The quadratic equation $ax^2+20x+c=0$ has exactly one solution. If $a+c=29$, and $a

Answers

Answer 1

Answer:

a² + c² = 641

Step-by-step explanation:

Given :-

ax² + 20x + c has exactly one solution .a + c = 29 .

For exactly one Solution ,

b² - 4ac = 0 20² - 4*a*c = 0 4ac = 400 ac = 100

Also ,

a + c = 29 ( a + c)² = 29²a² + c² + 2ac = 841 a² + c² + 2*100 = 841a²+ c² = 841 - 200 + = 641

Related Questions

NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!!!. Please help me with these math questions. Chapter 10 part 2

3. How do solving for solving to a rational function differ from solving for solutions to a rational inequality? How they are similar?

4. How is the difference quotient of a function determined? And how is the difference quotient related to the secant line? Is there a pattern for the difference quotient of linear functions?

Answers

9514 1404 393

Answer:

  3. sign changes in the denominator need to be taken into account

  4. difference quotient: (f(x+h) -f(x))/h; It is the slope of the secant line. For linear functions, the slope is constant, as is the difference quotient.

Step-by-step explanation:

3. When solving the equation f(x) = 0, where f(x) is a rational function, only the numerator zeros need to be considered.

When solving the inequality f(x) ≤ 0, or f(x) < 0, both numerator and denominator zeros need to be considered. As with solving any inequality, multiplying or dividing by a negative number changes the sense of the comparison.

Example

f(x) = x/(x-2) changes sign at both x=0 and x=2. Then three regions need to be considered when solving f(x) < 0. Those are x < 0, 0 < x < 2, and 2 < x.

__

4. The difference quotient is defined as ...

  dq = (f(x +h) -f(x))/h

The difference quotient is essentially the average slope between (x, f(x)) and (x+h, f(x+h)). That is, it is the slope of the secant line between those two points.

For linear functions, the slope is a constant. The difference quotient is a constant equal to the slope of the line.

Example

f(x) = ax +b . . . . . a linear function with a slope of 'a'

The difference quotient is ...

  (f(x+h) -f(x))/h = ((a(x+h)+b) -(ax+b))/h = (ax+ah+b -ax -b)/h = ah/h = a

The difference quotient is the slope of the line.

Angles 1 and 2 form a linear pair and the measure of angle two is 22 more than 4 times of the measure of angle 1. What degrees is angle 2

Answers

Answer:

m<2= 148.4

Step-by-step explanation:

A linear pair means that both angles add to 180.

m<2 = 4*m<1 +22

Together

m1 + m2 = 180

Put the value for m<2 into the above equation

m<1  + 4*m<1 + 22 = 180         Combine like terms\

5m<1 + 22 = 180                      Subtract 22

5m<1 = 180 - 22

5m<1 = 158                              Divide by 5

m<1 = 158/5

m<1 = 31.6

m<2 = 4*31.6 + 22

m<2 = 138.4

3/4 of the households in a rural area have pets. how many households have pets in this area if there are 1500 total households

Answers

Answer:

1,125 households would have pets in the area.

Step-by-step explanation:

We have 1,500 total households. We also know that 3/4 (or 0.75) of these households have pets. We would multiply 1,500 by 0.75 (which is equal to 3/4), resulting in 1,125. Therefore, 1,125 households would have pets in the area.

Answer:

1125 households

Step-by-step explanation:

3/4 of total households in area = # of households that have pets in the area

3/4 of 1500 = # of households that have pets in the area

3/4 · 1500 = # of households that have pets in the area

75/100 · 1500 = # of households that have pets in the area

0.75 · 1500 = 1125

1125 households

PLEASE ANSWER

The distance from the vertex of the curve to the focus is equal to _____.

Here’s the options

the distance from the vertex to the directrix

the distance from the vertex to the y-axis

the distance from the vertex to the origin

a constant

Answers

Answer:

The distance from the vertex to the directrix.

Step-by-step explanation:

According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.

