Complete the explanation of how you know whether the triangles are similar. If possible, find the Indicated length. A Р 2.0 1.7 во 1.2 C R. Because two pairs of angles are congruent, the triangles are similar by the select) QR =

Transform equation form Ax + By = C

to y = ax + b

THen

4x + 2y = -6

A= 4. B= 2. C= -6

y = (-A/B)•x +(D/B)

y= (-4/2)•x + (-6/2)

y = -2x -3

Therefore in new equation

Slope a = -2

Y intercept b = -3

Okay, here we have this:

Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:

We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:

Finally we obtain that the original expression is equal to tan(60°).

Given the two equations

7(x - 1) = 3y + 21

3.5x + 1.5y = 4.5

To determine if the lines are visible or perpendicular

Step 1: Expand the equations and make y the subject of the formula

7(x - 1) = 3y + 21

=> 7x - 7 = 3y + 21

=> 3y = 7x - 7 - 21

=> 3y = 7x -28

Divide both sides by 3

y = 7/3x - 28/3 ------equation 1

3.5x + 1.5y = 4.5

1.5y = -3.5x + 4.5

Divide both sides by 1.5

y = -3.5/1.5 x + 4.5/1.5

y = -7/3x + 3--------equation 2

Step 2: compare the two equations to the equation of a line, y = mx + c

For equation 1

m = 7/3

For equation 2

m= -7/3

The slopes are not the same

Also, the product of the gradients did not give -1

It can be seen that the lines are neither perpendicular nor parallel

The quotient is 113/21.

It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are  a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.

2 5/6 = (2·6 +5)/6 = 17/6

1 3/4 = (1·4 +3)/4 = 7/4

Here 17/6 is dived by 7/4,we get

(17/6) ÷ (7/4) = (17/6) × (4/7) = (17×4)/(6×7) = (17×2)/(3×7) = 34/21

Here 34/21 is converted into a mixed number.

34/21 = (21 +13)/21 = 1 13/21

Therefore, the quotient is 113/21

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The y-intercept is at the point where the line cut the y-axis.

Hence, the y-intercept is 1

Hence, the slope is -3

Comparing the values to the equation y = =-3x +1, the equation is valid for the line.

Remember that

where

μ=24,653

σ=778

n=441

X=24,745

substitute

using the values of the z-score table

we have that

P(x>2.4833) = 0.0065086

therefore

In this problem you can reflect the small triangle and you will see that the angle D is equal to the angle x, and the angle E is equal to the angle B so we can sum tyhe internal angles of the big triangle to find x so:

And we solve for x so:

the angles x is equal to 69º

The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,

then, the middle is between the 5th and 6th number:

then, we need to find the mean value of these numbers. So, the median is

Therefore, the answer is option C.

We have the following expression

In our case x is equal to 4, then, we will evalute the given function h(x) when x is 4. It yields,

which gives

Therefore, the asnswer is h(4)=24

The measure of length of GF is 16 cm.

Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:

[tex]\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}[/tex]

We are given the following;

FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]

GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]

ST = 8 cm

Substitute the given values, we will get the following;

[tex]\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2[/tex]

GF = 2 * 8 = 16 cm

Thus, the measure of the length of GF is 16 cm.

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The formula for compounding continuously is :

where A is the future amount

P is the principal amount

e is a constant

r is the rate of interest

and

t is the time in years.

The question stated that the investment will be doubled, so the future amount will be twice the principal amount.

A = 2P

The rate of interest is 3.7%

e is a constant approximately equal to 2.71828..

Subsitute the values to the formula and solve the value of t :

Take the natural logarithm of both sides,

note that ln e = 1

The answer is 18.73 years

Answer:

Explanation:

We want to find the product of 123 and 200;

Therefore, the product of 123 and 200 is;

El producto de 123 y 200 es;

Answer:

Im taking the test ill give the answers in 5 minutes

Step-by-step explanation:

The petrified stump is 4 ft tall and cast a shadow that is 2 ft long .

2 ft shadow has a 4 ft height

5 ft shadow will have ? height

cross multiply

1. y+10=7(x+2) (applying the distributive law to the right side of the equation)

y= 7x+14-10 (substracting 10 in both sides of the equality)

y=7x+4

2. y-1=-2(x-1) (applying the distributive law to the right side of the equation)

y-1=-2x+2 (adding 1 in both sides of the equality)

y=-2x+2+1 (simplifying)

y=-2x+3

3. y-2=1/4(x-1) (applying the distributive law to the right side of the equation)

y-2=x/4 -1/4 (adding 2 in both sides of the equality)

y=1/4(x) -1/4+2 (simplifying)

y=1/4(x) +7/4

4. y-4=3(x-3) (applying the distributive law to the right side of the equation)

y-4=3x-9 (adding 4 in both sides of the equality)

y=3x-9+4 (simplifying)

y=3x-5

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

Let:

We want to finde some number k such that we can express the volume of the iceberg below the water line as the product of k and the volume of the iceberg above the waterline, this is:

then, solving for k we have the following:

we have that k=2^3. This means that the volume of the iceberg above the water line is 2^3 times the volume of the iceberg below the water line

Answer: $1161

Step-by-step explanation: The equation for compound interest is A=P(1+r/n)^n*t. P is the principal, in this case, being $480 originally invested, r is the rate, in this case being 15% or 0.15, and n is 4 because it is compounded quarterly. t is 6 because the period invested is 6 years. A=480(1+0.15/4)^4*6. This can simplify to 480(1.0375)^24, which equals approximately $1161 dollars. If the question requires to the tenths, it is $1161.3, and for the hundredths, $1161.33.

Answer:

7

Step-by-step explanation:

opposite angles are the same

8z+18=74

8z=56

z=7

Answer:

7 is my final answer thank you

Step-by-step explanation:

set as brainliest

We want to calculate the following quotient

Note that using properties of radicals, given non zero numbers a,b we have that

So, using this fact, our quotient becomes

As we are taking the square root, this opearation is only valid if and only if the expression inside the square root is a non negative number. That is, we must have that

As this is a quotient, we should also that the quotient is defined.

To understand this last point, we should make sure that we are not dividing by 0. So first, we want to exclude those value s of 0 for which the denominator becomes 0. So we have the following auxiliary equation

which implies that x=0.

So, the second quotient is always defined whenever x is different from 0. However, assuming that x is not 0 we want to find the value of x for which

To start with this problem, we solve first the equality. So we have

since x is not 0, we can multiply both sides by 8x², so we get

If we divide both sides by 28, we have that

now, by adding 1 on both sides we get that

so, whenever x=1, we have that the quotient inside the radical becomes 0.

Now, we will solve the inequality, that is

Note that on the left, we are mostly dividing two expressions. Recall that the quotient of two expressions is positive if and only if both expressions have the same sign.

Note that the expression

is the product of number 8 (which is positive) with the expression x², which is also always positive for any value of x. This means that the expression 8x² is always positive.

So, taking this into account, we should focus on those values of x for which the numerator is positive, as the denominator is always positive. So we end up with the following inequality

If we divide both sides by 28 we get

So, if we add 1 on both sides, we get

So, whenever x is greater than 1, the expression inside the radical is positive.

This means that the original quotient is defined whenever x=1 and whenever x>1. Thus, we would have

we know that

the equation in slope intercept form is equal to

y=mx+b

In this problem

we have

b=-4 ------> because the y-intercept is (0,-4)

Find the slope

we need two points

we take

(-2,0) and (0,-4)

so

m=(-4-0)/(0+2)

m=-4/2

m=-2

therefore

Given data:

The given growth rate is r=7.8%=0.078.

The final number of bacteias in terms of initial is P'=2P.

The expression for the bacterias growth rate is,

Substitute the given values in the above expression.

Thus, after 9.23 hours population of the bacterias doubled.

Notice that the difference between the two equations is the +5 on the right side of the second equation.

The graph of the following equations are as folllows:

For y=x:

For y=x+5:

Thus, the graph of y = x was shifted 5 units upward to obtain the graph of y=x+5.

Therefore, each value or output of y=x+5 is 5 more than the corresponding output of y=x. Consequently, the graph of y=x+5 is the graph of y=x translated up by 5 units.

Thus, the correct answer is option C.

A function relates input to output. Functions can be one to one or many to one. The x values represent the input while the y values represent the output. In the case of one to one, it means that the output has only one corresponding input. Many to one means that there are many input values for one output value. An input value cannot have more than 1 output value. If this happens, then it is not a function. Looking at the options given,

Option A is a function since no input value has more than one output value

Option B is not a function since the output values of 7 and 1 has the same input value of - 1

For option C, the values are (- 3, - 2)' (- 1, 1), (- 1, - 5), (1, 4). It is not a function since the output values of 1 and - 5 has the same input value of - 1

Option D is not a function since the output values of 7 and 1 has the same input value of - 1

The correct option is A

Giving the funtion

m=2

n=-3

then the evaluated function in m=2 n=-3

has a value of 81/4

The product of the sum and difference binomials is

We will use this rule to solve the question

We need to find the product of (a - 1) and (2a + 2)

At first, we will take 2 as a common factor from the second bracket

Now, we will multiply (a - 1) by 2(a + 1)

By using the rule of the product of the sum and difference above, then

The answer is B

Explanation

From the image, angle x and 65 degrees form angles on a straight line. We will recall that the sum of angles on a straight line sums up to 180 degrees.

Therefore,

Angle y and 65 degrees form alternate angles, we will recall that alternate angles are equal

Therefore,

Angle x and angle z form corresponding angles, we will recall that corresponding angles are equal.

Therefore,

Answer:

Solution

What is the end behavior of the graph of the function?

The end behaviors of the function describe the functions of x as it approaches +∝ and as x approaches -∝

Therefore the correct answer is

Option D

Final answer = Down and Up

Turning points = 2

The number of groups of 4 magazines can she choose from the 7 magazines is 35

Total number of magazines that school librarian would like to buy subscription = 7 magazines

The number of subscription that she can afford = 4 new subscription

The different groups of 4 magazines can she choose from the 7 magazines = [tex]7C_4[/tex]

The combination is the method of selecting a particular items or objects from the group of collection. The combination can also be defined as the number of possible arrangement from the collection.

Then the value of

[tex]7C_4[/tex] = 7! / 4!(7 - 4)!

= 7! / (4! × 3!)

= (7 × 6 × 5 × 4!) / (4! × 3!)

= (7 × 6 × 5) / 3!

= (7 × 6 × 5) / 3 × 2 × 1

= 210 / 6

= 35

Hence, the number of groups of 4 magazines can she choose from the 7 magazines is 35

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