Which Similarity Theorem is described by the text below?If the lengths of three sides of one triangle are proportional to the lengths of three sides ofanother, then the triangles are similar.A. AAB. ASAC. SASD. SSS

The given figure can be divided into a rectangle and a triangle

The rectangle has the dimensions 10 m by 12 m

so, the area of the rectangle = 10 x 12 = 120 square meters

Now, we will find the area of the triangle:

Base = 12 - 10 1/4 = 1 3/4 m

Height = 15 - 10 = 5 m

Area = 1/2 x base x height =

So, the total area =

Answer:

Step-by-step explanation:

f(x)=|5x|    

f(2)= |5(2)|      Substitute 2 for x

f(2)= 10   Answer

Answer:

f(2) = | 5 • 2 | = | 10 | = 10

Step-by-step explanation:

Replace x with 2 then solve with the absolute value

Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

a division is a process of splitting a specific amount into equal parts.

We can stop the long division process when converting a fraction to a decimal number.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

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From the information given,

MAD for the heights of some sixth graders = 1.2

MAD for the heights of some seventh graders = 1

Number of times = MAD of data1/MAD of data 2 = 1.2/1

The answer is 1.2

Tristan should make 8 pieces of length 0.125 yards each to make a steps to the deck 1 yards above.

Division is breaking a number up into an equal number of parts. Mathematically, we can write "[a] divided by [b]" as a ÷ b. The division algorithm is given by -

D = dq + r

[D] - Dividend

[d] - Divisor

[q] - Quotient

[r] - remainder

Given is Tristan who is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height an he wants to make 8 steps.

Total number of steps to be made = [n] = 8

Height of deck = [h] = 1 yard.

Now, we have to divide 1 yard into 8 equal parts. Therefore, assume

that -

A = 1 ÷ 8

A = 1/8

0.125

We get the length of each step to be 0.125 yards.

Therefore, Tristan should make 8 pieces of length 0.125 yards each to make steps to the deck 1 yards above.

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The product of 21 and the difference between one whole number 1/2 and -1/2​ is; 42

We want to find the product of 21 and the difference between one whole number 1/2 and -1/2​. This can be expressed as;

21 * (1¹/₂ - (-¹/₂))

Let us first solve the bracket out using the order of operations rule named PEMDAS which stands for  P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;

1¹/₂ - (-¹/₂)

= 1¹/₂ + ¹/₂

= 2

Thus;

21 * (1¹/₂ - (-¹/₂)) = 21 * 2

= 42

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We solve as follows:

So, the value of "blank" is 80.

Answer:1,086

Step-by-step explanation: Initial Deposit

$400

Contributions

$0

Investment Time Span

20

Estimated Rate of Return

5.00%

Pencils: $0.25 each

Notebooks: $2.50 each

Backpacks: $32 each

The cost of the notebooks (C) must be equal to the price of each notebook (2.50) multiplied by the number of notebooks bought (x)

C = 2.50x

The prediction of outcomes of the number of 1 is 12

The given parameters are

Device = A die

Number of rolls = 72

From the question, the die is six-sided

This means that the sample space is

S = {1, 2, 3, 4, 5, 6}

So, the probability of rolling a 1 is

P(1) = 1/6

When the die is rolled 72 times, the number of outcomes of 1 is

Outcomes = P(1) * n

Where n = 72

So, we have

Outcomes = 1/6 * 72

Evaluate

Outcomes = 12

Hence, the prediction is 12

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The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.

It is given that:

Alicia wants to place her ten paintings side by side on the wall.

We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.

Alicia can arrange her six paintings:

6! = 6x5x4x3x2x1

6! = 720

Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

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Answer:

False

Step-by-step explanation:

Domain is the x-axis, range is the y-axis. In an ordered pair, the x-values go first, not second.

The measure of "a" in the above-given right-angled triangle is 32°

Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Key properties of a right-angled triangle to note are:

To solve for "a" recall the following. It is given that:

AB = BC

∠BEC=90°

∠DCE=42°

Because CD bisects ∠ACB, Hence,

∠ACD = ∠DCB = x.............................1

∠DCE= ∠BCE + ∠DCB .....................2

= ∠BCE + x = 42° ................................3

To find  ∠A, we use deductive reasoning to state:

∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)

Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:

∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°

Recall equation 2, where ∠DCB = x, hence

∠A +∠E +x + x + ∠BCE = 180°

Recall equation three where 3 where  ∠BCE + x = 42°, hence

∠A +∠E +x + (x + ∠BCE) = 180°

⇒ ∠A +∠E + x + 42° = 180°

Recall that ∠E = 90° so

⇒ ∠A +90° + x + 42° = 180° (Collect like terms)

⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence

∠A + x = 48°...........................4

Recall that in Δ ABC

AB =  BC (given)  

Hence, ABC is an Isosceles triangle. Since this is true, then

⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)

Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°

3x = 48

x = 48/3

x = 16°

Recall that

∠A = 2x...........equation 5, hence,

∠A = 2 * 16

∠A = 32°

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Hello!

What is an x-intercept:

 ⇒ value of x when the value of y equals '0'

       [tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]

  x-intercept is 25/8

What is a y-intercept:

 ⇒ value of y when the value of x equals '0'

       [tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]

   y-intercept is 5

Hope that helps!

