The graph of f(x) is shown.
For what values of x does f(x) = 0?
A) −1, 1, 2
B) −2, −1, 1
C) −3, −1, 1
D) −1, 1, 3

The tunnel A will be damaged and truck can pass through tunnel B.

Given that, tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² – 30x + 16y – 95 = 0.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y²= = 4ax.

Part A: x²+y²+30x+56=0

Add 15² on both the sides of a equation

That is, x²+30x+15²+y²=-56+15²

⇒ (x+15)²+y²=169

⇒ (x+15)²+y²=13²

Divide 13² on both the sides of the equation

⇒ (x+15)²/13² + y²/13² =1

Part B:

x²-30x+16y-95=0

Now, x²-30x+16y=95

Add 15² on both the sides of a equation

That is, x²-30x+15²+16y=95+15²

⇒ (x-15)²=320-16y

⇒ (x-15)²=16(20-y)

Part C:

Maximum height:

A: 13 feet

B: 20 feet

Width = 8 feet

A: x+15=8/2=4 y=12.37<13.5

B: x-15=8/2=4 y=19>13.5

Hence, the tunnel A will be damaged and truck can pass through tunnel B.

To learn more about the parabola equation visit:

https://brainly.com/question/21685473.

#SPJ1

Answer:

Step-by-step explanation:

Find the amount of time it takes for a beam of light from the Sun to reach Earth.

Hello!

Here are both solutions to your equation.

Fraction Form:

[tex]\frac{37}{100}[/tex]

OR

Decimal Form:

[tex]0.37[/tex]

Hope this helps!

The graph of the linear equation 4x - y = 8, with two points on the line is shown in the image attached below.

If we know the slope, m, of the linear equation, which is the rise of the line over the run of the line, and also know the y-intercept value, b, we can graph a linear equation such that the slope of the line would be the value of m, and the point where the line intercepts the y-axis would be the value of b in the linear equation that is represented as y = mx + b.

Given the linear equation, 4x - y = 8, we can rewrite this in slope-intercept form as y = mx + b:

4x - y = 8

-y = -4x + 8 [subtraction property of equality]

y = 4x - 8 [division property of equality]

The slope, m, is 4, while the graph of the linear equation must intercept the y-axis at y = -8, because the y-intercept of the linear equation is b = -8.

Thus, the graph of 4x - y = 8 is shown below.

Learn more about linear equation graph on:

https://brainly.com/question/28279384

#SPJ1

Answer:

Step-by-step explanation:

Find the burning rate of candle per hour:

The rate is the slope of the linear function and the initial length of the candle is the y-intercept:

The equation is:

Correct choice is the first one.

Answer:License plate numbers in certain state consists of seven characters: The first character is digit (0 through 9) The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore; license plate number in this state can be any string - of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit How many license plate numbers are possible if no digit appears more than once?

Step-by-step explanation: i don't know rm

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 2i [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3 {x}^{2} + 12 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3{x}^{2} = - 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{12}{3} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x {}^{2} = - 4 [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ (- 1)(4)} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 1} \sdot \sqrt{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = i \sdot2[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 2i[/tex]

[ i represents iota, i² = -1, (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=2i[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2+12=0[/tex]

Factor 3 from the left side of the equation:

[tex]\implies 3(x^2+4)=0[/tex]

Divide both sides of the equation by 3:

[tex]\implies\dfrac{3(x^2+4)}{3}=\dfrac{0}{3}[/tex]

[tex]\implies x^2+4=0[/tex]

Subtract 4 from both sides:

[tex]\implies x^2+4-4=0-4[/tex]

[tex]\implies x^2=-4[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{-4}[/tex]

[tex]\implies x^2=\sqrt{-4}[/tex]

Rewrite -4 as 2² · -1:

[tex]\implies x=\sqrt{2^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies x=\sqrt{2^2}\sqrt{-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies x=2\sqrt{-1}[/tex]

[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]

[tex]\implies x=2i[/tex]

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

Yes, the system of inequalities listed to the represent the wants of the campaign manager are correct

This refers to the term in mathematics that uses some expressions to typify statements.

