[tex](69)(5.6\times 10^{5})\implies (69)(560000)\implies 3\underset{\leftarrow 7\to }{\underline{8640000}}\implies 3.864\times 10^{7}[/tex]
The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is 132 centimeters, find the value of the shortest of the four side lengths.
The value of the shortest of the four side lengths of the quadrilateral is 30 cm
What is the length of the shortest side of the quadrilateral?The perimeter of a quadrilateral is the sum of all the sides.
Perimeter of the Quadrilateral = 132 centimeters
Let
The shortest side = x
Since, the sides are consecutive even integers;
Second side = (x + 2)
Third side = (x + 4)
Fourth side = (x + 6)
Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side
132 = x + (x + 2) + (x + 4) + (x + 6)
132 = x + x + 2 + x + 4 + x + 6
132 = 4x + 12
132 - 12 = 4x
120 = 4x
divide both sides by 4
x = 120/4
x = 30 centimeters
Therefore,
Second side = (x + 2)
= 30 + 2
= 32 cm
Third side = (x + 4)
= 30 + 4
= 34 cm
Fourth side = (x + 6)
= 30 + 6
=36 cm
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A dishwasher at a restaurant washes 9 forks. These forks represent 4% of the forks owned by the restaurant. How many forks does the restaurant own?
Answer:
The restaurant owns 225 forks
Step-by-step explanation:
We can get our answer by displaying as an equality
9 to 4/100
x to 100/100
You can multiply 4 by 25 to get 100 so to get the amount of forks, multiply 9 by 25
9 * 25 = 225
Answer:
225 forks
Step-by-step explanation:
9 to 4/100
x to 100/100
Multiply 4 by 25 to get 100 so to get the number of forks, multiply 9 by 25!
9 * 25 = 225
Hope this helps.
A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophomore, junior, and senior classes to complete the survey. This plan is an example of which type of sampling
This method is used when the population has distinct subgroups.
The plan to conduct a survey by randomly selecting 20 students from each of the freshman, sophomore, junior, and senior classes is an example of stratified random sampling.
In stratified random sampling, the population is first divided into subgroups or strata based on some characteristic, such as class level (freshman, sophomore, junior, senior), and a random sample is then selected from each stratum.
This method is used when the population has distinct subgroups and it is important to ensure that the sample is representative of each subgroup. In this case, by taking random samples of 20 students from each class level, the statistics class can ensure that the survey results accurately reflect the views of each class level and not just one particular group.
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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
The required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
The figure of the triangle is not given the quesiton, An figure is attached after the solution regarding the solution,
From diagram,
Consider the triangle RST and triangle VUT
ST/UT = 2
∠S = ∠U both are of 90°
RS/VU = 2.
So, triangles are similar by the SAS similarity theorem.
Thus, the required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.
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. Which of the following is the graph of the equation y = 2x + 3?
Answer:
The graph of the equation y = 2x + 3 is a straight line that passes through the point (0,3) and has a slope of 2.
It can be represented as a set of points in a coordinate plane. The slope of the line is 2, so for every unit increase in x (horizontal coordinate), y (vertical coordinate) increases by 2 units. The y-intercept of the line is 3, so when x is 0, y equals 3.
A line passing through (0,3) with a slope 2 can be represented as (x, 2x + 3)
It is important to note that an equation in the form of y = mx + c, with m being the slope and c being the y-intercept, always represents a straight line in a coordinate plane.
Step-by-step explanation:
(i) change 234mm into m
(ii) change 876m^2 into square cm
Answer: (i) 0.234m
(ii) 8760000cm^2
Step-by-step explanation:
234÷1000=0.2234m
876x10^4=8760000cm^
The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =
Answer:
x = 10
Step-by-step explanation:
the legs of an isosceles triangle are congruent.
the perimeter is the sum of the 3 sides of the triangle
sum the 3 sides and equate to 106
x + 5x - 2 + 5x - 2 = 106
11x - 4 = 106 ( add 4 to both sides )
11x = 110 ( divide both sides by 11 )
x = 10
Target offers a discount if you spend at least $50. Write an inequality to represent d, how much you must spend to receive the discount.
Answer:
d ≥ 50
Step-by-step explanation:
To receive the discount, you must spend at least $50, which can be represented by the inequality d ≥ 50. This inequality means that the amount you must spend (d) is greater than or equal to $50. If you spend more than $50, you will receive the discount. If you spend less than $50, you will not receive the discount.
Is the area of an equilateral triangle is 196 root 3 cm square then each of its side is?
Therefore , In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.
