Find the midpoint of the line segment with the endpoints A and B.
A(4.8): B(10,2)

Answer:

K = 3/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

k−9=5(k−3)

k+−9=(5)(k)+(5)(−3)(Distribute)

k+−9=5k+−15

k−9=5k−15

Step 2: Subtract 5k from both sides.

k−9−5k=5k−15−5k

−4k−9=−15

Step 3: Add 9 to both sides.

−4k−9+9=−15+9

−4k=−6

Step 4: Divide both sides by -4.

-4k/-4 = -6/-4

K = 3/2

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Answer: Number 2

Step-by-step explanation: yes

Answer:

the tax on a $90,000 salary is: $5175

Step-by-step explanation:

Given that the person earns a $90,000 annual salary, you need to use the last of the brackets , the one that reads "17,001 and up". That is, you need to find the 5.75% of the $90,000 in order to determine the taxes owed.

Recall that 5.75% in math terms is: 5.75/100 = 0.0575

Then the 5.75% of $90,000 is mathematically calculated as the product :

0.0575 x 90,000 = 5175

Therefore the tax on a $90,000 salary is: $5175

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

the 4th one hope right

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(2) = 3(2) - 3 = 6 - 3 = 3

h(3) = 3^2 - 4(3) = 9 - 12 = -3

A is the answer

56 and 79 am 12 and 68976

Answer: Dan Artes

Step-by-step explanation:

Well neither will be correct considering 35x103 is 3605

Since Dan is closer he would be correct considering kevin is way off.

Answer:

OMG

Step-by-step explanation:

I had the same question

Answer:

$10.79

Step-by-step explanation:

x =  original cost of one t shirt

We can build this equation

x - (20/100) x + 3x- 5 = 36

-1/5x + 4x = 41

-x + 20x = 205

19x  = 205

x = $10.79

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Okay, let's break this down step-by-step:

1) We need to choose a slope within 6 to 8 feet of vertical change for every 100 feet of horizontal change.

Let's choose a slope of 7 feet of vertical change for every 100 feet of horizontal change.

2) So for every 100 feet horizontally, the zip line will drop 7 feet vertically.

3) We know the ending point height, but we need to calculate the starting point height.

4) If the ending point height is 100 feet above the ground, then for every 100 feet of horizontal distance, the line drops 7 feet.

So to drop 100 feet vertically, the line would have to travel 100 / 7 = 14.29 ~ 15 100-foot segments.

5) So if the ending point is 100 feet above the ground,

the starting point will be 100 + (15 * 7) = 100 + 105 = 205 feet above the ground.

6) Therefore, the difference between the starting and ending point heights is 205 - 100 = 105 feet.

So the difference between the starting and ending point heights of the zip line is 105 feet.

Please let me know if any of the steps are unclear or if you have any other questions! I'm happy to explain further.

Answer:

The zip line needs to be 35 feet higher than the ending point.

Step-by-step explanation:

Assuming that we want to build a zip line with a slope of between 6 to 8 feet of vertical change for every 100 feet of horizontal change, we can choose a slope of 7 feet of vertical change for every 100 feet of horizontal change. This slope is within the given constraint of 6 to 8 feet of vertical change for every 100 feet of horizontal change.

To determine how much higher the starting point of the zip line needs to be than the ending point, we need to know the horizontal distance between the two points. Let's assume that the horizontal distance between the two points is 500 feet.

Using the slope of 7 feet of vertical change for every 100 feet of horizontal change, we can calculate the vertical change as follows:

Vertical change = slope * horizontal change

Vertical change = 7/100 * 500

Vertical change = 35 feet

Therefore, the starting point of the zip line needs to be 35 feet higher than the ending point.

Answer:

Kate owns Brain $5

Step-by-step explanation:

Answer:

C. -2

Step-by-step explanation:

4(y–3)+19=8(2y+3)+7

4y-12+19=16y+24+7

4y+7=16y+31

-12y=24

12y=-24

y=-2

Answer:

4(y-3)+19=8(2y+3)+7

4y -12 +19=16y+24+7...

-12+19-24-7=16y-4y

-24=12y÷12

-2=y...

•

•. • C.-2...

Answer:

because they made a mistake

This would be the average value of R(x) between 10 m and 50 m :

\(\displaystyle \frac1{50\,\mathrm m - 10\,\mathrm m} \int_{10\,\rm m}^{50\,\rm m} kx^2 \, dx\)

The average intensity of radiation between 10 meters and 50 meters from the source is 1033.33 k.