The following are the statements in inequalities

Considering the question here:

r = each 60-second radio spot

t = 30 seconds of television time

The budget is limited to $48,000 means less than or equal to

The manager wants at least 45 radio spots, but no more than 90

means radio spots from 45 to 90 hence 45≤ r ≤ 90

at least 20 means television spots of 20 and above hence t ≥ 20

Read more on inequalities here:

https://brainly.com/question/24372553

#SPJ1

Answer: x = 20

Step-by-step explanation:

The angles are corresponding angles so they are equivalent to each other. To solve for x, we set them equal and then solve for x.

65 = 3x + 5

60 = 3x

x = 20

Answer:

the other person has it right- it's x =20

The z-scores for a 67-inch- man and a 62-inch woman are -0.9667 and -0.5526, respectively.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

For a 67-inch- man, use the formula to solve for the z-score.

x = 67

μ = 69.9

σ = 3.0

z-score = (x – μ) / σ

z-score = (67 - 69.9) / 3.0

z-score = -0.9667

Do the same for a 62-inch- man, use the formula to solve for the z-score.

x = 62

μ = 64.1

σ = 3.8

z-score = (x – μ) / σ

z-score = (62 - 64.1) / 3.8

z-score = -0.5526

Learn more about z-score here: brainly.com/question/17489087

#SPJ4

Answer: the slope of this equation is 8

Step-by-step explanation: y = 8x - 15, the 8x represents the slope of this equation

The pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

The Janitor find the leakage in the pipe at a rate of [tex]23[/tex] fl oz per hour.

We have to find how fast was the pipe leaking in gallons per day​.

To find the leaking in gallons per day​ we have to convert [tex]23[/tex] fl oz per hour into gallons per day.

As we know that

[tex]1[/tex] gallon[tex]=128[/tex] fl oz

So [tex]1[/tex] fl oz[tex]=\frac{1}{128}[/tex] gallons

There are [tex]24[/tex] hours in a day so we multiply with [tex]24[/tex] to convert in day.

So the expression should be

[tex]=23[/tex] fl oz/hours[tex]\times\frac{1}{128}[/tex] gallons/fl oz[tex]\times24[/tex] hours/day

[tex]=\frac{23\times24}{128}[/tex] gallons/day

[tex]=\frac{23\times3}{16}\\[/tex] gallons/day

[tex]=\frac{69}{16}[/tex] gallons/day

Hence, the pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

To learn more about conversion of gallons and lb here link

https://brainly.com/question/22690673

#SPJ1

According to the given line, the points are L and M and the segment is LM.

Lines:

The line is defined as the one-dimensional figure, which has length but no width. It is made of a set of points which is extended in opposite directions infinitely.

Given,

Here we have the diagram.

Through the given diagram we have to identify the points and segments from it.

We know that, the points refers the is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape.

Based on this definition , we have two points that L and M in the given diagram.

Next one we have to identify from the graph is segment,

Segment means the part of the line that connects two points.

So, LM is the segment of the line.

To know more about Line here.

https://brainly.com/question/17188072

#SPJ1

The number of time Easton's song was played on commercials is 10 times.

The number of time Easton's song was played during a movie is 4 times.

The first step is to form a system of equations:

40c + 110m = 840 equation 1

c - m = 6

c = 6 + m equation 2

Where:

The system of equations would be solved using the substitution method.

Substitute for c in equation 1 using equation 2

40(6 +  m) + 110m = 840

240 + 40m + 110m = 840

40m + 110m = 840 - 240

150m = 600

m = 600 / 150

m = 4

Substitute for m in equation 2.

c = 6 + 4

c = 10

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1

The ages of Victoria and tyee are 72 and 74.

A linear equation is an algebraic equation of the form y=mx+b that only contains a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables. Ax+By=C is the accepted form for two-variable linear equations. Finding both intercepts of an equation in this form is rather simple (x and y). If an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is said to be linear. The point-slope form, standard form, and slope-intercept form are the three primary types of linear equations.

As given

ages are consecutive even integers

Victoria > Tyee

So

Victoria's age = x

Tyee's age = x + 2

x(x + 2) = 80

= x² + 2x - 80

= x²  + 8x - 10x - 80

Hence , the ages are 72 and 74.

To know more about linear equations ,visit:

brainly.com/question/11897796

#SPJ13

Width of the box is the dimension which gives the gives maximum value.

