The height of a triangle is 5 m less than its base. The area of the triangle is 42 m². Find the length of the base.
7m
8 m
11 m
12 m

-2z +2

-3z+z+2 distribute the - to make them positive

-3z+z equals -2z

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-\frac{9}{2}})~\hspace{10em} slope = m\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\left( -\cfrac{9}{2} \right)=-\cfrac{1}{4}[x-(-2)] \\\\\\ y+\cfrac{9}{2}=-\cfrac{1}{4}(x+2)\implies y+\cfrac{9}{2}=-\cfrac{1}{4}x-\cfrac{1}{2}\implies y=-\cfrac{1}{4}x-\cfrac{1}{2}-\cfrac{9}{2}[/tex]

[tex]\bf y=-\cfrac{1}{4}x-\cfrac{10}{2}\implies y=-\cfrac{1}{4}x\stackrel{\stackrel{b}{\downarrow }}{\boxed{-5}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

B. y = 2/3x + 4

Step-by-step explanation:

the equation is Y = mx + b

m = slope

b = y-intercept

your answer is B. y = 2/3x + 4

Answer:

Step-by-step explanation:

It's B

The general equation of a slope intercept line is

y = mx + b

m = the slope

m = 2/3

b = the y intercept

b = (0,4)

So the equation is

y = 2/3 x + 4

Your question is so confused. Are you looking for the measure of angle B?

Below is my work on how to find the angle B.

Answer:

B = 46°

Step-by-step explanation:

Cos(B) = Adj./Hypo.

Cos(B) = AB/BC

Cos(B) = 20/29

Cos(B) = 0.6897

B = Cos^-1(0.6897)

B = 46°

For this case we have to define trigonometric relations of rectangular triangles that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]cos (B)= \frac {20} {29}\\cos (B)= 0.689655172414[/tex]

So:

[tex]B = arccos (0.689655172414)\\B = 46.39718103[/tex]

Rounding off we have that B is 46 degrees

Answer:

46 degrees

ANSWER

One real root.

EXPLANATION

The graph of the function

[tex]f(x) = {x}^{3} + 6{x}^{2} + 12x + 8[/tex]

is shown in the attachment.

According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.

The x-intercepts gives the number of real roots.

Observe that the graph has only one intercept.

This implies that, the equation:

[tex]{x}^{3} + 6{x}^{2} + 12x + 8 = 0[/tex]

has only one real solution.

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Inverse proportion equation has this form:

[tex]y=\frac{k}{x}[/tex]

Where  "k" is the constant of variation.

We know that  "y" is inversely proportional to "x" and when [tex]x=3[/tex], [tex]y=6[/tex]

Then, we can substittute these values into the equation and solve for "k" to  find its value:

[tex]6=\frac{k}{3}\\\\6*3=k\\\\k=18[/tex]

Finally, we need to substitute "k" and [tex]y=9[/tex] into the equation and solve for "x":

[tex]9=\frac{18}{x}\\\\x=\frac{18}{9}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

y is inversely proportional to x is written as:

x ∝ 1/y

When the proportion is removed, a constant is introduced. We have to find the constant first to find the value of x in y = 9

So,

Removing the proportionality symbol will give us:

x=k/y

As we know that x=3 for y=6 so

3 = k/6

3*6=k

So,

k=8

Hence the value of proportionality constant is 8.

Now putting the value of y which is 9

x=k/y

=>x=18/9

=>x=2

Answer:

radius = 30 yd , cost of cement = $7065

Step-by-step explanation:

First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.

The area of the playground is ...

playground area = (109 yd)^2 = 11,881 yd^2

Then the area of the skating rinks is:

rink area = playground area - remaining field

rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2

Then the cost of cement for the rink area is ...

(2826 yd^2)($2.50 yd^2) = $7065

The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...

A = πr^2

Put the values in the formula:

2826 = 3.14r^2

Divide both sides by 3.14

900 = r^2

By taking square root at both sides we get,

30 = r

The radius of each quadrant is 30 yards....

Answer:

-1.25, 2, 3.5

Step-by-step explanation:

(x-2)(2x-7)(4x+5)=0

(2x^2-7x-4x+14)(4x+5)=5

from now on you know that either

(2x^2-7x-4x+14)=0 or

(4x+5)=0

By solving the first eqation (2x^2-7x-4x+14)=0

you get x = 2 or 3.5

By solving the second equation (4x+5)=0

you get x = -1.25

Answer:

The mean of this data set is  [tex]\mu = 24[/tex]

Step-by-step explanation:

By definition, the mean of a data set [tex]x_1, x_2, x_3, ..., x_n[/tex] is

[tex]\mu = \frac{\sum^n_i x_i}{n}[/tex]

Where n is the total number of data.

