Find the radius r of the circle. Round your answer to the nearest tenth.
M.
60°
N
10.2 yd
ס
ra
yd

Given:

The parent function is:

[tex]f(x)=x^2[/tex]

This function shift 1 unit left, vertically stretch by a factor of 3 and reflected over the x-axis.

To find:

The function after the given transformations.

Step-by-step explanation:

The transformation is defined as

[tex]g(x)=kf(x+a)+b[/tex]                ... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If k<0, then the graph of f(x) is reflected over the x-axis.

If 0<|k|<1, then the graph compressed vertically by factor |k| and if |k|>1, then the graph stretch vertically by factor |k|.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that the graph of f(x) shifts 1 unit left, so a=1.

The graph of f(x) vertically stretch by a factor of 3, so |k|=3.

The graph of f(x) reflected over the x-axis, so k=-3.

There is no vertical shift, so b=0.

Putting [tex]a=1,k=-3,b=0[/tex] in (i), we get

[tex]g(x)=-3f(x+1)+0[/tex]

[tex]g(x)=-3f(x+1)[/tex]

[tex]g(x)=-3(x+1)^2[/tex]                     [tex][\because f(x)=x^2][/tex]

Therefore, the correct option is B.

Answer:

1.24 m

Step-by-step explanation:

F ∝ 1/d²

F = k/d²

Use values given to solve for k

0.006 = k/3²

k  = 0.054 (I multiplied both sides by 3² in the equation above)

New equation is F= 0.054/d²

Plug in your numbers so 0.035 = 0.054/d²

0.054/0.035 = d²

You can simplify if you want so d² = 54/35

Square root both sides to solve for d

√54/35 = 1.24 m

Answer:

it will take 18 min

Step-by-step explanation:

1/45+1/30=2/90+4/90=5/90=90 divided by 5 is 18

Answer:

Step-by-step explanation:

let -2/3 be the rational number and 9 be the positive real number

according to the given of indices this tis can be written as

[tex]9^{-2/3}[/tex]

[tex](3)^{2*-2/3}[/tex]

[tex]3^{-4/3}[/tex]

1/3^4/3

Answer:

£16,050

Step-by-step explanation:

Mark's current pay is £15,000.

His pay raise is 0.07(£15,000), or £1,050

His new pay is the sum of these two results:  £15,000 + £1,050 = £16,050

Answer:

11/36

Step-by-step explanation:

Answer:

0.30555555555

Step-by-step explanation:

Answer:

$320

Step-by-step explanation:

12.5 % is 40

12.5% is 8% of 100%

so do 40 x 8 = 320

i think b. not sure sorry if im wrong

A + B are correct

via a p e x

The correct statements are A and B

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.'

According to the given problem,

cos(A−B) = cosAcosB + sinAsinB .

Let A=90∘, B = a

Therefore.

cos(90∘−a) = cos90∘cosa + sin90∘sina.

Here, we have,

cos90∘ = 0, sin90∘ = 1.

cos(90∘−a) = sina

Now, we know,

sin∅ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

cos∅ = [tex]\frac{Base}{Hypotenuse}[/tex]

For ∠BAC,

cosA = [tex]\frac{AB}{AC}[/tex]

For ∠ACB,

sinC =  [tex]\frac{AB}{AC}[/tex]

Hence, we can conclude, A and B are the true statements for the given right-angled triangle.

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Answer:

1) y= 2x

for every 5 x-steps to the right the graph goes up by ten. 10/5 is simplified to 2/1 or just 2

it starts at 0/0, so no need to add and absolute value

2) x: number of days

y: number of vidits (roughly2 per day, but you don't need to write this in the box)

3) 35 days. it's just y=70

and we could write this as

70 = 2*x | devide by 2 on both sides to get x

35 = x

Answer:

angle A = Angle E

ΔCAB ≅ΔFED

Step-by-step explanation:

ASA  means Angle side Angle Where the side is between the two angles

We have an angle C= F  and a side AC = EF

We need angle A = Angle E

ΔCAB ≅ΔFED

Answer:

she will make 78 dollars

Step-by-step explanation:

312 divided by 24 is `13

13 times 6 is 78

Answer:

7 groups

Step-by-step explanation:

1 hour = 60 minutes

3/4 of an hour = 3/4(60) = 45 minutes

therefore, 1 3/4 hours is 105 minutes

105 divided by 15 is 7

Answer:

10 quarts

thank you

i think

Answer:

29/60 of the crates are left behind.

Step-by-step explanation:

Total number of crates = 24 1/4= 97/4

Rotten tomatoes crates = 7 3/5= 38/5

Joe sold crates = 8 1/3= 25/8

Canned  crates of tomatoes =7 5/6= 47/6

Therefore

24 1/4 - 7 3/5 - 8 1/3 - 7 5/6

= 97/4-38/5-25/3-47/6

= (97*5-38*4)/20  - (25*2+47)/6

= 485-152/20 - 97/6

= 333/20-97/6

= 333*3-97*10/60

=999-970/60

=29/60

29/60 of the crates are left behind.

This question is solved in 2 steps.

First the LCM of fraction 1 and 2 is taken separately from the LCM of fraction 3 and 4 for simplification purposes.

Then again the LCM is taken for the answers obtained from fraction 1&2 and fraction 3& 4.

Absolute value of 7. Any real numbers in the absolute sign would equal to the positive value.

Definition

[tex] \large \boxed{ |x| = \begin{cases} x \: \: \: \: (x \geqslant 0) \\ - x \: \: \: \: (x < 0) \end{cases}}[/tex]

If we substitute x = 7 in. Answer by using the definition of absolute value. Note that we only substitute x = 7 in x and not -x since 7 is greater than 0 and not less than 0.

