Match each quadratic function with its respective graph.

f (x) = x^2 + 6x - 5
f (x) = x^2 - 4x + 5
f (x) = -x^2 - 2x +3
f (x) = x^2 + 4x - 5
f (x) = -x^2 + 2x - 3
f (x) = x^2 - 6x + 5

Answer:

Step-by-step explanation:

Angles: 45°: 45°: 90°

Ratio of sides: 1:1:√2

Given c= 55

a =c/√2

a=55/√2 = 38.9

b=a+2 = 38.9+2 =41.9

The length of the legs of the triangle is 41.9

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

Angles are: 45°: 45°: 90°

The ratio of sides: 1:1:√2

Given c = 55

a = c/√2

a = 55/√2

a = 38.9

b = a+2

b = 38.9+2

b =41.9

Thus, the length of the legs of the triangle is 41.9

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Answer:

(y + 8)(y - 2)

Step-by-step explanation:

Given

y² + 6y - 16

Consider the factors of the constant term (- 16) which sum to give the coefficient of the y- term (+ 6)

The factors are + 8 and - 2, since

8 × - 2 = - 16 and 8 - 2 = 6, thus

y² + 6y - 16 = (y + 8)(y - 2)

The values of f and g are;

f = 6

f = 6g = 8

We are given the trapezium ABCE where;

AD is parallel to BC

DE = 4 cm

Area of ABCE = 60 cm²

Area of ABCD = 48 cm²

f and g are sides of the rectangle ABCD. Thus;

fg = 48 - - - (eq 1)

Also,for the trapezium ABCE;

½(g + g + 4)f = 60

(2g + 4)f = 120 - - - (eq 2)

From eq 1, f = 48/g

Thus;

(2g + 4) × (48/g) = 120

96 + 192/g = 120

192/g = 120 - 96

192/g = 24

g = 192/24

g = 8

Thus;

8f = 48

f = 48/8

f = 6

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Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

Given four graphs of different nature as options.

We are required to find a graph that is not a continuous variable.

In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.

When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.

Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

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Answer: Graph B and Graph C

Step-by-step explanation:

Answer:55

Step-by-step explanation:addition

Answer:

171 square ft

Step-by-step explanation:

Area of side walk of the pool = Are of outer square - Area of inner square

[tex] = {30}^{2} - {27}^{2} \\ = (30 + 27)(30 - 27) \\ = 57 \times 3 \\ = 171 \: {ft}^{2} [/tex]

Answer:

[tex]105.625\pi cm^3[/tex]

Step-by-step explanation:

[tex]V=\pi r^2h=\pi *3.25^2*10=331.83072\\=331.83[/tex]

Answer in terms of [tex]\pi[/tex]

[tex]105.625\pi cm^3[/tex]

Answer:

(3x + 4)(2x - 5)

[tex]6x^{2}+7x-20=0[/tex]    =    (3x + 4)(2x - 5)

Hope this helped! Have a great day!

Answer: The answer is A

Step-by-step explanation: There are different ways to solve this type of problem. One way I would do it is to use a piece of wax paper to trace the shape then rotate the paper to get the answer.

Answer:

g(x) is a vertical compression of f(x)

Step-by-step explanation:

Equation of graph 1 :[tex]f(x)=x^2[/tex]

Equation of graph 2 :[tex]g(x)=\frac{2}{3}x^2[/tex]

f(x)→a f(x)

Its is case of vertical stretch or compression

Vertical stretch if |a|>1

Vertical compression if 0<|a|<1

f(x)→a f(x)

So, [tex]x^2[/tex] →[tex]\frac{2}{3}x^2[/tex]

So, [tex]a= \frac{2}{3}=0.67[/tex]

So,0<|a|<1

So,It is a case of vertical compression

So, g(x) is a vertical compression of f(x)

Answer:

$1407.15

Step-by-step explanation:

$1,770.00*0.25= $442.5

$1.770-$442.50 = $1327.5

$1327.5*0.06 = $79.65

$1327.50+$79.65 = $1407.15

Answer:

Answers are below

Step-by-step explanation:

Yes I was surprised by the scatter plot because I didn't know there would be the most rain at 77 degrees F on the red line.

If you switched which axis each variable is graphed on, your graph would look different because the graph could be sideways on the left or the right.

The graph has a trend of increasing temperature and amount of rain as you get up to the 7th column. After the 7th column, the trend shows decreasing rain and temperature.

Answer: Mary is cheaper than mike

Step-by-step explanation:

Hopes this Helps

Answer:

A) ΔABC ≅ ΔEDC

Step-by-step explanation:

To prove triangles congruent with the AAS method, you need two angles and the non-included side of one triangle to be congruent to the corresponding parts of another triangle.

Let's see what we have in these two triangles.

Side AB is congruent to side ED. This is one pair of sides.

Angle A is congruent to angle E. This is one pair of sides.

Now we need a second pair of angles, that will make the two sides not-included in the angles.

By the congruence of vertical angles, we see that angles ACB and ECD are congruent. This is another pair of congruent angles.

We have two angles and a non-included side of one triangle congruent to two angles and a non-included side of another triangle. The triangles are congruent by AAS.

Answer: A) ΔABC ≅ ΔEDC

Answer:

M = 20

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportion

To find k use the condition when r = 4, M = 160, that is

160 = k × 4³ = 64k (divide both sides by 64 )

2.5 = k

M = 2.5r³ ← equation of proportion

When r = 2, then

M = 2.5 × 2³ = 2.5 × 8 = 20

Answer:

M<varies>r³

M=kr³(k= constant)

when M=160,r=4

160=k(4)³

160=64k

k=2.5

therefore,M=2.5r³

when r=2

M=2.5r³

M=2.5(2)³

M=2.5(8)

M=20

Answer:

E

Step-by-step explanation:

I hope am right coz it seems most appropriate

Answer:

y= 3x +11

Step-by-step explanation:

slope-intercept form:

y= mx+c, where m is the gradient and c is the y-intercept.

Given that the slope is 3, m=3

substitute m=3 into the equation:

y= 3x +c

To find the value of c, substitute a coordinate.

When x= -3, y=2,

2= 3(-3) +c

c -9= 2

c= 9 +2 (+9 on both sides)

c= 11 (simplify)

Thus, the equation of the line is y= 3x +11.

Answer:

leg 1= 36  feet

leg2 = 15  feet

Step-by-step explanation:

Hi, we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the distance between Doreen’s house and the tower) and a and b are the other legs.  

leg1 = x

leg2 = x-21 (21 feet less than the other leg)

Replacing with the values given:  

39^2 = x^2 + (x-21)^2  

1,521 = x^2 + x^2 -42x +441

0 = 2x^2 -42x +441-1,521

0= 2x^2 -42x -1,080

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  (quadratic formula)

Replacing with the values given:  

x=-(-42)± √(-42)²-4(2)-1080] /2(2)  

x= 42± √10,404] /4

x = 42± 102 /4

Positive:

x = 42+102 /4 = 36

leg 1= 36

leg2 = 36-21 =15

Feel free to ask for more if needed or if you did not understand something.  

The length of shorter leg is 15 feet and other leg is 36 feet.

Let us consider that, length of shorter leg is x feet.

So that, length of other leg is [tex](x+21)[/tex] feet.

It is given that, the hypotenuse is 39 feet.

Apply Pythagoras theorem,

                 [tex]x^{2} +(x+21)^{2} =(39)^{2}\\ \\x^{2} +x^{2} +441+42x=1521\\\\2x^{2} +42x-1080=0\\\\x=15 ,-36[/tex]

Since, side can not be negative.

So that, we have to consider x=15 feet.

Length of other leg[tex]=x+21=15+21=36feet[/tex]

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Answer:

(5,6)

Step-by-step explanation:

I think you are asking whats the biggest sum you can get out of the ordered pairs. If you are I'm pretty sure (5,6) is correct. If you are not asking that, I am sorry.

Answer:

3/8

Step-by-step explanation:

1. We list all codes that start with 0 and have 0 as second digit:

2. We list all codes that start with 0 and have 1 as second digit:

3. We list all codes that start with 1 and have 0 as second digit:

4. We list all codes that start with 1 and have 1 as second digit:

5. We find the number of codes which have exactly 2 zeros: 6 codes

6. The total number of outcomes is: 16 codes

7. We find the probability that the number of codes has exactly 2 zeros: 6/16 3/8

Answer:

The probability of getting two 1's is 3/8

Step-by-step explanation:

Martha types a 4−digit code into a keypad to unlock her car doors.

