You are given the line, y=-2x-5. This line is in slope-intercept form, y=mx+b, where m is the slope (or gradient) and b is the y-intercept.
The gradient of the given line is -2 and the y-intercept is -5.
9. unit 7 homework 5 solve for x. round to the nearest tenth
x
54
12
The angle x in a right-angled triangle is 12.8°.
What is a right-angled triangle?
A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those with angles at 90 degrees, which are referred to as right angles.
The diagram shows a right-angled triangle with opposite = 12 units and hypotenuse as 54 units.
To find the angle x, apply the formula -
sin(x) = opposite/hypotenuse
sin(x) = 12/54
x = sin^-1(12/54)
x = sin^-1(2/9)
x = 12.84°
Rounding it to nearest tenth gives x = 12.8°.
Therefore, the value of x is 12.8°.
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A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = equals 6 cosine (2,000 pi x) + 11, where x is time in minutes.
With the help of cosine function, the amount fan rotates each minute is 1000 times.
We can use the cosine function:
Y = a cos ( b c - x ) + d
Y = equals 6 cosine (2000 pi x) + 11
Where x is time in minutes.
To find the period (p):
P = 2 pi/b
P = 2 pi/ 2000 pi
P = 1/1,000
P = 0.001
To find the rotation per minute we can use:
Rpm = 1/p
Rpm = 1/0.001
Rpm = 1,000
As the result, the amount of rotation is 1,000 times per minute
Your question is incomplete, but most probably your full question was:
A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = Equals 6 cosine (2,000 pi x) + 11, where x is time in minutes.
How many times does the fan rotate each minute?
A 1,000
B 2,000
C 4,000
D 6,000
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An architect creates a drawing in which a rectangular desk is 11 inches long and 6 inches wide. The drawing is at a scale of 1 inch = 2 feet. what is the actual area, in square feet, off the desk
The actual area of the rectangular desk is 264 feet²
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Scaling is used to increase or decrease the size of a figure by a scale factor.
The drawing is at a scale of 1 inch = 2 feet.
11 inches = 11 inches * 2 feet per 1 inch = 22 feet
6 inches = 6 inches * 2 feet per 1 inch = 12 feet
Area of the desk = length * width = 22 feet * 12 feet = 264 feet²
The actual area is 264 feet²
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solana purchased 50 boxes of ceramic pottery and 40 boxes of plates on Monday.On Thursday she purchased 58 boxes of ceramic pottery and 46 boxes of plates. the weekly total was 108 boxes of ceramic pottery and 96 boxes of plates. Let c represent the number of ceramic pottery pieces in each box, and let p represent the number of handpainted plates in each box.
Write two equivalent expressions to show the total number of ceramic pottery pieces and handpainted plates that Solana bought.
Both expressions are equivalent
What is the expression in mathematics?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to a specific value or result. Expressions can be simple or complex, and they can be used to represent mathematical relationships or to perform calculations.
Let c represent the number of ceramic pottery pieces in each box, and let p represent the number of handpainted plates in each box.
To find the total number of ceramic pottery pieces that Solana bought, we can use the following expression:
c* (50 + 58) = c*108
This expression shows that the total number of ceramic pottery pieces is equal to the number of ceramic pottery pieces in each box multiplied by the total number of boxes of ceramic pottery that Solana bought.
Alternatively, we can use the following expression:
c50 + c58 = 108*c
This expression shows that the total number of ceramic pottery pieces is equal to the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Monday plus the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Thursday.
Similarly, to find the total number of handpainted plates that Solana bought, we can use the following expression:
p* (40 + 46) = p*86
This expression shows that the total number of handpainted plates is equal to the number of handpainted plates in each box multiplied by the total number of boxes of handpainted plates that Solana bought.
Alternatively, we can use the following expression:
p40 + p46 = 86*p
This expression shows that the total number of handpainted plates is equal to the product of the number of handpainted plates in each box and the number of boxes Solana bought on Monday plus the product of the number of handpainted plates in each box and the number of boxes Solana bought on Thursday.
Both expressions are equivalent, as they provide the same value for the total number of ceramic pottery pieces and handpainted plates that Solana bought.