What is triangle?
Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.
What is polygons ?A polygon is a closed two-dimensional geometric shape that has three or more straight sides. The sides of a polygon are called edges and the points where the edges meet are called vertices.
Here,
We must apply the mathematical procedure for computing an equilateral triangle's area.
An equilateral triangle's area is equal to 3/4 of each side; assume that each side is x cm long.
[3/4 (a)2] cm2 is the equilateral triangle's surface area.
In light of the information mentioned in the query,
√3/4 × (a)² = 196√3
a²/4 = 196√3/√3
a²/4 = 196
a² = 196×4
a² = 784
a = √784
a = 28
In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.
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An online furniture store sells chairs for $200 each and tables for $450 each. Every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $4800 worth of chairs and tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution. Inequality 1
Using the provided values and the conditions, The inequality equations required are : [tex]x+y \leq 20[/tex] and [tex]450x+200y \geq 4800[/tex].
What do you mean by equation?An equation is a mathematical statement in which two expressions are set equal to each other. It is typically written using an "=" sign, with the expressions on either side of the sign representing equivalent values. For example, the equation 2 + 2 = 4 states that the value of 2 plus 2 is equal to the value of 4. Equations can be used to express relationships and to solve problems.
What are inequalities?An inequality is a mathematical statement that compares two values or expressions. It is similar to an equation, but instead of using the "=" sign to indicate that the two sides are equal, it uses one of the following symbols: ">", "<", "≥", "≤" to indicate that the two sides are not equal. For example, the inequality 2 + 2 > 4 states that the value of 2 plus 2 is greater than 4. Similarly, the inequality 2 + 2 < 4 states that the value of 2 plus 2 is less than 4. Inequalities can be used to express constraints in a problem or to define a range of solutions. They can also be represented graphically by using a number line.
x= number of tables sold
y= number of chair sold
max furniture in a day = 20
so, [tex]x+y \leq 20[/tex].
least selling amount = 4800
so, [tex]450x+200y \geq 4800[/tex]
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What are the 3 steps for solving a quadratic equation?
Determine what a, b, and c are worth. the quadratic formula in writing. After that, enter the values for a, b, and c. Simplify.
what is quadratic equation ?A quadratic polynomial in a single variable is represented by the expression x ax2+bx+c=0, which is a quadratic equation. a 0. Since it is a second order polynomial, the Fundamental Theorem of Algebra guarantees that it has at least one solution. Simple or difficult solutions are both possible. The term "quadratic equation" refers to an equation that is quadratic. It must square at least one word, according to this indication. One of the common solutions for quadratic equations is the formula "ax2 + bx + c = 0." where the variables "X" are undefined and are numerical coefficients or constants a, b, and c.
given
steps are
Find out what a, b, and c are worth.
Quadratic formula: write it down.
Add the values of a, b, and c after that. Simplify.
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Uncle Drew scored 28 points in 5 5/6 minutes during a game of basketball. How many points did he average per minute during that 5 5/6 minutes?
Answer:
He scored an average of 4.8 points per minute.
Complete the table for an object that goes 3/4 miles in 6 minutes.
Write any fraction as follows: 1/2 for one half
The speed of Ana is in miles per hour 7.5mph
By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.
Speed = distance ÷ time
Distance = 3/4
Time = 1/10
Speed = 3/4 ÷ 1/10
Speed = 3/4 x 10 = 15/2 miles per hour
or, 7.5mph
Divide the distance Ana covered by the time she ran to get her speed.
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The question is incomplete
Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour
Two cards are chosen at random from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a 10
The probability that the first card is a heart and the second card is a 10 is 1/51.
What is the probability?Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.
The following combinations are possible:
When we choose first card, total no. of card is 52 and card of heart is 13
so the probability of the first card to be heart is
P(1)= 13/52
= 1/4
When we choose second card, total no. of card is 51 and card of 10 is 4
so the probability of the first card to be 10 is
p(2)= 4/51
So the final probability is
= P(1)* P(2)
= 1/4 * 4/51
= 1/51
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Random students from a high school were surveyed to determine if there was enough interest to start a Ukulele Club.
Identify the population:
A. Students of high schools across the country
B. Students of the high school
C. Citizens of the city
D. Every citizen of the country
Answer:
b
Step-by-step explanation:
Answer:
B. Students of the high school
Step-by-step explanation:
It is high school because you just want to ask that area.
Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
TY
f(x)
18
f(x) =2(3ˣ) is an exponential function which has an initial value of 2.
What is an exponential function?Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.
A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.