Width of the box = 9 cm

Length of the box = 9 cm

Given,

The perimeter of the rectangular bottom of the box = 36 cm

The height of the box = 4 cm

We have to find the dimension which gives maximum value.

Volume = lwh

Perimeter = 2(l + w)

36 = 2l + 2w

l = (36 - 2w)/2

l = 18 - w

Now,

Volume = length × width × height

V = (18 - w) × w × 4

V = 72w - 4w²

Lets find w by using w = -b/2a

That is,

w = -72/2(-4) = -72/-8 = 9

That is,

Width of the box is 9 cm and it is the dimension which gives the maximum value.

Learn more about dimensions here:

https://brainly.com/question/2273504

#SPJ1

Answer:

27

Step-by-step explanation:

x + y = 23

x - y = 27

(x + y) + (x - y) = 23 + 27

2x = 50

x = 25

y = - 2

How to find distance:

|25 -(-2)| = |27| = 27

Answer:-4+27

Step-by-step explanation:

Answer:

3 feet

Step-by-step explanation:

s= sandra

L= Lamp

if you know that the lamp is four feet away, and the bird is five feet away. go vertically up from the lamp until the distance from the lamp vertically equals five feet back to sandra.

The correct options are that the functions share a y intercept of -1 and both functions have a range of all real numbers.

A function may be defined as the expression in which for one input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Real number may be defined as the set of numbers that has integers, rational numbers, and natural numbers. Here, from the graph we can see that both the functions meet on the y-axis at a point (0, -1). Thus, both these functions share a y intercept of -1. Now, both the functions have a certain value of y for a given value of x. Hence, both functions have a range of all real numbers.

Learn more about Real numbers at:

brainly.com/question/10547079

#SPJ1

Answer:b n d

Step-by-step explanation:

Answer:

   -6.4, -5 1/2, -5, and -2 6/4.

Step-by-step explanation:

Arranging these negative values in order from least to greatest may be tricky if you are not familiar with your integer rules and operations. However, if you seem to understand, even a little, this way may be helpful to you.

All you need to know is this. positive and negative are opposites. Thus, if, for example, +2 is greater than +1 in positives, then -2 is less than -1 in negatives. So, in other words, think about it this way when you see a negative number, but you are used to positive numbers, just assume that the biggest number on the positive side is the smallest number on the negative side.

Therefore, if we were to use this method, we would result in -6.4, -5 1/2, -5, and -2 6/4. Since it would be the opposite in positives.

We need to take the derivative, which is:

[tex]f'(x) = 10x + 2[/tex]

and see where it is positive (increasing) and negative (decreasing). We see that [tex]f'(x) = 0 at x = -1/5, f'(x) < 0 for x < -1/5, and f'(x) > 0 for x > -1/5[/tex]. Therefore, we have

f(x) increasing: (-1/5, ∞)

f(x) decreasing: (-∞, -1/5)

The range of F(x) = 7.4* is all positive real numbers is true

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Currently, the function is

f(x) = 7 x 4^x

Suppose,

y = f(x) = 7 x 4^x.

=> y = 7 x 4^x

Hence,

lny = ln (7 x 4^x).

We obtain using the logarithm equation

Hence,

ln y = ln7 + ln 4^x.

= ln y = ln7 + x ln4 .

Hence,

y equals e^(ln7 + x ln4).

=> y = e^ln7.e^(xln4) (xln4)

Using the exponential formula, we obtain

=> y = 7xln4

Consequently, y=f(x)=7.x.ln4

To determine function f's value (x)

7.x.ln7 = 0

As a result, For all possible values of x (x€R). To date,

=> 7x ≥ 0

=> 7xln4 ≥ 0

Therefore interval notation will be (0,∞)

Notation for set builders:

{y|y>0}

The graph will be plotted as follows if all the values of x (x€R) are used:

Hence, it is true that the range of f(x)=7*4x is all positive real integers.

To learn more about Range click on the link

https://brainly.com/question/26098895

#SPJ9

Answer:

the answer is 29              

Answer:

C

Step-by-step explanation:

I'm to lazy to type it out so...I took a photo

I hope this helps :D

and I need brainiliest so bad...

ANSWER: x = 3

z = 100

Answer:

38333333333333/10000000000000

Step-by-step explanation: