Juan's work for solving by completing the square is below. In which step (if any) does Juan make a mistake?
(SEE PICTURE FOR STEPS)



Step 4

Step 1

Juan does not make a mistake.

Step 3

Answer:

a. angle 4 is congruent to angles 1, 2, 3, 5

b angle 5 is congruent to angles 1, 2, 3, 4

c. the sum of angles 1, 4, and 5 is 180°

d. The sum of angles 1, 2, and 3 is 180 °

Step-by-step explanation:

a. all angles are the same measurement

b. all angles are the same measurement, you know this by measuring

c. they are on a striaght 180 degree line

d. the sum of a triangles angles are always 180 degrees

Step-by-step explanation:

let n be the number of working hour

so total income is 24n + 6

now 1/6 of the income will be into saving

so the saving is (24n + 6) /6

The expression representing the amount that will go into his savings each week is $4h + $1.

An expression is combination of variables, numbers and operators.

Mike's weekly pay is given by:

Pay = (hourly rate) x (hours worked) + sales bonus

Pay = $24h + $6

To find one-sixth of his weekly pay, we can multiply his pay by 1/6:

Savings = (1/6) x Pay

Savings = (1/6) x ($24h + $6)

Savings = $4h + $1

Therefore, the simplified expression representing the amount that will go into his savings each week is $4h + $1.

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Answer:

A

Step-by-step explanation:

First you simplify both sides to get -2.4x+14.4 > 52.8

then you need to subtract the 14.4 from both sides giving -2.4x> 38.4

then divide both sides by -2.4 giving an answer of

x is less than or equal to -16 meaning you point to the left with a closed circle

Answer:The answer is 4.06

Step-by-step explanation:

Okay I am 98% sure my math could be wrong since I don’t know what the possible answers to the question are but this is what I got.

but am not pretty sure

the volume of cone is =1/3 pie r² h

I think this is the formula to calculate it

Answer:

$120

Step-by-step explanation:

constant fee = (204-183) /(140-105)

= 21/35 = $0.6 per km

so, initial fee =

183 - (105 × 0.6)

= 183 - 63

= 120

Answer:

120

Step-by-step explanation:

trust me.

Answer:

[tex] - \frac{9}{2} [/tex]

Step-by-step explanation:

Rate of change of y with respect to x

[tex] = \frac{60 - 96}{ - 12 - ( - 20)} \\ \\ = \frac{ - 36}{ - 12 + 20} \\ \\ = \frac{ - 36}{ 8} \\ \\ = - \frac{9}{2} [/tex]

Answer:

the missing angle will be 140°

Answer: 140

Step-by-step explanation:

Answer:

ans : it is order wise

a) 6/125 cm³

b) 8/125 cm³

c) 1/125 cm³

d) 36/125 cm³

Step-by-step explanation:

a)

for rectangular prism = length × width × height

= (1/5) × (2/5) × (3/5)

= 6/125 cm³

b)

for cube = length³

= (2/5)³

= 8/125 cm³

c)

for cube = (1/5)³

= 1/125 cm³

d)

for rectangular prism = (3/5) × (4/5) × (3/5)

= 36/125 cm³

Answer:

x = 1.50

Step-by-step explanation:

We can use a ratio to solve

2 papers      1 paper

-------------  = --------------

3 dollars        x dollars

Using cross products

2x = 3*1

2x=3

Divide by 2

2x/2 = 3/2

x = 1.50

Answer:

$1.50

Step-by-step explanation:

example;

2/3=1.50

Have a great day <3

Answer:

[tex]{ \tt{yes \: it \: describes \: a \: functional \: equation \: of \: a \: line}}[/tex]

Answer:

????????????????????

Answer:

10x +30

Step-by-step explanation:

2(3 + 5x) + 24

Distribute

2*3 + 2*5x+24

6+10x+24

Combine like terms

10x +30

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

D

Step-by-step explanation:

Given

- (x + 1)² - 4 = 0 ( add 4 to both sides )

- (x + 1)² = 4 ( multiply both sides by - 1 )

(x + 1)² = - 4 ( take the square root of both sides )

x + 1 = ± [tex]\sqrt{-4}[/tex] = ± 2i ( subtract 1 from both sides )

x = - 1 ± 2i , then

x = - 1 + 2i, x = - 1 - 2i → D

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

Answer:

188

Step-by-step explanation:

SR and ST are equal in length so the arc SR and arc ST also have same measurement

since the perimeter of the circle is equal to 360 and arc RT is given as 64

x = (360 - 64) / 2

x = 188

Answer:

U = 1

V = -5

Step-by-step explanation:

U = -1 - (-2) = 1

V = -4 -1 = -5

Answer:

the answer will be - 9

Step-by-step explanation:

because 4plus 3 is 7 and minus one is 6 and then plus one is 7 and then plus the 2 and the ans will be x = -9

Answer:

0

Step-by-step explanation:

when the term has a coefficient of, it does not have to be written.

x- X/1

The sum of two opposites equals o

So the solution would be o

Answer:

48 ANS.

MAY IT HELPED U

Answer:

a. See below for the Frequency and Relative frequency Table.

b. Pitcher (P) is the position provides the most Hall of Famers.

c. 3rd base (3) is the position that provides the fewest Hall of Famers.

d. R is the outfield position that provides the most Hall of Famers.

e. Th number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.