The equation of a line in point-slope form is given by

Where

Thus, if we substitute the above values into the equation:

The equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words is w = 30t .

In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity. Velocity and speed are denoted by the letters v and v, respectively (boldface). The symbol has a bar over it for average values. How swiftly something is going, being done, or something that is moving quickly is measured in terms of speed. Driving an automobile 45 miles per hour is an illustration of speed. Someone cleaning a room in 10 minutes would be an example of quickness. the definition of speed. a direction or speed at which an object's location changes.

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Hello there. To solve this question, we'll need to remember how to find the variance and standard deviation of a data set.

First, given a data set with values:

The variance can be calculated by the formula:

In this case, μ is the arithmetic mean of the data set and x_i is the i-th element of the data set.

The data set given is:

{4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

To calculate the mean, we add every term and divide by the number of terms:

Now, we calculate the square of the difference between every term and mean.

Notice we have some repeated terms, we rewrite the sum like this:

Adding the terms and calculating the squares, we have:

This is the variance of the values of this data set. We can round it up to the nearest tenth as 1.6

The standard deviation is the square root of the variance.

Then, we calculate:

Again, rounding it to the nearest tenth, we have 1.3;

The final answer is: The variance of this data set is 1.6 and its standard deviation is 1.3.

Solving the second question:

We apply the same formula. First, find the mean of the values:

Now, as every term is different from each other, we apply the formula and get the following:

Calculating the difference, squaring it, adding the values and dividing by 9, we get:

Variance is approximately equal to 4.84

The Standard deviation is the square root of the variance, namely 2.2

In the small triangle

There are a right angle and an acute angle of measure 53 degrees

Since the sum of the angles of a triangle is 180 degrees

Then 90 + 53 + < 1 = 180 degrees

Then 143 + < 1 = 180

Subtract 143 from both sides

Then < 1 = 37 degrees

Since <2 is an exterior angle of the small triangle

Then its measure = the sum of <1 and 90 degrees

Then < 2 = 37 + 90 = 127 degrees

In the triangle of angles 2, n3 and 30

< 2 + < 3 + 30 = 180

127 + < 3 + 30 = 180

Add 127 and 30

157 + <3 = 180

<3 = 23

The answer is < 2 = 127 degrees and < 3 = 23 degrees

The form of quadratic is:

Since (0,6) is given, we know c = 6, thus we have:

Point 2 is (2,8), replace x and y and find equation:

Putting point 2 (3,0), we have:

Solving the 2 simulatenous equations for a and b, we get:

a = -3

b = 7

Now u have all the values, a, b, and c.

Just put it in the general form of parabola :

y = -3x^2 + 7x + 6

Answer:

Step-by-step explanation:

x/7=12

The pre-image ABC in order to become the reflection at A'B'C' is reflected across the x-axis.

The pre-image ABC in order to become A"B"C" both are CONGRUENT, because the image and pre-image are BOTH RIGID.

**Please note that the rules for the transformation from ABC to A"B"C" were not provided**

Solution

For this case we have the following:

g = 12 and h=19

And we want to find 3h(h-g)

If we replace we got:

3*19 (19-12) =57*7=399

Then the answer would be:

D. 399​

Answer:

7

Step-by-step explanation:

14/2=7

The population after 5 years is approximately 337,465 people

The population of the city is 250,000

Annual growth rate is 6%

The population after t years is:

After 5 years, t = 5 and the population becomes:

The population after 5 years is approximately 337,465 people

Answer:

a) DE = 15 cm

b) AB = 6 cm

Step-by-step explanation:

Explanation #a)

- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;

[tex]{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = \frac{24}{8} }} \\ \\ { \rm{\bar{DE}} = \frac{24 \times 5}{8} } \\ \\ { \rm{\bar{DE}} = 15 \: cm}[/tex]

Explanation #b)

[tex]{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ \frac{24}{8} = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = \frac{18 \times 8}{24} }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}[/tex]

- Therefore, the scale factor is 2, triangle CDE = 2ABC

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]

Part A.

From the given table, we can see that the variable occupation is a Categorical variable becasue the occupation can divide a set of people into groups. Then, the level of measurement is Nominal because the occupation describes the objects by labels, with no quantitative value.

Part B.

Temperature is a Quantitave variable because we can measure the temperature of an object. Regarding the level of measurement, the temperature is an Interval variable because zero temperature is not the lowest possible temperature.

Part C.

The price is a Quantitative variable because the price is a numerical value with a meaningful order. Regarding the level of measurement, the price is a Ratio variable because it has a true zero, meaning that we can take ratios of values.

Based on the graph of the function shown, we can logically deduce the following:

The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Similarly, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph of the given function shown above, we can reasonably and logically deduce the following:

In conclusion, the function which this graph represent is a continuous function because both the domain and range is defined for all set of values in the interval above.

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[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}[/tex]

Let the total number of offices in the building be x.

We can represent the information provided in the question mathematically as:

Solving for x:

Cross-Multiply:

Hence, there are 140 offices in the building.

Answer: 140 offices