Hence, the right answer is: The distance from the vertex to the directrix.

what is the value of g​

Answers

Answer:

the value of g is gram .

may this answer is helpful for you

Four spinners are spun. Spinner 1 has outcomes Spinner 2 has outcomes Spinner 3 has outcomes Spinner 4 has outcomes The outcomes for each spinner are equally likely. is the sum of the numbers that come up on the spinners. What is the expected value of

Answers

Complete Question

Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?

Answer:

[tex]E(s)=14.5[/tex]

Step-by-step explanation:

From the question we are told that:

Spinner 1 ={1,2,3,4,5,6,7,8}

Spinner 2=  {1,2,3,4,5,6}

Spinner 3 = {1,2,3,4,5,6}

Spinner 4  {1,2,3,4,5}

Generally the equation for expected outcome is mathematically given by

[tex]E(s)=\sum P(x).x[/tex]

Where

[tex]x=\frac{n(n+1)}{2}[/tex]

For Spinner 1

[tex]E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}[/tex]

[tex]E(s_1)=4.5[/tex]

For Spinner 2

[tex]E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_2)=3.5[/tex]

For Spinner 3

[tex]E(s_2)=E(s_3)[/tex]

For Spinner 3

[tex]E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_4)=3[/tex]

Therefore The Expected Value

[tex]E(s)=\sum E(s 1..4)[/tex]

[tex]E(s)=4.5+2(3.5)+3[/tex]

[tex]E(s)=14.5[/tex]

If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.

A. 13
B. 52
C. 208
D. 104

Answers

Answer:

D. 104

Step-by-step explanation:

[tex]y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } [/tex]

when y is 26, x is 4:

[tex]26 = \frac{k}{ {(4)}^{2} } \\ k = 416[/tex]

when x is 2:

[tex]y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104[/tex]

Answer:

D; 104

This is the correct answer

what is the least common factor for 9 8 7

Answers

Answer:504

This is the answer

504

Least common factor is 504

Please I need the answer ASAP!!!!

Answers

Step-by-step explanation:

D

*not sure about this answer pls tell me i ak right or wrong

The answer is B.

The points are written as (X,Y)
So if the number written in the place of “x” is negative, that means it is underneath the “X” axis.

14. The data below show the average ages and number of volunteer hours for five randomly chosen persons. Given the equation of the regression line is y' = 9.309x - 167.012, predict the number of hours a person will volunteer if her age is 27.5 years. Age, x Volunteer Hours, y 24.9 66.5 25.6 70.0 26.1 74.8 27.3 89.6 27.0 82.6​

Answers

The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.

Given equation is,

→ [tex]\hat{y}=9.309x - 167.012[/tex]

Her age,

→ x = 27.5 years

By substituting the value of "x" in the given equation, we get the predicted time,

hence,

→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]

     [tex]= 255.9975- 167.012[/tex]

     [tex]=88.9855 \ months[/tex]

Thus the above is the right answer

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The diagram shows APQR. Which term describes point S?

Answers

Answer:

c) centroid

Step-by-step explanation:


add 10 and g, then subtract f from the result​

Answers

Answer:

(10+g) -f

Step-by-step explanation:

Add 10 and g

10 +g

Subtract f from the result

(10+g) -f

A prism and two nets are shown below: Prism 1 E 3 Net A Net Part A: Which is the correct net for the prism? Explain your answer. (2 points) Part B: Write the measurements of Sides AB. BC, and CD of the correct net. (4 points) Part C: What is the surface area of the prism? Show your work. (4 points)​

Answers

Answer:

A) Net A (see explanation)

B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.

C) SA = 98.4 in²

Step-by-step explanation:

Part A

Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.

Part B

AB = This is the height of the prism.

= 3 in.

BC = This is the slant on the front of the prism.

= 5 in.

CD = This is the length of the prism.

= 7.2 in.

Part C

* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.

