand-ins.When there is a decimal point, zeros following a nonzero digit are important.When there is no decimal point, zeros that follow a nonzero digit are not meaningful.The equation is given as:
= 19.948 - 8.57
On subtracting.
= 11.378
On converting in the significant figures:
= 1.1378 x 10⁻¹
Thus, the correct number of significant figures is found as 1.1378 x 10⁻¹ .
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After school, Terrell skateboards directly from school to a skate park and then from the skate park to a movie theater. The skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park. What is the straight-line distance between the school and the movie theater?
Answers
We can use the Pythagorean theorem to find the straight-line distance between the school and the movie theater. Let's call the straight-line distance "d".
d^2 = 8^2 + 6^2 = 64 + 36 = 100
d = sqrt(100) = 10
So the straight-line distance between the school and the movie theater is 10 miles.
Let's call the straight-line distance between the school and the movie theater d. Then, we can represent the trip as a right triangle with sides 8 miles (the southward distance to the skate park) and d (the eastward distance from the skate park to the movie theater). The third side, connecting the school and the movie theater, has a length of 6 miles (the distance between the skate park and the movie theater).
Using the Pythagorean theorem, we can write the equation:
d^2 + 8^2 = 6^2
Expanding and solving for d, we get:
d^2 + 64 = 36
d^2 = 36 - 64
d^2 = -28
d = sqrt(-28)
Since the square root of a negative number is not a real number, this solution is not possible. This means that the path from the school to the movie theater cannot be a straight line. Terrell would have to take a curved path or a path with multiple turns to reach the movie theater
This stuff is so confusing please help
Answers
The measure of angle D of the isosceles triangle given above would be = 16°
What is an isosceles triangle?An isosceles triangle is defined as the type of triangle that has all its three sides less than an acute angle, that is less that angle 90°. Also, all the internal angles of an isosceles triangle= 180°
Total internal angles of the isosceles triangle = 180°
Angle C = 2x + 17
Angle E = 8x - 13
Angle D = X
To calculate D the following is carried out:
180 = 2x+ 17 + 8x - 13 + X
180-17+13 = 2x+8x+X
176 = 11x
X = 176/11
X=16°
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80. Rochester, New York (43. 2°N, 77. 6°W). And Richmond.
Virginia (37. 5°N, 77. 5°W), have approximately the same
longitude, which means that they are roughly due north-
south of each other. Use the difference in latitude to
approximate the distance between the cities.
Answers
The approximate latitudinal distance of cities Rochester and Richmond is 394 miles
Let us assume the angle between the 2 cities as θ
θ = 43.2° - 37.6°
=5.7°
hence for finding the latitudinal distance between the cities (given that the Earth is approximately spherical) we can use the formula
distance= [tex]\frac{\theta}{360} *2\pi r[/tex]
= [tex]\frac{5.7}{360} *2 (3.14)(3960)[/tex]
= 393.756 miles ≈394 miles
therefore the distance comes out to be 394 miles
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15 is what percent of 40
Answers
The correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The algebraic representation of the statement 15 is what percent of 40 is:
40 (x/100) = 15
40x / 100 = 15
40x = 1500
x = 1500/40
x = 37.5
Hence, the correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.
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In the Walking Dead, the number of zombies doubles every episode. If, in episode 1, there were 75 zombies, how many zombies are in episode 16??
Please help ;-;
Answers
There are 4915200 zombies in the episode 16.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
In the Walking Dead, the number of zombies doubles every episode.
In the episode 1,
there were 75 zombies.
Then,
y = 75(2)¹⁶
y = 4915200
Therefore, 4915200 zombies.
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Question 1 Multiple Choice Worth 5 points) (06.01 LC) Segment AB has point A located at (5, 4). If the distance from A to B is 7 units, which of the following could be used to calculate the coordinates for point B?
a. 7 = √(x-4)^2 + (y+5)^2
b. 7 = √(x+5)^2 + (y+4)^2
c. 7 = √(x-4)^2 + (y-5)^2
d. 7 = √(x-5)^2 + (y-4)^2
Answers
To calculate the coordinates of B, we use 7 = √(x-4)^2 + (y-5)^2
What is Pythagoras Theorem?Pythagoras Theorem states that "In a right- angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".
The sides of this triangle have been named Perpendicular, Base and Hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Given:
To calculate the coordinates for point B, we can use the Pythagorean Theorem.
In this case, we are given point A located at (5, 4).
We also know that the distance from A to B is 7 units.
We can represent this as a right triangle, with point A being one of the legs and the distance of 7 units being the hypotenuse.
Now, using the Pythagorean Theorem, we can calculate the coordinates for point B.
Let consider the coordinates of B (x, y)
The distance between A and B be 7 units. So, we use distance formula,
7 = [tex]\sqrt{ (x - 4)^{2} + (y - 5)^{2}[/tex]
We can do this by setting up the equation 7 = [tex]\sqrt{ (x-4)^2 + (y-5)^2 }[/tex]and then solving for x and y.
To solve for x, we can start by subtracting 4 from both sides of the equation, giving us 3 = [tex]\sqrt{x^2 + (y-5)^2}[/tex]. Now,
we can take the square root of both sides to get x = √3.
Similarly, to solve for y, we can start by subtracting 5 from both sides of the equation,
giving us 2 = [tex]\sqrt{(x-4)^2 + y^2}[/tex]. Now, we can take the square root of both sides to get y = √2.
Therefore, the coordinates for point B are (√3, √2).
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Refer to the T-account below:
Manufacturing Overhead
(2)
4,000
(9)
150,000
(3)
15,000
(4)
80,000
(5)
30,000
(6)
25,000
154,000
150,000
Bal.
4,000
Entry (4) could represent which of the following except?
A) Indirect labor cost incurred.
B) Factory insurance cost.
C) Overhead cost applied to Work in Process.
D) Depreciation on factory equipment.
Answers
Overhead cost applied to Work in Process. and hence Option (c) is correct for the production
Refer to the T-account below:
Manufacturing Overhead
(2)
4,000
(9)
150,000
(3)
15,000
(4)
80,000
(5)
30,000
(6)
25,000
154,000
150,000
Bal.
4,000
Labor costs = $175,000
Production order = $150,000
General factory use = $25,000
Factory overhead applied to production = $23,000
Therefore, the journal entry is as follows:
Work in process A/c Dr. $23,000
To Factory overhead $23,000
(To record the factory overhead applied to production
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whats the original price if the sale price is 72 with a 64 disscount
Answers
If the sale price is 72 with a 64% discount. Then the original price will be $200.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If the sale price is 72 with a 64% discount. Then the original price is given as,
⇒ $72 / (1 - 0.64)
⇒ $72 / 0.36
⇒ $200
If the sale price is 72 with a 64% discount. Then the original price will be $200.
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Maggie has decided to collect Hot Wheel cars. She is allowed to buy 15 cars a week with her allowance and she currently has 2 cars in her room. Identify
the rate of change, the initial value and write the function that best models the situation.
O Rate of Change: 2; Initial Value: 15; y = 2 + 15x
O Rate of Change: 2; Initial Value: 15; y = 2x + 15
O Rate of Change: 15; Initial Value: 2; y = 2x + 15
O Rate of Change: 15, Initial Value: 2; y = 15x + 2
Answers
Maggie's rate of change for her car is 15; her initial value is 2; and the best function to model her situatioon is y = 2 + 15x (D).
Based on the given case, we know that:
"Maggie can buy 15 cars per week with her allowance."This statement gives information about Maggie's rate of change, showing how many cars Maggie can buy per week.
"She currently has 2 cars in her room."This statement shows that currently, she already has 2 cars. 2 cars are her initial value.
This situation represents that, Maggie might buy 15 cars every week as an additional to her current 2 cars. This situation can be formulated as:
y = 15x + 2
where:
y = total cars
x = number of weeks
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What is 100 °F in °C?
Answers
The conversion factor from Celsius to Fahrenheit is 37.78.
How can you quickly translate F to C?We employ conversion formulae that are similar to those found in most textbooks. Add 32 and multiply by.5556 (or 5/9) to convert temperatures from degrees Fahrenheit to degrees Celsius. Add 32 and multiply by 1.8 (or 9/5) to convert temperatures from degrees Celsius to Fahrenheit.Let's take a closer look at how to convert between Celsius and Fahrenheit scales. Explanation: °F = °C (9/5) + 32 is the conversion formula from Celsius to Fahrenheit.The conversion factor from Celsius to Fahrenheit is 37.78. Let's take a closer look at how to convert between Celsius and Fahrenheit scales.To learn more about Fahrenheit refer to:
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Ten less than twice a number is equal to at most 52. What are all the possible values of the number? Inuk wrote the inequality 2x−10≤52, where x equals the number, to help solve this problem. Solve his inequality. Use the letter x as your variable and write your x term first.
Answers
The all possible values of x in the given inequality are all the numbers less than or equal to 31.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Ten less than twice a number is equal to at most 52.
The linear inequality representing this is,
2x − 10 ≤ 52
Adding both sides with 10,
2x ≤ 62
Dividing both sides by 2,
x ≤ 62 / 2
x ≤ 31
Hence all the numbers less than or equal to 31 satisfy the given equation.
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Your local pizza parlor has four (4) sizes of crust (personal, medium, large, and family), two (2) types of crust (New York thin and Chicago deep dish), seven (7) toppings from which to select (pepperoni, sausage, chicken, bacon, tofu, mushroom, and spinach), and three (3) shakables (Parmesan cheese, red pepper flake, and butter flavor). How many different pizza pies consisting of any two servings of toppings, any one size of pizza, any type of crust, and any of the shak- ables (0, 1, 2, or all 3) could you order if you have no say in how the toppings are placed on the pizza (that is, a small deep-dish pepper-oni and mushroom with red pepper flake is the same as a small deep-dish mushroom and pepperoni with red pepper flake)?
Answers
The total number of different pizzas you can order is 8 x 21 x 4 = 672.
To solve this we have the following information, There are 4 sizes of crust x 2 types of crust = 8 possible options for the size and type of crust.
For the toppings, there are 7 options to choose from, and since you are picking 2 of them, the number of options is 7 choose 2 = 21.
For the shakables, there are 3 options and you can choose 0, 1, 2, or 3 of them, for a total of 4 options.
So the total number of different pizzas you can order is 8 x 21 x 4 = 672.
Therefore, The total number of different pizzas you can order is 672.
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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 15\le x \le 3015≤x≤30.
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The average rate of change over the interval 15 ≤ x ≤ 30 is equal to -6/5.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [15, 30]:
a = 15; f(a) = 40
b = 30; f(b) = 22
For the average rate of change over the interval 15 ≤ x ≤ 30, we have the following:
Average rate of change = [f(b) - f(a)]/(b - a)
Average rate of change = [22 - 40]/(30 - 15)
Average rate of change = -18/15
Average rate of change = -6/5
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at the start of 2014 lucy's house was worth £200000 the value of the house increased by 5% every year. work out the value of her house at the start of 2017
Answers
You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.
200,000 x 5/100 = 10,000
Therefore by 2015 the house's value was= 200,000 + 10,000= 210,000
however, you cannot keep adding 10,000 thrice over to find the value of the house for the year 2017 as the amount the value increases by each year will change as it is a percentage difference
value for 2016,
210,000x5/100=10,500
Therefore by 2016 the house's value was= 210,000 + 10,500= 220,500
value for 2017,
220,500x5/100=11,025
Therefore by 2017 the house's value was= 220,500 + 11,025= 231,525gbp
Answer:
You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.
200,000 x 5/100 = 10,000
200,000+10,000+10,000+10,000=231510
Amount it has increased: 11,025
Step-by-step explanation: