What similarity statement can you write relating the three triangles in the diagram?

Answer:

Angle E = 73 degrees

Step-by-step explanation:

Supplementary means it equals 180 degrees.

So to find x, you add the 2 equations.

2x + 15 + 5x - 38 = 180

which equals 7x + (-23) = 180 = 7x - 23 = 180

7x = 203  You move the -23 to the other side

203/7 = 29  So x = 29 degrees

So to find angle E, you put in 29 degrees for x.

2 x 29 + 15 = 73 degrees

Answer:

23

Step-by-step explanation:

Basically, (f o g)(1) is saying f(g(1))

So let's plug in 1 into the g(x) equation.

[tex]g(1)=2(1)-6 \\ \\ g(1)=2-6 \\ \\ g(1)=-4[/tex]

Now we can plug in -4 into the f(x) equation.

[tex]f(-4)=-4(-4)+7 \\ \\ f(-4)=16+7 \\ \\ f(-4)=23[/tex]

23

Step-by-step explanation:

This is a problem of composition of function. We can define this as follows:

[tex]The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f[/tex]

So [tex](f.g)(x)=f(g(x))=h(x)[/tex]:

[tex]h(x)=-4(2x-6)+7 \\ \\ h(x)=-8x+24+7 \\ \\ h(x)=-8x+31[/tex]

Therefore:

[tex]h(x)=f(g(1))=-8(1)+31=23[/tex]

Answer:

Step-by-step explanation:

Answer:

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

Explanation:

(

sin

x

)

2

=

3

(

cos

x

)

2

(

sin

x

)

2

=

3

(

1

−

(

sin

x

)

2

)

(

sin

x

)

2

=

3

−

3

(

sin

x

)

2

4

(

sin

x

)

2

=

3

(

sin

x

)

2

=

3

4

sin

x

=

±

(

√

3

2

)

x

=

π

3

,

π

−

π

3

,

π

+

π

3

,

(

2

π

)

−

π

3

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

If this was in the region

0

≤

x

≤

2

π

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)=3cos^2(x)\implies sin^2(x)=3[1-sin^2(x)] \implies sin^2(x)=3-3sin^2(x) \\\\\\ sin^2(x)+3sin^2(x)=3\implies 4sin^2(x)=3\implies sin^2(x)=\cfrac{3}{4}[/tex]

[tex]\bf sin(x)=\pm\sqrt{\cfrac{3}{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{2} \\\\\\ sin^{-1}[sin(x)]=sin^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies x= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]

that is, on the interval [0, 2π].

Answer:

a. 18.67 + 3.456 + 0.2 + 3.21

=25.536

b. 3.256 + 4.21 + 3.009 + 0.35

=10.825

c. 7 – 3.06

=3.94

d. 62.98 – 3.555

=59.425

e. 5.3 × 12

=63.6

f. 4.35 × 2.11

=9.1785

g. 56/0.7

= 80

h. 5.6/7

=0.8

Perform addition, subtraction, and multiplication operations with decimal numbers.

a. To perform the addition, we simply add the numbers together:

18.67 + 3.456 + 0.2 + 3.21 = 25.536

b. Add the numbers together:

3.256 + 4.21 + 3.009 + 0.35 = 10.825

c. Subtract 3.06 from 7:

7 - 3.06 = 3.94

d. Subtract 3.555 from 62.98:

62.98 - 3.555 = 59.425

e. Multiply 5.3 by 12:

5.3 × 12 = 63.6

f. Multiply 4.35 by 2.11:

4.35 × 2.11 = 9.1785

g. Divide 56 by 0.7:

56 ÷ 0.7 = 80

h. Divide 5.6 by 7:

5.6 ÷ 7 = 0.8

https://brainly.com/question/36349392

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Answer:

A

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{10x^6y^3+20x^3y^2}{5x^3y}=2x^3y^2+4y}[/tex]

Step-by-step explanation:

[tex]\dfrac{10x^6y^3+20x^3y^2}{5x^3y}=\dfrac{(5x^3y)(2x^3y^2)+(5x^3y)(4y)}{5x^3y}\\\\=\dfrac{5x^3y(2x^3y^2+4y)}{5x^3y}\qquad\text{cancel}\ 5x^3y\\\\=2x^3y^2+4y[/tex]

Answer:

he would make one out of the two shots

Step-by-step explanation:

Answer with explanation:

Probability of getting shoot from free throw line= 80% =0.80

Probability of not getting shoot from free throw line = 100% - 80% = 20% = 0.20

A student attempt throwing ,twice from free throw line.

A= First Attempt

B= Second Attempt

→If Events , A and B are Independent,then Probability of A and B is given as

P (A ∩ B)= P(A) × P(B)

→And,Conditional probability of event A has definitely occurred  and then probability that event B will occur,when these two events A and B are not Independent, is given by:

[tex]P(\frac{B}{A})=\frac{P(B\cap A)}{P(A)}[/tex]

Option 4:  The conditional probability of Event B given Event A is P(B|A)=P(A and B)/P(A) when two events are not independent.

