8. Olivia's brother is twice her age
minus 9 years. He is also as old
as half the sum of the ages of
Olivia and both of her 12 year-
old twin brothers. Write and
solve an equation to find the
ages of Olivia and her brother.

The right triangle that shows the length of the two sides is 5.2 and 3.1.

It is required to find the triangle.

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Given:

In trigonometry function, in a right triangle, a tangent of an angle x is equal to the ratio of the opposite side to angle x to the adjacent side to angle x.

According to given question we have:

Given that angle x will be:

[tex]x=tan^{-} \frac{3.1}{5.2}[/tex]

The opposite to angle x or perpendicular = 3.1 units

The adjacent side to angle x or base angle  = 5.2 units

Therefore, the right triangle that shows the length of the two sides is 5.2 and 3.1.

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Answer:

b

Step-by-step explanation:

Answer:

x= 5

Step-by-step explanation:

2x+ 15=25

-15 -15

2x= 10

/2 /2

x=5

Answer:

x = 5

Step-by-step explanation:

2x + 15 = 25

2x + 15 - 15 = 25 - 15            (subtract 15 from both sides)

2x = 10

2x/2 = 10/2                           (divide by 2 on both sides)

x = 5

Step-by-step explanation:

[tex] {13}^{ \frac{4}{5} } + 2.6 \\ [/tex]

[tex] \sqrt[5]{(13) {}^{4} } + 2.6 \\ [/tex]

[tex] \sqrt[5]{28561} + 2.6 \\ [/tex]

[tex]7.78 + 2.6 = 10.38 \\ [/tex]

Answer:

true

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want a table of values of the function sin(3x)/x as x nears zero, and an estimate of the limit of the function value as x → 0.

The function f(x) = sin(3x)/x is an even function. That is ...

  f(-x) = sin(-3x)/(-x) = -sin(3x)/-x = sin(3x)/x = f(x)

When f(-x) = f(x), the function is even. It is a reflection of itself across the y-axis. This means all of the function values for negative x-values are the same as for the corresponding positive x-values. We only need to fill in half the table to know what the other half looks like.

See the attachment for values calculated by a spreadsheet and rounded to 8 decimal places.

The table shows the difference from 3 gets smaller as x gets closer to 0. If we add more rows to the spreadsheet table (2nd attachment), we see that the value gets even closer to 3 as x nears zero. At x = 10^-7, we run up against the accuracy limits of the spreadsheet.

The limit of the expression is 3 as x approaches 0.

Answer:

42

Step-by-step explanation:

x + x + 2 + x + 4 = 120

3x + 6 = 120

3x = 114

x = 114/3

x = 38

38, 40, 42

The three integers are 38, 40, and 42.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that the sum of three consecutive even integers (3 integers in a row) is 120. The value of integers will be calculated as below:-

x + x + 2 + x + 4 = 120

3x + 6 = 120

3x = 114

x = 114/3

x = 38

1st integer = x = 38

2nd integer = x+2 = 38 + 2 =  40

3rd integer = x+4 = 38 + 4 = 42

Therefore, the three integers are 38, 40, and 42.

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The angle that the vector  [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is (B) tan⁻¹ 2/3.

To find the angle of the given vector:

Given: [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]

So,

[tex]\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}[/tex]

Using the formula [tex]\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}[/tex], we obtain:

[tex]\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}[/tex]

Therefore, the angle that the vector  [tex]\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is (B) tan⁻¹ 2/3.

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The correct question is given below:

The angle that the vector  [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is:

(A) tan⁻¹ 3/2

(B) tan⁻¹ 2/3

(C) sin⁻¹ 2/3

(D) cos⁻¹ 3/2

KJSAnflkadfalkdmnfaldskjfnasd...

Based on the given parameters, the domain of the situation is 10 <= x <= 15

The domain of the function is the set of input values of the graph

The equation of the function is given as:

y= 50 + 15x

Where

From the question, we understand that:

At least 10 students but no more than 15 are going on the trip

When the above is represented as an inequality, we have

10 <= x <= 15

Where x is the number of students

Hence, the domain of the situation is 10 <= x <= 15

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The standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}[/tex]

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

∑(x(i) - X)² = 400

n = 51

SD = √(400/51-1)

SD = √8

SD = 2.828 ≈ 2.83

Thus, the standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.

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Answer:

- p / 2

Step-by-step explanation:

4 / -8 =   - 1/2

p^3 / p^2   = p

- 1/2  * p   =  - p / 2

Answer:

This problem has been solved! See the answer Show transcribed image text Expert Answer Transcribed image text: Decide whether or not the functions are inverses of each other. f (x) = 2x + 4, g (x) = x – 2 no yes The function fis one-to-one.

Step-by-step explanation:

The test statistic value calculated by the statistical procedure selected is known as the T-test.

The mean difference between two sets of observations is zero using the T-test, also known as the dependent sample t-test. When the population standard deviation is unknown, the student's t-test is a statistical tool for assessing assumptions about the mean of a small sample taken from a normally distributed population.

Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

Therefore, the test statistic value calculated by the statistical procedure selected is known as the T-test.

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By using the concept of dilation, we find that scale factor from A to B is equal to l' / 5, where l' is the length of the shortest side of the quadrilateral B.

Scale factor is a key variable used to dilate lengths and distances by rigid transformations. Then, the length of the shortest side of the quadrilateral B is equal to the product of the scale factor and the length of the shortest side of the quadrilateral A. Mathematically speaking, this kind of rigid transformation is represented by the following formula:

r = l' / l      

Where:

If we know that l = 5, then the length of the shortest side of the quadrilateral B is equal to the following linear equation:

l' = 5 · r

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Answer: 83

Step-by-step explanation:

you travill 25 feet long

Option B (22,16,18,36)

Mean- Mean is an average of the data collected in the data set. It can be found by dividing the sum of the values by the number of values. Median is the middle value of the data set when the values are placed in order from least to greatest.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

Add all the numbers (22+16+18+36) = 92

Avarage = sum of the all given numbers/ total numbers

total numbers =4

so avarage= mean= 92/4 =23

(22,16,18,36) has the most spread because one number as low as 16 and one as high as 36. Our mean is 23, so that means that the spread is huge.

Hence the answer is (22,16,18,36).

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Answer:

the answer is clear

Step-by-step explanation:

you have to get the answer by completing the answer

Answer:

$1,820

Step-by-step explanation:

The math problem is $35 times 52 weeks

Answer:

Step-by-step explanation:

the answer you end up getting is D

2x/2 > 12/2x > 6

Because x is greater than 2

Answer:

Ama is an elephant so she is 2 years old

Step-by-step explanation:

The value of FG is 32.

The drawing is attached with this.

Given that,

Value of EF = 11

Value of EG = 21

From the above given data we can assume that F and G be the corner points.

E is the point lie between F and G.

We have to find the value of FG. It may be a straight line.

So,

Value of FG = Value of EF + Value of EG

FG = 11 + 21

FG = 32

That is, the value of FG is 32.

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Answer is

A. False

B. True

C. False

According to the graph,

A (1, -2), B(b, - 2), C(1, -7), A'(-b , b), B'(-1 ,b), C'(-b , 1).

A. if ABC is reflected across x-axis. (x, y) reflected x-axis→ (x-y)

    so A'(1,2), B' (b-2), C'(1-7) , it's no equal to title .

    so A is false.

B. if ABC is translated 7 units to the left , up 8 units.

    (x, y)→(x-7,y+8),

    so  A'(-b , b), B'(-1 ,b), C'(-b , 1)

    it's equal to title. so B is true.

C.  if ABC is translated 8 units down, 7 units to right

    (x y)→(x+7, y-8),

   so A' (8,-10),B'(13,-10), C'(8,-15)

   it's not equal to title. so C is false.

A transformation is the movement of a figure. There are four types of transformations: reflection, rotation, translation, and dilation. Of these four types of transformations, a transformation can either be a congruent or similar shape to the original image. Congruent means that the shape or figure retains its size, shape, length, and angles of the original shape.