Step-by-step explanation:

Note: This question not complete. The complete question is therefore provided before answering the question as follows:

Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).

L P C H 2 P R 1 S S 1 L P R P

P P P R C S L R P C C P P R P

2 3 P H L P 1 C P P P S 1 L R

R 1 2 H S 3 H 2 L P

a. Use frequency and relative frequency distributions to summarize the data.

b. What position provides the most Hall of Famers?

c. What position provides the fewest Hall of Famers?

d. What outfield position (L, C, or R) provides the most Hall of Famers?

e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).

The explanation of the answers is now provided as follows:

a. Use frequency and relative frequency distributions to summarize the data.

The frequency is the number of times a position occurs in the sample, while the relative frequency is calculated as the frequency of each position divided by the sample size multiplied by 100.

Therefore, we have:

Frequency and Relative frequency Table  

Position           Frequency          Relative frequency (%)

P                               17                             30.91%

H                               4                               7.27%

1                                5                               9.09%

2                               4                               7.27%

3                               2                               3.64%

S                               5                               9.09%

L                               6                               10.91%

C                              5                                 9.09%

R                              7                                12.73%

Total                       55                               100%  

b. What position provides the most Hall of Famers?

As it can be seen from the frequency table in part a, Pitcher (P) has the highest frequency which is 17. Therefore, Pitcher (P) is the position provides the most Hall of Famers.

c. What position provides the fewest Hall of Famers?

As it can be seen from the frequency table in part a, 3rd base (3) has the lowest frequency which is 2. Therefore, 3rd base (3) is the position that provides the fewest Hall of Famers.

d. What outfield position (L, C, or R) provides the most Hall of Famers?

As it can be seen from the frequency table in part a, we have:

Frequency of L = 6

Frequency of C = 5

Frequency of R = 7

Since R has the highest frequency which is 7 among the outfield position (L, C, or R), it implies that R is the outfield position that provides the most Hall of Famers.

e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).

Total frequency of infielders = Frequency of 1 + Frequency of 2 + Frequency of 3 + Frequency of S = 5 + 4 + 2 + 5 = 16

Total frequency of outfielders = Frequency of L + Frequency of C + Frequency of R = 6 + 5 + 7 = 18

The calculated total frequencies above imply that number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.

Answer:

[tex]3w + 6 = 21 \\ 3w = 15 \\ w = 5[/tex]

Hey there!

[tex]\mathsf{3w + 6 = 21}[/tex]

[tex]\mathsf{3w + 6 - 6 = 21 - 6}[/tex]

[tex]\mathsf{21 - 6 = \boxed{\bf 15}}[/tex]

[tex]\mathsf{\dfrac{3w}{3}=\dfrac{15}{3}}[/tex]

[tex]\mathsf{\dfrac{15}{3}=\boxed{\bf 5}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer: \huge \bf w = 5}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

The surface area of the balloon is [tex]S(t) = \frac{100}{49} \pi t^8[/tex]

Step-by-step explanation:

Given;

S(r) = 4πr²

where;

S is the surface area of the balloon

r is the radius of the surface

The radius of the balloon at time "t" is given as;

[tex]r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0[/tex]

The surface area of the balloon as a function of time "t" is calculated as;

[tex]S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8[/tex]

Answer:

32

Step-by-step explanation:

The base angles of the triangle are the same since the sides are the same

<C = 74

A+B+C = 180 since the sum of the angles of a triangle = 180

74+B+74=180

Combine like terms

148+B =180

B = 180-148

B = 32

Answer:

[tex]\text{A. }32^{\circ}[/tex]

Step-by-step explanation:

From the Isosceles Base Theorem, the two base angles of a isosceles triangle are equal. Therefore, [tex]\angle A=\angle C=74^{\circ}[/tex].

Since the sum of the interior angles of a triangle is always equal to 180 degrees, we can write the following equation:

[tex]\angle A+\angle B+\angle C=180[/tex]

Substitute [tex]\angle A=\angle C=74^{\circ}[/tex] into this equation to solve for [tex]\angle B[/tex]:

[tex]74+\angle B+74=180,\\\angle B=180-74-74=\boxed{32^{\circ}}[/tex]

Answer:

The point estimate for p is of 0.12.

The 90% confidence interval for p is 0.0862 < p < 0.1538.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg.

This means that [tex]n = 250, \pi = \frac{30}{250} = 0.12[/tex]

The point estimate for p is of 0.12.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.0862[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.1538[/tex]

The 90% confidence interval for p is 0.0862 < p < 0.1538.