It is the reverse of differentiation.

The intensity of radiation at a distance x meters from a source is modeled by the function given by

R(x)=kx²

where k is a positive constant.

The average intensity of radiation between 10 meters and 50 meters from the source will be

\(\rm Average \ intensity = \dfrac{1}{50 - 10} \int_{10}^{50} \ kx^2 \ dx\\\\\\Average \ intensity = \dfrac{k}{50 - 10} [ \dfrac{x^3}{3} ]_{10}^{50}\\\\\\Average \ intensity = \dfrac{k}{40} [ \dfrac{50^3}{3} - \dfrac{10^3}{3} ]\\\\\\Average \ intensity =1033.33k\)

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9514 1404 393

Answer:

  (a) 3%

Step-by-step explanation:

Nathan's actual mileage was ...

  (2882 mi)/(131 gal) = 22.0 mi/gal

The error can be computed from ...

  error % = (predicted/actual -1) × 100% = (22.6/22 -1) × 100% ≈ 2.73%

Nathan's prediction was high by about 3%.

Step-by-step explanation:

500 ×1.07^t <-- function (I think)

500 × 1 07^2 = $572.45 <-- balance after 2 years

x-12= 36

x-12= 36

x= 36 - 12

x= 24

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.

Answer:

5 is the answer

Step-by-step explanation:

\(\dfrac{ \left( 44+ { 9 }^{ 2 } \right) }{ { 5 }^{ 2 } }\)

Calculate 9 to the power of 2 and get 81

\(\dfrac{ 44+81 }{ { 5 }^{ 2 } }\)

Add 44 and 81 to get 125

\(\dfrac{ 125 }{ { 5 }^{ 2 } }\)

Calculate 5 to the power of 2 and get 25

\(\frac{125}{25}\)

Divide 125 by 25 to get 5

\(5\)

The exponential function represented by the given graph is:

y = 2(.5^x)

Here we have an exponential decay, the general form of these functions is:

y = A*(b)^x

Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.

Now let's look at the y-intercept, we can see that it is y = 2, then:

2 = A*(b)^0

2 = A

The function is of the form:

y = 2*(b)^x   with 0 < b < 1.

The option that meets these conditions is the first one: y = 2(.5^x)

So that is the correct option.

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Answer:

12

Step-by-step explanation:

The hypotenuse is always 2x the short!

6 x 2 = 12!

probably 1 and 2, I'm only in 6th grade tho so I forgot (love the pfp btw)

The measure of the smallest angle of a tree with a hill is 60°.

The measure of the greatest angle of a tree with a hill is 120°.

Given:

A tree on a 30° slope grows straight up.

To find:

The measures of the

greatest and smallest angles the tree makes with the hill.

Solution:

In figure drawn:

\(\angle PQR = 30^o\)

AB= Straight three

Construction:

Draw a parallel line CA to QR through point A.

Now,

\(\angle PQR = \angle PAC = 30^o\\\\\angle PAC +\angle PAB = 90^o \text{(Complimentary angles)}\\\\\angle PAB = 90^o -\angle PAC\\\\angle PAB=90^o-30^o=60^o\)

The measure of the smallest angle of a tree with a hill is 60°.

\(\angle PAB + \angle BAQ= 180^o\text{(Supplementary angles)}\\\\ \angle BAQ= 180^o-\angle PAB \\\\ \angle BAQ=180^o-60^o=120^oC\)

The measure of the greatest angle of a tree with a hill is 120°.

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Answer:

Neither; see below

Step-by-step explanation:

Your acceleration: \(a=\frac{\Delta v}{\Delta t}=\frac{25-0}{25}=1m/s^2\)

Your friend's acceleration: \(a=\frac{\Delta v}{\Delta t}=\frac{6-0}{6}=1m/s^2\)

Therefore, since both you and your friend accelerate at the same rate, neither is faster.

This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.

The coordinates are given as:

First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).

Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)

Calculate the distance AB and A'B' using:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ AB = √ (-4 + 3)² + (9 - 7)²

⇒ AB = √1 + 4

⇒ AB = √5

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ A'B' = √ (3 - 3)² + (6 + 4)²

⇒ A'B' = 10

This gives, Divide A'B' by AB to determine the scale factor (k)

k = 10 / √5

k = 2√5

Hence, this transformation is a by a factor of 2√5

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Answer:

Reflection and 2

Step-by-step explanation:

for plato