△ ABC ~ △DEF The perimeter of △ ABC is 6 and its area is 5
The perimeter of △DEF is 18 and its area is x^2+9
1.) Determine the scale factor of △DEF to △ ABC :
2.) let b represent the base of △ ABC and h represent height. Write expressions to represent the base and height of △DEF.
Base: Height:
3.) Use these expressions along with the information above to find all values of x that satisfy the given conditions and calculate the area of △DEF X=
4.) area of △DEF=
5.)What is the ratio of the area of △DEF to △ ABC?

By using Pythagoras theorem we get the height of the roof of dog house is 21 inches.

The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. 

This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. born. 

According to the question:

Given, Hypotenuse(h) = 29 inches

           Base(b) = 40/2 = 20 inches

Using Pythagoras theorem, we get

h² = b² + p²

⇒ 29² = 20² + p²

⇒ p² = 29² - 20²

⇒ p² = 841 - 400

⇒ p² = 441

⇒ p = √441

⇒ p = 21

∴ The height of the roof of dog house is 21 inches.

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The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer:

If the safe dose is .5 to 1 mg/kg/dose, the safe limit depends on the side of the child.  Using the more conservative limit of .5mg/kg, you have 36mg(kg/.5mg)=72kg, which is roughly 160lbs,  Even with the upper limit of 1mg/kg, you still have 36mg(kg/1mg) = 36kg, or 80lbs, which is a larger child.  I would say this dose isn't "safe", but you really need the weight of the child to calculate what is a safe dose.

Step-by-step explanation:

The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term  \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.

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Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer:

\(2abCosC = 1\)

Step-by-step explanation:

The cosine rule is

=> \(a^2= b^2+c^2-2abCosC\)

For 2abCosC, it becomes

=> \(2abCosC = b^2+c^2-a^2\)

=> \(2abCosC = (2)^2+(1)^2-(2)^2\)

=> \(2abCosC = 1\)

Answer:

-1.6666666666667.

Step-by-step explanation:

.

Answer:

-1.666666666

Step-by-step explanation:

we have a whole number which in this case is 1 and a fractional part which is 2/3.

wed can either turn 1 into a part of the mixed fraction which would be 5/3 so when we divide it gives you 1.666666666

or divide 2/3 which gives you 0.666666666 then just add the oone which gives you the same answer

The answer for this question is Celsius for Fahrenheit.

To convert temperatures from degrees Fahrenheit to degrees Celsius, multiply the result by.5556 (or 5/9) after subtracting 32.

(50°F - 32) x.5556 = 10°C, for instance.

When converting from degrees Celsius to Fahrenheit, multiply the result by 1.8 (or 9/5) and then by 32.

For instance, (30°C x 1.8) + 32 = 86°F'

Here are two useful charts that translate between F and C as well as between C and F.

The temperature of f degrees Fahrenheit converted to degree Celsius.

(( f)=5/9 (f-32)

represent the temperature of f degrees Fahrenheit converted to degree Celsius.

The function C(F) will be "C of F" it will be converted Fahrenheit to Celsius.

So that means if the temperature is in Fahrenheit it will be converted to Celsius.

So that means the C(F) represents the Celsius temperature.

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Complete Question -

For one month diera calculated her home town's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees FAhrenheit to degrees Celsius using the function C(F) = 5/9(F-32). What does C(F) represent?

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer: D: Square Root Of 5

Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)

Answer:

1. 55.5

2. 54.5

Step-by-step explanation:

Use division to convert the fraction to a decimal:

1/4 = 1 ÷ 4 = 0.25

Multiply by 100 to get percent value:

0.25 × 100 = 25%

Answer:

1. 0.56

percentage: 56%

2. 0.55

percentage: 55%

Step-by-step explanation:

5/9 to decimal= 0.56

to percentage multiply by 100

same for the second one

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Answer:

A.  The probability of event B​ occurring, given that event A has occurred

Step-by-step explanation:

Conditional probability

A probability is conditional if is depends on what has already happened.

The probability that event B happens, given that event A has already happened is "B given A" or P(B | A)

Therefore, P(B | A) means "The probability of event B​ occurring, given that event A has occurred"

Additional information:

P(A | B) means "A given B", i.e. the probability of event A​ occurring, given that event B has occurred

P(A ∩ B) means the probability of event A and event B both happening.

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Answer:

37.8

Step-by-step explanation:

Change 12 mm to 1.2 cm

Then apply the volume rule

Area * height

A = 1.2*7=8.4

H=4.5

Volume 8.4*4.5 =37.8

The annual interest rate on the account is 7.5%.

Option D

Using the formula for simple interest:

Simple Interest = Principal (P) * Rate (R) * Time (T)

We know that the principal (P) is $6,000, the time (T) is 5 years, and the balance at the end of 5 years is $8,250.

So, we can rearrange the formula to solve for the interest rate (R):

Rate (R) = (Simple Interest) / (Principal * Time)

The simple interest can be calculated as the difference between the final balance and the principal:

Simple Interest = $8,250 - $6,000 = $2,250

Now, let's substitute the values into the formula:

Rate (R) = $2,250 / ($6,000 * 5)

Rate (R) = $2,250 / $30,000

Rate (R) = 0.075 or 7.5%

Therefore, the annual interest rate on the account is 7.5%.

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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The sum of the series b 2 b 4 b 6 b 8 b {10} is \($\dfrac{180}{3}$\) since it is a geometric series with a common ratio of \($\dfrac{7}{4}$\).

