Select the description that is true of the equation 3x + y =9
x-intercept equals
x-intercept equals
y-intercept equals 3
y-intercept equals 9

The question appears to be about finding the midpoint of segment AH, which involves dividing the segment into two equal parts, either by measurement or by averaging the coordinates of A and H if available.

The question seems to be asking about identifying the midpoint of a line segment in a geometric construction. However, the provided text alludes to various geometric proofs and theorems, rather than directly providing information about finding midpoints.

To find the midpoint of segment AH, one would need to measure the length of AH and then divide it by 2 to find the center point. If the points A and H are on a coordinate plane, the midpoint can be found by calculating the average of the x-coordinates and the y-coordinates of the endpoints A and H. Without specific coordinates or measurements, a more detailed answer cannot be provided.

The midpoint of AH is (0, 4).

Let's assign coordinates to the points A and H to make it easier to calculate the midpoint. Suppose A is at (x1, y1) and H is at (x2, y2).

The formula for finding the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is:

[tex]M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)[/tex]

If we assume A is at (0, 0) and H is at (0, 8) (since H is directly 'below' A on a vertical line), the coordinates are as follows:
A = (0, 0)
H = (0, 8)

Now, applying the midpoint formula:

[tex]M = \left( \frac{0 + 0}{2}, \frac{0 + 8}{2} \right) = (0, 4)[/tex]

Answer:

The slope is 2.

Step-by-step explanation:

The given line has equation: [tex]f(t)=2t-6[/tex].

This is a linear equation in [tex]t[/tex].

The slope is the coefficient of the independent variable [tex]t[/tex].

The coefficient of [tex]t[/tex] in  [tex]f(t)=2t-6[/tex] is 2.

Therefore the slope is 2.

Alternatively,  [tex]f(t)=2t-6[/tex] is of the form  [tex]f(t)=mt+c[/tex], where [tex]m=2[/tex] is the slope.

Answer:

Step-by-step explanation:

The slope is 2 and the y intercept is -6

Answer:

Mary: 16

Kevin: 22

Ahmed: 88

Step-by-step explanation:

This could be written as the following formula.

Mary + Kevin + Ahmad = 126

and we know that

Mary + 6 = Kevin

Kevin * 4 = Ahmed

so Ahmed = (Mary + 6) * 4

When filling this in you get

Mary + Mary + 6 + (Mary + 6) * 4 = 126

Mary + Mary + 6 + 4Mary + 24 = 126

6Mary + 30 = 126

6Mary = 96

Mary = 16

So Mary served 16 orders.

Using the earlier formulas you get

Kevin = Mary + 6 = 16 + 6 = 22

Ahmed = Kevin * 4 = 22 * 4 = 88.

Now we just need to double check it.

Mary + Kevin + Ahmad = 16 + 22 + 88 = 126. Which matches what it should be.

Answer:

A = 64 pi inches ^2

Step-by-step explanation:

Circumference is equal to

C =2*pi*r  where r is the radius

16 pi = 2 * pi *r

Divide each side by 2 pi

16pi/2pi = 2pir/2pi

8 = r

The radius is 8

To find the area, we use

A = pi r^2

   =pi (8)^2

  = 64 pi

The graph shows the solutions:

x1 = -3    ⇒  x + 3 = 0

x2 = 1     ⇒  x - 1 = 0

x3 = 5     ⇒  x - 5 = 0

The polynomial follows:   y = (x + 3)(x - 1)(x - 5)

.

Answer:

y= (x+3) (x-1) (x-5)

Step-by-step explanation:

The graph crosses the x axis at the points -3,1,5

These are also called the zeros

f(x) =k (x-a) (x-b) (x-c) .....

where a,b,c,... are the zeros of the function and k is a constant

f(x) = k * (x--3) (x-1) (x-5)

f(x) = k(x+3) (x-1) (x-5)

To help determine the value of k

Take another point  at x = 0, we know the value is positive

f(0) = k(3) (-1) (-5)

f(0) = k(15)

That means k must be greater than 0  Looking at the graph, it should be around 1

f(x) = (x+3) (x-1) (x-5)

The perimeter of a rectangle with sides of 14 ft and 8 ft is 44 ft.

