A father who is 42 years old has a son and a daughter. The daughter is three times as old as the son. In 10 years the sum of all their ages will be 100 years. How old are the two siblings at present?

Well this series is neither arithmetic or geometric as said in the other solution but since there are addition signs I will find the sum

The sum is 522.24

Answer:

Final answer is C. 28°.

Step-by-step explanation:

Given equation is [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex].

Now we need to find the missing value of [tex]\theta[/tex] using cosine formula. So let's compare the given equation [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex] with cosine formula [tex]b^2+c^2-2\left(b\right)\left(c\right)\cos\left(A\right)=a^2[/tex].

we get [tex]\theta =A[/tex]

which is basically the angle between given sides 15 and 17

Hence A=28°.

So the final answer is 28°.

Answer:

A child's dinner costs $4

Step-by-step explanation:

7 + 7 = 14

22 - 14 = 8

8 / 2 = 4

Answer

5^2 + 12^2 = 25 + 144 = 169 = 13^2

Therefore, it is a right triangle.

Step-by-step explanation:

Answer:

5² + 12² = 25 + 144 = 169 = 13²

Therefore, it is a right triangle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The population doubles every 20 minutes, so:

x = 200 (2)^(t / 20)

[tex]

S=14\times14+4(\frac{14}{2}\times18) \\

S=196+4(7\times18) \\

S=196+4\times126 \\

S=196+504 \\

S=\boxed{700}

[/tex]

Answer:

B. [tex]700\text{ inches}^2[/tex].

Step-by-step explanation:

We have been given an image of a pyramid. We are asked to find the total surface area of the given pyramid.

[tex]\text{Surface area of pyramid}=A+\frac{1}{2}*ps[/tex], where,

A = Area of base of pyramid.

p = Perimeter of base,

s = Slant height,

Upon substituting our given values, we will get:

[tex]\text{Surface area of pyramid}=14^2+\frac{1}{2}*4*14*18[/tex]

[tex]\text{Surface area of pyramid}=196+2*14*18[/tex]

[tex]\text{Surface area of pyramid}=196+504[/tex]

[tex]\text{Surface area of pyramid}=700[/tex]

Therefore, the total surface area of given pyramid is 700 square inches and option B is the correct choice.

Answer:

Step-by-step explanation:

The last option, option D is not linear.

In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.

Now, specifically, in Algebra, a linear expression refers to an expression which has variables with an exponent equal to 1, like option A, B and V. As you can see option D has an expression which variable is squared, that means it's not linear, and its graph is not a line, but a parabola.

The function which is not linear equation is f(x) =x²+ 9.

Thus, option (D) is correct.

A linear equation is an equation that represents a straight line on a graph.

It is an algebraic equation in which the variables are raised to the power of 1, and there are no exponents or radicals involved.

The general form of a linear equation in two variables, x and y, is given by:

ax + by = c

a) f(x) =x have the highest degree 1.

So, it is linear equation.

b) f(x) = 10x + 100 have the highest degree 1.

So, it is linear equation.

c) f(x) = 1/5x - 2 have the highest degree 1.

So, it is linear equation.

d) f(x) =x²+ 9 have the highest degree 1.

So, it is not a linear equation.

Thus, option (D) is correct.

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Answer:

Dave rode his bicycle 17 miles in the morning

Dave rode his bicycle 40 miles in the afternoon

Step-by-step explanation:

* Lets study the information to solve the question

- Dave rod his bicycle in the morning and again in the afternoon

- Six more than twice as many miles in the afternoon as in the morning

  means the distance in the afternoon is 6 more than twice the distance

  in the morning

- The entire trip was 57 miles means the total distance in the morning

  and in the afternoon was 75

* To solve the question let the distance in the morning is x miles

∵ The distance in the morning = x miles

∵ The distance in the afternoon is 6 more than twice the distance

  in the morning

∴ The distance in the afternoon = 2x + 6 miles

∵ The distance in entire trip = 57 miles

- The distance in the morning and the distance in the afternoon = 57 miles

∴ x + (2x + 6) = 57 ⇒ simplify

∴ 3x + 6 = 57 ⇒ subtract 6 from both sides

∴ 3x = 51 ⇒ divide both sides by 3

∴ x = 17 miles

∵ The distance in the morning is x miles

∴ Dave rode his bicycle 17 miles in the morning

∵ The distance in the afternoon = 2x + 6 miles

- Substitute the value of x

∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles

∴ Dave rode his bicycle 40 miles in the afternoon

Answer:

