Mathematics College

which three statements are true about the line segment CBit's the radius of the circleit is the circumference of the circleit is a cordit is 6cm longit is diameter of the circle it is 7cm longit is 1.75cm long

Answers

Answer 1

Answer:

It is the diameter of the circle

it is 7 cm

it is a chord

Explanation:

First, we notice that the line segment CB passes through the centre of the circle and its endpoints touch the circumference - this tells us that CB is the diameter.

Furthermore, any line segment whose endpoints lie on the circumference of the circle is a chord (meaning that the diameter is the longest chord), and so we deduce that CB is also a chord.

Since CB is the diamter, its length is 2 times the radius. The raduis of the circle we know is DA = 3.5 cm; therefore, the dimater is CB = 2 DA = 2 * 3.5 = 7 cm.

Hence, the correct choices are:

It is the diameter of the circle

it is 7 cm

it is a chord

Related Questions

The ages of three siblings, Ben, Bob and Billy, are consecutive integers. The square of the age of the youngest child Ben is four more than eight times the age of the oldest child, Billy. How old are the three boys?

Answers

Let the age of the youngest child (Ben) be x years.

Since the ages are consecutive integers, the ages of the other 2 are (x + 1) and (x + 2).

It was given that the age of the youngest child is four more than eight times the age of the oldest child. This means that:

[tex]x^2-4=8(x+2)[/tex]

We can rearrange the equation above and solve for x as a quadratic equation:

[tex]\begin{gathered} x^2-4=8x+16 \\ x^2-8x-20=0 \end{gathered}[/tex]

Using the factorization method, we have:

[tex]\begin{gathered} x^2-10x+2x-20=0 \\ x(x-10)+2(x-10)=0 \\ (x-10)(x+2)=0 \\ \therefore \\ x-10=0,x+2=0 \\ x=10,x=-2 \end{gathered}[/tex]

Since the age cannot be negative, the age of the youngest child is 10.

Therefore, the ages are:

[tex]\begin{gathered} Ben=10\text{ }years \\ Bob=11\text{ }years \\ Billy=12\text{ }years \end{gathered}[/tex]

Determine whether each linear function is a direct a variation. If so, state the constant of variation. If not, explain why notI need help for number 6

Answers

In direct variation function, variables x and y are related by the next formula:

y = kx

where k is the constant of variation.

Isolating k for the above formula, we get:

k = y/x

Computing y divided by x with the values of the table:

[tex]\frac{5}{10}\ne\frac{6}{11}\ne\frac{7}{12}\ne\frac{8}{13}[/tex]

Given that all the quotients are different, then the linear function is not a direct variation

Translate and solve: The difference of a and 7 is 11

Answers

Answer:

(B)a=18

Explanation:

The difference of a and 7 translated as an expression is:

[tex]a-7[/tex]

Thus, the equation is:

[tex]a-7=11[/tex]

To solve for a, add 7 to both sides of the equation:

[tex]\begin{gathered} a-7+7=11+7 \\ a=18 \end{gathered}[/tex]

The correct choice is B.

the length of the rectangle is two feet less than 3 times the width.if the area is 65ft^2.find the dimension.

Answers

Given:

The area of the rectangle, A=65ft^2.

Let l be the length of the rectangle and w be the width of the rectangle.

It is given that the length of the rectangle is two feet less than 3 times the width.

Hence, the expression for the length of the rectangle is,

[tex]l=3w-2\text{ ----(A)}[/tex]

Now, the expression for the area of the rectangle can be written as,

[tex]\begin{gathered} A=\text{length}\times width \\ A=l\times w \\ A=(3w-2)\times w \\ A=3w^2-2w \end{gathered}[/tex]

Since A=65ft^2, we get

[tex]\begin{gathered} 65=3w^2-2w \\ 3w^2-2w-65=0\text{ ---(1)} \end{gathered}[/tex]

Equation (1) is similar to a quadratic equation given by,

[tex]aw^2+bw+c=0\text{ ---(2)}[/tex]

Comparing equations (1) and (2), we get a=3, b=-2 and c=-65.