In this case we have 7 data

12, 13, 15, 28, 28, 30, 42

So the mean is:

[tex]\mu = \frac{12+ 13 +15 +28 +28 +30+ 42}{7}[/tex]

[tex]\mu = 24[/tex]

Final answer:

To find out how much Julia's movie ticket cost, we subtracted the cost of the popcorn ($7) from the total amount spent ($15) to get the movie ticket price of $8.

Explanation:

The student's question asks how much Julia's movie ticket cost if she spent a total of $15 on a movie ticket and popcorn combined, given that the popcorn cost $7. To solve this, we subtract the cost of the popcorn from the total amount spent.

Here's the calculation step by step:

Start with the total amount spent: $15.

Subtract the cost of the popcorn: $15 - $7.

The result gives us the cost of the movie ticket: $8.

Therefore, Julia's movie ticket cost $8.

Answer:

13 x + 6

Step-by-step explanation:

Perimeter of triangle  =  All the sides added together

( 5 x + 3 ) + ( 5 x + 5 ) + ( 3 x - 2 ) = 13 x + 6

Final answer:

The perimeter of the triangle, given its side lengths as linear expressions 5x + 3, 5x + 5, and 3x – 2, is found to be 13x + 6 after combining like terms.

Explanation:

To calculate the perimeter of the triangle, we simply need to add together the lengths of its three sides. The expressions for the side lengths are given as 5x + 3, 5x + 5, and 3x – 2.

The perimeter (P) can be written as a linear expression by summing these expressions:

P = (5x + 3) + (5x + 5) + (3x – 2)

Now, let's combine like terms:

P = 5x + 5x + 3x + 3 + 5 – 2

P = 13x + 6

Hence, the linear expression for the perimeter of the triangle is 13x + 6, which is the simplified form.

Answer:

Jenn

Step-by-step explanation:

Natalie and Beth swim at about the same speed. Kara swims twice as fast as Beth so she also swims twice as fast as Natalie. So Kara is faster than Natalie and Jenn is faster than Kara. Therefore Jenn is faster than Natalie.

Hope This Helps :]

Final answer:

Jenn is faster than Natalie because she swims faster than Kara who swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth.

Explanation:

The question pertains to comparing the speeds of different swimmers, which is a logical, rather than numerical comparison. Kara swims almost twice as fast as Beth, and Natalie swims about the same speed as Beth. Jenn swims faster than Kara.

Therefore, Jenn is the fastest swimmer among the four. Since the comparison is between Natalie and Jenn, and we have already established that Jenn swims faster than Kara, who in turn swims faster than Beth (and Natalie swims at the same speed as Beth), it is logical to conclude that Jenn is faster than Natalie.

Answer:

[tex]648\ yd[/tex]

Step-by-step explanation:

step 1

Find the circumference of the complete circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=35\ yd[/tex]

substitute

[tex]C=2\pi(35)[/tex]

[tex]C=70\pi\ yd[/tex]

step 2

Find the measure of the arc length for a central angle of 280 degrees

Remember that the circumference subtends a central angle of 360 degrees

so by proportion

[tex]\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd[/tex]

step 3

Find the perimeter of the playground

[tex]P=54.44\pi+45=54.44*3.14+45=215.96\ yd[/tex]

Multiply by 3

[tex]215.96*(3)=647.87\ yd[/tex]

Round to the nearest integer

[tex]647.87=648\ yd[/tex]

Answer: I'm pretty sure it's 200x - 120x = 1,200

Step-by-step explanation:

Answer:

200x - 120x = 1,200

Step-by-step explanation:

The break-even point is when the amount of money he spends equals the amount he earns.  

Let's see how much he earns and how much he spends per month:

He earns $200 per hour. If x represents the number of hours per month, we can write the earns as 200x.

He spends $1,200 per month and $120 per hour. We can write it as 1,200 + 120x.

So, we need 200x = 1,200 + 120x

We don't have this exact equation in our options but if we subtract 120x from both sides, we have:

200x - 120x = 1,200 + 120x - 120x

200x - 120x = 1,200

The correct answer is the first equation.

Answer:

3

Step-by-step explanation:

You add the total number of pets, and get 15. Then divide it by the number of people and get 3.

