Find the distance from the point (8, 4) to the line y =
x+ 2.

[tex](x+1)^2=25​\\x+1=5 \vee x+1=-5\\x=4 \vee x=-6[/tex]

Answer:

b) L+S=80 and 2.75L+3.25S=245

Step-by-step explanation:

L stands for larger softballs. S stands for smaller softballs.

If you are ordering 80 softballs, then L and S represent the number of softballs of each one (large or small) to get a total of 80.

2.75 is the price of a large softball

3.25 is the price of a small softball.

You multiply the amount of each softball to how many of those kinds of softballs you get, you will then get the sum of the amount you ordered for 80 softballs: 245 dollars.

So thus the answer is B

Answer:

L+S=80

2.75L+3.25S=245

Choice B

Step-by-step explanation:

Larger ball costs $2.75.

Smaller ball costs $3.25.

You order a total of 80 softballs for $245.

So L is for number of large balls.

S is for number of small balls.

So we have 80 balls in all, some are small and some are large. This means the number of large plus the number of small equals 80.

So we have this equation L+S=80.

Now if you buy L balls, you spend 2.75 times L on large balls altogether.

If you buy S balls, you spend 3.25 times S on small balls altogether.

So together you spend 2.75L+3.25S.  They gave us that this amount should be equal to 245.

So this equations is 2.75L+3.25S=245

We are looking for the choice that contains these equations:

L+S=80

2.75L+3.25S=245

Answer:

equation: y=-150m+2250

Height after:

6 Minutes: 1350 ft

8 Minutes: 1050 ft

10 Minutes: 750 ft

Step-by-step explanation:

We know that the hot air balloon has an initial height of 2250 ft, so that is our y-intercept (in the equation, y =mx+b, the y-intercept is b). Next you know that after every minute, the balloon goes down 150 ft. So that means -150 ft per minute. Now put it together, the equation is written as "y = 150m+2250" (since m is the required variable, that's what is written in the equation instead of x).

Next, to make a table, you need to determine what value goes in the left side, the x values (the independent variables) and what goes in the right side, the y values (the dependent variables). The two variables here are Height and Time. Time is not dependent on the height of the balloon-- the height depends on how much time has passed. So Time on the left and height on the right. Next just plug in the values 6, 8, and 10 into your equation. Your answer will be the output, aka the height of the hot air balloon after x minutes.

Your table should look something like this:

m       y

6       1350

8       1050

10       750

Hope this helps :)

Answer:

0.17

Step-by-step explanation:

The numbers are from 1 to 6 on each side.

The total sample space will be 6.

Denoted as:

n(S) = 6

There will be only one outcome as 1

So,

Let A be the event that the number is 1

Then,

n(A) = 1

[tex]P(A) = \frac{n(A)}{n(S)} \\=\frac{1}{6} =0.166[/tex]

Hence the theoretical probability of the number cube showing a 1 is 0.166 ..

Rounding off to the nearest hundred

0.17 ..

Answer:

Option A) f(2)=0 and g(-2)=0

Step-by-step explanation:

we know that

The vertex of f(x) is equal to (2,0)

The vertex of g(x) is equal to (-2,0)

step 1

Find the value of f(x) and g(x) for x=2

Observing the graph

For x=2

f(2)=0 ----> the y-coordinate of the vertex

g(2) > 12

step 2

Find the value of f(x) and g(x) for x=-2

Observing the graph

For x=-2

f(-2)> 12

g(-2)=0 ----> the y-coordinate of the vertex

therefore

The statement that is true regarding the graphed functions is

f(2)=0 and g(-2)=0

Answer:

105

Step-by-step explanation:

Evaluate 4 a^3 - 2 b^2 + 5 where a = 3 and b = -2:

4 a^3 - 2 b^2 + 5 = 4×3^3 - 2×(-2)^2 + 5

3^3 = 3×3^2:

4×3×3^2 - 2×(-2)^2 + 5

3^2 = 9:

4×3×9 - 2×(-2)^2 + 5

3×9 = 27:

4×27 - 2×(-2)^2 + 5

(-2)^2 = 4:

4×27 - 24 + 5

4×27 = 108:

108 - 2×4 + 5

-2×4 = -8:

108 + -8 + 5

| | 1 |  

| 1 | 0 | 8

+ | | | 5

| 1 | 1 | 3:

113 - 8

| | 0 | 13

| 1 | 1 | 3

- | | | 8

| 1 | 0 | 5:

Answer:  105

Answer:

105

Step-by-step explanation:

4a^3 -2b^2 +5

Let a=3 and b= -2

4 (3)^3 -2 (-2)^2 +5

4 *27 -2 (4) +5

108 -8+5

105

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

As data we have that[tex]r = 6 \ ft[/tex]