The exponential function that has an initial value of 2 is f(x) = 2ˣ.
f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.
f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3
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Given that there are 4 quarts, 8 pints, or 16 cups in 1 gallon, which of the following amounts is greater than 2 gallons? Select all that apply.
A) 5 quarts, 2 pints
B) 1 gallon, 3 quarts
C) 9 quarts
D) 40 cups
E) 1 gallon, 9 pints
Answer:
C, D, E
Step-by-step explanation:
A sookeeper weighted an African elephant to be 9 x 10 (to the 3rd power) pounds, and an African lion to be 4 x 10 (to the second power) pounds. Hiw many times greater is the weight of the elephant than the weight of the lion
2.25×10 times greater is the weight of the elephant than the weight of the lion.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a zookeeper weighted an African elephant to be 9 x 10³ pounds.
An African lion to be 4 x 10² pounds
We need to find how many times greater is the weight of the elephant than the weight of the lion
Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,
N=9×10³/4×10²
=2.25×10
Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.
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express √832 in the form 4n where n is the integral
We can express √832 as 4(2√13).
What is definite integral?A definite integral of a function can be represented as the signed area of the region bounded by its graph.
Given is the root of 832 or √832.
Assume that {4n} is equal to {y}. So, we can write -
y = 4n
Squaring both sides, we get -
y² = (4n)² = (√832)²
y² = 16n² = 832
16n² = 832
n² = (832/16)
n² = 52
n = √52
n = 2√13
So, we can write (√832) as 4(2√13).
Therefore, we can express √832 as 4(2√13).
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What is the value of 3 in tan?
The value of tan 3° is 0.0524.
tangent is the trigonometric ratio.
we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.
tan Q = perpendicular of the triangle /base of the triangle.
sine theta divided by cos theta gives the value of tan theta.
tan Q = sin Q/ cos Q.
some formula of the tan Q are as follows,
1- tan Q = sin Q/cos Q
2- tan Q= 1 /cot Q
3-tan^2 Q =sec^2 Q -1
4- tan(90 - Q)=cot Q
5- tan (Q+π) = tan Q
6- tan (π-Q) = -tan Q
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What is the measure of ∠A if it is complementary to ∠B that has a measure of 55?
For the given complementary angles, the measure of angle A is found to be 45°.
Define the term complementary angles?When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are referred to as supplementary angles.When two angles sum up to 90 degrees, they are complementary (a Right Angle). They don't even have to be close to one another for the total to be 90 degrees. Examples: The complimentary angles of 40° and 50°.For the stated question-
Angle A is complementary to Angles B.
So,
Angle A + Angles B = 90°
Angle A + 55° = 90°
Angle A = 90° - 55°
Angle A = 45°
Thus, the measure of angle A is found to be 45°.
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I have no clue about this.
Help!
Answer: 294 feet^2
Step-by-step explanation:
Find the volume of the cube.
Find the cube root of the volume.
Plug this answer into the formula for finding the surface area of a cube.
(area = 6 · s2)
Answer:
294cm[tex]^{2}[/tex]
Step-by-step explanation:
A cube has 6 faces
To find out the area of one face, you'd have to do 7x7 (7[tex]^{2}[/tex]).
To find out the total surface area of the cube, use this equation to help you:
AREA= 6(the amount of faces of the cube) × 7[tex]^{2}[/tex](the area of ONE face)
so in other words...
AREA=6×7[tex]^{2}[/tex]
AREA= 294cm[tex]^{2}[/tex]
hope this helped:)
How do you find the f of G in a pair of functions?
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
f of G in a pair of functions ,
Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2
To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).
f(x) = x2
f(g(x)) = g(x)2
= (√x + 2)2
= x + 2√x + 4
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
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Simplifying algebraic expressions
Answer:
-8
Step-by-step explanation:
7-6x+3x
You have to replace x for a 5.
7-6(5)+3(5)
After this you would multiple all of it.
7-30+15
Then add
7+15=22
-30+22=-8
Answer:
[tex] \sf \: 7 - 6x + 3x = - 8[/tex]
Step-by-step explanation:
Now we have to,
→ find the value of expression.
The expression is,
→ 7 - 6x + 3x
→ using (x = 5)
Let's solve the expression,
→ 7 - 6x + 3x
→ 7 - 6(5) + 3(5)
→ 7 - 30 + 15
→ 7 - 15
→ -8 => final answer
Hence, the answer is -8.
help help help help use slope form to write the equation of a line that passes through the point (7,-16) with slope 3.
required equation is, y=3x-37.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here, given that,
we have to find,
the equation of a line that passes through the point (7,-16) with slope 3.
we know,
y = mx+c
i.e. -16 = 3*7+c
so, c= -37
hence, required equation is, y=3x-37.