They are clearly written to be able to find a clear solution, it clearly tells you what to do, and how, you just have to find out the way to be able to use the hints in a simple word problem, so it finds its way to be solved

Step-by-step explanation:

the difference between 100,000,000 and -100,000,000 is greater than a hyphen. Mathematical sentences without symbols would be as nonsensical as regular sentences without verbs: they tell you what to do

Answer:

B

Step-by-step explanation:

I love these!  Ok, the expanded formula you need for this is

[tex]6(cos\frac{5\pi }{6}+sin\frac{5\pi }{6}i)[/tex]

From the unit circle we get the cos and sin of that angle and fill them in:

[tex]6(-\frac{\sqrt{3} }{2}+\frac{1}{2}i)[/tex]

Distributing through the parenthesis gives you

[tex]-\frac{6\sqrt{3} }{2}+\frac{6}{2}i[/tex]

which simplifies to

[tex]-3\sqrt{3}+3i[/tex]

To convert 6cis (5pi)/6 from polar form to rectangular form, use the formula r*cos(theta) + r*sin(theta)*i. The magnitude (r) is 6 and the angle (theta) is 5pi/6. The rectangular form results to be B. -3 Square root of 3 +3i.

The student is asked to convert the complex number 6cis (5pi)/6 from polar form to rectangle form. In polar form, a complex number can be represented as rcis(theta), where r is the magnitude and theta is the angle. To convert this to rectangular form, we use the formula r*cos(theta) + r*sin(theta)*i. In this case, r=6 and theta=5pi/6. Therefore, the rectangular form of the given number is (6*cos(5pi/6)) + (6*sin(5pi/6))*i which equals -3 +

3 square root

of 3*i. Hence, the correct answer is B. -3 Square root of 3 +3i.

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Answer:

A and E

Explanation:

A.the space the bottom of a tent takes up- Area

B.the distance around the outside of a tent- Perimeter

C.the measure from the top to the bottom of a tent- Height

D.the measure from the top to the bottom of a flat sleeping bag-length

E.the space a flat sleeping bag takes up-area

F.the distance around the outside of a flat sleeping bag- perimeter

Answer:

Step-by-step explanation:

You can use the same formula in each case. The area of a triangle with sides "a" and "b" separated by angle α is ...

  A = (1/2)ab·sin(α)

1. The area of the square is 4 times the area of the right triangle whose legs are radii of the square:

  square area = 4·(1/2)·(13 m)(13 m)sin(90°) = 2·(13 m)² = 338 m²

__

2. The area is ...

  A = (1/2)(8 cm)(12 cm)sin(81°) ≈ 47.4 cm²

For this one, you don't need to work out the answer in detail. You know it will be less than, but nearly, 48 cm², which is half the product of the side lengths.

The normal distribution is symmetric about its mean. For any symmetric distribution, the mean is the same as the median. So the answer is B.

In a normal distribution, the mean and median are equal due to its symmetrical nature. Therefore, if the mean is 315, then the median is also 315.

The question asks about the relationship between the mean and median in a normal distribution. In a normal distribution, the mean, median, and mode are all equal. This is due to the symmetrical nature of the normal distribution around its mean. So, if the mean of the normal distribution is 315, the median is also 315.

The answer to the student's question is: B.315.

Answer:

Distributive property

Step-by-step explanation:

The given equation is:

[tex]2q(q+4)=10[/tex]

To solve this equation, we expand the left hand side using the distributive property to obtain:

[tex]2q^2+8q=10[/tex]

That was exactly what Miskai did.

Therefore the property that justifies his step shown is the distributive property.

