pls help with Trigonometric

Pls Help With Trigonometric

Answers

Answer 1

The value of the given trigonometry function is 2√15/15

Half angles

Half angles are trigonometric identities used to express sine, cosine and tangent of half angles.

For instance the value of cos theta is expressed as shown below;

cosФ = cos(Ф/2+Ф/2)

cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ  = 1 - 2cos²Ф/2

Given the following parameters

cosФ = -7/15

Substitute

cosФ  = 1 - 2cos²Ф/2

-7/15  = 1 - 2cos²Ф/2

-2cos²Ф/2 = -7/15 - 1

-2cos²Ф/2 = -8/15

cos²Ф/2 = 4/15
cosФ/2 = 2/√15

Rationalize

2/√15 * √15/√15

2√15/15

Hence the value of the given trigonometry function is 2√15/15

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Related Questions

Susan drove 4 hours. Her average speed was 60 mph. Finish the chart below to give her an average speed of 60 mph.

║hour ║ speed║
______________
║1st ║ 65 ║
║2nd ║ 70 ║
║3rd ║ ____ ║
║4th ║ 55 ║

Answers

Answer:

Its 50

Step-by-step explanation:

60 times 4 it gives you 240.

Now minus all the numbers on the table like this

240 - 55 - 70 - 65 which equals to 50

240 would be the miles

Joey paints old furniture and sells the pieces at craft fairs. the function f(t) approximates how many pieces of furniture he paints per hour. the function w(h) represents how many hours per week joey spends painting the pieces of furniture. what are the units of measurement for the composite function f(w(h))?

Answers

the units of measurement for the composite function f(w(h)) are - furniture/weeks

What are composite functions?

function composition is an operation. that takes two functions f and g, and produces a function h = g . f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

Let as consider the work f(t) approximates how numerous pieces of furniture he paints per hour. It implies unit of this work is furniture/hours. The work w(h) speaks to how numerous hours per week Joey spends portray the pieces of furniture. It implies unit of this work is hours/weeks. We have to be discover the units of estimation for the composite work f(w(h)). It the work f(w(h)), to begin with we ought to apply the work w(h) after that f(t).

                               [tex]f(w(h)) = \frac{furniture}{hours} (\frac{hours}{week} )\\f(w(h)) = \frac{furniture}{week}[/tex]

The units of measurement for the composite function f(w(h)) is furniture/weeks.

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Men consume on average 15 grams of protein a day. Assume a normal distribution with a standard deviation of 3 grams. A sample of 40 men was studied. What is the probability that the sample mean is between 15 and 16 grams per day

Answers

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For this problem, the parameters are given as follows:

[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]

The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:

X = 16:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16 - 15}{0.4743}[/tex]

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 15}{0.4743}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

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pleaseeee hurrryyyyyyyy

Answers

Answer:I THINK IT IS 1,-3

Step-by-step explanation:

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. What is the probability of a value less then $1?

Answers

Find the probability of a value less than $1
Since nickels, dimes and quarters are all less than $1 and there are a total of 70+100+80 = 250 coins of them
And the total coins in the jar is 250+50=300 coins
We get, the probability of a value less than $1 is 250/300 = 5/6.

What are the parts of an algebraic expression, and how do they relate to polynomial expressions?

Answers

The parts of algebraic expressions related to polynomials are variables and coefficients.

What are the parts of algebraic expressions?

The parts of algebraic expressions are;

Variables which are letters that represent numbersCoefficients are numbers that multiply the variables Constant is a number that is not multiplied by any variable

Polynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication

Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.

Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.

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what is the answer (3*5)^6

Answers

The solution of the given expression is:

(3*5)^6 = 11,390,625

How to solve the given expression?

Here we have an expression with an exponent, which is:

(3*5)^6

First, we can solve the thing inside the parenthesis is:

3*5 = 15

Replacing that we get:

(3*5)^6 = (15)^6

Now, the exponent 6 means that we need to multiply the number by itself 6 times, so we get:

(15)^6 = 15*15*15*15*15*15 = 11,390,625

Then we conclude that:

(3*5)^6 = 11,390,625

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Volume=
Help me please! Thank u so much I appreciate it

Answers

the volume of the oblique pyramid is 16 cubic units

How to determine the volume

The formula for finding the volume of a oblique pyramid is given as;

Volume = [tex]\frac{1}{3}[/tex] × base area/ height

Where

base area = area of a right triangle

From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit

let's put in the values to the formula

Base area = 10 × 24

Base area = 240 units

height = 5 units

Since we have both the height and the base area, let's find the volume

Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{240}{5}[/tex]

Volume = [tex]\frac{1}{3}[/tex] × [tex]48[/tex]

Find the division

Volume = 16 cubic units

Thus, the volume of the oblique pyramid is 16 cubic units

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A soccer ball is kicked across a field at an angle of 45° with an initial speed of 16m/s.
Determine how long the soccer ball was in the air.
1.94 s
3.89 s
2.16 s
O2.30 s

Answers

Answer:

it's C. 2.26s

but you wrote 2.16s nearly

The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds,  option D.

How to determine how long the soccer ball was in the air

To determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.

In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:

Vertical component (Vy) = initial speed (v) * sin(angle)

Vy = 16 m/s * sin(45°)

Vy = 11.31 m/s

Now, we can use the vertical motion equation to find the time the ball spends in the air:

Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2

Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:

0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2

Simplifying the equation:

4.9 * time^2 = 11.31 * time

Dividing both sides by time:

4.9 * time = 11.31

time = 11.31 / 4.9

time ≈ 2.31 seconds

Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.

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A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side that will allow the angle at B to be bisected?

A diagram shows a triangle ABC. BD is a line drawn to the base AC. The length of AB is 5 m, BC is 7 m, AD is x m, DC is 4 m, and AC is 12 m.

Answers

The AD's length of 3m will enable the angle at B to be divided in half.

Angle Bisector Theorem: What is it?

The angle bisector of a triangle divides the opposing side into two portions that are proportional to the other two sides, according to the angle bisector theorem, in simpler words the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

The triangle has sides of 5, 7, and (x+4) m.

Angle B's angle bisector will only be the BD if

x/4 = 5/7

x = 5 *4 / 7

x = 20/7 = 2.85 ≈ 3m

Thus if AD has length of 3m then it will enable the angle at B to be divided in half.

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Answer:

AD = 3m

Hope this helps!

Step-by-step explanation:

John, Jim and Joe each went for a medical examination. Their combined height was 5.25 m. If John was 12 cm shorter than Jim and Jim was 0.09 m taller than Joe, how tall, in metres, was Joe?

Answers

The 5.25 m combined height of John, Jim, and Joe, the 12 cm height difference between John and Jim and the 0.09 m difference in height between Jim and Joe, indicates that solution to the word problem is Joe was 1.73  meters tall

What is a word problem?

A word problem is a presentation of a math problem using verbal description rather than numbers, variables and operators.

The combined height of John, Jim and Joe = 5.25 m

John's height = Jim's height - 12 cm = Jim's height - 0.12

Jim's height = Joe's height + 0.09 m

Let h represent Joe's height, we get;

Jim's height = h + 0.09

John's height = h + 0.09 - 0.12 = h - 0.03

John's height = h - 0.03

The sum of the heights is therefore; h + h + 0.09 + h - 0.03 = 3·h + 0.06

The sum of their heights = Their combined height = 5.25 meters

Therefore; 3·h + 0.06 = 5.25

h = (5.25 - 0.06)/3 = 1.73

Joe's height, h = 1.73 meters

Jim's height = 1.73 + 0.09 = 1.82

Jim's height = 1.82 meters

John's height = 1.73 - 0.03 = 1.7

John's height is 1.7 meters

Joe was 1,73 meters tall

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I NEED HELP ASAP! The two cylinders below are similar. What is the volume of the larger cylinder?

Answers

Answer:

E

Step-by-step explanation:

We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.

I chose the second way to work out.

Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:

[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]

The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.

Thus, we have

[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]

A data value is considered​ _______ if its​ z-score is less than 2 or greater than 2.

Answers

A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

A positive z-score indicates the raw score is higher than the mean average.For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.A negative z-score reveals the raw score is below the mean average.For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.

What does a standard deviation of 2 mean?

Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean.In any distribution, about 95% of values will be within 2 standard

         deviations of the mean.

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

Let R be the region bounded by
y
=
7
sin
(
π
2
x
)
,
y
=
7
(
x

2
)
2
, and
y
=
x
+
6
, and containing the point (2,7).

