what is the length of BC in the right triangle below?

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

Answer:

If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases

Step-by-step explanation:

Let

x ----> the number of pieces of fruit

y ----> the total pay for the purchase

we know that

Todd

[tex]y=1.25x+4[/tex] ----> equation A (peaches plus a carton of vanilla yogurt)

Agnes

[tex]y=1.00x+6[/tex] ----> equation B (apples plus a jar of honey)

Equate equation A and equation B and solve for x

[tex]1.25x+4=1.00x+6[/tex]

[tex]1.25x-1.00=6-4[/tex]

[tex]0.25x=2[/tex]

[tex]x=8\ pieces\ of\ fruits[/tex]

therefore

If the number of fruits is 8, then Todd and Agnes will pay the same amount for their purchases

Answer:

The length of rectangular panel is 6.4 cm.

Step-by-step explanation:

We are given the following information in the question:

Area of rectangular solar panel = 128 square cm

Width of panel = 20 cm

We have to find the length of the panel

Formula:

[tex]\text{Area of rectangular panel} = \text{Width}\times \text{Length}\\\Rightarrow 128 = 20\times \text{Length}\\\\\text{Length} = \displaystyle\frac{128}{20} = 6.4\text{ cm}[/tex]

Hence, the length of rectangular panel is 6.4 cm.

This is an example of direct variation as greater would be length and breadth, the greater would be the area.

Answer:

Step-by-step explanation:

[tex]x = x^{2} - 20[/tex]

[tex]x^{2} - x - 20 = 0[/tex]

[tex](x - 5)(x + 4) = 0[/tex]

[tex]x = -4, 5[/tex]

The two numbers are 5 and -4.

To find a number that is 20 less than its square, we can set up an equation where the number is represented by x. The equation then becomes x = x^2 - 20.

By re-arranging the equation, we get x^2 - x - 20 = 0. This is a quadratic equation which can be solved by factoring or using the quadratic formula.

The factored form of the equation is (x - 5)(x + 4) = 0. Therefore, the solutions for x are 5 and -4, meaning 5 and -4 are the numbers that are 20 less than their squares.

The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.

To find out how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon.

Length of Iditarod Trail ultra-marathon = 1.6x106 meters

Length of Boston Marathon = 4.2x104 meters

Dividing the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon:

1.6x106 / 4.2x104 = 38.09524

The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.

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The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.

To determine how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail (1.6×106 meters) by the length of the Boston Marathon (4.2×104 meters). Performing the division, we get:

(1.6×106 meters) / (4.2×104 meters)

= 38.095

The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.

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The value 503.782 to the nearest tenth is 503.8

Rounding up to the nearest tenth means we want only a digit to be placed after the decimal point.

Given the value 503.782, this value to the nearest tenth will be 503.8.

Note that 1 was added to the value "7" after the decimal point. This was because the adjacent value "8" is more than 4.

Hence the value 503.782 to the nearest tenth is 503.8

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Final answer:

To round 503.782 to the nearest tenth, the digit in the hundredths place is 8, which is greater than or equal to 5. Therefore, the rounded number is 503.8.

Explanation:

To adjust 503.782 to the closest 10th, we really want to take a gander at the digit in the hundredths place, which is the second digit after the decimal point. It is 7 in this instance.

Since 7 is more prominent than or equivalent to 5, we gather together the digit in the tenths place, which is the primary digit after the decimal point. For this situation, it is 8.

Therefore, 503.8 is obtained by rounding 503.782 to the nearest tenth.

To round 503.782 to the nearest tenth, we look at the digit in the hundredths place, which is 8. Since 8 is greater than or equal to 5, we round up. Therefore, the rounded number is 503.8.

Answer:

The electrician charges $46 per hour

Step-by-step explanation:

we know that

An electrician charges $322 for 7 hours of work

so

using proportion

Find out how much does the electrician charge per hour

Let

x ----> the charge per hour

[tex]\frac{322}{7}\frac{\$}{h}=\frac{x}{1}\frac{\$}{h}\\\\x=322/7\\\\x=\$46[/tex]

therefore

The electrician charges $46 per hour

The electrician charges $46 per hour.