This property says that, if a, b, and c are real numbers then,

[tex]a(b+c)=ab+bc[/tex]

5 people , 1 wall ~ 20/5 = 4 minutes

1 person, 1 wall ~ 4/5 minutes

9 people, 1 wall ~ (4/5) x 9 = (36/5) minutes

Therefore 9 people, 9 walls ~ (36/5) x 9

= 64.8 minutes

= 1h 4 min 48 s

Answer:

It takes 20 minutes :)

Step-by-step explanation:

You're buying two items, we can represent them as X. First you set one of the X's to be the dryer, and since we know that the washer costs 46 more than the dryer, that can be represented as X + 46. The equation can be written as follows:

x + (x + 46) = 696

2x + 46 = 696

2x = 650

x = 325

Therefore, the dryer costs $325, and the washer costs $371

The cost of the dryer is found by setting up an equation where x represents the dryer's cost and solving for x. The calculation steps reveal that the dryer costs $325.

The student is asking how to find the cost of a dryer when given the combined cost of a washer and dryer, and that the washer costs $46 more than the dryer. To solve this, we first let the cost of the dryer be x dollars. Therefore, the cost of the washer would be x + $46. We are told that combined they cost $696.

Setting up the equation: x + (x + $46) = $696.

Combine like terms: 2x + $46 = $696.

Subtract $46 from both sides: 2x = $696 - $46.

Calculate the remaining balance: 2x = $650.

Divide both sides by 2 to find the cost of the dryer: x = $325.

Therefore, the cost of the dryer is $325.

Answer:

(-3, 8)

Step-by-step explanation:

We are given two equations and we have to find the solution to the given equations. We can do this by using substitution method as shown below:

[tex]2x+y=2[/tex]                                          Equation 1

[tex]x-3y=-27[/tex]                                     Equation 2

From Equation 1, we can get the value of y as:

[tex]y=2-2x[/tex]                                          Equation 3

Using this value of y in equation 2, we get:

[tex]x-3(2-2x)=-27\\\\ x-6+6x=-27\\\\ 7x=-21\\\\ x=-3[/tex]

Thus value of x is -3. Using this value in Equation 3, we get:

[tex]y=2-2(-3)\\\\ y=2+6\\\\ y=8[/tex]

Thus the solution to the given equations is (-3, 8)

Answer:

The correct option is option B. It has one solution, and it's x=-3

Step-by-step explanation:

We have the following system of equations:

5x+7 = 2y                        (1)

y-9x=23                            (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

5x + 7 = 18x + 46

Step 3: Solve for x:

7 - 46 = 18x - 5x

-39 = 13x

x= -3

So the correct option is option B. It has one solution, and it's x=-3

Answer: Option B

The system has 1 solution

Step-by-step explanation:

We must solve the following system of equations

[tex]5x+7=2y\\\\y-9x=23[/tex]  

To solve it, clear y from the second equation and then substitute in the first equation

[tex]y=23 + 9x[/tex]

Now substitute in the first equation

[tex]5x+7=2(23 + 9x)\\\\5x +7 = 46 + 18x\\\\5x -18x = 46-7\\\\-13x = 39\\\\x = -\frac{39}{13}\\\\x=-3[/tex]

Answer:

option B and option D

0 and 2

Step-by-step explanation:

Given in the question two functions

f(x) = x² - 4x + 3

g(x) = -x² + 3

f(x) = g(x)

x² - 4x + 3 = - x² + 3

Rearrange the like terms, x terms to the left and constant term to the right.

x²+ x² - 4x = 3 - 3

2x² - 4x = 0

Divide by two

2x²/2 - 4x/2 = 0/2

x² - 2x = 0

Take x as a common term

x(x-2) = 0

so

x = 0

or

(x-2) = 0

x = 2

Answer:

0

3

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2-4x+3[/tex]

We can rewrite this function in the vertex form to obtain;

[tex]f(x)=(x-2)^2-1[/tex]

This is the graph of the parent function [tex]h(x)=x^2[/tex] shifted, 2 units to the right and 1 unit down.

The second function is

[tex]g(x)=-x^2+3[/tex]

This is the graph of the parent function [tex]h(x)=x^2[/tex] reflected in the x-axis and shifted up 3 units.

The graph of the two functions are shown in the attachment.

