Consider the quadratic inequality, x^2 - 3x < 10. When you solve the inequality the solution is -2

we have that

[tex]y=-x^2+36[/tex]

we know that

Is the equation of a vertical parabola open down

so

the vertex is a maximum

step 1

convert the equation of the parabola in the vertex form

[tex]y=-x^2+36[/tex]

[tex]y-36=-x^2[/tex]

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0

so

for y=0

[tex]-x^2+36=0[/tex]

[tex]x^2=36[/tex]

[tex]x=(+/-)6[/tex]

the points are (-6,0)  and (6,0)

see the attached figure

Answer:

Step-by-step explanation:

Answer: 76 degrees

Step-by-step explanation: 63 + 13 = 76

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

As we know,

[tex] \sf \qquad density = \dfrac{mass}{volume} [/tex]

So, we can infer that :

[tex] \sf \qquad mass= {density} \cdot{volume} [/tex]

Now, let's calculate the mass of gases in each case :

[tex]\qquad \sf  \dashrightarrow \:mass = 0.09 \times (15) {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \:mass = 0.09 \times 3375 {}^{} [/tex]

[tex]\qquad \sf  \dashrightarrow \:mass = 303.75 \: \: mg {}^{} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:mass =0. 30375 \: \: g {}^{} [/tex]

[tex]\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: (14 \sdot 12 \sdot10)[/tex]

[tex]\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: 1680[/tex]

[tex]\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: 294 \: \: mg[/tex]

or

[tex]\qquad \sf  \dashrightarrow \:mass = 0.294 \: \: g[/tex]

[tex]\qquad \sf  \dashrightarrow \:mass = 1.251\: \cdot \: \dfrac{4}{3} \cdot3.14 \cdot(4) {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \:mass = 0.417\: \cdot \: 803.84[/tex]

[tex]\qquad \sf  \dashrightarrow \:mass = 335.201 \: \: mg[/tex]

or

[tex]\qquad \sf  \dashrightarrow \:mass = 0.335 \: \: g[/tex]

So, the arrangement of masses from least to greatest is :

Answer:

Helium<Hydrogen<Nitrogen

Step-by-step explanation:

Answer:

4+(n-1)2

Step-by-step explanation:

Because its an arithmatic series for which the formula is

n-term=first term+(n-1)d.

where "d" is the common difference.

Answer:

30 min

Step-by-step explanation:

1 /  ( 1/20 + 1/ x) =  12

1 = 12/20 + 12/x

8/20 = 12/x

x = 12 * 20 / 8 = 30 min

p=20+25c because it i did this on paper so i got what it equals to

Answer:

The length of AC is 12.08cm

Step-by-step explanation:

hope it's help

;)

Answer:

see photo for detailed analysis

Answer:

The original value of the car.

Step-by-step explanation:

The 21,500 would be the a value of the function, as it is before the parentheses. The a value of an exponential function is a constant, and it is the y-intercept of that function, meaning in a real-world application, it would be where the values start at. In this case, the 21,500 is where the price of the car starts at, i.e., the original value of the car.

The equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]

The equation is given as:

x² - 10x + 13 = 0

The solution to a quadratic equation is represented by:

[tex]x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

So, we have:

[tex]x =\frac{10 \pm \sqrt{(-10)^2 -4 * 1 * 13}}{2 * 1}[/tex]

Evaluate the radicand

[tex]x =\frac{10 \pm \sqrt{48}}{2}[/tex]

Take the square root of 48

[tex]x =\frac{10 \pm 4\sqrt{3}}{2}[/tex]

Divide

[tex]x =5 \pm 2\sqrt{3}[/tex]

Hence, the equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]

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Answer:

mode and median

Step-by-step explanation:

both are 80

mode - value that appears most often

median- list values lowest to highest find the value in the middle position

Answer:

C. 50 + 80 + 2 + 8

Step-by-step explanation:

this would give you an answer 8 greater then the original equation 52+80

Answer:

18.84

Step-by-step explanation:

The diameter is 2 times the radius, so just multiply 6 by 3.14

please mark brainliest ( :

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate the circumference ~

[tex]\qquad \sf  \dashrightarrow \: c = \pi d[/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 3.14 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: c =18.84 \: ft[/tex]

Answer:

  h(x), g(x), f(x)

Step-by-step explanation:

The axis of symmetry of a parabola is the vertical line through its vertex.

__

The equation is written in vertex form:

  f(x) = a(x -h)² +k . . . . . vertex (h, k), scale factor 'a'

The vertical line through the vertex is x=h.

Your equation is ...

  f(x) = -2(x -4) +2

so (h, k) = (4, 2) and the line of symmetry is x=4.

__

The given equation can be written in vertex form:

  g(x) = 5x² -10x +7

  g(x) = 5(x² -2x) +7

  g(x) = 5(x² -2x +1) +7 -5 . . . . complete the square

  g(x) = 5(x -1)² +2

so (h, k) = (1, 2) and the line of symmetry is x=1.

__

Your problem statement tells us ...

  h(x) = -(x +2)² +2

so (h, k) = (-2, 2) and the line of symmetry is x=-2.

The coordinates of the vertex can also be read from the graph: (-2, 2).

__

The rank of the functions is the order of {-2, 1, 4}, or h(x), g(x), f(x).