The total charge is $322, and the total number of hours worked is 7.

To find the charge per hour, use the formula:

Charge per hour = Total charge / Number of hours

Substitute the given values into the formula:

Charge per hour = 322 / 7

Perform the division:

322 divided by 7 equals 46. Therefore, the electrician charges $46 per hour.

So, the calculation is:

Charge per hour = 46

Answer:

$45

Step-by-step explanation:

Multiply 4.5 by 5 to give you the total amount lost over 5 days,which is 22.5. If you lost 22.5 and started with 67.5, subtract the two to get your answer

Answer:

55%

Step-by-step explanation:

all you have to do is divide 114.4 by 208 to get 0.55, then turn that into a percentage by moving the decimal 2 times to the right.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\begin{array}{ccc}208&-&100\%\\\\114.4&-&p\%\end{array}\qquad\text{cross multiply}\\\\208p=(100)(114.4)\\\\208p=11440\qquad\text{divide both sides by 208}\\\\p=\dfrac{11440}{208}\\\\p=55[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Calculate the quotient of given numbers and convert it to the percent:}\\\\\dfrac{114.4}{208}=0.55\\\\0.55\cdot100\%=55\%[/tex]

Answer:Communitive Property

Step-by-step explanation: You can only do this property with addition and multiplication because you are able to switch the places and still get the same answer

Answer:

She should earn $540 in a 40 hour week

Step-by-step explanation:

we know that

Her pay for 22 hours is $297

so

using proportion

Find out how much should she earn in a 40 hours week

[tex]\frac{22}{297}=\frac{40}{x}\\\\x=297*40/22\\\\x= \$540[/tex]

Answer:

$528.92

Step-by-step explanation:

The subscription given is $499 plus 8% tax

Add tax

108/100 * $499 = $538.92

$538.92 for 30 days.

If its being promoted for 7 days there is a $10 off coupon, this will be;

$538.92-$10 = $528.92

Final cost = $528.92

Answer: 7/12

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

The problem is asking us to find what fraction of students watch between 0 and 2 hours of TV a day:

The information we have is:

0 - 1 hours = 1/6

1 1/2 - 2 hours = 5/12

We only need this information because it is asking us for 0 to 2 hours.

Now we have to add the fraction of students that watch TV 0-1 hours and the fraction of students watch TV 1 1/2 - 2 hours:

1/6 + 5/12

To be able to solve this we have to have the same denominator and to do it we have to multiply the first fraction by 2:

(1/6) *2 = 2/12

Now we can add:

2/12 + 5/12 = 7/12

We add the numerators and the denominator stays the same.

Answer:

two hundredths

Step-by-step explanation:

6 is in the ones place. 3 is in the tenths place. 2 is in the hundredths place

5 is in the thousandths place.

Answer:

two hundredths

Step-by-step explanation:

its two places after the decimal point

Answer:

630

Step-by-step explanation:

if you add the percentages of the trucks, sport cars and vans you get:

30% + 25% + 10% = 65%. So to find the percentage of vehicles that aren't in this categories you substract this percentage from 100%.

100% - 65% = 35%

This means that 35% of the vehicles aren't in those categories, so to find the amount you just multiply the total of vehicles with the percentage an then divide by 100

(1,800*35)/100 = 630 vehicles

In order to get the answer to this question you will have to multiply the whole number as many times as it's exponent so in this case you will have to multiply 10, 15 times.

[tex]10^{15}[/tex]

[tex]10^{15} = 10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10[/tex]

[tex]10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10 = 1000000000000000[/tex]

[tex]= 1000000000000000[/tex]

Therefore your answer is "1,000,000,000,000,000."

Hope this helps.

Answer:

x = 2.8 hours

Explanation

Total distance = 350 km

Time period = 3 hrs

Hence we need to formulate an equation...,

Distance = Speed × Time

; Distance covered travelling at 120 = 120x Since the total time period was 3hrs...then the remaining time is (3 - x)

;Distance covered travelling at 60 = 60(3- x)

The equation is going to be...,

; 120x + 60(3 - x) = 350...since total distance is 350 km

; 120x + 180 - 60x = 350

; 60x = 170....divide both sides by 60

Hence..., x = 2.8 hours

For this case we have the following solutions:

[tex]x_ {1} = 1 + \sqrt {5}\\x_ {2} = 1- \sqrt {5}[/tex]

Then, the factorized equation is of the form:

[tex](x- (1+ \sqrt {5})) (x- (1- \sqrt {5})) = 0\\(x-a) (x-b) = 0[/tex]

We apply distributive property:

[tex]x ^ 2-bx-ax + ab = 0\\x ^ 2- (1- \sqrt {5}) x- (1+ \sqrt {5}) x + (1+ \sqrt {5}) (1- \sqrt {5}) = 0\\x ^ 2-x + \sqrt {5} x-x- \sqrt {5} x + (1 ^ 2- \sqrt {5} + \sqrt {5} - (\sqrt {5}) ^ 2) = 0\\x ^ 2-2x + (1-5) = 0\\x ^ 2-2x-4 = 0[/tex]

ANswer:

The equation is [tex]x ^ 2-2x-4[/tex]

Good evening ,

____________________

Step-by-step explanation:

it’s a rational function then it’s continue at all real numbers except when x=3

[tex]\frac{1}{x-3}[/tex] ; x≠3.

:)

This is an arithmetic sequence

The value of the 3rd term is 72

There are 4 terms in this sequence

The sequence starts at 60 and adds 6 repeatedly

Answer:

b, c, f, g

Step-by-step explanation:

The answer is [tex]-28w^2[/tex]

Answer:

[tex]\large\boxed{f(x)-g(x)=x^2+2x+6}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+1\\\\g(x)=2x-5\\\\f(x)-g(x)=(x^2+1)-(2x-5)\\\\f(x)-g(x)=x^2+1-2x-(-5)\\\\f(x)-g(x)=x^2+1-2x+5\qquad\text{combine like terms}\\\\f(x)-g(x)=x^2+2x+(1+5)\\\\f(x)-g(x)=x^2+2x+6[/tex]

Answer:

2.5

Step-by-step explanation:

Use the given functions to set up and simplify  

D

.

x

=

0.5

x

+

4

+

0.9

x

=

x

+

5

=

x

=

2.5

A

=

x

=

2.5

x

=

2.4

=

x

=

2.5

B

=

x

=

2.5

x

=

0.42

=

x

=

2.5

C

=

x

=

2.5

x

=

0.4

=

x

=

2.5

D

=

x

=

2.5

x

=

2.5

=

x

=

2.5

The solution for x in the equation 0.5x + 4 + 0.9x = x + 5 is 2.5.

Given that:

0.5x + 4 + 0.9x = x + 5

It is required to find the value of x.

In order to find the value of x, first operate the like terms together and then solve it to find the value of x.

Consider,

0.5x + 4 + 0.9x = x + 5

1.4x + 4 = x + 5

Subtract both sides by x.

0.4x + 4 = 5

Subtract both sides by 4.

0.4x = 5 - 4

0.4x = 1

Now, divide both sides by 0.4.

x = 1 / 0.4

x = 2.5

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The expression [tex]\(5x + 2x - 3\)[/tex] is a linear expression.

The expression [tex]\(5x + 2x - 3\)[/tex] represents a linear expression because it consists of terms involving only the variable \(x\) raised to the power of 1. In other words, each term is a linear term.

Linear expressions depict relationships that are straight lines when graphed on a Cartesian plane. In this case, \(5x\) and \(2x\) are both linear terms since they involve the variable \(x\) raised to the first power, while the constant term \(-3\) does not involve \(x\) at all.

The expression simplifies to [tex]\(7x - 3\),[/tex] maintaining its linear form. Linear expressions are fundamental in algebra and represent relationships with constant rates of change.

Answer: the correct answer is B

Answer:

Part 1) The number is 0.008

Part 2) The number is 0.05

Step-by-step explanation:

Part 1) we have

0.08 is ten times great as ...

That means----> 10 times a number is equal to 0.08

Let

x -----> the number

To find the number divide 0,08 by ten  

so

0.08=10x

x=0.08/10

x=0.008

Part 2) we have

0.5 is ten times great as...

That means----> 10 times a number is equal to 0.5

Let

x -----> the number

To find the number divide 0,5 by ten  

so

0.5=10x

x=0.5/10

x=0.05

The correct option is C. 3 ÷ 1 > 3 ÷ 3.

To solve this problem, we need to evaluate each of the given number sentences to determine which one is true.

A. 3 ÷ 1 < 0 ÷ 3

First, we perform the divisions:

3 ÷ 1 = 3

0 ÷ 3 = 0

Now we compare the results:

3 < 0

This statement is false because 3 is not less than 0.

B. 0 ÷ 3 > 3 ÷ 3

Again, we perform the divisions:

0 ÷ 3 = 0

3 ÷ 3 = 1

Now we compare the results:

0 > 1

This statement is false because 0 is not greater than 1.

C. 3 ÷ 1 > 3 ÷ 3

We perform the divisions:

3 ÷ 1 = 3

3 ÷ 3 = 1

Now we compare the results:

3 > 1

This statement is true because 3 is greater than 1.

D. 3 ÷ 3 < 4 ÷ 4

We perform the divisions:

3 ÷ 3 = 1

4 ÷ 4 = 1

Now we compare the results:

1 < 1

This statement is false because 1 is not less than 1; they are equal.

Therefore, the only true statement is C. 3 ÷ 1 > 3 ÷ 3.

Answer:

In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list statements and the reasons the statements are true.

A paragraph proof is a two-column proof in sentence form.

Step-by-step explanation:

A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column

The statements regarding proofs are,

(1)In a paragraph proof, statements and their justifications are written in sentences in a logical order.

2. A two-column proof consists of a list of statements and the reasons the statements are true and

(4) A paragraph proof is a two-column proof in sentence form.

We have given that the statement is,In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list of statements and the reasons the statements are true.

A flowchart proof gives a visual representation of the sequence of steps without justifications.

A paragraph proof is a two-column proof in sentence form.

A flowchart proof gives a visual representation of the sequence of steps without justifications.

A paragraph proof is a two-column proof in sentence form.

A two-column proof lists only the given information and what is to be proven.

Logical order is when all of the messages and segments within a group are in their logical sequence.

So we have the correct statements are

A paragraph proof is only a two-column proof written in sentences. However, since it is easy to leave steps out when writing a paragraph proof.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true.

The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column

Therefore the statement 1. 2 and 4 are true.

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Answer:

x = 45

Step-by-step explanation:

The average is calculated as

average = [tex]\frac{score}{count}[/tex]

here the average = 50 , thus

[tex]\frac{36+44+75+x}{4}[/tex] = 50

Multiply both sides by 4

36 + 44 + 75 + x = 200

155 + x = 200 ( subtract 155 from both sides )

x = 45

The required, 5.241 divided by 3 equals approximately 1.747.

To divide 5.241 by 3, we can perform the division as follows:

    1.747

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

3 | 5.241

To start, we divide the whole number part, 5, by 3. The result is 1, which becomes the whole number part of the quotient.

Next, we bring down the decimal point and consider the decimal part of the dividend, which is 0.241. We can continue the division process by adding a decimal point to the quotient and placing a 0 to the right of the decimal point.

   1.747

 3 | 5.241

     - 3

     -----

       24

Now, we divide 24 by 3, which gives us 8. We bring down the next decimal digit, which is 1, and continue the division:

   1.747

 3 | 5.241

     - 3

      -----

       24

     - 24

      -----

         1

Since there are no more decimal digits to bring down, we have finished the division. The final quotient is 1.747, rounded to three decimal places.

Therefore, 5.241 divided by 3 equals approximately 1.747.

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