Answer:

Are there answer choices?

Step-by-step explanation:

Answer: 13°

Step-by-step explanation: The correct answer is 13°. Since you know the opposite and adjacent you will use tangent tan x= 12/50

Final answer:

To find the angle of elevation between the diver and the diving board, we use the tangent function of a right triangle, which results in an angle of approximately 13 degrees. Thus, option B (13 degrees) is the correct answer.

Explanation:

The question is asking for the measure of the angle of elevation from the diver looking up to the top of the diving board. To calculate this, we can use trigonometry, specifically the tangent function, which relates the opposite side to the adjacent side of a right-angled triangle. We have a right triangle where the height of the diving board is the opposite side (12 feet), and the distance from the diver to the base of the diving board is the adjacent side (50 feet).

The tangent of the angle \heta is the ratio of the opposite side to the adjacent side:

tan(\ heta) = opposite / adjacent = 12/50

To find \ heta, we take the inverse tangent (arctan) of the ratio:

\heta = arctan(12/50)

Using a calculator, we find that:

\heta\approx 13.4\extdegree

Finally, we round to the nearest whole number:

\heta\approx 13\extdegree

Therefore, the angle of elevation is approximately 13 degrees, which corresponds to option B.

If both machines are working at once, 200 tshirts (100 in each machine) could be made in 100 minutes, if 200 shirts can be made in machine 1 in 50 minutes, it will take 25 minutes to make 100. machine b takes 150 minutes per each 200, 150 divided by two is 75. 75 + 25 = 100 minutes

It would work better just to use machine one and take 50

minutes, but i dont think thats an answer choice.

edit: i think from the choices your answer would be: 37.5 as if both machines run at once more tshirts can be made

Multiply the bracket by 1/2

1/2(2n +6)

cross out 2 and 2n and divide by 2.

cross out 6 and 2 and divide by 2

n+3

Answer is n+3

Distribute 1/2 into (2n+6): 1/2 * 2n + 1/2 * 6. Simplify: n + 3. The equivalent expression is n + 3.

Let's break down the process step by step:

Given expression:[tex]\( \frac{1}{2}(2n+6) \)[/tex]

1. Distribute [tex]\( \frac{1}{2} \)[/tex]into the parentheses:

  We multiply each term inside the parentheses by [tex]\( \frac{1}{2} \):[/tex]

  [tex]\( \frac{1}{2} \times 2n + \frac{1}{2} \times 6 \)[/tex]

2. Simplify each term:

  a. [tex]\( \frac{1}{2} \times 2n \):[/tex]

     The [tex]\( \frac{1}{2} \)[/tex] and the [tex]\( 2 \)[/tex] cancel out, leaving [tex]\( n \).[/tex]

  b. [tex]\( \frac{1}{2} \times 6 \):[/tex]

     Multiply [tex]\( \frac{1}{2} \) by \( 6 \) to get \( 3 \).[/tex]

3. Combine the simplified terms:

  Add the simplified terms together:

  [tex]\( n + 3 \)[/tex]

So, the expression equivalent to [tex]\( \frac{1}{2}(2n+6) \) is \( n + 3 \).[/tex]

Answer:75

Step-by-step explanation:3/5x=45

X=45÷3/5

×=45×5/3

×=75

For this case we must find the value of the variable "x" of the following equation:

[tex]\frac {3} {5} x = -45[/tex]

We multiply by 5 on both sides of the equation:

[tex]3x = -45 * 5\\3x = -225[/tex]

We divide between 3 on both sides of the equation:

[tex]x = \frac {-225} {3}\\x = -75[/tex]

Answer:

[tex]x = -75[/tex]

Answer:

Ryan has 2H + 5 stickers.

Step-by-step explanation:

Let J = Janice

Let M = Melvin

Let R = Ryan

J = 2*M

R = J + 5

=============

J = 2*H

R = 2H + 5

The answer is:

The distance between the two jets is 63.5 mi.

From the statement we know that the first jet is located 56 mi due to the east city while the second jet is located 30 mi due to the north, so, we can calculate the distance between the two jets using the Pythagorean Theorem.

The Pythagorean Theorem states that:

[tex]c^{2}=a^{2} +b^{2}[/tex]

So,

[tex]Distance=\sqrt{(Jet_{1}Location)^{2}+(Jet_{2}Location)^{2}}\\\\Distance=\sqrt{(56mi)^{2}+(30mi)^{2}}=\sqrt{3136mi^{2}+900mi^{2}} \\\\Distance=\sqrt{3136mi^{2}+900mi^{2}}=\sqrt{4036mi^{2}}=63.5mi[/tex]

Hence, the distance between the two jets is 63.5 mi.