One triangle:

A = 1/2bh

= 1/2 (4) (3)

= 6 in²

Back rectangle:

A = bh

= 7.2 (3)

= 21.6 in²

Front rectangle:

A = bh

= 7.2 (5)

= 36 in²

Bottom rectangle:

A = bh

= 7.2 (4)

= 28.8 in²

Total:

A = 6 + 6 + 21.6 + 36 + 28.8

= 98.4 in²

HELP SOMEONE FOR 20 POINTS

Answers

Use the quadratic formula, and it will give you x= 8/3 and 2/5
You can also just use photo math
Using the quadratic formula, your answer will be
X= 2/5 and 8/3

Need the value of P please

Answers

Answer:

B. 35°

Step-by-step explanation:

First, find the two interior angles that are adjacent to angles 90° and 125° respectively.

Thus:

Interior angle 1: 180° - 90° = 90° (linear pair)

Interior angle 2: 180° - 125° = 55° (linear pair)

P + 90° + 55° = 180° (sum of interior angles in a triangle)

P + 145° = 180°

Subtract 145° from each side

P = 180° - 145°

P = 35°

Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?

Answers

Answer:

The state can issue 456,976,000 license plates.

Step-by-step explanation:

For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.

For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.

For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:

[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]

= 10*26*26*26*26*10*10

=456,976,000.

Therefore, the state can issue 456,976,000 license plates.

the cost of using 19 hcf of water is $36.48 and the cost of using 32 hcf is 56.63 what is the cost of using 28 hcf of water?

Answers

Answer:

$54.32

Step-by-step explanation:

19=$36.48/19 =1.94

1=$1.94 * 28= 54.32

28=54.32

What are the measures of Angles a,b, and c? show your work and explain your answers.​

Answers

Answer:

a=35

b=55

c=110

Step-by-step explanation:

a=35

Opposite angles which are non-adjacent angles formed by two intersecting lines are equal

b+35+90=180 sum of interior angle of a triangle equal to 180

b=180-125

  =55

c+70=180  Angles on a straight line add up to 180°

c=180-70

 =110

Suppose an average student can answer 6 homework questions in 30 minutes. If X follows an exponential distribution and measures the length of time between starting two homework questions. What is the value of μ?

Answers

Answer:

10

Step-by-step explanation:

Make a ratio like

6 : 30

2 : x

Then cross multiple

6x = 60

Make x subject formula

x = 10

I hope it helped

What percent is modeled by the grid?
A grid model with 100 squares. 33 squares are shaded.
23%
30%
33%
40%

Answers

Answer

33 percent

Step-by-step explanation:

Answer:

33 squares are shaded 23%

Step-by-step explanation:

I hope this answer works out for you if it doesn't I'm really sorry have a great day

if i pay 15300 interest capital on a loan for 25 years how much will i pay?

Answers

Answer:

i dont know soory

Step-by-step explanation:

Can someone help me with this

Answers

Answer:

Step-by-step explanation:

If two triangles have two congruent sides and a congruent non included angle, then triangles are not necessarilly congruent.

I need help with these questions

Answers

9514 1404 393

Answer:

  17.  25 mile per gallon

  18. Eduardo did should have divided by -4.

Step-by-step explanation:

17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...

  (450 mi)/(18 gal) = 25 mi/gal

__

18. The appropriate method for solving this inequality is ...

  -4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)

  x < -30

The step Eduardo took of adding 4 will give ...

  -4x +4 > 124 . . . . . puts him one step farther away from a solution

Eduardo chose an operation to perform that did not get him closer to a solution.

Given f (x) = 3x - 5 find f (x - 2)

Answers

Answer:

3x-11

Step-by-step explanation:

f (x) = 3x - 5

f(x-2)

Replace x in the function with x-2

f (x-2) = 3(x-2) - 5

           =3x-6 -5

           =3x-11

In ∆ ABC,AD is the altitude from A to BC .Angle B is 48°,angle C is 52° and BC is 12,8 cm. Determine the length of AD

Answers

9514 1404 393

Answer:

  7,6 cm

Step-by-step explanation:

The law of sines can be used to find the length AB.

