Throughout this activity, the scale factor, n, has been a positive value. However, a scale factor for dilations can also be negative. When a set of coordinates on a preimage is multiplied by -n instead of n, the coordinates of the image rotate about the center of dilation by 180°. Consider all the potential intervals of n in the table. Enter information in the table to indicate whether the scale factor produces an enlargement, a reduction, or no size change. Also indicate whether the image rotates 180° about the center of dilation. The first one has been done for you.

The solution of the system of equation is (-7, -2).

The system of the equations;

\(\rm y^2 + x^2 = 53 \\\\y -x = 5\)

From equation 1

\(\rm y -x=5\\\\y = 5+x\)

Substitute the value of y in equation 1

\(\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2\)

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\(\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2\)

Hence, the solution of the system of equation is (-7, -2).

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Answer:

i think it might be c but i might be wrong sorry if i am

Step-by-step explanation:

TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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Answer:

The coordinates of Q are (1.5,3)

Step-by-step explanation:

Here, we simply want to divide the line segment in the given ratio

We can use the internal division formula here;

The coordinates of Q will be;

(x,y) = (nx1 + mx2)/(n + m) , (ny1 + my2)/(n + m)

m = 5, n = 3

(x,y) = (3(-1) + 5(3))/(5 + 3) , (3(-2) + 5(6)/(5 + 3))

(x,y) = (-3 + 15)/8 , (-6 + 30)/8

(x,y) = 12/8, 24/8

(x,y) = (1.5,3)

Answer:

a=m-b-z

Step-by-step explanation:

Answer:

a = -z + m -b

Step-by-step explanation:

Sorry my handwriting is a bit messy,  but hopefully it helps. Have a great day!

Answer:

rearrange the question

y - 5x = 8.................(1)

y - 8x = 9..................(2)

make y the subject formula in eqn. (1)

y = 8 + 5x................(3)

substitute

8 + 5x - 8x = 9

-3x = 1

x = -⅓

y = 8 + 5x

y = 8 + (-⅓)

y = 23/3

Answer:

Step-by-step explanation:

The model of the growth is:

Annual sales after 7 years:

Answer: The answer is C, 1/3 cup.

Answer:

C and D

Step-by-step explanation:

C and D can both be used to determine how much she did drink

C finds the difference between the initial amount of water and the final amount of water.

D finds that the change in water and the final amount of water combined together should equal the initial amount of water.

The simplest form of expression 125^(2/3) is 25.

This expression can be solved using exponents. Exponent means a quantity, describing the power to which base number is raised. In other words , Exponent refers to the number of times a number is used in a multiplication. The 4 types of exponents are: positive, negative, zero, and rational. Positive exponents tell you how many times to multiply a base by itself.

In order to solve this expression , we use properties of exponents.

Hence , using the property - \(x^{m} x^{n} = x^{mn}\)

and rewriting 125 as cube of 5

i.e. \(125=5^{3}\)

→ \((5^{3})^{2/3}\)

Now , cancelling the 3s

→ \(5^{2}\) = 25

Therefore the answer after simplification is 25.

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We are asked to find the sum of the series 3, 7, 15, 31,... for the first 110 terms. To calculate the sum, we can use the formula for the sum of an arithmetic series, which is given by Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.

In this series, we can observe that each term is obtained by multiplying the previous term by 2 and adding 1. Therefore, the common difference (d) is 1 and the first term (a) is 3.

Using the formula for the sum of an arithmetic series, we can substitute the values into the formula. Plugging in n = 110, a = 3, and d = 1, we get Sn = (110/2)(2(3) + (110-1)(1)).

Simplifying this expression, we have Sn = (55)(6 + 109) = (55)(115) = 6325.

Therefore, the sum of the series for the first 110 terms is 6325.

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Answer:

3

Step-by-step explanation:

-4 x (3/-4)

= -4 x (-0.75)

= + 3                                      

Answer: 155

Step-by-step explanation:

To round 154.98 to the nearest tenth, remember that in the hundredths place is 8 and is more than 5. Therefore, the tenths value of 154.98 increases by 1 to 0.

The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Answer:

B.

right scalene triangle

Step-by-step explanation:

The approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

The change of base rule of the log is used to write the given logarithmic number in terms of ratio of two log numbers.

For example,

\(\log_ba=\dfrac{\log_xa}{\log_xb}\)

Here, a,b is the real number and x is the base.

