Verify that $\triangle ABC\sim\triangle DEF$ . Find the scale factor of $\triangle ABC$ to $\triangle DEF$ .

$\triangle ABC:\ BC\ =\ 18,\ AB\ =\ 15,\ AC\ =\ 12$

$\triangle DEF:\ EF\ =\ 12,\ DE\ =\ 10,\ DF\ =\ 8$

The ratio as a unit rate is 0.8 meters per second.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

The given statement is "8 meters in 10 seconds".

It can be written as:

= 8/10 meters per second

= 0.8 meters per second

Thus, the ratio as a unit rate is 0.8 meters per second.

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The Question attached here seems to be incomplete, the complete Question is

Write the ratio as a unit rate. 8 meters in 10 seconds.

A. 0.8 meters per second

B. 1.125 meters per second

C. 2 meters per second

D. 80 meters per second

Step-by-step explanation:

From the image, let Angle 1 be x, and angle 2 be 16°

\({ \tt{x + 16 = 180}} \\ { \tt{x = 164 \degree}}\)

Answer:

∠ EHK

Step-by-step explanation:

Adjacent angles are positioned next to each other on a straight line and are supplementary.

∠ IHK is next to ∠ EHK on the line DI and are adjacent

Answer:185

Step-by-step explanation:the answer is 185 because you have to add

Answer:

5%

Step-by-step explanation:

Given the following question:

The item costs 60 dollars
The shipping costs was 3 dollars

What was the percent of 60 is 3?

To find the answer we divide the shipping fee by the cost and then multiply the answer by 100.

\(\frac{3}{60} =3\div60=0.05\times100=5\)
\(=5\)

3 dollars is "5 percent" of 60 dollars.

Hope this helps.

Answer:

hey how r u doing ?

Step-by-step explanation:

........aags

Answer:

its 2:14 and I'll never sleep

Answer:

The X intercepts would be -1 and 2

Answer:

There are two x-intercepts.

Step-by-step explanation:

They are in the picture attached below.

Answer:1925g=1kg 925g

Step-by-step explanation:

1kg=1000g

2kg=2000g

2kg 300g=2300g

2300-375=1925g=1kg 925g

Answer:

two ratios

Step-by-step explanation:

you need two to be able to solve it

Answer:

2 ratios

Step-by-step explanation:

The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b\(\sqrt{3}\) = \(\frac{1}{2 - \sqrt{3} }\)

Rationalizing the right hand side by the conjugate surd which is 2 + \(\sqrt{3}\)

\(\frac{1}{2 - \sqrt{3} }\)  x \(\frac{2 + \sqrt{3} }{2 +\sqrt{3} }\) = \(\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}\) = \(\frac{2 + \sqrt{3} }{1}\) = 2 + \(\sqrt{3}\)

Equating,

a + b\(\sqrt{3}\) = 2 + \(\sqrt{3}\)

Comparing the variables,

a = 2,   b\(\sqrt{3}\) = \(\sqrt{3}\), b = 1

The ratio, a: b = 2:1

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The length of Ad is x.

The hypotenuse and legs of a right triangle are the two sides that are directly across from the right angle. The Pythagorean theorem, which asserts that the hypotenuse's square is equal to the sum of the legs' squares, can be used:

\(c^2 = a^2 + b^2\)

This formula can be used to determine the length of the third side of a right triangle if we know the lengths of any two of its sides.

We are aware that the hypotenuse of the right triangle Abc in this instance is Ab. Ad is also one of the right triangle's legs, although we don't know how long it is. Give it the name x:

c = Ab

a = x

b = ?

Using the Pythagorean theorem, we can solve for b:

\(Ab^2 = x^2 + b^2\\b^2 = Ab^2 - x^2\\b = \sqrt{(Ab^2 - x^2)}\)

Therefore, the length of Ad is x.

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Thus, the unique solution to the given differential equation with the initial condition y(1) = 13 is \(y = 1 / (- (1/4) * x^4 + 17/52).\)

To solve the given differential equation, we'll use the method of separation of variables.