Since the given series \($b 1 b 2 b 3 \cdots b {10}$\) has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of\($\dfrac{7}{4}$\). This means that the ratio of any two consecutive terms in the series is a constant, \($\dfrac{7}{4}$\). Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

\($S = b2 + b4 + b6 + b8 + b_{10}$\)

\($= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$\)

\($= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$\)

\($= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Since the sum of the series\($b 1 b 2 b 3 \cdots b {10}$\) is 180, we can substitute $b2$ with \($\dfrac{180}{3}$\)nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

\($S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

\($= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Therefore, the sum of the series \($b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$\).

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Using the Empirical Rule, it is found that:

It states that, for a normally distributed random variable:

Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:

68% are within 1 standard deviation of the mean, hence, out of 100:

0.68 x 100% = 68 scores.

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According to the equation does the graph of the systems of equations solve is B.

1/3x+1=2x-4 is correct.

A graph is a structure consisting of a group of items, some of which are "linked." The objects are mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.

It is evident from the graph that the two lines intersect at the location:

(3, 2).

To put it another way,

at x =3, y = 2

The point where two lines intersect is:

(x, y) = (3, 2) (3, 2).

Now,

x = 3 is the point  of the x-coordinate

y = 2 is the point of the y-coordinate

Now, examine the equation, 1/3x+1=2x-4, to see if it contains the correct x-coordinate value.

(1/3)x + 1 = 2x -4

subtracting 1 from both side:

(1/3)x + 1 -1  = 2x -4 -1

We get:

(1/3)x = 2x -5

subtract 2x from both sides:

(1/3)x -2x = 2x -5 -2x

We get:

-(5/3)x = -5

on simplifying the equation we get:

x = 3

the value of x = 3

this show that the 1/3x+1=2x-4 is correct.

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Answer:

its D

bc 3 is grater

The length of each edge of the cube =  6 inches, Thus option B is correct.

The volume of a cube = 216 cubic inches,

length of each edge of a cube is an inch

To find the value of a:

The formula for the volume of a cube is \(a^{3}\)

The volume of cubic = \(a^{3}\)

V = \(a^{3}\)

substitute the volume value given in the equation in the above formula

216 = \(a^{3}\)

\(a = \sqrt[3]{216}\)

\(a\) = 6

a = 6inches

Therefore, the length of each edge of the cube is 6 inches.

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Answer:

what is

Step-by-step explanation:

The sample proportion of the teenagers 13 to 17 years of age who use social media​ is 0.236.

Sample proportion is defined as the proportion of something from a given sample which has a particular characteristic.

The formula to calculate the sample proportion is,

p = Number of successes in a particular sample / Sample size

Given that,

a random sample of n = 330 teenagers 13 to 17 years of age was asked if they use social media.

Sample size = 330

Of those surveyed, 252 stated that they do use social media.

We have to find the proportion of teenagers 13 to 17 years of age who use social media​.

Number of failures = 252

Number of successes = 330 - 252 = 78

Sample proportion = 78 / 330 = 0.236

Hence the sample proportion is 0.236.

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Answer: The digit in the thousand place is '9'.

Step-by-step explanation: The given number is 5_278.

The difference between the values of the digits in the thousandth place and the tenth place is 8930.

The digits in the tenth place is already given, which is 7

Let's assume the digits in the thousandth place is x,

we get 6 = 6 , in   42= 6x7 using commutative law of multiplication.

What do associative law and commutative law mean?

using the Commutative Law of Multiplication.

42 = 6 x 7

42 / 7 = 6

 6  =  6

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Answer:

12.7 cm

Step-by-step explanation:

We can obtain CB using Pythagoras :

CB = √12² - 6²

CB = √108

CB = 10.39

Using CB,

We can apply trigonometry on triangle BCD to obtain the length of CD

Sin θ = opposite / hypotenus

Sin 55 = CB / CD

Sin 55 = 10.39 / CD

CD = 10.39 / sin 55

CD = 12.68

CD = 12.7 cm

Answer:

2 : 3

6 : 9

10 : 15

12 : 18

Given complete row:

\(\rightarrow 6:9\)

make it in simplest form:

\(\rightarrow 2 : 3\)

\(\rightarrow 1 : 1.5\)

now solve for others:

1st row:

\(\sf \rightarrow \frac{3}{1.5} :3\)

\(\sf \rightarrow 2:3\)

2nd row:

\(\sf \rightarrow 6:9\)

3rd row:

\(\sf \rightarrow \frac{15}{1.5} :15\)

\(\sf \rightarrow 10 :15\)

4th row:

\(\sf \rightarrow 12 : 12*1.5\)

\(\sf \rightarrow 12 :18\)

Answer:

2 : 3

6 : 9

10 : 15

12 : 18

Step-by-step explanation:

Equivalent ratios are ratios that have the same proportion to each other when put in simplest form.  Two ratios are considered equivalent if one can be expressed as a multiple of the other.

Therefore,  ? : 3 = 6 : 9 = ? : 15 = 12 : ?

Or,   ? / 3 = 6 / 9 = ? / 15 = 12 / ?

You have been given one complete ratio:  6 : 9 or 6 / 9

Therefore, from this, you can determine the other equivalent ratios by working out the multiples.

? / 3 = 6 / 9

To get from 3 to 9, the denominator has been multiplied by 3, therefore divide 6 by 3 to find ?

Answer:

A. Reflection

Step-by-step explanation:

I believe the answer would be reflection