The logarithmic equation given in the problem is,

\(log_5(15) = x+ 3\)

Using the change of base formula, the above equation can be written as,

\(\dfrac{log{15} }{log{5} }= x+ 3\)

Isolate the x variable as,

\(x=\dfrac{log{15} }{log{5} }- 3\\x=\dfrac{1.17609}{0.69897}- 3\\x\cong-1.317\)

Hence, the approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

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Answer:

B

Step-by-step explanation:

B) -1.317

Answer:

First one

Step-by-step explanation:

rearrange x + y = 2 in the form y = mx + c

y = -1x + 2

means gradient is -1 and y-intercept is 2. such line is shown in the first graph

see where x = 1 and draw a straight line. Such line is also only shown in the first graph.

it should be the first graph

Answer:

keeping the value of x as -1

then we have

\(f( - 1) = {1}^{2} + 5 \times 1 - 7\)

=1 +5-7

= -1

6 possible ways to order 3 couples in a row

Given,

We have three married couples. that is six persons in total.

a, b, c, d, e, f may taken as the six persons.

Considering the statement:

Elder partner on the left, assume a, c and e as elders.

Then we have, (a, b) ------ ( 1)

                        (c, d) ------ (2)

                        (e, f) ------ (3)

There is no change in position between the couples.

So, we get three persons in total.

Possible ways to order these three persons will be like this: 3! = 3×2×1

                                                                                                        = 6

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Answer:

m∠D = 109

Step-by-step explanation:

This is a parallelogram.

In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:

9x - 44 = 6x + 7

9x - 6x = 7 + 44

3x = 51

x = 17

Now we can calculate measure of m∠D:

m∠D = 9x - 44

9×17 + 44 = 109

Answer:

148cm^2

Step-by-step explanation:

The formula for surface area of a rectangular prism is 2(hl)+2(hw)+2(wl).

we just plug in the values.

2(6 x 5) + 2(6 x 4) + 2(4 x 5)

= 2(30) + 2(24) + 2(20) then simplify

= 60 + 48 + 40

= 148

Notice that points ( i ), ., (vi) are approaching x=1 from the right and points

(vii), ., (xi) are approaching from the left.

The closer is a point Q to x=1, the closer is the slope of the line PQ to the slope of the tangent at x=1.

For this articular function you can treat a pair like (xi),(vi) as an upper and lower

bound on the slope of the tangent.

If you can find a pair (something like Q1=0.999, Q2=1.001) so close to x=1 that the two secant lines PQ1 and PQ2 have identical slopes within two decimal places, then you have your estimate.

The exact value of the slope at x=1 is -14π.

The thing about this function is that it alternates between up and down extremely quickly.

If I could attach a graph I would; I would recommend that you look at it in some graphing tool.

Just imagine what is happening around x=1:

The argument of sin is 14π, making the value of the function 0.

If you keep increasing x beyond 1, the argument of sin gets smaller;

when the argument of sin gets to 13.5π the value of the function reaches -1

and the direction of the slope reverses.

That means that to get any meaningful estimate of the slope you need x

such that 14π/x is in the interval (13.5π, 14.5π).

That means x must be in the interval (0.97, 1.03).

And you probably need to try values even closer to 1 to get accuracy to 2 decimal digits.

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The maximum and minimum voltage for an outlet can vary, but in standard residential outlets in the US, the voltage is typically 115 volts.

For alternating electric current, the number of oscillations per second is determined by its frequency. The frequency is measured in hertz (Hz), which represents the number of complete oscillations per second.

a) In 0.05 seconds, the number of oscillations can be calculated by dividing the time (0.05s) by the period (T), which is the inverse of the frequency. The formula is: Number of oscillations = Time / Period. However, the period can also be expressed as 1/frequency. So, the formula becomes:

Number of oscillations = Time x Frequency.

Given that the time is 0.05 seconds, you need to know the frequency of the alternating current to determine the number of oscillations.

b) The maximum and minimum voltage for an outlet depend on the type of alternating current.

In the case of standard residential outlets in the United States, the voltage is 115 volts.

However, it's important to note that the voltage is not always equal to 115 volts.

In summary, to determine the number of oscillations in 0.05 seconds, you need to know the frequency of the alternating current.

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Answer:

B

Step-by-step explanation:

3(x +1) =3x +3

Plug it in

3(5+1)=3(5)+3

3(6)=15+3

18=18

Answer:

$9.9

Step-by-step explanation:

the key word in this is markdown or a decrease so multiply the original and the markdown 45 * 22% or .22

Answer:

1

Step-by-step explanation:

3x + 5 = 8

Subtract 5 from both sides of the equation

3x + 5 -5 = 8 -5

Simplify

3x =3

Divide both sides of the equation by the same term

3x/3 = 3/3

Simplify

x = 1

Hence, 1 will make the equation True.

[RevyBreeze]

Answer:

Slope m (Gradient) = 3

y-intercept: (0, -5)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 3x - 5

Step 2: Break function

Slope m = 3

y-intercept b = -5

Answer:

SLOPE: 3

Y INTERCEPT: -5

The number with the X is always the slope, and the number without the X is the y intercept, it depends if you are adding or subtracting.