First, we rewrite the equation in the form\(dy/dx = y^2 * x^3\)

Separating the variables, we get:

\(dy/y^2 = x^3 * dx\)

Next, we integrate both sides of the equation:

\(∫(dy/y^2) = ∫(x^3 * dx)\)

To integrate \(dy/y^2\), we can use the power rule for integration, resulting in -1/y.

Similarly, integrating \(x^3\) dx gives us \((1/4) * x^4.\)

Thus, our equation becomes:

\(-1/y = (1/4) * x^4 + C\)

where C is the constant of integration.

Given the initial condition y(1) = 13, we can substitute x = 1 and y = 13 into the equation to solve for C:

\(-1/13 = (1/4) * 1^4 + C\)

Simplifying further:

-1/13 = 1/4 + C

To find C, we rearrange the equation:

C = -1/13 - 1/4

Combining the fractions:

C = (-4 - 13) / (13 * 4)

C = -17 / 52

Now, we can rewrite our equation with the unique solution:

\(-1/y = (1/4) * x^4 - 17/52\)

Multiplying both sides by -1, we get:

\(1/y = - (1/4) * x^4 + 17/52\)

Finally, we can invert both sides to solve for y:

\(y = 1 / (- (1/4) * x^4 + 17/52)\)

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The normal price is gotten by find the 5% discounted price and adding it to the amount paid.

The normal price is  £580

Given Data

Discount = 5%

Amount paid = £551

Let the normal price be x

let us find 5% of x

= 5/100 *x

=0.05x

Hence the discounted amount is £0.05x

We know that the amount paid = Normal Price - Discount

Substituting our data

551 = x-0.05x

551 = 0.95x

Divide both sides by 0.95

x = 551/0.95

x =  £580

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Answer:

48

Step-by-step explanation:

Bridget = 2      x 12 = 24

Jim = 1              x 12 = 12

Krutika = 1        x 12 = 12        ---> 24 + 12 + 12 = 48

80.49% of Brookland voters support increasing funding for mental health services.

To estimate the number of voters in favor of increased funding for mental health services in Brookland, one can use the percentage of voters who participated in the survey and apply it to the total number of voters in the city.

The percentage of supporters of the financial increase is calculated by dividing the number of supporters by the total number of survey respondents:

Ratio = (482 / 600) = 0.8033

To estimate the number of voters, we multiply the proportion by the total number of voters in the city:

Estimated number of voters = 0.8033 * 19,310 = 15,541

An estimated 15,541 voters in Brookland support increasing funding for the city's mental health services.

To calculate the percentage of voters, we divide the estimated number of voters by the total number of voters in the city and multiply by 100:

Percentage of voters = (15,541 / 19,310) * 100 = 80.49%

Therefore, approximately 80.49% of Brookland voters support increased funding for mental health services.

If you increase the number of randomly selected voters to 1200, the margin of error decreases. A larger sample size usually provides a more accurate representation of the population.

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Answer:

A. <DEC and <AEB

Step-by-step explanation:

Angles AEB and DEC are vertical angles.

Answer:db

Step-by-step explanation:

Reina's driving time from Squamish to Whistler would have to be approximately 11.78 minutes for this situation to represent a proportional relationship.

To determine if the given situation represents a proportional relationship, we need to check if the ratios of distance to time are the same for both parts of the trip.

a) Let's calculate the ratios of distance to time for both segments of the trip:

Segment 1 (West Vancouver to Squamish):
Distance: 55 km
Time: 45 minutes
Ratio: 55 km / 45 min = 11/9 km/min

Segment 2 (Squamish to Whistler):
Distance: 60 km
Time: 50 minutes
Ratio: 60 km / 50 min = 6/5 km/min

The ratios for the two segments are not equal (11/9 is not the same as 6/5). Therefore, this situation does not represent a proportional relationship.

b) For the situation to represent a proportional relationship, the ratios of distance to time for both segments must be equal. Let's assume Reina's driving time from Squamish to Whistler is represented by "t" minutes.

Segment 2 (Squamish to Whistler):
Distance: 60 km
Time: t minutes
Ratio: 60 km / t min = 6/5 km/min

To make the ratios equal, we need to set up the equation:

11/9 = 6/5

To solve for "t," we can cross-multiply:

(11/9) * t = (6/5) * 60

11t/9 = 72/5

Cross-multiply again:

5 * 11t = 9 * 72

55t = 648

t ≈ 11.78 minutes

Therefore, Reina's driving time from Squamish to Whistler would have to be approximately 11.78 minutes for this situation to represent a proportional relationship.