  AB/sin(C) = BC/sin(A)

A = 180° -48° -52° = 80°

  AB = BC·sin(C)/sin(A) = 12,8·sin(52°)/sin(80°)

The sine function can be used to find AD from AB.

  AD/AB = sin(48°)

  AD = AB·sin(48°) = 12,8·sin(48°)sin(52°)/sin(80°)

  AD ≈ 7,61 cm

__

The dimension of interest is ha in the attachment, the height from vertex A.

Find x. Round your answer to the nearest tenth of a degree.

Answers

Answer: x=52.6°

Step-by-step explanation:

To find the value of x, we have to use our SOHCAHTOA. We can eliminate sine and cosine because both uses hypotenuse, which is not labelled. Therefore, we use tangent.

[tex]tan(x)=\frac{17}{13}[/tex]

To find x, we want to use inverse tangent.

[tex]x=tan^{-1}(\frac{17}{13} )[/tex]      [plug into calculator]

[tex]x=52.6[/tex]

Now, we know that x=52.6°.

What is 9,000,000 + 8,000 + 90,000,000 + 100 + 2 + 90,000 + 90 in standard form?

Answers

Answer:

9×10^7 + 9×10^6 + 9×10^4 + 8×10^3 + 1 ×10^2 + 9×10 + 2

9000000+8000+90000000+100+2+90000+90 = 99098192

please mark this answer as brainlist

Twice a certain number is subtracted from 9 times the number. The result is 21. Find the number.​

Answers

Answer:

3

Step-by-step explanation:

Let x represent the number.

Create an equation to represent the situation, and solve for x:

9x - 2x = 21

7x = 21

x = 3

So, the number is 3.

Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.

Answers

When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.

The domain and the range of the given function are:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex](3,\infty)[/tex]

 The given function is:

[tex]g(x) = 3^x + 3[/tex]

First, we plot the graph of g(x)

To do this, we need to generate values for x and g(x). The table is generated as follows:

[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]

[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]

[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]

[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]

[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]

The generated values in tabular form are:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]

Refer to the attached image for graph of g(x)

To determine the domain, we simply observe the x-axis.

The curve stretches through the x-axis, and there are no visible endpoints on the axis.  This means that the curve starts from [tex]-\infty[/tex] to [tex]+\infty[/tex]

Hence, the domain of the function is: [tex](-\infty,\infty)[/tex]

To determine the range, we simply observe the y-axis.

The curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.  This means that the curve of g(x) is greater than 3 on the y-axis.

Hence, the range of the function is: [tex](3,\infty)[/tex]

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Function: [tex]g(x) = 3^{x} + 3[/tex]. Domain: [tex]Dom \{g(x)\} = \mathbb{R}[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex], respectively.

In Function Theory, the domain of a function [tex]f(x)[/tex] represents the set of values of the independent variable ([tex]x[/tex]), whereas the range of the function is the set of values of the dependent variable.

The Domain of the Function represents the set of values of [tex]x[/tex] (horizontal axis), whereas the Range it is the set of values of [tex]y[/tex] (vertical axis). After analyzing the existence of Asymptotes, we complement with graphic approaches and conclude where domain and range (in Interval notation) are.

Analytically speaking, the domain of exponential functions is the set of all real numbers and the range of [tex]g(x)[/tex] is any number between [tex]\lim_{x \to -\infty} g(x)[/tex] and [tex]\lim_{x \to +\infty} g(x)[/tex]. In a nutshell, we get the following conclusions in interval notation:

Domain: [tex]Dom \{g(x)\} = (-\infty, +\infty)[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex]

Lastly, we proceed to complement this analysis by graphing function with the help of a graphing tool.

According to the image, domain and range coincides with outcomes from analytical approaches.

Which proportion could be used to determine if the figure ms represent a dilation

Answers

Step-by-step explanation:

Three-halves = 4 = 6

HOPE SO IT HELP'S YOU

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