Then, replacing we have:

[tex]A = \pi * 6 ^ 2\\A = 36 \pi[/tex]

Taking [tex]\pi = 3.14[/tex]

A = 113.04

So, the pool area is [tex]113.04 \ ft ^ 2[/tex]

Answer:

[tex]113.04 \ ft ^ 2[/tex]

Answer:

9π ft²

Step-by-step explanation:

Answer:

=8/3m⁷n⁶

Step-by-step explanation:

Given the expression (2mn)⁴/6m⁻³n⁻², we first solve the numerator

(2mn)⁴ = 16m⁴n⁴

The new expression becomes 16m⁴n⁴/6m⁻³n⁻²

We now divide the coefficients and the exponents as follows:

=16/6ₓ(m⁴/m⁻³)×(n⁴/n⁻²)

Division between indices to the same base we subtract the powers.

4-⁻3=7

4-⁻2=6

=8/3m⁷n⁶

Answer:

the asnwer is A

Step-by-step explanation:

Answer:

20.

Step-by-step explanation:

P(5,3)  = 5! / 3!

= (5*4*3*2*1) / (3*2*1)

= 20.

Answer:

There is a multiplication error

Step-by-step explanation:

Long division method is used to divide greater  number by a smaller number.

Here, greater number is known as the dividend and smaller number is known as divisor.

As per division algorithm,

Dividend = Divisor [tex]\times[/tex] quotient + remainder

Here, dividend = [tex]8x^3-36x^2+54x-27[/tex]

Divisor = [tex]2x-3[/tex]

Here, we need to find the error in the long division .

In step:

[tex]18x+27[/tex] , it should be 18x-27 as [tex]-3\times 9=-27[/tex] not +27

So, there is a multiplication error .

The correct option is c) she makes a multiplication error.

Step-by-step explanation:

Given :

Dividend = [tex]8x^3-36x^2+54x-27[/tex]

Divisor = [tex]2x-3[/tex]

Solution :

In step [tex]18x +27[/tex] there is mistake. It should be [tex]18x - 27[/tex] because [tex]-3 \times 9= -27[/tex] not +27.

Therefore the correct option is c) she makes a multiplication error.

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Answer:

6√10 ≈ 19.0

Step-by-step explanation:

The length of the diagonal is:

d² = w² + l² + h²

Given d = 36, l = 30, and h = 6:

36² = w² + 30² + 6²

1296 = w² + 900 + 36

w² = 360

w = 6√10

w ≈ 19.0

The box should be approximately 19 inches wide.

Answer:

A = 1024π units², A ≈ 3216.99 units²

Step-by-step explanation:

The equation of the area of a circle is A = πr², where A = area and r = radius.

Given that, we can plug in r as 32 units: A = π(32 un.)²

Simplifying that gives us A = 1024π units², or A ≈ 3216.99 units²

Answer:

B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex]  are perpendicular lines.

Step-by-step explanation:

We can quickly plot the points in the cartesian plane as shown in the attachment.

A visual representation will help us see that A,B,C, and D do not lie on the same line.

The slope of AB  is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]

The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]

The two slopes are negative reciprocals of each other.

It is true that line AB and line CD are perpendicular.

These two lines cannot be perpendicular and parallel at the same time.

It is also not possible that, the two lines are perpendicular but will not intersect

Therefore the correct choice is B

Answer:

B

Step-by-step explanation:

plato/edmentum

Answer:

Step-by-step explanation:

Option 3 is correct

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram

Step-by-step explanation:

Slope formula is given by:

slope = y2-y1

over      x2-x1

Properties of the parallelogram:

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)

⇒Slope of AB =Slope of CD and Slope of BC = Slope of AD

By property of parallelogram:

⇒A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram

Answer: OPTION C.

Step-by-step explanation:

A parallelogram is defined as a quadrilateral which has two pairs of parallel sides.

Attached is shown in the parallelogram obtained by plotting the vertices provided in Option C.

If that figure is a parallelogram, then:

[tex]Slope\ AB=Slope\ CD\\\\Slope\ BC=Slope\ AD[/tex]

Let's check this:

[tex]Slope\ AB=\frac{-2-3}{-5-(-3)}=\frac{5}{2}[/tex]

[tex]Slope\ CD=\frac{0-5}{1-3}=\frac{5}{2}[/tex]

[tex]Slope\ BD=\frac{3-5}{-3-3}=\frac{1}{3}[/tex]

[tex]Slope\ DA=\frac{-2-0}{-5-1}=\frac{1}{3}[/tex]

Therefore, the set of vertices that forms a parallelogram is:

[tex]A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)[/tex]

Answer:

9 geese

11 cows

Step-by-step explanation:

Say x is cows, and y is geese.

x + y = 20 animals

x * 4 + y * 2 = 62

x = 20 - y

(20 - y) * 4 + y * 2 = 62

80 - 4y + 2y = 62

- 2y = -18

y = 9 geese

x = 20 - 9 = 11 cows

Lisa has 11 cows and 9 geese.

To solve the problem involving Lisa's barn with 20 animals having 62 legs in total, and knowing she only has cows and geese, we can use a system of linear equations. We can denote the number of cows as c and the number of geese as g. Cows have 4 legs and geese have 2 legs.

We can then set up the following equations based on the information given:

Cows and geese equation: c + g = 20 (since there are 20 animals in total)

Legs equation: 4c + 2g = 62 (because cows have 4 legs and geese have 2 legs)

Now, let's solve the system of equations:

Multiply the first equation by 2 to match the number of geese legs in the second equation: 2c + 2g = 40

Subtract the modified first equation from the legs equation: (4c + 2g) - (2c + 2g) = 62 - 40, which simplifies to 2c = 22, and then c = 11. Lisa has 11 cows.

Substitute the number of cows back into the first equation to find the number of geese: 11 + g = 20, which leads to g = 9. Lisa has 9 geese.

Therefore, Lisa has 11 cows and 9 geese.

Answer:

[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]

Step-by-step explanation:

I don't know where [tex]\theta[/tex] is so there is going to be two possibilities for cosine value, one being positive while the other is negative.

A Pythagorean Identity is [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].

We are given [tex]\sin(\theta)=\frac{7}{25}[/tex].

So we are going to input [tex]\frac{7}{25}[/tex] for the [tex]sin(\theta)[/tex]:

[tex]\cos^2(\theta)+(\frac{7}{25})^2=1[/tex]

[tex]\cos^2(\theta)+\frac{49}{625}=1[/tex]

Subtract 49/625 on both sides:

[tex]\cos^2(\theta)=1-\frac{49}{625}[/tex]

Find a common denominator:

[tex]\cos^2(\theta)=\frac{625-49}{625}[/tex]

[tex]\cos^2(\theta)=\frac{576}{625}[/tex]

Square root both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{576}{625}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{576}}{\sqrt{625}}[/tex]

[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]

Answer:

A is most likely the next step in the series

Step-by-step explanation:

Each step, the number of sides is increasing by 1.

4,5,6 means that the next number of sides would be 7. Option A has 7 sides.

Answer: it’s B 0

Step-by-step explanation:

The mathematical expression is 6 + 8x

The sum of 6 and the product of 8 and x  can be written  mathematically by first  getting the product of  8 and x  which equals 8x

Sum means addition( +)

So the sum of 6 is written as 6 +

We  thus have  the mathematical expression Translated as  6 + 8x

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The mathematical expression for 'the sum of 6 and the product of 8 and x' is 6 + 8x.

A mathematical expression is a combination of numbers, variables, and mathematical operators (e.g., +, -, *, /) that represents a calculation or relationship. Expressions can be simple, like 2x + 3, or complex, serving various purposes in mathematical modeling, calculations, and problem-solving.

To translate the phrase 'the sum of 6 and the product of 8 and x' into a mathematical expression, we can use the symbols and operations of algebra. The sum of 6 and the product of 8 and x can be written as 6 + 8x. Here, 8x represents the product of 8 and x, and the addition symbol, '+', represents the sum of 6 and 8x.

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Answer:

x     y

6     36

9     54

12    72

Step-by-step explanation:

The options are shown in the pictures attached.

Data:

a single dog costs about $6 per day

y-variable represents the total cost

x-variable represents days

So, 1 day costs $6, 2 days costs 2*$6 = $12, 3 days costs 3*$6 = $18 and so on. Then, the table is:

x     y

6     6*6 = 36

9     9*6 = 54

12    12*6 = 72

Answer:

The first term (2x) represents Jillian's earnings at the end of the week. Where the 2 represents the amount of money she earns per pag, and the 'x' is the number of bags sold.

Let us explain this with an example: if Jillian sells 36 bags, then she will earn 2×36 = $72

Answer:

option C is true.

Step-by-step explanation:

We are given that Jack and Jillian sell apples at a produce stand .

We are given that an expression which shows Jack's earning=2x-8

We have to find that first term what represent in the given expression

Jillian earns for each bag  of apples she sells=$2

Let Jillian sold number of bags of apples =x

Then ,Jillian earn total at the end of the week =[tex]2\timesx=$2x[/tex]

Jack has earned $ 8 less than Jillian earn

Therefore, total earning of jack=[tex]2x-8[/tex]

In the given expression the first term 2x represent the earning of Jillian.