A rotation is a turn around a centre point. In a rotation, the distance from each point on the shape to the centre remains the same. A rotation is identified by a shape turning a specific amount degrees, usually 90, 180, or 270 degrees, around a point either clockwise or counter clockwise. This means with each rotation performed four things are given.

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The equivalent expression using the additive inverse property is -17- 25

The expression is given as:

-17- (25)

The additive inverse property states that:

-x + x = 0

This also states that

-(x) = -x

Using the above as a guide, we have the following equation

-17- (25) = -17- 25

Hence, the equivalent expression using the additive inverse property is -17- 25

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Answer:I would say c

Step-by-step explanation: because it is the only one that makes sense

The magnitude of the vector is 10√2 and the direction of the vector is 78.69°

Magnitude and the direction of the vectors:

A vector is a directed line segment with an initial point and a terminal point.

To calculate the magnitude of the vector using the Pythagorean Theorem or the distance formula, and to find its direction using the inverse tangent function.

The formula for the magnitude of the vector is

|v|=√(a²+b²)

And the formula for the direction of the vector is,

θ=tan⁻¹(b/a)

where

(a, b) represents the given point.

Given,

Vector u,

Magnitude = 10 in

Direction angle = 45°

Vector v,

Magnitude = 10 in

Direction angle = 225°

Now we have to find the magnitude by apply the value on it,

=> |v|=√(10² + 10²)

=> |v|=√(100 + 100)

=> |v|=√200

=> |v|=√2 x 100

=> |v|=10√2

Similarly, the direction of the vector is,

=> θ = tan⁻¹ (225 / 45)

=> θ = tan⁻¹ (5)

=> θ = 78.69°

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Yes, 9/16 gallon of white paint is enough for Liam to make  8 gallons of light green paint.

For the given conditions; use unitary method.

3/8 gallons white paints ------> 6 gallons of light green paint.

Thus, from 1 gallons of white paint.

1 gallons white paints ------> (6×8)/3 gallons of light green paint.

For preparing 8 gallons of light green paint, multiply both side of equation by 9/16.

9/16 gallons white paints ------> (6×8)/3 × (9/16) gallons of light green paint.

on solving.

9/16 gallons white paints ------> 9 gallons of light green paint.

The requires value for light green paint is 8 gallons, we have prepared more than that that is 9 gallons.

Thus, Liam has sufficient white paint to make 8 gallons of light green paint.

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The side length of the cube is 4 feet. Then the surface area of the cube will be 96 square feet.

Suppose that: The side length of the considered cube is L units. Then, we get:

The volume of that cube = L³ cubic units.

The surface area of that cube = 6L² square units.

In February 2003, the Battlefords Chamber of Commerce in Saskatchewan placed a cage containing a 64-cubic foot ice cube along Yellowhead Highway. Then the side length of a cube will be

64 = L³

L = ∛64

L = 4 feet

Then the surface area of the cube will be

SA = 6 x 4²

SA = 6 x 16

SA = 96 square feet

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The dimensions of her scale drawing is 9 centimeters high and 101.25 centimeters long.

As we are informed from the question -

Measurement in real = measurement on scale

The 4 feet height measures 3 centimeters on scale

So, height of 12 feet on scale will be = (3/4) × 12

Performing multiplication and division to find the height of scale drawing

Height 12 feet on scale = 9 centimeters

The length of 135 feet will measure on scale = (3/4) × 135

Performing multiplication and division to find the height of scale drawing

Length 135 feet on scale = 101.25 centimeters

So, the dimensions of scale drawing will be 9 centimeters high and 101.25 centimeters long.

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Answer: 4

Step-by-step explanation:

f=factor

24=6*f

24/6=f

f=4

Answer:

4 is paired with 6 to get 24

Step-by-step explanation:

Here are some examples I got from my math teacher:

So How do you find the factor pairs?

Factor pairs are a set of two integers that give a particular product when multiplied together. For example, 2 and 5 are a factor pair for the product of 10. Factor pairs can be negative numbers, but they must be whole numbers – that means that they can't be a fraction or a decimal.