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What is the motion of displacement?
Displacement is the change in the position of an object relative to a reference point over a period of time.
It is usually represented by a vector quantity and is measured in meters (m). The formula for displacement is displacement = final position - initial position. Mathematically, displacement is denoted by s and is equal to the final position (x2) minus the initial position (x1), or s = x2 - x1. As an example, if a person walks a path of length 10 meters, starting at the origin (x1 = 0) and ending at x2 = 10, then their displacement would be s = 10 - 0 = 10 meters. To calculate displacement, we need to know the initial and final positions of the object, and the direction in which it moves.For example, if an object moves from position 5 m to position 10 m, the displacement is 5 m. This can be calculated by subtracting the initial position (5 m) from the final position (10 m). The result is 5 m, which is the displacement of the object.
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How do you find the domain and range of a function in Class 12?
In Class 12, to find the domain and range of a function, you can use the following steps:
Domain: The domain of a function is the set of all input values for which the function is defined. To find the domain of a function, you need to look at the function and identify any values of x that would make the function output undefined. These values of x are not in the domain of the function.For example, if the function is f(x) = 1/x, the domain of the function is all real numbers except 0, because dividing by 0 is undefined. In this case, the domain of the function is (-∞,0) U (0,+∞)
Range: The range of a function is the set of all possible output values of the function. To find the range, you can look at the function and identify any restrictions on the output values.For example, if the function is f(x) = √x, the domain of the function is all non-negative real numbers, because √x is only defined for non-negative values of x. In this case, the range of the function is [0,+∞)
Note that some functions may have more complex expressions, in such cases, you may have to use algebraic methods to find the domain and range.
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Write an expression, in its simplest form, for the perimeter of this shape.
The diagram is not drawn to scale.
The expression that represents the perimeter of the triangle is 3x
How to determine the perimeter of the triangleFrom the question, we have the following parameters that can be used in our computation:
Side length = x
Triangle type = equilateral triangle
The perimeter of an equilateral triangle can be calculated as
P = 3 * side length
substitute the known values in the above equation, so, we have the following representation
P = 3 * x
So, we have
P =3x
Hence, the perimeter expression is 3x
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find the scale factor
Answer:
[tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Method 1To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.
[tex]\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}[/tex]
[tex]\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]
Therefore, the scale factor is 2/3.
Method 2To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
From inspection of the given diagram:
Q = (-3, 9)R = (3, 6)[tex]\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}[/tex]
[tex]\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}[/tex]
[tex]\implies QR=\sqrt{(6)^2+(-3)^2}[/tex]
[tex]\implies QR=\sqrt{36+9}[/tex]
[tex]\implies QR=\sqrt{45}[/tex]
[tex]\implies QR=3\sqrt{5}[/tex]
From inspection of the given diagram:
Q' = (-2, 6)R' = (2, 4)[tex]\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}[/tex]
[tex]\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}[/tex]
[tex]\implies Q'R'=\sqrt{(4)^2+(-2)^2}[/tex]
[tex]\implies Q'R'=\sqrt{16+4}[/tex]
[tex]\implies Q'R'=\sqrt{20}[/tex]
[tex]\implies Q'R'=2\sqrt{5}[/tex]
To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:
[tex]\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}[/tex]
Therefore, the scale factor is 2/3.
what is the Least common denominator of 7/10 and 1/15
Answer:
30
Step-by-step explanation:
10 = 2 × 5
15 = 3 × 5
LCD = 2 × 3 × 5 = 30
What is the principle of factorization Mcq?
Answer:
The principle of factorization is that every square matrix can be expressed as a product of a lower triangular matrix and upper triangular matrix. On the basis of this fact, these lower and upper triangular matrices help us in finding the unknowns.
Step-by-step explanation:
Hope it helps!
7over 5=n over 60 what is n ???
PLEASE HELP
Answer:
n= 84
Step-by-step explanation:
After setting each fraction to equal each other, cross multiply. Multiply 7 and 60, and multiply 5 and n.
You will get 60 x 7 = 5 x n
60 times 7 equals 420.
420=5n
Divide 5 from both sides to get n= 84.