Using discriminant method, the solution of equation (1) is,

[tex]\begin{gathered} w=\frac{-b\pm\sqrt[]{^{}b^2-4ac}}{2a} \\ w=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times3\times(-65)}}{2\times3} \\ w=\frac{2\pm\sqrt[]{4^{}+780}}{2\times3} \\ w=\frac{2\pm\sqrt[]{784}}{6} \\ w=\frac{2\pm28}{6} \end{gathered}[/tex]

Since w cannot be negative, we consider only the positive value for w. Hence,

[tex]\begin{gathered} w=\frac{2+28}{6} \\ w=\frac{30}{6} \\ w=5\text{ ft} \end{gathered}[/tex]

Now, put w=5 in equation (A) to obtain the value of l.

[tex]\begin{gathered} l=3w-2 \\ =3\times5-2 \\ =15-2 \\ =13ft \end{gathered}[/tex]

Therefore, the length of the rectangle is l=13 ft and the width is w=5 ft.

Dianne is 23 years older than her daughter Amy. In 5 years, the sum of their ages will be 91. How old are they now?Amy is ? years old, and Dianne is ? years old.

Answers

Currently

Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.

In 5 years

Amy's age will be (x + 5) years.

Dianne's age will be:

[tex]x+23+5=(x+28)\text{ years}[/tex]

The sum of their ages in 5 years is 91. Therefore, we have:

[tex](x+5)+(x+28)=91[/tex]

Solving, we have:

[tex]\begin{gathered} x+5+x+28=91 \\ 2x=91-5-28 \\ 2x=58 \\ x=\frac{58}{2} \\ x=29 \end{gathered}[/tex]

Amy is 29 years old. Therefore, Dianne will be:

[tex]29+23=52\text{ years old}[/tex]

ANSWER:

Amy is 29 years old, and Dianne is 52 years old.

What is 10/12 written in simplest form?

Answers

ANSWER:

[tex]\frac{5}{6}[/tex]

STEP-BY-STEP EXPLANATION:

We have the following fraction

[tex]\frac{10}{12}[/tex]

Now to reduce to its simplest form, we must simplify

[tex]\frac{2\cdot5}{2\cdot6}=\frac{5}{6}[/tex]

How do I solve this and what is the answer

Answers

Answer:

Answer is 20 degrees
:)

How much money would you have if you deposited $100.00 in an account thatearned 8% interest after 20 years?

Answers

Problem:

How much money would you have if you deposited $100.00 in an account that earned 8% interest after 20 years?.

Solution:

Step 1: Calculate 8% of the given amount ($100.00):

[tex]100.00\text{ x 0.08 = \$8 }[/tex]

Step 2: Add the above value to the money deposited:

$100.0 + $8 = $108.0

Thus, we can conclude that the money in this account after 20 years is $108.0

Consider the equation cos(2t) = 0.8. Find the smallest positive solution in radians and round your answer to 2 decimal places.

Answers

Given:

cos(2t) = 0.8

Take the cos⁻' of both-side of the equation.

cos⁻' cos(2t) = cos⁻'(0.8)

2t = cos⁻'(0.8)

Calculate the value of the right- hand side with your calculator in radians.

2t =0.6435

Divide both-side of the equation by 2

t ≈ 0.32

How long does it take Tina to type 864 words, if she took 15 minutes to type out an assignment that comprised 720 words?

Answers

Given data:

The given time taken by Tin to type 720 words is t=15 min.

The given expression can be wriiten as,

720 word=15 min

720 words= 15(60 sec)

720 words= 900 sec

1 word = 900/720 sec

=1.25 sec

Multiplying the above equation with 864 on both sides .

864 words= 864(1.25) sec

= 1080 sec

=1080/60 min

= 18 min.

Thus, the time taken bby Tine to type 864 words is 18 min.

two functions are given below: f(x) and h(x) state the axis of symmetry for each function and explain how to find it f(x)=3(x+4)^2+1

Answers

The axis of symmetry for each function are x = -4 and x =1

How to determine the axis of symmetry for each function?

The functions are given as

f(x) and h(x)

As a general rule of functions;

The axis of symmetry for a function is the x-coordinate of the vertex of the function

In f(x), we have

f(x)=3(x+4)² + 1

The vertex of this function is

(x, y) = (-4, 1)

So, the axis is x = -4

For function h(x), we have

The vertex of this function is

(x, y) = (1, -3)

So, the axis is x = 1

Hence, the axis of symmetry are x = -4 and x =1

Answers

Using the triangle sum theorem:

[tex]\begin{gathered} m\angle L+m\angle K+20=180 \\ 2m\angle L=180-20 \\ 2m\angle L=160 \\ m\angle L=\frac{160}{2} \\ m\angle L=80 \end{gathered}[/tex]

Using the exterior angle theorem:

[tex]\begin{gathered} m\angle E=m\angle L+m\angle J \\ m\angle E=80+20 \\ m\angle E=100 \end{gathered}[/tex]

Answer:

100

If the point (-6, 4) is dilated by a scale factor of 1/2, the resulting point is (-3,2).TrueFalse

Answers

(-6,4)

Multiply each coordinate by 1/2

( -6 * 1/2 , 4 * 1/2) = (-3,2)

True

find the slop of the line passing through the points (1,-1) and (-1,1)

Answers

Answer:

I think its done this way. But I don't know if the answer is correct.

I don’t know what im doing wrong. Can someone help?

Answers

We want to write

[tex]\frac{\sqrt[]{5}+1}{2}[/tex]

as decimal, doing it on a calculator we have

[tex]\frac{\sqrt[]{5}+1}{2}=1.61803398875[/tex]

But we only need three decimal places, then the result is

[tex]\frac{\sqrt[]{5}+1}{2}=1.618[/tex]

Please help quick :/

Answers

Answer:

The design fee is $40.

Step-by-step explanation:

The y intercept means the cost when the number of shirts ordered is 0. This means that in the context of this problem the y intercept is the design fee.

Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.

Answers

The given information is:

The starting population of bacteria is 390.

The population quadruples every 20 minutes.

To find the equation of the population in terms of minutes, we can apply the following formula:

[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]

Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.

If we replace the known values, we obtain:

[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]

To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:

[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]

Thus, after 1 hour there are 24960 bacterias.

−1= 8x+2i need help with this problem,

Answers

Given

-1 = 8x + 2

Answer

-1 = 8x + 2

-1 -2 =8x

-3 = 8x

x = -3/8

A granite pyramid is 50 feet high and has a square base 30 feet on a side. If granite weighs 180 pounds per cubic foot, what is the weigh in tons of the pyramid?

Answers

The weight of the granite pyramid in tons is 1350 tons.

How to find the weight of the pyramid granite in tons?

A pyramid is a three-dimensional shape.

The granite pyramid is 50 feet high and has a square base of 30 feet on a side.

Granit weighs 180 pounds per cubic foot.

Therefore, the weight in tons of the pyramid can be calculated as follows;

Hence,

volume of the granite pyramid = 1 / 3 b² h

Therefore,

volume of the granite pyramid = 1 / 3 × 30² × 50

volume of the granite pyramid = 45000 / 3

volume of the granite pyramid = 15000 ft³

Hence,

1 ft³ = 180 pounds

15000 ft³ = ?

weight = 2700000 pounds

1 pounds = 0.0005 tons

2700000 pounds = ?

Therefore,

weight of the pyramid granite in tons = 1350 tons

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Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.If x-8>10, then x_18.

Answers

GIVEN

The inequality:

[tex]x-8>10[/tex]

SOLUTION

The inequality is to be solved.

Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:

[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]

ANSWER

[tex]x>18[/tex]

Consider the following expression 9x+4y + 1 Select all of the true statements below 1 is a constant. 9x and 1 are like terms. 9x is a factor, 9x + 4y + 1 is written as a sum of three terms. ( 9x is a coefficient. None of these are true.

Answers

ANSWER:

1st option: 1 is a constant

4th option: 9x + 4y + 1 written as a sum of three terms

STEP-BY-STEP EXPLANATION:

We have the following equation:

[tex]9x+4y+1[/tex]

From the following equation we can say the following:

• The only constant term is 1

• None of the terms are similar

• There are a total of 3 terms

• The coefficients are 9 and 4

• The factors are 9, 4, 1, x and y

From the above we can affirm that the true statements are:

• 1 is a constant

• 9x + 4y + 1 written as a sum of three terms

Find x, for which 7x+8=4x-10

Answers

We are given the equation 7x+8=4x-10 and we want to find the value of x, such that the equality holds. To do so, we will start with the equation and the solve it for x. That is, we will apply mathematical operations on both sides of the equation, so we end up "ilosating" the x on one side of the equality sign. We start by

[tex]7x+8=4x\text{ - 10}[/tex]

First, we subtract 4x on both sides, so we get

[tex]\text{ -10=(7x-4x)+8=3x+8}[/tex]

Now, we subtract 8 on both sides, so we get

[tex]3x=\text{ -10-8=-18}[/tex]

Finally, we divide both sides by 3, so we get

[tex]x=\frac{\text{ -18}}{3}=\text{ -6}[/tex]

so x=-6.