The solution to f(x)=g(x) is where the two graphs meet.

The two graphs intersected at

(0,3) and (2,-1)

Answer:

6x ≥ 3 + 4(2x - 1)

⇔ 6x ≥ 3 + 8x - 4        => remove the parentheses

⇔ 6x - 8x ≥ 3 - 4

⇔ -2x ≥ -1

⇔ 2x ≤ 1 (or 1 ≥ 2x)

⇔ x ≤ 1/2

⇔ x ≤ 0.5

The answer for the question should be:

1 ≥ 2x

6x ≥ 3 + 8x – 4

and the first graph.

Answer:

1 ≥ 2x

6x  ≥ 3 + 8x - 4

and the first line graph.

Step-by-step explanation:

6x ≥ 3 + 4(2x – 1)

6x  ≥ 3 + 8x - 4

6x -  8x ≥  -1

-2x   ≥ -1

x  ≤ 1/2

or 1 ≥ 2x.

Answer:

see explanation

Step-by-step explanation:

Using Euler's formula for Polyhedra, that is

F + V - E = 2

where F is faces, V is vertices and E is edges

1

Rearrange formula for E

F + V - E = 2 ( add E to both sides )

F + V = 2 + E ( subtract 2 from both sides )

E = F + V - 2

  = 25 + 17 - 2 = 40

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

2

Rearrange formula for F

F + V - E = 2 ( add E to both sides )

F + V = 2 + E ( subtract V from both sides ) F = 2 + E - V, so

F = 2 + 34 - 11 = 25

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

3

Rearrange formula for V

F + V - E = 2 ( add E and subtract F from both sides )

V = 2 + E - F

  = 2 + 36 - 22 = 16

Answer:

1. use Euler's formula to find the missing number f=25 vertices=17 Edges=?

40

2. Mario's company makes gemstones Faces=12 vertices=? edges=20

10 vertices

3. Pierre built the model shown in the diagram for a social studies project

pentagon

4. A jewelry store buys small boxes find the surface area of the box to the nearest whole number

266 cm^2

5. Find the lateral area of the prism below Round your answer to the nearest whole number

322 m^2

6. Find the surface area of the cylinder in terms of pi

350pi cm^2

7. Allison is planning to cover the lateral surface of a large cylindrical can diameter 3 feet height 3.5 feet

33. ft^2

8. Find the surface area of the regular pyramid shown to the nearest whole number

740 m^2

9. is the figure below drawn in one point or 2 point perspective

Answer:

B 0.34

Step-by-step explanation:

If 34% of all people are expected to get the flu, then that means 34% of any sample size should also expect to be infected.  If they choose 1 person at random from either the population or a preselected random sample, then that person has a 34% chance of getting the flu.  0.34 is the decimal corresponding to 34%. So the probability is 0.34

Convert the percentage to a decimal. The answer is 0.34.

Answer:

The height of the pyramid is [tex]50\ in[/tex]

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

we have

[tex]V=1,800\ in^{3}[/tex]

The area of the base B is equal to

[tex]B=\frac{1}{2}(12)(18)=108\ in^{2}[/tex]

substitute and solve for H

[tex]1,800=\frac{1}{3}(108)H[/tex]

[tex]5,400=(108)H[/tex]

[tex]H=5,400/(108)=50\ in[/tex]

Answer:Add T with e and thats your answer.

Step-by-step explanation:

Answer:

The distance of the dot above the ground is 28.9 in

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangle ABC is an isosceles triangle

CA=CB=15 in ------> is the radius of the circle

∠ACD+112°=180° ---> because the diameter divide the circle into two equal parts

∠ACD=180° -112°=68°

In the right triangle ACD

Find AD we have sin(68°)=AD/AC AD=AC*sin(68°) substitute the value AD=15*sin(68°)=13.9 in

Find the distance AB

AB=2*AD AB=2*13.9=27.8 in

The diameter is equal to

2*15=30 in

The distance of the dot above the ground is equal to

AB+(30-27.8)/2

27.8+1.1=28.9 in

Answer:

45

Step-by-step explanation:

Two tangents drawn to a circle from an outside point form arcs and an angle, and this formula shows the relation between the angle and the two arcs.

m<EYL = (1/2)(m(arc)EVL - m(arc)EHL)      Eq. 1

The sum of the angle measures of the two arcs is the angle measure of the entire circle, 360 deg.

m(arc)EVL + m(arc)EHL = 360

m(arc)EVL = 360 - m(arc)EHL      Eq. 2

We are given this:

m<EYL = (1/3)m(arc)EHL       Eq. 3

Substitute equations 2 and 3 into equation 1.

(1/3)m(arc)EHL = (1/2)[(360 - m(arc)EHL) - m(arc)EHL]

Now we have a single unknown, m(arc)EHL, so we solve for it.

2m(arc)EHL = 3[360 - m(arc)EHL - m(arc)EHL]

2m(arc)EHL = 1080 - 6m(arc)EHL

8m(arc)EHL = 1080

m(arc)EHL = 135

Substitute the arc measure just found in Equation 3.

m<EYL = (1/3)m(arc)EHL

m<EYL = (1/3)(135)

m<EYL = 45

Answer:

D

Step-by-step explanation:

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence

(BC)² = 10² + 30² → D

The equation that is needed to find the length of BC is [tex]BC^2 = 10^2 + 30^2[/tex].

The correct option is D.

To find the length of side BC in the triangle ABC, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, triangle ABC has a right angle at angle BAC.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can use this theorem to find the length of BC.

Let BC be denoted as x. According to the Pythagorean theorem, we have:

[tex]BC^2 = AB^2 + AC^2[/tex]

Substituting the given values, we get:

[tex]BC^2 = 10^2 + 30^2[/tex]

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Answer:

49 minutes

Step-by-step explanation:

knowing that the more people, the lower the time (divide), and the more walls, the more time (multiply)

1. find how long it takes 1 person to paint 1 wall:

63 minutes/9 walls = 7 minutes/wall with 4 people

7 minutes * 4 people = 28 minutes/wall with 1 person

2. Find for 7 people and 4 walls: 28 minutes * 7 people/4 walls = 196/4 =

49 minutes

Answer:

The correct answer is 16 minuets!

Step-by-step explanation:

You can use the formula PRT=w

(P=people) (R=rate) (T=time) (w-work)

You would start by plugging the numbers in for the given information:

(4 people)*(r)*(63min)=9walls

then solve for r

in this case r=.035714286

You can use this infromation to find what is being asked and the previously mentioned formula:

(7 people)*(.035714286)*(t) = 4 walls

Now all you have to do is solve for t to get the answer.

In this case t=16

(I also just had this question asked on an online quiz and got it correct so I know the answer is right)

Hope this helps!

Answer:

The expression is [tex]x=100-15-10+20-40+35[/tex]

Jake has in his wallet [tex]\$90[/tex]

Step-by-step explanation:

Let

x-----> the money that Jake has in his wallet

we know that

The expression that represent the situation is equal to

1) Jake has $100 of birthday money in his wallet

so

[tex]x=100[/tex]

2) He spends $15 at Twistee Treat and $10 at Wawa

so

[tex]x=100-15-10[/tex]

3) He finds a $20 bill on the ground

so

[tex]x=100-15-10+20[/tex]

3) His friend borrows $40 from Jake

so

[tex]x=100-15-10+20-40[/tex]

4) At home, Jake mows the lawn and earns $35

so

[tex]x=100-15-10+20-40+35[/tex]

[tex]x=\$90[/tex]

Jake has $90 in his wallet after accounting for all his expenses, earnings, and the money borrowed by his friend. This calculation includes his birthday money, spending, found money, and earnings from mowing the lawn.

To determine how much money Jake has in his wallet, we need to account for all his spending, earnings, and borrowings.

Therefore, Jake has $90 in his wallet.

Answer:

0.25%

Step-by-step explanation:

To change a fraction to a percentage, we multiply the fraction by 100%.

1/400 = 1/400 x 100 = 0.25%

hope this helps

The value of the Percentage 1/400 as a percent is: 0.25%

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Thus:

1/400 as a percent is calculated as:

1/400 * 100/1

= 100/400

= 0.25%

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