Answers

a. The area of [tex]R[/tex] is given by the integral

[tex]\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36[/tex]

b. Use the shell method. Revolving [tex]R[/tex] about the [tex]x[/tex]-axis generates shells with height [tex]h=x+6-7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le 2[/tex], and [tex]h=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With radius [tex]r=x[/tex], each shell of thickness [tex]\Delta x[/tex] contributes a volume of [tex]2\pi r h \Delta x[/tex], so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral

[tex]\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56[/tex]

c. Use the washer method. Revolving [tex]R[/tex] about the [tex]y[/tex]-axis generates washers with outer radius [tex]r_{\rm out} = x+6[/tex], and inner radius [tex]r_{\rm in}=7\sin\left(\frac{\pi x}2\right)[/tex] if [tex]1\le x\le2[/tex] or [tex]r_{\rm in} = 7(x-2)^2[/tex] if [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each washer has volume [tex]\pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x[/tex]. As more and thinner washers get involved, the total volume converges to

[tex]\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16[/tex]

d. The side length of each square cross section is [tex]s=x+6 - 7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le2[/tex], and [tex]s=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each cross section contributes a volume of [tex]s^2 \Delta x[/tex]. More and thinner sections lead to a total volume of

[tex]\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70[/tex]

A line has a slope of 2 and passes through the point -3, 6 what is the equation in slope intercept form

Answers

Answer:

y=2x+12

Step-by-step explanation:

A regular decagon is rotated n degrees about its center the decagon onto itself . This value of n could be

Answers

value of n could be 252 degree. Option 4

How to determine the value

It is important to note that a decagon is a ten-sided polygon.

Since, a decagon has 10 sides

And we know that the angle made in one complete rotation is 360 degree.

Now find angle made in each rotation by the decagon is 360,

= 360/ 10

= 36 degrees

Now, we have to find possible values of n, and 'n' must be a multiple of 36

Apply hit and trial from given options.

We observe that from given options, only 252 degree is multiple of 36.

Therefore, value of n could be 252 degree. Option 4

The complete question is ;

A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be:

1. 10 degrees

2. 150 degrees

3. 225 degrees

4. 252 degrees

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Select the correct answer.

Which function does this graph represent?

A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.

A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2

Answers

The parabola represented by this graph has the following equation:

y = -16.67(x + 1)² + 2

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:

(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:

y = a(x - h)² + k

y = a(x + 1)² + 2

We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:

y = a(x + 1)² + 2

-4 = a(-0.4 + 1)² + 2

a = -6/0.6²

a = -16.67

Hence the equation is:

y = -16.67(x + 1)² + 2

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Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

B

Step-by-step explanation:

If x and y vary inversely, then as x increases, y decreases. That eliminates answers A, C, and D.

Answer: B

What is a sample statistic give examples give examples. (select all that apply.)

Answers

A sample statistic is a numerical descriptive measure of a sample.

What is a sample statistic?A sample statistic is a numerical metric that describes a sample. A statistic (plural) or sample statistic is any quantity generated from values in a sample for statistical purposes. Estimating a population parameter, characterizing a sample, or testing a hypothesis are all statistical goals. A statistic is the average (or mean) of sample values. The term statistic refers to both the function and the function's value on a particular sample. When a statistic is utilized for a certain purpose, it may be given a name that indicates that purpose.The three examples are - x bar, s, s^2, p hat

Therefore, a  sample statistic is a numerical descriptive measure of a sample.

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The complete question is given below:

What is a sample statistic?

A _____descriptive measure of  a _____.

Give three examples. (Select all that apply.)

The high school athletics department is installing a new rectangular addition to their current practice field. the length of the new addition will be at least 10 meters more than twice the width of the new addition. the original field has an area of 300 square meters. the area of the entire practice field, with the addition, must be no more than 1,200 square meters. if a represents the area of the entire practice field, including the new addition, and x represents the width of the new addition, in meters, which system of inequalities can be used to represent this situation?

Answers

The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

What are word problems?

Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.

We have a new addition to the current rectangular field,

Let that new addition to the current rectangular field be x

Length of the new addition = 10x

Twice the width of the new addition = 2x²

Original area of the field = 300

From the above information, we can derive a quadratic equation:

2x² + 10x + 300

Also, we exist given a constraint that the total area of the practice field should be no more than 1200.

It can be less than 1200 or equivalent to 1200.

Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

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solve the equation
14x+7y=28

Answers

STEP BY STEP EXAMPLES
y = 4 - 2x

Haley conducted a study which found that a cup of coffee contains 150 milligrams of caffeine. the amount of caffeine in the body each hour after consumption of one cup is 9% less than the previous hour. if haley conducted her study for a total of 10 hours, which inequality represents the range of the exponential function that models this situation?