Two seamstresses sew 5 curtains in 3 hours. How many curtains will 12 seamstresses sew in the same time if the seamstresses all work at the same rate?

Answers

Answer:

30 curtains

Step-by-step explanation:

You have 6 times as many seamstresses so you will get 6 times as many curtains

6 * 5 = 30 curtains

open up or down, vertex:(0,-4), passes through: (-3,5)

Answers

open up or down, vertex:(0,-4), passes through: (-3,5)

In this problem we have a vertical parabola open upward

the equation in vertex form is equal to

y=a(x-h)^2+k

where (h,k) is the vertex

we have

(h,k)=(0,-4)

substitute

y=a(x)^2-4

Find the value of a

with the point (-3,5)

substitute in the equation

5=a(-3)^2-4

5=9a-4

9a=5+4

9a=9

a=1

therefore

the equation is

y=x^2-4

answer is

f(x)=x^2-4

The band is selling T-shirts for $15.00 each. They make $5.00 profit from each shirt sold. Write an equation to represent the profit earned,y,for selling,x,number of shirts.

Answers

The equation to represent the profit earned y, for selling x, number of shirts is y = 5x.

Given that:-

Selling Price of T-shirt = $ 15

Profit earned per T-shirt = $ 5

We have to form an equation to represent the profit earned y, for selling x, number of shirts.

We know that,

Profit earned by selling 1 T-shirt = $ 5

Hence, profit earned by selling x T-shirts = 5*x

We know that,

Profit earned by selling x T-shirts = y

Hence, we can write,

y = 5x

Hence, the equation that represents the profit earned y, for selling x, number of shirts is y = 5x.

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Write an expression in terms of Pi that represents the area of the shaded part of N.

Answers

Answer:

The area of the shaded part is:

[tex]=(PN)^2\lbrack\pi-\frac{1}{2}(75-\sin 75)\rbrack[/tex]

Explanation:

The area of the shaded part is the subtraction of the area of the unshaded part from the area of the whole circle.

Area of the ushaded part is:

[tex]\frac{1}{2}\times(PN)^2\times(75-\sin 75)[/tex]

Area of the circle is:

[tex](PN)^2\pi[/tex]

Area of the shaded part is:

[tex]\begin{gathered} (PN)^2\pi-\frac{1}{2}(PN)^2(75-\sin 75) \\ \\ =(PN)^2\lbrack\pi-\frac{1}{2}(75-\sin 75)\rbrack \end{gathered}[/tex]

select all reasons that support one or more statements in ghe proof.

Answers

Answer:

B, C, D and E.

Explanation:

The proof and reasons for each step is given below:

Step 1:

Statement: RSTU is a parallelogram.

Reason: Given

Step 2:

Statement: RS is parallel to TU and RU is parallel to TS

Reason: (B)Definition of a parallelogram

Step 3:

Statement: ∠RSU≅∠TUS and ∠RUS≅∠TSU.

Reason: (C)Alternate Interior angles are congruent

Step 4:

Statement: SU≅US.

Reason: (E)corresponding parts of congruent triangles are congruent.

Step 5:

Statement: Triangle RSU≅Triangle TUS.

Reason: AAS Congruence Theorem

Step 6:

Statement: RS≅TU and RU≅TS

Reason: (D)Opposite sides of a parallelogram are congruent.

The reasons that support the proof are B, C, D and E.

P(B) = 2/3P(An B) = 1/6What will P(A) have to be for A and B to be independent?1/211/121/45/6

Answers

P(B) = 2/3

P(An B) = 1/6

What will P(A) have to be for A and B to be independent?

Remember that

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true

substitute given values

1/6=P(A)*(2/3)

solve for P(A)

P(A)=1/4

Solve for x. 8x-2x+7>21+10

Answers

Answer: [tex]x > 4[/tex]

Step-by-step explanation:

[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]

Which of the following is only true sometimes? A. The sum of a rational number and a rational number is rational. B. The sum of a rational number and an irrational number is irrational. C. The product of an irrational number and an irrational number is irrational. D. The product of a nonzero rational number and an irrational number is irrational.

Answers

The sum of a rational number and a rational number is rational. ALWAYS

The sum of a rational number and an irrational number is irrational.

The product of an irrational number and an irrational number is irrational. SOMETIMES

For example, the product of multiplicative inverses like √2 and 1/√2 will be 1

The product of a nonzero rational number and an irrational number is irrational.

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