[tex] \large{ |7| = 7 \: \: \: \: (x \geqslant 0)}[/tex]

You may also be wondering what will happen if we substitute x = any negative numbers.

[tex] \large{ | - 7| = - ( - 7) \: \: \: \: (x < 0)} \\ \large \boxed{ | - 7| = 7}[/tex]

Because -7 is less than 0. We substitute in -x and not x. This is the definition of absolute value. But to understand it easily, any numbers in absolute value have to equal to their positive value.

Conclusion

Let me know if you have any doubts regarding the absolute value through comment!

Answer:

The given parameters of the study are;

The number of people in the sample, n = 200

The p-value = 0.013

The average increase between fall and spring semester = $0.35

Therefore, we have;

Given that the p-value is less than 0.05, we reject the null hypothesis, and that there is significant statistical evidence to suggest that there is a difference between the fall and spring semester tuition at universities across the U.S.

Step-by-step explanation:

The result of the test hypothesis is incorrect or should be rejected.

Researchers frequently use P-values to determine if a trend they've seen is statistically significant. The p-value of a statistical test is small enough to reject the null hypothesis of the test, which is referred to as statistical significance.

The likelihood that the null hypothesis is true is P > 0.05. The likelihood that the alternative hypothesis is correct is (1-P) the P-value. The test hypothesis is incorrect or should be rejected if the test result is statistically significant (P≤0.05). There was no effect if the P-value was bigger than 0.05.

We reject the null hypothesis since the p-value is less than 0.05, and there is strong statistical evidence to imply that there is a difference between autumn and spring semester tuition at institutions across the United States.

Hence, the result of the test hypothesis is incorrect or should be rejected.

Learn more about P-Value:

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Answer:

y=-1

Step-by-step explanation:

y=-1 just shows the y value which means its just a horizontal line which is parallel to the x axis.

48 ÷ (7 x 5 - 3 x 9)

= 48 ÷ (35 - 27)

= 48 ÷ 8

= 6

Step-by-step explanation:

only half of your points for each answer ;)

Answer: 6

Step-by-step explanation:

Because of PEMDAS, you do 7x5 which is 35 than 3x9 which is 27. Then you subtract those and get 8. After you finish what's in the parenthesis, you divide 48 by 8 which is 6.

Answer:

The correct answer is - 103.13

Step-by-step explanation:

Given:

Circumference (C) = 36

Area =?

Formula:

Formula of area

A=πr2

formula of circumference

C=2πr

Solution:

C= 36 given so

36 = 2*3.142*r (r is radius)

r = 36/6.284

= 5.729

Putting the value of r in the formula of Solving for Area

A = 3.142*(5.729)^2

= 3.142*32,821

= 103.1124 or 102.3

Answer: 3/4

Step-by-step explanation:

Did the test

The required multiplicative rate in the given function is 3 / 4. Option B is correct.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
From the table of the exponential functions,
The multiplicative factor is given as,
K = y₂/y₁
K =  [9 / 8] / [3/2]
K = 3 / 4

Thus, the required multiplicative rate in the given function is 3 / 4. Option B is correct.

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Answer:

Hi, there for x it will be x=−2y+6

But if your solving for y it will be [tex]y=-\frac{1}{2}x+3[/tex]

Hope this Helps :)

Step-by-step explanation:

Let's solve for x.

2x+4y=12

Step 1: Add -4y to both sides.

2x+4y+−4y=12+−4y

2x=−4y+12

Step 2: Divide both sides by 2.

[tex]\frac{2x}{2}=\frac{-4y+12}{2}[/tex]

x=−2y+6

2.

Let's solve for y.

2x+4y=12

Step 1: Add -2x to both sides.

2x+4y+−2x=12+−2x

4y=−2x+12

Step 2: Divide both sides by 4

[tex]\frac{4y}{4} =\frac{-2x+12}{4}[/tex]

[tex]y=-\frac{1}{2} x+3[/tex]

Answer:

a = 32

b= 27

c = 9

Step-by-step explanation:

a= 5+ b from the second equation

c= b/3 from the third equation

substitute the above equations to the first equation then solve for b your answer will be 27

substitute the value of b in the second equation you will solve for a

perform the same substitution to the third equation you will get the answer for c

Step-by-step explanation:

a-b=5<=>a=5+b (1)

b:c=3<=>b=3c (2)

a+b+c=68<=>5+b+3c+c=68<=>5+3c+3c+c=68

<=>7c=63<=>c=9

Fill in (2), we have b=3c=3.9=27

and in (1), we have a=5+b=5+27=32

So, a=32, b=27, c=9

Answer:

63/10,  6.396,  6.99,  7 4/11

Step-by-step explanation:

Convert all to fraction or decimal

umm I don't know hehe oops

Answer:

Length of old board = 68.2cm

Step-by-step explanation:

Let old board length be x

Given new board is 120 % longer than old board = x + 120% of x

Length of new board = 150cm

Therefore,

x + 120% of x = 150

[tex]x + \frac{120}{100} x = 150\\\\x + 1.20x = 150\\\\2.2x = 150 \\\\x = 68.18 = 68.2cm[/tex]

Answer:

C

Step-by-step explanation:

.........................

Answer:

21 is the answer

Step-by-step explanation:

from the figure it can be seen that

angle G = angle J

angle H = angle K and

angle I = angle L

thus triangle GHI is similar to triangle JKL and in 2 similar triangles the ratio of their corresponding sides is same. that means

[tex] \frac{hi}{kl} = \frac{gi}{jl} \\ \frac{18}{30} = \frac{x}{35} \\ x = \frac{18}{30} \times 35 \\ x = \frac{3}{5} \times 35 \\ x = 3 \times 7 \\ x = 21[/tex]

Answer:

35square meters

Step-by-step explanation:

5×7=35