Hence, option C is true.

Answer: C: JIllian's earning at the end of the week

Answer:

  3 seconds

Step-by-step explanation:

The given equation describes a parabolic curve with zeros at x=-1 and x=7. The line of symmetry of the curve is halfway between the zeros, at ...

  x = (-1 +7)/2 = 6/2 = 3

The maximum of the curve is on the line of symmetry. The ball will reach its maximum height 3 seconds after being thrown.

_____

Additional comment
The maximum height will be 16 meters.

The ball will reach its maximum height 3 seconds after being thrown.

To find the time when the ball reaches its maximum height, we need to determine the vertex of the quadratic equation representing the ball's height. The equation h(x)=-(x+1)(x-7) can be rewritten in vertex form as h(x)=-x^2+6x-7. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -1 and b = 6. Plugging these values into the formula, we get x = -6/-2 = 3. Therefore, the ball reaches its maximum height 3 seconds after being thrown.

Answer:(4, 7)

Step-by-step explanation:

This question is about changing the coordinates of the function.

They want you to choose a value of x that will make the sentence inside the function (-3x/4) equal to -3.

-3 x / 4 = -3

x = 4

Hence, the correspondig point is (4, 7)

Answer:

Second option: False

Step-by-step explanation:

We need to remember this property:

 [tex]\sqrt[n]{x^n}=x^{\frac{n}{n}}=x[/tex]

In this case we have the following expressions provided in the exercise:

[tex]\sqrt{3x}[/tex] and [tex]x\sqrt{3}[/tex]

Based on the property mentioned before the expression [tex]\sqrt{3x}[/tex] cannot be simplified. So 3 and  [tex]x[/tex] stays inside the square root.

Therefore, the conclusion is: The expression [tex]\sqrt{3x}[/tex] is not equivalent to the expression [tex]x\sqrt{3}[/tex]

Deciphering the expressions reveals that 'square root 3x' is not equivalent to 'x square root 3'. They interpret differently on the terms inside and outside of the square root, thus they are not the same.

The statement 'the expression square root 3x is equivalent to the expression x square root 3' is False. To understand why, we need to understand the properties of square roots and multiplication. The expression square root 3x means that the square root is being taken over the entire product of 3x. This is not the same as x square root 3, where the square root is only being applied to 3, and then that result is being multiplied by x.

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Answer:

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

Step-by-step explanation:

sin(x)=sqrt(3)/2

This happens twice in the first rotation on our unit circle.

It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.

So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.

This is at pi/3 and 2pi/3.

So we can get all the solutions by adding +2pi*k to both of those.  This gives us a full rotation about the circle any number of k times. k is an integer.

So the solutions are

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

An equation is formed of two equal expressions. The solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of sinx=√3/2 are,

sin(x) = √3/2

x = sin⁻¹ √3/2

x = (π/3 ± 2πn), (2π/3 ± 2πn)

Hence, the solution to the equation sin(x)=√3/2 is (π/3 ± 2πn), (2π/3 ± 2πn), where n is any natural number.

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Answer:

c. $280

Step-by-step explanation:

first you times the total profits by the percent that the girls get then the percent the boys get to find out how much of the profit the girls and boys basketball teams each get, then you subtract the profits the boys get by the profits the girls get to find out how much more the boys get than the girls.

7,115.03 x .07 = 498.0521

7,115.03 x .11 = 782.6533

782.6533 - 498.0521 = 284.6012

the boys receive 284.6012 more in profits than the girls

so c. $280 would be the best estimate of how much more the boys team will receive

Answer:160

Step-by-step explanation:

To solve the problem we must know the concept of the Center angle theorem. The measure of the center angle ∠AOC  is 160°.

According to the central angle theorem, if an arc of a circle makes an angle with any point on the circumference of that circle then the measure of that angle is half the angle made by that arc at the center of the circle.

Given to us

∠ABC = 80°

As we already know the angle made by Arc AC at point B, therefore, the center angle made by ARC AC at the center will be twice of it. Therefore,

∠AOC = 2∠ABC

∠AOC = 2(80°)

∠AOC = 160°

Hence, the measure of the center angle ∠AOC  is 160°.

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Answer:

71.4

Step-by-step explanation:

For this, we will use Heron's Formula, or

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex],

with p as the perimeter divided by 2, and a, b, and c are the side lengths.

Plugging our values in, (11.6+20+13)/2 = 22.3 = p, and

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex] = [tex]\sqrt{5103.8679} =71.4[/tex] rounded to the nearest tenth

Answer:

$894

Step-by-step explanation:

$27,000+$2,200+$600= $29,800

$29,800*0.03=$894