Answers

[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

[tex]y = a(1-r)^t[/tex]

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

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Determine whether each pair of triangles is congruent. If yes, include the theorem or
postulate that applies and describe the series of rigid motions that map one triangle onto the
other.
A.
4
B.
ΔΔ
C.
D.

Answers

A and B are not congruent

C is congruent because it’s has two sides that are the same length and an angle

D is congruent because it has two angles the same and a side

The pair of triangles in option A, C and D are congruent triangles.

Pair of triangles are given.

What is the congruence theorem?

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle

By AAS congruence, two triangles are congruent.

B) In the given figure, one angle and one side is equal

So, two triangles are not congruent

C) Here, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle

D) Here, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.

Therefore, the pair of triangles in option A, C and D are congruent triangles.

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Which of the following equation is an example of inverse variations?

Answers

f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

What are inverse variations?

Inverse variation can be defined as the relationships between variables represented in the form of y = k/x

where;

x and y are two variables k is the constant value

From the options given, we can see that;

f(x) = -1/ 3x

f(x) = -z/xy

Both take the form of inverse variations

Thus, f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

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A right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. a right pyramid with square base has a base edge length of 24 feet and slant height of 20 feet. what is the height of the pyramid?

Answers

The height of the pyramid is [tex]16ft.[/tex]

What does it mean by right pyramid?

The centroid of the base sits just above the right pyramid. Oblique pyramids are non-right pyramids. A right pyramid is typically assumed to be a regular pyramid because it has a regular polygon base.

To find the height of the pyramid:

l=the slant height of the right pyramid.

b=the length side of the square base of the right pyramid.

h=the height of the right pyramid.

Pythagorean Theorem: [tex]l^{2} =h^{2} +(\frac{b}{2} )^{2}[/tex]

Solve:h

[tex]h^{2} =l^{2} +(\frac{b}{2} )^{2}[/tex]

[tex]h^{2} =20^{2} -12^{2}[/tex]

[tex]h^{2} =256[/tex]

[tex]h=16ft[/tex]

Therefore, The height of the pyramid is [tex]16ft.[/tex]

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Answer:

The height of the pyramid is 16ft

Step-by-step explanation:

The ratios of teachers:male students :female students is 2:17:18 the total number of students is 665 find the number of teachers

Answers

2: 35
X 19
38 : 665
38 teachers!

Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.


Find the area of the shape.

Answers

r = 6
A=πr^2

A = 113.09734

Quarter circle formula = πr^2 / 4

113.09734 / 4 = 28.274335

113.09734 - 28.274335 = 84.824005 is the answer

what is the solution to the inequality 14 - 2(x+1)< -4

Answers

Answer: x>8.

Step-by-step explanation:

[tex]14-2*(x+1) < -4\\ 14-2x-2 < -4\\12-2x < -4\\12-2x+4 < 0\\16-2x < 0\\16-2x+2x < 0+2x\\16 < 2x\\Divide \ both\ sides\ of \ the\ equation \ by \ 2:\\8 < x.[/tex]

A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five times the age of the son. Six years from now the son’s age will be?

Answers

Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

     +s          +s

6 - 4s = 60

-6         -6

---------------------

-4s = 54

-----   -----

 -4     -4

   s ≅ 14

14 + 6 = 20

Answer:

20.

Step-by-step explanation:

x = father's age and y = son's age,

x + y = 60

x - 6 = 5(y - 6)

x - 5y = -24

Subtract this from first equation:

6y = 84

y = 14

So the son's age is 14.

Six years time son will be 20.

Bernie owns Bernie’s Bike Shop and is advertising his company by
taking his logo and placing it around town on different sized signs. After creating a few signs, he
noticed a relationship between the amount of ink he needs for his logo and the size of the sign.
1. The table below represents some of the signs Bernie has created and the relationship
between the amount of ink needed versus the size of the sign. Complete the information
below to help Bernie see this relationship

Answers

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

f(x) = x²Domain = 2, 3, 4, 15 and x.Range = 4, 9, 16, 225 and x².

What is a graph?

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:

f(x) = x²

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

Domain = 2, 3, 4, 15 and x.Range = 4, 9, 16, 225 and x².

Read more on domain here: brainly.com/question/17003159

#SPJ1

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