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Answer:

c

Step-by-step explanation:

The required logarithmic equation which equivalent to eˣ = 4 is  x = ln4.

Given that,
To determine the logarithmic equation which is equivalent to eˣ = 4.

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,
eˣ = 4
Taking ln both side
lneˣ = ln4
x lne = ln 4

Since lne = 1
x = ln 4

Thus, the required logarithmic equation which is equivalent to eˣ = 4 is x = ln4.

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Answer:

407.3725

Step-by-step explanation:

The value of the F ratio for testing the significance of this model is not 15.56.

For question 10, in a simple linear regression analysis, SST represents the total sum of squares, which measures the total variation in the dependent variable. SSE represents the sum of squared errors, which measures the variation that is not explained by the regression model.

To determine which statement is true, we need to compare the values of SST and SSE.


Now let's move on to question 14. The standard error of estimate is a measure of the variability of the observed values around the regression line. It is not directly related to the sum of the residual squared.

Therefore, the statement that the sum of the residual squared must be 120 is not necessarily true.

Lastly, for question 15, the F ratio is used to test the overall significance of a multiple regression model. It compares the explained variation (SST - SSE) with the unexplained variation (SSE) and takes into account the number of observations and number of explanatory variables.

Given that SST is 900 and SSE is 460, we can calculate the F ratio as follows:

F = ((SST - SSE) / number of explanatory variables) / (SSE / (number of observations - number of explanatory variables))

F = ((900 - 460) / 5) / (460 / (35 - 5))

F = 440 / 460

F ≈ 0.9565

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Answer:

f(2) = 11

hope this helps

Step-by-step explanation:

3(2)+5

6+5

11

Answer:

11

Step-by-step explanation:

3(2)+5=11

Substitution -- :D

Answer:

Given that,

To find the distance between the points (2,2) and (-2,-1)

we know that,

Distance formula,

The distance between the two points (x1,y1) and (x2,y2) is,

Substitute the value we get,

the points (2,2) and (-2,-1)

Answer is: The distance between the point (2,2) and (-2,-1) is 5 units.

The result of a histogram of the given data is 0.8.

There are a few steps to use a TI-83, TI-83 plus, or TI-84 calculator is used to create the histogram.

1. First, the process is to press the STAT key and then press ENTER.

2. Enter the data into column L1.

3. In the third step with all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu.

4. After that press ENTER and make sure that Plot1 is set to On.

5. Use the directional keys to navigate to the Type selector, move the selection to the third type in the top row, and press ENTER.

6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1.

7. Finally, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is finished, the correct histogram will display on the calculator.

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We know that the volume of a sphere is given by the formula:

V = (4/3)πr^3

where r is the radius of the sphere.

To find how fast the volume is increasing with respect to time, we need to differentiate the volume formula with respect to time:

dV/dt = 4πr^2(dr/dt)

where dV/dt is the rate of change of volume with respect to time, and dr/dt is the rate of change of radius with respect to time.

We are given that dr/dt = 2 mm/s, and we need to find dV/dt when the diameter of the sphere is 100 mm.

Since the diameter is twice the radius, when the diameter is 100 mm, the radius will be 50 mm.

So, substituting r = 50 mm and dr/dt = 2 mm/s into the equation for dV/dt, we get:

dV/dt = 4π(50)^2(2) = 20,000π mm^3/s

Evaluating numerically, we get:

dV/dt ≈ 62,831.853 mm^3/s (rounded to 3 decimal places)

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The slope-Intercept form of the given line is y=1.5x.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,

Slope of the line, m = (-2 - 3)/(4 - 2)

                                = 3 / 2

                                = 1.5

Now, the equation of the line passing through (2, 3) can be written as,

y = mx + c

(3) = 1.5(2) + C

3 = 3 + C

3 - 3 = C

C = 0

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1.5(x) + 0

y = 1.5x

Hence, the equation of the given line is y=1.5x .

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Answer:

its 10.08

Step-by-step explanation:

Answer:

f(x)

Step-by-step explanation: