2) The Allen's rectangular backyard has a
perimeter of 144 feet. If the backyard is 40
feet wide, what is the area of their yard?

Answer:

Part A:

Option 1

3x + 8 = 5x - 20 (vertically opposite angles)

2x = 28

x = 14

3x + 8 + 5x + 4y = 180° (adjacent angles on a straight line)

8x + 4y = 172

Substitute x = 14 into equation to find y.

8(14) + 4y = 172

4y = 60

y = 15

Hence, x = 14 and y = 15.

Part B:

Option 4

Unlabeled angle = 5x + 4y (vertically opposite angles)

Substitute x and y to find angle measure.

5(14) + 4(15) = 130°

Hence, measure of unlabeled angle is 130°.

We have a line defined by two points, P(-4,9) and Q(12,1).

Knowing two points of the line, we can calculate the slope with the formula:

In this case, the slope will be:

With the slope and one point we can express the equation in slope-point form:

The x-intercept is the value of x that makes the function f(x) become 0.

In this case, we have to find x so that y = 0.

We can replace y in the equation and calculate x as:

Then, for the x-intercept is x = 14.

Answer:

a) The equation of the line is y = (-1/2)*x+7

b) The x-intercept is x = 14.

Answer: 22

Step-by-step explanation:

Let the sides have lengths [tex]x-4, x-2, x[/tex]. Since the perimeter is 60,

[tex]x-4+x-2+x=60\\\\3x-6=60\\\\3x=66\\\\x=22[/tex]

So, the length of the longest side is 22 units.

For the description "The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations." Graphing method for solving systems is in play. Option A

This is further explained below.

Generally, Construct a graph using the first equation.

Create a graph using the same rectangular coordinate system for the second equation.

Find out whether the lines overlap, if they run parallel to one another, or if they are the same line.

In conclusion, Find a solution to the problem that we are having. In the event that the lines meet, locate the location where they do so.

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CQ.

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

answer choices

Graphing

Substitution

Elimination (adding or multiplying)

The fraction of gasoline used is:

We need to convert this fraction to decimal and to percentage to find the answer.

Converting 7/8 to decimal:

For this we have to do the division between 7 and 8:

Thus, the decimal form of 7/8 is 0.875

Converting 7/8 to percentage:

we use the result that we previously get of 7/8 as a decimal: 0.875, and to convert it to percentage we multiply it by 100:

7/8 to percentage is equal to 87.5%

Answer: 0.875 and 87.5%

You will need to make b the subject of the formula:

This you do by subtracting 0.25 from both sides of the equation:

b + 0.25 = 1.15 becomes:

Answer:

  U'(12, 15)

Step-by-step explanation:

Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.

Dilation about the origin multiplies each coordinate value by the scale factor:

  U' = 3U

  U' = 3(4, 5) = (12, 15)

The coordinates of U' are (12, 15).

Answer:

Step-by-step explanation:

You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.

We like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...

  (minutes, population) = (110, 60000)

We can put these numbers in the form ...

  p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))

where the growth factor (2) is applicable over the growth period (15 minutes).

This makes our equation ...

  p(t) = 60000(2^((t-110)/15))

We want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.

The population at t=0 was about 372.

The population after 4 hours will be 24,382,480.

__

Additional comment

A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...

  p(t) = 372·e^(0.0452098t)

where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15

These rounded numbers don't give the problem statement values exactly:

  p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).

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[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]

The equation of a linear model to describe the data is 14x - y = 26904

To find a linear equation of the provided data,

Let us put the number of legislature on the y axis and the year corresponding at the x axis,

According to provided information,

In year 2003, the number of legislature is 1138.

In year 2009, the number of legislature is 1222.

So here we have two points,

A(2003,1138) and B(2009,1222).

As we have two points now,

We can use the two point form of the line to find the equation of line,

It says if we have two point (a,b) and (c,d), then the equation of line is,

(y-b)/(x-a) = (d-b)/(c-a)

So, our equation of line is with points A and B is,

(y - 1138)/(x-2003) = (1222-1138)/(2009-2003)

(y-1138)/(x-2003) = 14

y - 1138 = 14x - 28042

14x - y = 26904

When,

x = 2000, y = n,

14(2000) - n = 26904

n = 1096.

The Linear Equation is 14x - y = 26904

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Given the equation : 2x + 3y = 12?

We will find the slope of the equation by re-arranging the equation into the standard form of slope intercept formula:

Re-arranging the equation will be :

Answer:

Yes

Explanation:

A set S is said to be closed under addition if:

For a, b in S, a+b is in S.

If we add two even numbers, the result will always be an even number.

Therefore, the set of even number is closed under the operation of addition

[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]

ATTACHED IS THE SOLUTION

BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is twenty one lesser or equal to minus four z minus twenty one.

21 ≤ −4z − 21.

We need to solve for z

Let us add twenty one on both sides

21+21≤ −4z − 21+21

42≤ −4z

Divide both sides by 4

10.5≤ -Z

-10.5≥Z

Z≤ -10.5

Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

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The Volume of the model sphere is given as

Given that the diameter is 5inches, the radius will be

substituting r in the formula will give

Hence, the volume of the model sphere is approximately 321.39 cubic inches

The number of people who ride the bus is 70 students.

From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.

Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.

This will be illustrated as:

4/7 = 40/x

Cross multiply

4x = 40 × 7

4x = 280

Divide

x = 280/4

x = 70

Therefore there are 70 students.

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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?

The height of cylinder when volume of 480 cubic meters is  480/r^2.

Volume serves as a measure for an object's storage capacity. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water when filled to the brim. The amount of space a three-dimensional object occupies is another way to define volume.

A solid's volume can be calculated by counting how many unit cubes it contains, such as in the case of a cube or cuboid. The best way to understand volume is to think of it as the area surrounded or occupied by any solid object or object with three dimensions. This can be seen by performing the following easy exercise at home:

volume of cylinder V is = πr²h

where, r  = radius of cylinder

h = height of cylinder

V = 480π cubic meters

Now, calculate its height in terms of cylinder radius using the volume of cylinder formula:

V = πr²h

480π =  πr²h

h = 480π/ πr²2

h = 480/r²

Therefore, The height of cylinder when volume of 480π is  480/r².

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Answer:

900

Step-by-step explanation:

because I know answer

Step 1: State the given in the question

Given that 3 out 20 cars passing through an intersection did not fully stop

Step 2: State what to be determined

We are to determine the probability that a car arriving at this intersection that will not fully stop

Step 3: State the formula for finding probability

The formula for finding the probability of an en event, E, from a sample S, is the ratio of the number of elements of event E to the total number of elements in the sample S.

This can be represented mathematically as

Step 4: Use the formula to solve the probability

If the event E is cars passing through an intersection did not fully stop. Then, the number of elements in the event E is given as 3. That is:

The sample is the total number of cars, which is given as 20. This means that

Therefore, the probability of the event occuring would be P(E). This is as calculated below:

Hence, the probability that a car arriving at this intersection will not fully stop is 3/20 or 0.15

The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.

By Binomial probability distribution,

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,

[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074

P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

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Mrs. long bought 4 types of fruits at the market:

- 2 cantaloupes that weighed 2.3 pounds each:

that is, a total of 2.3x2 = 4.6

- 6 peaches that weighed a total of 1.7 pounds.

- 4 apples that weighed a total of 1.25 pounds.

- and 3 pounds of grapes.

The total weight of the four fruits is:

4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.

Answer:

this is true

Step-by-step explanation:

Answer:

-5  < x < 17/5

Step-by-step explanation:

add three onto all sides -10 < 5x < 17

then divide all sides by -5  < x < 17/5

Take into account that vector v can be written as follow:

where (x,y) and (xo,yo) are two points on the vector.

In this case, we can use (xo,yo) = R(-2,12) and (x,y) = S(-7,6). By replacing these values into the expression for vector v, we obtain:

Now, consider that the magnitude of v is the square root of the sum of the squares of the components. Then, we have for the magnitud of v:

Hence, the magnitude of v is approximately 7.810.

Now, consider that the tangent of the angle of the direction of the vector is equal to the quotient between the y component over the x component of the vector:

Hence, the direction of vector v is approximately 230.194 degrees.

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18

Given the following question:

Part A:

75 dollars to spend on gaS

Gas per gallon costs $2.80

With 75 dollars you can buy "26.8 gallons of gas."

Part B:

We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.

"10.4 miles" per gallon

1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula

And R(-3,7) , S(-4,-5)

Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.

3) So the answer is GH is not parallel nor perpendicular.

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

How to find the soccer portion of the pie chart?

In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.

According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.

Therefore, the soccer portion is:

= Total hours spent on walking / Total sports hours x 360°

= 10 / 50 x 360°

= 72°

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

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A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?​

Let

A -----> you

B-----> a bird

C-----> top of the tree

see the following image

step 1

In the right triangle ABD

tan(42)=BD/AD

substitute given values

tan(42)=BD/40

BD=40*tan(42)

BD=36 ft

step 2

In the right triangle ACD

tan(32)=CD/AD

CD=AD*tan(32)

CD=40*tan(32)

CD=25 ft

step 3

Find the difference BD-CD

36-25=11 ft

therefore