Have a nice day!

Answer:

1- exponential

2- constant multiplicative rate of change

Step-by-step explanation:

Answer:

Exponential

Constant multiplicative rate of change

Step-by-step explanation:

It is not a linear function because in order to be linear it should decrease or increase the same amount from one moment to another.

Nor is it a quadratic function, since to be quadratic it should have values that increase and then decrease (a point of return).

So the correct option is that it is an exponential function because the values do not change the same amount each time, they change constantly but by a multiplication factor.

So for the second of the options it will be: constant multiplicative rate of change

In summary:

The data in the table can best be described as exponential because there is a constant multiplicative rate of change.

Correct option is C. The independent variable in the equation y = 10x is 'x', which represents the number of questions answered correctly on the exam.

In the equation y = 10x, the independent variable is the variable that you have control over or can set the value of freely, which in this context is the number of questions answered correctly on the exam represented by 'x'. The dependent variable, represented by 'y', is the total number of points you score on the exam, which depends on the number of questions you answered correctly. Therefore, the correct answer to the question is C) The number of questions answered correctly on the exam.

Break it into squared and rectangles and find the area of those first then add it all together

For your square you would get 16 ft squared

For your rectangle you would get 32 ft squared

For your other rectangle you would get 32 ft squared as well

Then add those all together to get the full answer

80 ft squared

Hope this helps :)

Answer:

The coefficient of the squared expression in the parabola equation is [tex]a=4[/tex]

Step-by-step explanation:

The equation of a parabola in its vertex form is:

[tex]y = a(x-h) ^ 2 + k[/tex]

Where the vertex of the parabola is the point (h, k)

a is the ceoficiente of the term to the square.

We need to find the equation of a parabola that has its vertex in the point:

(-5, -2)

So:

[tex]h = -5\\\\k = -2[/tex]

Therefore the equation is:

[tex]y = a(x - (-5)) ^ 2 -2\\\\y = a(x + 5) ^ 2 -2[/tex]

We know that the point (-4, 2) belongs to this parable. Then we can find the value of a by replacing the point in the equation of the parabola

[tex](2) = a((-4) + 5) ^ 2 -2\\\\2 = a(1) ^ 2 -2\\\\2 = a -2\\\\a = 4[/tex]

Finally the coefficient is a = 4

Answer:

The answer is 4

Step-by-step explanation:

This is the correct answer

Answer:Classifying Polynomials. Polynomials can be classified two different ways - by the number of terms and by their degree. A monomial has just one term. For example, 4x2 .Remember that a term contains both the variable(s) and its coefficient (the number in front of it.)

Step-by-step explanation:Hope this helps. Please name me brainliest

The answer is:

⇨ look at its highest exponent

Work/explanation:

To classify polynomials by their degree, look at the highest exponent of the polynomial.

For instance, if we have [tex]\rm{x^2+2x}[/tex] then we have a second-degree binomial.

(binomial because we have 2 terms)

This is a quadratic equation. You have to factor it.

You have to find two numbers that meet the following requirement:

-When multiplied, is equal to -18.

-When added, is equal to 3.

The two numbers are 6 and -3.

Now factor it:

(x + 6)(x - 3)

So x = -6 or x = 3

Answer

0.024, 0.030,0,036

Step-by-step explanation:

+0.06 everytime

Answer:

Step-by-step explanation:

Thank you for responding.

Let's pretend you are not dealing with a decimal. Suppose the sequence was

6   12    18 ... and you wanted the next three entries. You would notice that you add 6 to go from 6 to 12. You could also see that you would add 6 to get from 12 to 18.

So the next 3 entries would be 24   30   36.

Now go back to what you are given

0.024

0.030

0.036

No need to be formal. It is just a disguised arithmetic sequence.

The answer is:

The correct option is:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Inversing a function means switching the range and domain of the function. To inverse a function we need to rewrite the variable (x) with the function (f(x) or y), and rewrite the function (f(x) or y) with the variable (x), and then, isolate "y" or "f(x)".

Also, we need to remember how to isolate the variable from a logarithmic function.

[tex]ln(x)=a\\\\e^{a}=e^{ln(x)}\\\\e^{a}=x[/tex]

So, we are given the function:

[tex]f(x)=ln(10x)[/tex]

Which it's equal to write:

[tex]y=ln(10x)[/tex]

Then, inversing the function we have:

[tex]y=ln(10x)[/tex]

[tex]x=ln(10y)[/tex]

[tex]x=ln(10y)\\\\e^{x}=e^{ln(10y)} \\e^{x}=10y\\\\y=\frac{e^{x}}{10}[/tex]

Hence, we have that the correct answer is the option:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Have a nice day!

[tex]f(x) = \ln(10x)\\ \\ f^{-1}\Big(f(x)\Big) =x \\ \\ f^{-1}\Big(\ln(10x)\Big) = x\\ \\ \ln(10x) = t \Rightarrow 10x = e^t \Rightarrow x = \dfrac{e^t}{10} \\ \\ \Rightarrow f^{-1}(t) = \dfrac{e^t}{10} \Rightarrow \boxed{f^{-1}(x) = \dfrac{e^x}{10}}[/tex]

I’m assuming you need to find y

So what you would do is

3x + y = 2

Subtract 3x from both sides and get:

y = 2 - 3x

From this, we can see the y-intercept is 2. Therefore, the correct graph is the first one.

Answer:

Step-by-step explanation:

Answer:

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

Step-by-step explanation:

The stem-and-leaf plot is a semi-graph that allows presenting the distribution of a quantitative variable. It consists of separating each data in the last digit (which is called a leaf) and the remaining front numbers (which form the stem).

It is especially useful for medium-sized data sets and that your data is not grouped around a single stem. With it we can get the idea of ​​what distribution the data have, the asymmetry, etc.

The name of stem and leaves refers to the branch of a plant, with the front digits marking the stem where the number is located and the final digit of the leaf.

1. First at all, we have to sort the data from lowest to highest

64, 69, 88, 88, 91, 92, 93, 94, 95, 97, 97, and 100

2. Draw a table with two columns, the first column for the stem and the second for the leaves. Arrange all the stems in the first column in descending order. Each stem is written only once.

Stem            Leaf

3.  Record all the leaves in the second column, in increasing order, next to the corresponding stem.

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

Answer:

[tex]g(n-7)=\frac{n^2-14n+44}{3n-21}[/tex]

Step-by-step explanation:

The given function is

[tex]g(x)=\frac{x^2-5}{3x}[/tex]

To find g(n-7), we substitute x=n-7 to obtain;

[tex]g(n-7)=\frac{(n-7)^2-5}{3(n-7)}[/tex]

Expand the parenthesis to obtain;

[tex]g(n-7)=\frac{n^2-14n+49-5}{3n-21}[/tex]

Simplify:

[tex]g(n-7)=\frac{n^2-14n+44}{3n-21}[/tex]

Answer:

hello : x=2 and x = -8 is solution

Step-by-step explanation:

x² +6x -16=0

for : x = 2

2² +6(2) -16 = 4+12-16 = 16-16 = 0

for x = - 8

(-8)² +6(-8) -16 = 64 - 48 -16 = 64 -64 = 0

For this case we must solve the following equation of the second degree:

[tex]x ^ 2 + 6x-16 = 0[/tex]

The solution is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Where:

[tex]a = 1\\b = 6\\c = -16[/tex]

Substituting:[tex]x = \frac {-6\pm \sqrt {6 ^ 2-4 (1) (- 16)}} {2 (1)}[/tex]

[tex]x = \frac{-6\pm\sqrt{36+64}}{2}[/tex]

[tex]x = \frac {-6 \pm \sqrt {100)}} {2}\\x = \frac {-6 \pm10} {2}[/tex]

So:

[tex]x_ {1} = \frac {-6 + 10} {2} = \frac {4} {2} = 2\\x_ {2} = \frac {-6-10} {2} = \frac {-16} {2} = - 8[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 8[/tex]

Answer:

$1.45-$0.25=x

x=$1.20

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have three triangles with base b = 9yd and height h = 10yd, and one triangle in the base of pyramid with base b = 9yd and height h = 7.8yd.

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]LA=4\cdot\dfrac{(9)(10)}{2}=(2)(90)=180\ yd^2\\\\B=\dfrac{(9)(7.8)}{2}=(9)(3.9)=35.1\ yd^2\\\\SA=B+LA\to SA=180+35.1=215.1\ yd^2[/tex]

Answer:

Step-by-step explanation: first u need to write a division equation 8 ÷ 1/3. Then u have to solve. Well first u have to probably turn the whole number 8 into a fraction 1/8. Then u have to multiply 1/8 times 1/3 equals to?

1/24 as ur answer

The answer is:

The value of "x" is 90.16

To solve the problem we need to use the trigonometric identity of the sine that establish that:

[tex]Sin(\alpha )=\frac{OppositeSide}{Hypotenuse}[/tex]

So, we are given the following information:

[tex]\alpha =48(degrees)\\\\OppositeSide=67[/tex]

Then, applying the trigonometric identity, we have:

[tex]Sin(48)=\frac{67}{Hypotenuse}[/tex]

[tex]Sin(48)=\frac{67}{Hypotenuse}\\\\Hypotenuse=\frac{67}{sin(48)}=90.157=90.16[/tex]

Hence, the value of "x" is (rounded to the nearest hundreth) 90.16.

Have a nice day!

Due To My Calculations, The Answer Is 90.16.