The code uses the numbers 1 and 0

So the sample space of all the possible combinations is given by

1. 0 0 0 0

2. 0 0 0 1

3. 0 0 1 0

4. 0 0 1 1

5. 0 1 0 0

6. 0 1 0 1

7. 0 1 1 0

8. 0 1 1 1

9. 1 0 0 0

10. 1 0 0 1

11. 1 0 1 0

12. 1 0 1 1

13. 1 1 0 0

14. 1 1 0 1

15. 1 1 1 0

16. 1 1 1 1

So there are total 16 possible outcomes.

Now count the number of combinations that has exactly two 1's

4. 0 0 1 1

6. 0 1 0 1

7. 0 1 1 0

10. 1 0 0 1

11. 1 0 1 0

13. 1 1 0 0

So there are 6 possible outcomes with exactly two 1's

The required probability is

P(two 1's) = Number of outcomes with two 1's/Total number of outcomes

P(two 1's) = 6/16

P(two 1's) = 3/8

Therefore, the probability of getting two 1's is 3/8

Answer:

Make N alone

There is an 8 so we subtract 8 from both sides so the equation is still equal

-4 - 8 = -12

Because we are subtracting N it is positive

N = 12

8 - 12 = -4

Hope this helps

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

32cos 85≈2.8

Answer:

Step-by-step explanation:

Answer:

Distance of segments AB and CD = 12

Step-by-step explanation:

AB+BC + CD = 6+6+6 = 18inch

midpoint AB = 6/2 = 3

midpoint CD =6/2 = 3

Midpoint AB+Midpoint CD = 3+3 = 6

To solve we just 18-6 = 12

Distance of segments AB and CD = 12

Answer:

its 12

Step-by-step explanation:

Distance of segments AB and CD = 12

Answer:

x < -7

Step-by-step explanation:

-5x + 7 > 42

Subtract 7 from each side

-5x + 7-7 > 42-7

-5x > 35

Divide each side by -5, remembering to flip the inequality

-5x/-5 <35/-5

x < -7

Answer:

The answer is A and D.

Step-by-step explanation:

Acute angles are angles that are less than 90°.

0° < θ < 90°.

So by looking at the diagram, any angles that are smaller than a L-shaped(90°) are all acute angle.

Answer: Expressed powers

Step-by-step

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 700

x = 46

p = 46/700 = 0.066

q = 1 - 0.066 = 0.934

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, the z score for a confidence level of 90% is 1.645

Therefore, the 90% confidence interval is

0.066 ± 1.645√(0.066)(0.934)/700

= 0.066 ± 0.0094

The lower limit of the confidence interval is

0.066 - 0.0094 = 0.0566

The upper limit of the confidence interval is

0.066 + 0.0094 = 0.0754

Answer:

(0.0503, 0.0811).

Step-by-step explanation:

The confidence interval for the unknown population proportion p is (p^−z⋆p^(1−p^)n−−−−−−−−√,p^−z⋆p^(1−p^)n−−−−−−−−√). The confidence interval can be calculated using Excel.

1. Identify α. Click on cell A1 and enter =1−0.90 and press ENTER.

2. Thus, α=0.1. Enter the number of successes, x=46, and sample size, n=700, in the Excel sheet in cells A2 and A3. To find the proportion of successes, p^, click on cell A4 and enter =A2/A3 and press ENTER.

3. Thus, p^≈0.0657. Use the NORM.S.INV function in Excel to find z⋆. Click on cell A5, enter =NORM.S.INV(1−A1/2), and press ENTER.

4. The answer for z⋆, rounded to two decimal places, is z⋆≈1.64. To calculate the standard error, p^(1−p^)n−−−−−−−−√, click on cell A6 and enter =SQRT(A4∗(1−A4)/A3) and press ENTER.

5. The answer for the standard error, rounded to four decimal places, is p^(1−p^)n−−−−−−−−√≈0.0094. To calculate the margin of error, z⋆p^(1−p^)n−−−−−−−−√, click on cell A7 and enter =A5*A6 and press ENTER.

6. The answer for the margin of error, rounded to four decimal places, is z⋆p^(1−p^)n−−−−−−−−√≈0.0154. The confidence interval for the population proportion has a lower limit of A4−A7=0.0503 and an upper limit of A4+A7=0.0811. Thus, the 90% confidence interval for the population proportion of people in the region who would order calzones if they were on the menu, based on this sample, is approximately (0.0503, 0.0811).