Answer:

the answer is c

Step-by-step explanation:

I already did that

Answer:

C that's the answer

no explanation I'm jus saying

Answer:

1.2378×104

Step-by-step explanation:

The number 10 is called the base because it is this number that is raised to the power n. Although a base number may have values other than 10, the base number in scientific notation is always 10.

Answer:

Step-by-step explanation:

10b + -2

or

10b - 2

8b + 2b = 10b

7 - 9 (or 9 - 7, which equals 2) = -2

you can add -2 which is

10b + -2

or subtract

10b - 2

Answer:

10b-2

Step-by-step explanation:

8b+2b is 10b. Then 7+(-9) is -2. Combine the answer to get 10b-2

Answer:

The correct option is C. if you express the problem in terms of ㏑ three and seven.

Answer:

4

2

one-half

Step-by-step explanation:

Hope this helps!! :)

Using the interactive ruler, we can determine that it is 4 Units from the dilation's center to the image and pre-image.

This virtual instrument, which appears on the computer screen and is also known as an Interactive Teaching Program (ITP) ruler, is used to measure a shape's lines and sides.

Given, we need to find the distance in units between points C and A

Using the interactive ruler, we can determine that the separation between points C and A is 2 units.

Therefore, it takes 1.5 units to get from point C to point A'.

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y = -4x - 1

the gradient of the parallel line will be the same as the given line so you just need to change the y intercept

[tex]~~~~~~~\dfrac 25 x - \dfrac 12= n(4x-5)\\\\\\ \implies \dfrac{4x}{10}- \dfrac{5}{10} = n(4x-5)\\\\\\\ \implies \dfrac 1{10}(4x-5) = n(4x-5)\\\\\\\implies n = \dfrac 1{10}~~~~~;\left[x \neq \dfrac 54 \right][/tex]

Answer:

C   [tex]3 \frac{7}{8} + (-6\frac{1}{4})[/tex]

Step-by-step explanation:

+ × - = -

Example:

5 × -3 = -15

+(-5) = -5

then:

3 7/8 - 6 1/4

= 3 7/8 + (-6 1/4)

Answer:

1) 125

2) 113

Step-by-step explanation:

Hope it helps :)

Answer:

x = 70°

Step-by-step explanation:

Since in triangle ABC (Check the image)

=> AB = AC

Therefore, ∠B = ∠C

From Angle Sum property of a triangle,

=> ∠A + ∠B + ∠C = 180°

=> x + 55 + 55 = 180

=> x +110 = 180

=> x = 70°

Hope you've understood the solution.

The quadratic equation with the given characteristics is:

f(x) = (x + 3)*(x - 7).

We know that the vertex must be (2, -25) and it passes through (7, 0).

For a quadratic equation:

y = a*x^2 + b*x +c

The x-value of the vertex is:

x = -b/2a

Then we have:

2 = -b/2a

We also have:

-25 = a*4 + b*2 + c

And because the function passes through (7, 0) we know that 7 is one of the roots, then:

0 = a*49 + b*7 + c

Then we have 3 equations to work with:

2 = -b/2a

-25 = a*4 + b*2 + c

0 = a*49 + b*7 + c

If we subtract the third and second equations we get:

25 = a*45 + b*5

Now, with the first equation we can rewrite:

a  = -b/4

Replacing that in the other equation:

25 = a*45 + b*5

25 = (-b/4)*45 + b*5 = b*(-25/4)

25*(-4/25) =b = -4

Now we know the value of b.

2 = -(-4)/2a

a = 1

Now we need to find the value of c, we have that:

0 = 1*49 + -4*7 + c

0 = 49 - 28 + c

0 = 21 + c

Then c = -21

The equation is:

[tex]y = x^2 - 4x - 21[/tex]

It can be factorized to:

f(x) = (x + 3)*(x - 7).

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Answer:

B.  The equation of the linear function is y = 3x + 2

D.  The rate of change of the linear function is 3.

Step-by-step explanation:

First find the slope by choosing two ordered pairs and using the slope formula:

[tex]\textsf{let}\:(x_1,y_1)=(2,8)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(3,11)[/tex]

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{11-8}{3-2}=3[/tex]

Now use the Point-slope form of linear equation with the found slope and one of the points to create the equation of the linear function:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]\implies y-8=3(x-2)[/tex]

[tex]\implies y=3x + 2[/tex]

The rate of change of a linear function is its slope.

Therefore,

B.  The equation of the linear function is y = 3x + 2

D.  The rate of change of the linear function is 3.

Answer:

A function table

Step-by-step explanation:

Hope this helped

Answer:

C, Negative x coordinates, positive y coordinates.

Step-by-step explanation:

Note that the original points are all in the third quadrant, i.e., sign will be (-,-). When reflected across the x axis, the y coordinate becomes negative => (x,-y) => (-,-) becomes (-,+)

Answer: D. Negative-x and Negative-y

Step-by-step explanation: quadrant one are both positive quadrant 2 is positive and negative. Quadrant 3 is negative and negative and quadrant 4 is negative and positive.

Answer:

A

Step-by-step explanation:

Here [ a, b ] = [ 2, 6 ], thus

f(b) = f(6) = -  + 70 = - 64 + 70 = 6

f(a) = f(2) = - 2² + 70 = - 4 + 70 = 66

average rate of change =  =  = - 15 → A