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Lewis uses a half-cup of lemon juice for
every pitcher of lemonade he makes. If he
starts with a gallon of lemon juice and makes
19 pitchers of lemonade, is it reasonable to
assume he'll have enough juice left to make at
least 9 more pitchers? Explain.
Answer:
Yes
Step-by-step explanation:
there are 16 cups in a gallon. if he uses 1/2 a cup to make 1 pitcher, there would be 32 pitchers made. 19+9 is 28 so the answer is yes.
^^mark brainliest pls:D
Practice 2-2 Using number sense to solve Equations (PLEASE HELP)
The solutions for all the equations would be
1. p = 30
2. h = 99
3. t = 31.4
4. r = 57
5. t = 5
6. w = 8
7. y = 9
8. p = 7
9. a = 13
10. w = 12
11. h = 24
12. g = 128
13. a = 21
14. y = 39
15. d = 16
16. w = 25
What is an equation?
An equation is a statement that asserts the equality of two expressions. The expressions on either side of the equation are separated by an equals sign (=), and they must have the same value for the equation to be true.
1) 30p = 900
p = 900/30
p = 30
2) h/9 = 11
h = 9 * 11
h = 99
3) t + 32.4 = 62
t = 62 - 32.4
t = 31.4
4) r - 17 = 40
r = 40 + 17
r = 57
5) 5t = 25
t = 25/5
t = 5
6) 8w = 64
w = 64/8
w = 8
7) 9y = 81
y = 81/9
y = 9
8) p + 5 = 12
p = 12 - 5
p = 7
9) a + 2 = 15
a = 15 - 2
a = 13
10) w + 8 = 20
w = 20 -8
w = 12
11) h/6 = 4
h = 6 * 4
h = 24
12) g/8 = 16
g = 16 * 8
g = 128
13) a/7 = 3
a = 3 * 7
a = 21
14) y - 11 = 28
y = 28 + 11
y = 39
15) d - 4 = 12
d = 12 + 4
d = 16
16) w - 10 = 15
w = 15 + 10
w = 25
Hence, solutions for all the equations would be
1. p = 30
2. h = 99
3. t = 31.4
4. r = 57
5. t = 5
6. w = 8
7. y = 9
8. p = 7
9. a = 13
10. w = 12
11. h = 24
12. g = 128
13. a = 21
14. y = 39
15. d = 16
16. w = 25
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3. Tell whether the set of ordered pairs {(3, 2), (4, 3), (5, 4), (6, 5)} satisfies a linear function. Explain.
a. No; there is no constant change in x that corresponds to a constant change in y.
b.
No; there is a constant change in x that corresponds to a constant change in y.
Yes; there is a constant change in x that corresponds to a constant change in y.dd T
Yes; there is no constant change in x that corresponds to a constant change in y.
d.
Find the x and
conto
The given set of ordered pairs does not satisfy a linear function.
What is a linear function?A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.
Given:
The given set of ordered pairs is:
{(3, 2), (4, 3), (5, 4), (6, 5)}
To find:
Whether the given set of ordered pairs satisfies a linear function or not.
Explanation:
The slope of a linear function is:
m = (y₂ - y₁)/ (x₂ -x₁)
The slope of the linear function passes through the points and is:
m₁ = (3-1)/(3-1)
m₁ = 2/2
m₁ = 1
The slope of the linear function passes through the points and is:
m₂ = (9-3)/(5-3)
m₂ = 6/2
m₂ = 3
Therefore m₁ ≠ m₂ therefore the given set of ordered pairs does not satisfy a linear function.
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What is math trying to do with me?
seriously
:^
Answer:
1.
Y would equal to 449 after plugging in 12 for x
2.
Y would equal to 239 after plugging 7 in for x
Step-by-step explanation:
We just have to plug in the values give too us and find what y equals.
1.
y=42(12)-55
y=504-55
y=449
2.
y=42x-55
we just have to plug in 7 for x.
y=42(7)-55
42*7=294
y=294-55
y=239
The table shows the approximate area
in square miles of the largest and smallest
states in the United States. What is the
difference between the areas in
square miles?
State
Area (mi?)
873
Alaska
Rhode Island
392
The difference between the areas is 481 square miles.
Given information:
Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.
To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:
Let X be the total difference:
873 - 392 = X
481 = X
Therefore, the difference in the areas in square miles is 481.
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