The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with sides of 14 ft and 8 ft, the perimeter is found by adding twice the length and twice the width:

Perimeter = 2(length + width)
Perimeter = 2(14 + 8) = 2(22) = 44 ft

Answer:

33 feet

Step-by-step explanation:

We can draw a triangle in this situation.

Note:

The height of the tree is the side "opposite" of the 35 angle. The squirrel's distance of 47 feet from the base of the tree is the side "adjacent" to the angle.

Which trig ratio relates "opposite" and "adjacent"?

It is Tan

Thus we can write and solve (let height of tree be h):

[tex]Tan(35)=\frac{h}{47}\\h=Tan(35)*47\\h=32.91[/tex]

To the nearest foot, the height of tree is about 33 feet

Answer:

<-6,-4>

Step-by-step explanation:

To find u+v, all you have to do is add the corresponding components of each.

That is for example on this problem, you would do

<-3,-5>+<-3,1>

=<-3+-3,-5+1>

=<-6,-4>.

Answer:

8 1/8 hours

Step-by-step explanation:

1 5/8 * 5 = 5 25/8

5 28/5 = 5 + 3 + 1/8

= 8 1/8 hours

I think the answer is 8 1/8

Answer:

=2.83 the second option

Step-by-step explanation:

Using the trigonometric ratios we can find the sides of the triangle with the acute angles.

In the triangle provided we will use COSINE

Cos ∅=adjacent/hypotenuse

Let us substitute with the values in the question into the formula.

Tan 45 =2/x

x=2/Cos 45

=2.83 units

Answer: SECOND OPTION.

Step-by-step explanation:

You can use the following identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=45\°\\adjacent=2\\hypotenuse=x[/tex]

Therefore, in order to calculate the value of "x", you need to substitute values into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for "x".

This is:

[tex]cos(45\°)=\frac{2}{x}\\\\xcos(45\°)=2\\\\x=\frac{2}{cos(45\°)}\\\\x=2\sqrt{2}[/tex]

[tex]x[/tex]≈[tex]2.83[/tex]

The two lines are parallel, which means they never touch, cross or meet.

Answer: No solution

Answer:

no solution

Step-by-step explanation:

Answer:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Step-by-step explanation:

Rule of exponents:

[tex] a^{\frac{1}{n}} = \sqrt[n]{a} [/tex]

Apply the rule to this case:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Answer:

Wrong

Step-by-step explanation:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Answer:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\14\%=\dfrac{14}{100}=0.14\\\\3540\%=\dfrac{3540}{100}=35.40=35.4\\\\14\%\ of\ 3540\%\ of\ 35\to(0.14)(35.4)(35)=173.46[/tex]

Answer:

D.

Step-by-step explanation:

The data is symmetric for Shop A but not for Shop B ( note the values 10 and 11 for Shop B which are a lot lower than the other values).

Mean for Shop A and Median for Shop B.

Answer:

The correct option is B.

Step-by-step explanation:

The number of lattes sold daily by two coffee shops is shown in the table.

The data set for shop A is

55, 52, 56, 48, 57, 30, 45, 41

Arrange the data in ascending order.

30, 41, 45, 48, 52, 55, 56, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{30+41+45+48+52+55+56+57}{8}=48[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50[/tex]

The data set for shop B is

45, 42, 57, 48, 11, 10, 46, 43

Arrange the data in ascending order.

10, 11, 42, 43, 45, 46, 48, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{10+11+42+43+45+46+48+57}{8}=37.75[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44[/tex]

Both data distribution are not symmetric, so it is better to describe the centers of distribution in terms of median for both coffee shops. Therefore the correct option is B.

Answer:

I believe the answer rqould be B since only 1 thing happened

Answer: Option B

Step-by-step explanation:

Simple event is an event where all the possible outcomes have the same probability.

Are the type of events that we can write as:

P = number of a given outcome/total posible outcomes.

Here we have 3 combined options (A, C and D) that, while in parts can be described in that way, not as whole events.

The correct option is B, where the probability of getting a given number in a dice is the number of times that the number repeats (1) divided the total number of options (6), P =  1/6 for all the numbers, so this is a simple event.

Answer:

The answer is equal to. Each equation equals 1.

Answer:

[tex]3-\sqrt{11}[/tex]

Step-by-step explanation:

If you want rational coefficients then you would want the conjugate of any irrational zero given.

The question is equivalent to what is the conjugate of [tex]3+\sqrt{11}[/tex].

The conjugate of [tex]3+\sqrt{11}[/tex] is [tex]3-\sqrt{11}[/tex].

In general, the conjugate of a+b is a-b

or the conjugate of a-b is a+b.

Or maybe you like this explanation more:

Let [tex]x=3+\sqrt{11}[/tex]

Subtract 3 on both sides:

[tex]x-3=\sqrt{11}[/tex]

Square both sides:

[tex](x-3)^2=11[/tex]

Subtract 11 on both sides:

[tex](x-3)^2-11=0[/tex]

Use difference of squares to factor. I apply [tex]u^2-v^2=(u-v)(u+v)[/tex].

[tex]([x-3]-\sqrt{11})([x-3]+\sqrt{11})=0[/tex]

So you have either

[tex][x-3]-\sqrt{11}=0[/tex] or [tex][x-3}+\sqrt{11}=0[/tex]

Solve both for x-3 and then x.

Add sqrt(11) on both sides for first equation and subtract sqrt(11) on both sides for second equation:

[tex]x-3=\sqrt{11}[/tex] or [tex]x-3=-\sqrt{11}[/tex]

Add 3 on both sides:

[tex]x=3+\sqrt{11}[/tex]  or [tex]x=3-\sqrt{11}[/tex]

Answer:

the answer is C.

Step-by-step explanation:

Answer:

204 in^3

Step-by-step explanation:

The volume of the base square is V=lwh.

When we substitute our givens, it becomes V=6(4)(2). This equals 48 in^3.

The volume of the triangle is V=.5lwh.

When we substitute our givens, it becomes V=.5(6)(4)(15-2). This equals 156 in^3.

When we add 48 and 156, we get 204 in^3.

Hope this helps :)

Answer:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

Step-by-step explanation:

Using:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

we will have two solutions.

x^2-3x+1=0

So, a=1   b=-3  c=1

[tex]x_{1}=\frac{+3+\sqrt{-3^{2}-4*1*1} }{2*1}\\\\x_{2}=\frac{+3-\sqrt{-3^{2}-4*1*1} }{2*1}[/tex]

We have two solutions:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

The answer is in the picture below! :)

|

V

Step-by-step explanation:

x - y = 7...eqn 1

x^2 + y = 125...eqn 2

making y the subject of the formula in eqn 1

=> y = x -7...eqn 3

subst for y from eqn 3 in eqn 2

=> x^2 + x-7 = 125

=> x^2 + x - 132 = 0

=> (x + 12) (x -11) =0

x = 11 or -12

when x = 11, y = 4

when x = -12, y = -19

Answer:

The largest numbers is either -12 or 11

Step-by-step explanation:

Let the numbers be a and b and a be the largest number.

The difference of two numbers is 7

        a - b = 7 ------------------------- eqn 1

The sum of the smaller number and the square of the larger number is 125

        a² + b = 125 ------------------------- eqn 2

eqn 1 + eqn 2

       a² + a - 132 = 0

       ( a + 12 ) (a - 11) = 0

        a = -12 or a  = 11

So the largest numbers is either -12 or 11

Answer:

2πrh unit^2.

Step-by-step explanation:

The lateral area is  the circumference of the base * the height =  2πrh.

The lateral area of a right cylinder with height equal to h and r as the radius is 2πrh. Therefore, option C is the correct answer.

All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

The surface area that a cylinder's curved surface alone covers is known as the curved surface area (CSA) or lateral surface area. The curved surface area of a cylinder is computed using the formula 2πrh, where  height of the cylinder is h and the radius of the base is r.

Therefore, option C is the correct answer.

Learn more about the lateral surface area here:

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"Your question is incomplete, probably the complete question/missing part is:"

Which of the following formulas would find the lateral area of a right cylinder with height equal to h and r as the radius?

A. LA = 2πr²

B. LA = 2πr

C. LA = 2πrh

D. LA = 2πr² + 2πrh

Answer: B. Rhombus.

Step-by-step explanation: B. Rhombus is the answer because a rectangle has 2 pairs of equal sides. A pentagon has 5 sides. A trapezoid doesn’t have all equal sides. A rhombus is like a squished square.

ANSWER

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

EXPLANATION

The given equation is :

[tex] \frac{2}{5}(x - 2) = 4x[/tex]

We multiply both sides by [tex] \frac{5}{2} [/tex]

[tex] \frac{5}{2} \cdot\frac{2}{5}(x - 2) = 4x \times \frac{5}{2} [/tex]

We simplify to obtain:

[tex]x - 2 = 10x[/tex]

Group similar terms to obtain:

[tex] - 2 = 10x - x[/tex]

Simplify the right hand side.

[tex] - 2 = 9x[/tex]

Divide both sides by 9.

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

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

Or

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

The second choice is correct

The solution for [tex]x[/tex] is [tex]x = -\frac{2}{9}[/tex].

To solve the equation [tex]\frac{2}{5} (x - 2) = 4x[/tex], we need to perform the following steps:

Distribute the Fraction:
We start by distributing [tex]\frac{2}{5}[/tex] to both terms inside the parentheses:
[tex]\frac{2}{5}x - \frac{2}{5} \cdot 2 = 4x[/tex]
This simplifies to:
[tex]\frac{2}{5}x - \frac{4}{5} = 4x[/tex]

Isolate the Variable:
Next, we want to get all terms involving [tex]x[/tex] on one side. We can do this by subtracting [tex]\frac{2}{5}x[/tex] from both sides:
[tex]-\frac{4}{5} = 4x - \frac{2}{5}x[/tex]

Now, we can combine the [tex]x[/tex] terms on the right:
[tex]4x - \frac{2}{5}x = \left(4 - \frac{2}{5}\right)x = \left(\frac{20}{5} - \frac{2}{5}\right)x = \frac{18}{5}x[/tex]
Thus, we have:
[tex]-\frac{4}{5} = \frac{18}{5}x[/tex]

Solve for x:
Now, we want to solve for [tex]x[/tex] by multiplying both sides of the equation by the reciprocal of [tex]\frac{18}{5}[/tex], which is [tex]\frac{5}{18}[/tex]:
[tex]x = -\frac{4}{5} \cdot \frac{5}{18} = -\frac{4}{18} = -\frac{2}{9}[/tex]

Given the multiple-choice options of [tex]\frac{2}{9}[/tex], [tex]9[/tex], [tex]-\frac{2}{9}[/tex], and [tex]-\frac{9}{2}[/tex], the correct answer is negative 2 over 9.

Answer:

B. & E.

Step-by-step explanation:

First, to find your slope, put your line into slope-intercept form.

[tex]y=mx+b\\[/tex]

[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4} x-\frac{7}{4}[/tex]

Your slope is [tex]\frac{3}{4}[/tex].

Now, you can find the y-intercept of your parallel line by plugging your given point and your slope into point-slope form.

[tex]y-y1=m(x-x1)\\y-(-2)=\frac{3}{4} (x-(-4))\\y+2=\frac{3}{4} (x+4)\\y+2=\frac{3}{4} x+3\\y=\frac{3}{4} x+1[/tex]

Your y-intercept is 1.

If you notice, answer choice E is equivalent to one of our steps in converting it to point-slope form. Therefore, E is one of your answers.

The equation of your parallel line is:

[tex]y=\frac{3}{4} x+1[/tex]

B is also a correct answer.

If you put B into slope-intercept form, you get the following:

[tex]3x-4y=-4\\-4y=-3x-4\\y=\frac{3}{4} x+1[/tex]

This, of course, is equivalent to the parallel line which we already found, so we know it is parallel.

Answer:

-2

Step-by-step explanation:

Within the provided points list for the graph, there is the coordinate (1, -2). Hence, by definition of a function and how to read graphs, f(1) is -2.

In this scenario, you're being asked to read the value of f(1) from a given graph. The line passing through the listed points is irrelevant provided one of the plotted points has an x-coordinate of 1. You directly read this from the graph - not calculate it or interpolate it. The list of points you've provided includes (1, -2), so, in your case, f(1) = -2. This is exactly how you would refer to the y-value at x=1 on a visual graph.

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Answer:first equation is 4 units shifted down from the second

Step-by-step explanation:

Answer:

The graph of y = 5x²-4 differs from the graph of y = 5x² by difference of 4 units

Step-by-step explanation:

In y = 5x²-4, when y is 0 x is not 0 and when x is 0 , y is not 0

but

In y = 5x² , when y is 0 , x is 0 and vise versa.

In y = 5x² the value of y will always increase as the value of x increase.

Answer:

A closed circle on the graph indicates that the point is included in domain and range. An open circle indicates that the point is not included in the domain and range.

Now based on this, we will evaluate the given options:

Option A. The function g(x) is defined for all real numbers x.

The lines on the graph contain a limited values. Hence its obvious that the domain and range is not the set of all Real numbers. Hence this option is Wrong.

Option B. The maximum value of the range is 4.

From the graph we can see that the maximum/highest value along y-axis is 4. Since there is a closed circle at (-4, 4), this value is included in the range. Hence this option is True.

Option C. The maximum value of the domain is 3

There is an open circle at the point when x is 3. Hence this point is not included in the Domain. Value of domain is numbers less than 3. Hence this option is Wrong.

Next two options are incomplete. Here are the complete options and listed correctly.

Option D. The range of g(x) is {yl -1 < y ≤ 4}

This is correct because there is an open circle at point (3, -1). Hence -1 would not be included in the range. The range will be set of all values from -1 to 4, including 4 as there is a closed circle at (-4, 4)

Option E. The domain of g(x) is {x| x ≤ -4 ≤ -1 or 0 ≤ x <3}

Since there are closed circles at points where x is -4, -1 and 0, these points would be included in the Domain. 3 wont be included in the Domain as there is an open circle.

Answer:

B and D are correct.

The sum of the geometric series is approximately 435.4, according to the formula for geometric series summation.

To find the sum (Sn) of a geometric series, you can use the formula:

[tex]\[ Sn = \frac{{a_1 \cdot (1 - r^n)}}{{1 - r}} \][/tex]

Where:

[tex]- \( a_1 \) is the first term\\- \( r \) is the common ratio\\- \( n \) is the number of terms[/tex]

Given:

[tex]\( a_1 = 0.28 \)\( a_5 = 362.88 \)\( r = 6 \)[/tex]

We need to find [tex]\( n \)[/tex]. Since [tex]\( a_5 \)[/tex] is the fifth term, we can use the formula for the nth term of a geometric series:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

Substitute the values we have:

[tex]\[ 362.88 = 0.28 \cdot 6^{(5-1)} \]\[ 362.88 = 0.28 \cdot 6^4 \]\[ 362.88 = 0.28 \cdot 1296 \]\[ 362.88 = 363.648 \][/tex]

So, [tex]\( n = 5 \).[/tex]

Now, plug the values into the sum formula:

[tex]\[ S_5 = \frac{{0.28 \cdot (1 - 6^5)}}{{1 - 6}} \]\[ S_5 = \frac{{0.28 \cdot (1 - 7776)}}{{-5}} \]\[ S_5 = \frac{{0.28 \cdot (-7775)}}{{-5}} \]\[ S_5 = \frac{{-2177}}{{5}} \]\[ S_5 = -435.4 \][/tex]

Since the sum of a series cannot be negative, the correct answer is option:

a. 435.4

Answer:

(x^2)/3 + 4

Step-by-step explanation:

4 more means add four and the quotient of x squared and 3 shows that x squared must be divided by three before added to 4

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