Answer: The mean is 3

Step-by-step explanation: In order to find the mean, you must add all the numbers (4+2+5+1+3) and then in this problem, you have to divide it by five since Spencer surveyed only five of his friends.

4+2+5+1+3=15

15 divided by 5 equals 3

Answer: im sorry i dont knoey888888888888888888888hjk.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y-2z=-3&(1)\\3x+2y-z=12&(2)\\-x-y+4z=3&(3)\end{array}\right\\\\\text{add both sides of the equations (1) and (3):}\\\\\underline{+\left\{\begin{array}{ccc}x-3y-2z=-3\\-x-y+4z=3\end{array}\right}\\.\qquad-4y+2z=0\qquad\text{add 4y to both sides}\\.\qquad2z=4y\qquad\text{divide both sides by 2}\\.\qquad\boxed{z=2y}\\\\\text{Put it to (2)}:\\\\3x+2y-2y=12\\3x=12\qquad\text{divide both sides by 3}\\\boxed{x=4}\\\\\text{Put the value of x to (1) and (3):}[/tex]

[tex]\left\{\begin{array}{ccc}4-3y-2z=-3&\text{subtract 4 from both sides}\\-4-y+4z=3&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3y-2z=-7&\text{multiply both sides by 2}\\-y+4z=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-6y-4z=-14\\-y+4z=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-7y=-7\qquad\text{divide both sides by (-7)}\\.\qquad\boxed{y=1}\\\\\text{Put the value of y to the second equation:}[/tex]

[tex]-1+4z=7\qquad\text{add 1 to both sides}\\4z=8\qquad\text{divide both sides by 4}\\\boxed{z=2}[/tex]

Answer:

Step-by-step explanation:

To graph the function h(x) = 8|x+1| - 1, plot key points at (-3, 15), (-1, -1), and (1, 15). The graph exhibits vertical stretching due to the coefficient 8 and symmetry around the line x = -1.

To graph the function (h(x) = 8|x+1| - 1), follow these steps:

1. Identify Key Points:

  Determine critical points where the expression inside the absolute value becomes zero. Here, when (x = -1), (h(x) = -1). Additionally, consider points on either side of -1.

2. Plot Points:

  Plot these points on the coordinate plane: (-3, 15), (-1, -1), and (1, 15).

3. Determine Behavior:

  Understand that the absolute value function |x+1| ensures symmetry around the vertical line x = -1. The coefficient 8 stretches the graph vertically, and the constant -1 shifts it downward.

4. Connect Points:

  Draw a smooth curve connecting the points, considering the shape of the absolute value function.

5. Label Axes:

  Label the x-axis and y-axis appropriately.

The resulting graph represents the function [tex]\(h(x) = 8|x+1| - 1\)[/tex].

Answer:

Step-by-step explanation:

Put the value of x = 0.3 to the equation 5x + 2y = 20, and solve it for y:

5(0.3) + 2y = 20

1.5 + 2y = 20           subtract 1.5 from both sides

2y = 18.5          divide both sides by 2

y = 9.25

Answer:

29

Step-by-step explanation:

(5k-3) + (9+k) = 180

6k + 6 = 180

6k = 174

k = 29

mark brainliest please (button next to the thanks button)

Answer:

k equals 29 degrees

Step-by-step explanation:

a line equals 180 degrees so you set the sum of the variables equal to 180 and solve for k

Answer:a -10

Step-by-step explanation:

-10 +8 = 2

ANSWER

[tex]x = - 10[/tex]

EXPLANATION

The given equation

[tex]x + 8 = - 2[/tex]

This is a linear equation in x.

To solve this equation, we add the additive inverse of 8 to both sides to get;

[tex]x + 8 + - 8 = - 2 + - 8[/tex]

We simplify to get:

[tex]x + 0 = - 10[/tex]

This implies that,

[tex]x = - 10[/tex]

The correct answer is A.

Answer:

[tex]\sqrt{13}\ units[/tex]

Step-by-step explanation:

we have

[tex]R(1, -1), S(6, 1),T(8, 5),U(3, 3)[/tex]

Plot the vertices

see the attached figure

The shorter diagonal is SU

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]S(6, 1),U(3, 3)[/tex]

substitute

[tex]SU=\sqrt{(3-1)^{2}+(3-6)^{2}}[/tex]

[tex]SU=\sqrt{(2)^{2}+(-3)^{2}}[/tex]

[tex]SU=\sqrt{13}\ units[/tex]

Answer:

Man cant really get more in depth than the other answer!

Answer is √(13) :D

From the given histogram, the mean of the distribution is 5. Therefore, option B is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram, the frequency distribution is

Number      Frequency

     1                    1

     2                   2

     3                   3

     4                   1

     5                   1

     6                   2

     7                   3

     8                   1

     9                   1

Now, the mean is (1×1+2×2+3×3+4×1+5×1+6×2+7×3+8×1+9×1)/15

= (1+4+6+4+5+12+21+8+9)/15

= 70/15

= 4.67

≈ 5

Therefore, the mean is 5.

To learn more about an arithmetic mean visit:

https://brainly.com/question/15196910.

#SPJ7

The mean of the data distribution is 6.3.

The mean of a data distribution can be calculated by summing all the values and dividing by the total number of values. Considering the data set 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the mean is:

(4 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8) / 10 = 63 / 10 = 6.3

To simplify the expression √(5/8), you can simplify the numerator and denominator separately. The square root of 8 can be simplified to 2√2. Rationalizing the denominator, the final simplified form is √10 / 4.

To simplify the expression √(5/8), we can first simplify the numerator and denominator of the fraction separately. The square root of 5 is not a perfect square, so we cannot simplify it further. The square root of 8, however, can be simplified. We can write 8 as 4 * 2, and since 4 is a perfect square, we can take its square root. So, we have √(5/8) = √5 / √8.

Next, we can simplify the square root of 8. √8 can be written as √4 * √2, and since √4 is 2, we have √8 = 2√2. Substituting this back into our expression, we get √(5/8) = √5 / 2√2.

Finally, we can simplify the expression further by rationalizing the denominator. We can multiply the numerator and denominator by √2 to get rid of the radical in the denominator. This gives us the final simplified form: √(5/8) = (√5 * √2) / (2√2 * √2) = (√10) / (2 * 2) = √10 / 4.

Answer:

Step 2: Olivia incorrectly determined 1/2 of 10% of 720

Step-by-step explanation:

1/2 of 720 = 360

10% of 720 = .10*720 = 72

1/2 of 72 = 36

This is not the same as 31

This is the incorrect step

Step 2

Answer:

Step 2: Olivia incorrectly determined One-half of 10% of 720.Step-by-step explanation:

Answer:

-9x^3(x - 7)(x + 3)

Step-by-step explanation:

Answer:

The value of (g*h) (-3)  is [tex]=-\frac{112}{3}[/tex]

Step-by-step explanation:

If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]

We have to find (g*h) (-3)

First multiply g(x) with f(x)

[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]

[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]

simplify

[tex]=-x^2+6x+\frac{4}{x}-9[/tex]

Now, put x= -3 in above expression

[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]

[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]

[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]

[tex]=7\left(-\frac{16}{3}\right)[/tex]

[tex]=-\frac{16}{3}\cdot \:7[/tex]

[tex]=-\frac{112}{3}[/tex]

Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]

Answer:

(2, 0)

Step-by-step explanation:

Given

y = x² + 3x - 10

To find the x- intercepts let y = 0, that is

x² + 3x - 10 = 0 ← in standard form

Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

The factors are + 5 and - 2, since

5 × - 2 = - 10 and 5 - 2 = + 3, hence

(x + 5)(x - 2) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 5, 0) and (2, 0)

Answer:

x = -8   &   at x = 3

Step-by-step explanation:

This is a rational function.

We can get the values of x at which vertical asymptotes occur by setting the denominator equal to 0 and solving for x.

Let's do this:

[tex]x^2+5x-24=0\\(x+8)(x-3)=0\\x=-8,3[/tex]

Hence, vertical asymptotes occur at x = -8 & at x = 3

Answer:

Average rate of change = -6

Step-by-step explanation:

The average rate of change over the interval (a,b) is given by;

[ f(b) - f(a)] / (b-a)........................where interval is (a,b)

(a,b) interval =(-3,1)

Where;

f(x)= -12 (x+2)² +5

[tex]f(a)=f(-3)=-12(-3+2)^2+5\\f(a)=f(-3)=-12(-1)^2+5\\f(a)=f(-3)=-12(1)+5\\=-12+5=-7\\\\\\f(b)=f(1)=-12(1+2)+5\\f(b)=f(1)=-12(3)+5\\=-36+5=-31\\\\f(b)-f(a)=-31--7=-24\\\\b-a=1--3=4\\\\f(b)-f(a)/b-a=\frac{-24}{4} =-6[/tex]