4. Complete the table. (10 points: 1 point for each row)
a. Identify the actual number of sales at each price.
b. Use your line of best fit to calculate the predicted sales at each price. Round
the predicted sales to the nearest tenth.
c. Calculate the residuals at each price by subtracting predicted sales from actual
sales.
Price
1.5
1.6
1.8
2.0
2.1
2.2
2.5
2.7
2.9
3.0
Actual sales
96
94
91
85
83
79
73
70
64
63
Coffee:
Predicted sales
96
94
89
85
83
80
74
69
64
62
Residual I have to figure out the residual by subtracting the Actual sales by the predicted sales .but I need someone to help me put them back in the decimal form at first when they were first calculated
For this kind of issue, you can select any option and the procedure will remain the same. Let's choose coffee as the beverage to analyse for the purposes of this response.
What does a 0.5 Pearson correlation indicate?When a correlation coefficient's magnitude is between 0.5 and 0.7, it means that the variables are moderately correlated. Low correlation between the variables is indicated by correlation coefficients with magnitudes between 0.3 and 0.5.
In this equation, x stands for price, and y for sales.
-22.7x+130.3
The slope indicates the number of units that the sales would change by if we raised the price by one unit. Since our slope is -22.7, this indicates that a 1 unit price increase would result in a 22.7 decrease in sales.
The scatterplot's points are all intersected by the line of best fit, as can be seen. We can also calculate the Pearson correlation coefficient, which gives us -0.998, to add to the evidence. This suggests a very adverse relationship.
For this item we will just need the equation for the line of best fit and the data that has been given in the problem. For the actual sales, we will just refer to the given while we will compute for the predicted sales using the line of best fit.
PRICE ACTUAL SALES PREDICTED SALES
1.5 96 96
1.6 94 94
1.8 91 89
2.0 85 85
2.1 83 83
2.2 79 80
2.5 73 74
2.7 70 69
2.9 64 64
3.0 63 62
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Classifying Triangles Card Sort
The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.
Describe the triangle.A triangle is a polygon since it has three parts and three vertices. It is a basic geometric shape. A triangle with the corners A, B, & C is referred to as a triangle ABC. A singular plane & triangle in Geometric shapes are found so when three components are not collinear. Due to its right side and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations at which its three sides meet. 180 degrees is obtained by multiplying three triangle angles.
Here,
Given: Triangle STU is a right triangle in this instance.
Thus,
We learn:
parts s, t, and u
Their connection is as follows:
Given that it's a right triangle
So,
The Pythagoras Theorem states that
=>u²= t²+s²
The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.
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Please I need help!!
In the diagram DO and TO of rectangle OUTD are extended as shown.
Find the value of X
Show your work
Value of X is 8.
What is rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given,
Figure OUTD is a rectangle.
Each angle in a rectangle measures 90 degrees.
Therefore,
(7X + 2) + 4X = 90
7X + 2 + 4X = 90
11X + 2 = 90
Subtract 2 from both sides of the equation
11X = 88
Divide both sides of the equation by 11
X = 8.
Hence, 8 is the value of x.
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You have 47 total coins for a total of $9.95. You only have quarters and dimes. Choose the two equations that make up the system of equations that represents this situation.
One equation that represents the total value of the coins in cents is:
0.25x + 0.10y = 995
where x is the number of quarters and y is the number of dimes.
Another equation that represents the total number of coins is:
x + y = 47
These two equations make up a system of equations that can be used to find the number of quarters and dimes that add up to $9.95 and have a total of 47 coins.
Answer:
[tex]\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}[/tex]
Step-by-step explanation:
To solve this problem, we can create and solve a system of equations.
Define the variables:
Let x be the number of quarters.Let y be the number of dimes.Values of the coins:
The value of a quarter is $0.25.The value of a dime is $0.10.Given there are a total of 47 coins:
[tex]x+y=47[/tex]
Given there is a total of $9.95 in quarters and dimes:
[tex]0.25x+0.1y=9.95[/tex]
Therefore, the system of equations that represents the problem is:
[tex]\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}[/tex]
To solve the system of equations, rewrite the first equation to isolate y:
[tex]y=47-x[/tex]
Substitute this into the second equation to eliminate y:
[tex]0.25x+0.1(47-x)=9.95[/tex]
Solve the equation for x to find the number of quarters:
[tex]\begin{aligned}0.25x+0.1(47-x)&=9.95\\0.25x+4.7-0.1x&=9.95\\0.15x+4.7&=9.95\\0.15x&=5.25\\x&=35\end{aligned}[/tex]
Therefore, there are 35 quarters.
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}35+y&=47\\y&=12\end{aligned}[/tex]
Therefore, there are 12 dimes.
Please somebody help with this question!
According to angle symmetry, the value of x=125°
What is an example of an alternate angle?The two parallel lines intersected by a transversal form alternate angles. Consider the following figure, where EF and GH are two parallel lines. The transversal line RS intersects EF at L and GH at M. If a transversal cuts two parallel lines, the alternate angles are equal.
Since, AK and BL are parallel lines.
Hence,
∠ADC=∠BED=72°
∠EIH=∠DHG=55°
∠DHG+∠GHK=180°
∠GHK=180°-55°
∠GHK=125°=x
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Which value of X satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y
The value of X that satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y is X = -8/7.
What is an equation?An equation is a mathematical statement that shows that two mathematical algebraic expressions are equal. For example, x + 7 = 10 is an equation, in which x + 7 and 10 are two expressions separated by an 'equal to' sign.
An equation also has two sides, the let hand side and the right hand side.
Solving the two equations simultaneously we have:
-9x + 4y = 8 --- (1)
-3x - y = 4 --- (2)
Multiply 2 by 3 and subtract from (1) as shown below
-9x + 4y = 8
-9x - 3y = 12
------------------
0 + 7y = - 4
7y = -4
y = -4/7
Substituting the value of y in equation 2 we get the value of x.
-3x - (- 4/7) = 4
-3x + 4/7 = 4
-3x = 4 - 4/7
-3x = 24/7
x = -8/7
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3v-12=15
show work
check
Answer: 9
Step-by-step explanation:
Given equation is
3v-12 = 15
Now let's add 12 to both sides of the equation.
You'll get
3v = 27
Divide 3 from both sides, and you get
v = 9
Let's check.
Substitute 9 for v in the equation and you get
27 - 12 = 15
Which is true.
Final Answer: v=9
The solution to the given equation 3v - 12 = 15 is x = 9.
What is the solution to the equation?
A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
The equation is given in the question, as follows:
3v - 12 = 15
We have to determine the solution to the given equation.
As per the question, we have
3v - 12 = 15
Rearrange the terms in the above equation, and solve for v:
3v = 15 + 12
3v = 27
Divided by 3 into the above equation, we get
v = 27/3
v = 9
Thus, the solution to the given equation is x = 9.
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Write the solution to the system of equations as an ordered pair using decimals.
5x + 6y = 30
1.5x - 3y = 12
On solving the provided question we can say that the given equation yield solution as x=27.4 and y= -5/8.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
On solving simultaneously,
x=27.4
y= -5/8
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answer choices:
circle
ellipse or parabola
hyperbola
A-
B-
C-
a) Vertical plane not passing through the cone's topmost point - hyperbola.
b) Horizontal plane - circle.
c) Diagonal plane - ellipse or parabola
What is a cone?
A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the center of the base).
Cross section of a cone:
A cross section is a representation of a shape's axis of symmetry intersected by a plane. When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.
When a cone's cross-section is split horizontally, it is circular.
When a cone is cut vertically, its cross-section is an isosceles triangle, and this plane slices through the center of the cone.
When a cone is cut vertically, the cross-section is parabolic except for the plane running through the center.
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I need help pleaseee with work
Answer:
Step-by-step explanation: add i'll the sides togetheir
What will be the area of triangle if its length and breadth is 14cm and 7cm?
The area of the triangle would be 49 cm².
Area of a triangle = (length x breadth)/2
Area of the triangle = (14cm x 7cm)/2
Area of the triangle = (98cm)/2
Area of the triangle = 49 cm²
The area of a triangle can be calculated by using the formula (length x breadth)/2. In this scenario, the length and breadth of the triangle is 14cm and 7cm respectively. Therefore, the area of the triangle can be calculated by using the formula. The area of the triangle would be (14cm x 7cm)/2 = (98cm)/2 = 49 cm². Hence, the area of the triangle with the given length and breadth would be 49 cm².
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what kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?
In order to make the stream of water from a garden hose approximate a sine curve, the nozzle of the hose should be moved in an up-and-down motion.
The reason is because a sine curve is a smooth wave-like pattern that oscillates between positive and negative values. If the nozzle is moved up and down, it will cause the water to be released in a similar wave-like pattern, creating a stream that approximates a sine curve. This is due to the nozzle moving in a sinusoidal motion, which causes the water to be released in the same motion. This kind of motion is known as a harmonic motion, and it's the same motion that causes a wave to have a sinusoidal shape.
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use pascal’s triangle to expand (m+4)^4
Using Pascal's triangle we can find the binomial coefficient, by which we get 1m^4 + 16m^3 + 96m^2 + 128m + 256
What is pascal's triangle?Pascal's triangle is a triangular array of numbers in which each number is the sum of the two numbers directly above it. It is named after the French mathematician Blaise Pascal, who studied its properties in the 17th century. The rows of the triangle are numbered starting from 0, and the first number in row n is always 1. The other numbers in row n are the sum of the corresponding number in row n-1 and the number directly above it. The nth number in the kth row of Pascal's triangle is denoted by C(n,k) and it is called binomial coefficient, it is also denoted by nCk. It is used in many areas of mathematics, particularly in combinatorics and algebra, and it can be used to expand binomial expressions using the binomial theorem.
The binomial theorem states that for any non-negative integer n and any binomial expression (a+b)^n, the expansion is given by:
(a+b)^n = C(n,0)a^n*b^0 + C(n,1)a^(n-1)*b^1 + C(n,2)a^(n-2)b^2 + ... + C(n,n)a^0b^n
where C(n,k) = n!/(k!(n-k)!) is the binomial coefficient, which can be found using Pascal's triangle.
Using this theorem:
(m+4)^4 = C(4,0)m^44^0 + C(4,1)m^34^1 + C(4,2)m^24^2 + C(4,3)m^14^3 + C(4,4)m^0*4^4
Using Pascal's triangle we can find the binomial coefficient:
C(4,0)=1, C(4,1)=4, C(4,2)=6, C(4,3)=4, C(4,4)=1
So the expanded form of (m+4)^4 is:
1m^4 + 4m^34 + 6m^24^2 + 4m4^3 + 14^4
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40. The area of a square is 45 m², what is the measurement of its side? (no choices)
41.) What is the square root of -4? a. 2 b.-2 c.0 d.undefined
42.) Which of the following DOES NOT belong to the group?
a. (3/4)-2 b. 9/16 c. 16/9 D.9 m
43.) Evaluate 8x0.
a.0 b.1 c.8 d.x
44.) If y varies directly as x, and y is 15 when x-3, find y when x-5.
a. 25 b. 15 C.45 D.35
45. If N varies inversely as M, and N=5 when M-3, find N when M=10.
a. 3/2 b. 15 c. 5/3 d. 5
46.)If y varies jointly as x ad z, and y-6 when x-10 and z-8, find y when x-4 and 2-40. a. 12 b. 10 c. 8 d. 16
47.) If z varies directly as x and inversely as y, and z-9 when x-6 and y=2, find z when x=8 and y=12. a. 2 b. 4 c. 6 d. 16
48. If 3 men can do a portion of a job in 8 days, how many men can do the same job in 6 days? a. 7 b. 6 c. 5 d. 4
49.) Jordan's income varies directly as the number of days that he works. If he earns 8,000 pesos in 20 days, how much will he earn if he worked 3 times long? a. 26,000 b. 24,000 c. 20,000 c. 16,000
50.) The amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed. Suppose a car used 25 litres on a 100 km trip at 100 kph, about how many litres will be use on a 1000 km trip at 64 kph? a. 100 L b. 200 L c. 300 L c. 400 L
The solutions to the different sides and values of square are given below. The length of the side of the square is 6.71m.
What is a square?Square is a polygon which four equal sides and all angles are right- angles.
Given area of square = 45 m²
Area = side²
Side = √Area = √45 = 6.71 m
Therefore side of the square is 6.71m.
41) Negative numbers do not have square roots.
Therefore √-4 is undefined.
42) Option D is correct as it is not a fraction.
43) Any number multiplied by zero is zero.
Therefore (a) is the correct option.
44) When y = 15, x = 3
For direct variation, y =kx
so k = y/x =15/3 = 5
When x=5, y = kx =5*5 = 25
Therefore (a) is correct.
45) For inverse variation
MN = k
Given 5*3 = k
k=15
When M = 10 , N = k/M = 15 /10 = 3/2
Therefore option a is correct.
48) Let the amount of work be W
For 3 men,
8 days = W
1 day = W/8
Now work done by 1 man in one day = (W/8) /3 =W/24
In six days, work done by one man = W/24 * 6 = W/4
Therefore for the work to be completed, the number of men required is 4 (W/4 *4 = W).
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The first term of a sequence is 4.
1. Choose a growth factor and list the next 3 terms of a geometric sequence.
2. Choose a different growth factor and list the next 3 terms of a geometric sequence.
1. The sequence is 2, 8, 16, 32.
2. The sequence is 4, 16, 64, 256.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
For example, 3, 7, 11, 15, ... is a sequence as there is a pattern where each term is obtained by adding 4 to its previous term.
Given:
The first term of a sequence is 4.
1. let the common ratio 2.
Then, second term= 4 x 2= 8
third term = 8 x2 =16
fourth term = 16 x 2= 32
So, the sequence is 2, 8, 16, 32..
2. let the common ratio 4.
Then, second term= 4 x 4 = 16
third term = 16 x 4 = 64
fourth term = 64 x 4 = 256
So, the sequence is 4, 16, 64, 256.
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Use the explicit rule given to write the first three terms for each sequence. F(n)=16+(1/2)(n-1)
From the explicit rule the first three terms of sequence is 16, 16.5, 17.
What is the explicit rule?The explicit formulae for L-functions are relationships introduced by Riemann for the Riemann zeta function between the sums over complex number zeroes of an L-function and sums over prime powers.The difference between each consecutive term in an arithmetic sequence is constant. An explicit formula for an arithmetic sequence is a = d (n - 1) + c, where d is the common difference between consecutive terms and c = a1.Here given,
F(n) = 16+(1/2)(n-1)
We have to find first three terms.
F(1) = 16 + (1/2)(1-1)
= 16 + 1/2 x 0
= 16
F(2) = 16 + (1/2) (2-1)
= 16 + 1/2
= 16 + 0.5
= 16.5
F(3) = 16 + (1/2) (3-1)
= 16 + 1/2 x 2
= 16 + 1
= 17
So the first three terms in the sequence is 16, 16.5, 17 with common difference of .05.
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5. You overhear a friend discuss how Americans are frivolous in their spending and waste lots of
money. Use this data on family budgets to argue against his position.
The statement if False.
What is the family budget?A family budget is a game plan for your family's money. Your plan identifies where and how your money comes and goes by focusing on income and expenses. Importantly, it also reflects your family's goals and values by how you spend and save.
Given statement,
You overhear a friend discuss how Americans are frivolous in their spending and waste lots of money.
The most expensive items in American spending are needs like housing, taxes, and transportation, while wants like wants are the least expensive.
In America, besides taxes three largest cost categories are households, transportation and food.
A family's transportation costs are $1,847 more than its food expenses.
Typically, needs make up 80% of expenses rather than wants.
Housing, fees, and medical expenses, continuing to be the same each month. The cost of clothing, entertainment, food, and transportation changes every month.
Hence, we can conclude that, Americans don't necessarily waste money on wants because they have to spend on needs before wants, which results in a lot of spending on things like housing and taxes.
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Two angles are complementary. The measure of
one angle is 125% of the other. Find the
measures of both angles.
Answer:
2
Step-by-step explanation:
what is the slope of 9/10x + 3/10
Answer:
3/10(3x+1)
Step-by-step explanation: