What is the length of Line BC?

Answer:

x = 4

Step-by-step explanation:

4x+41=3x+45

Subtract 3x from both sides

x + 41 = 45

Subtract 41 from both sides

x = 4

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer: $58.40 Multiply 4 times 17.59 and add 237 times 0.19

Final answer:

The total cost of renting a car for 4 days at $17.59 per day and driving 237 miles at 19¢ per mile would be $115.39.

Explanation:

To calculate the cost of renting a car for 4 days:
For the rental cost, we multiply the daily rental rate by the number of days:

Rental cost=Number of days × Daily rental rate

Cost of renting the car for 4 days = 4 days x $17.59 per day = $70.36
Next, to find the cost of driving 237 miles, we multiply the distance driven by the cost per mile:

Cost of driving=Distance driven × Cost per mile

Cost of driving 237 miles at 19¢ per mile = 237 miles x $0.19 = $45.03
Total cost = Cost of renting + Cost of driving = $70.36 + $45.03 = $115.39

Answer:

Step-by-step explanation:

lets say in the shown triangle x=165

so speed [tex]\frac{dx}{dt} =25[/tex]

and  [tex]\frac{dy}{dt} =35[/tex]

Also since distance = speed* time

time = pi minutes = pi/60 seconds

y = [tex]\frac{35\pi \pi }{60}[/tex]

y = [tex]\frac{7\pi }{12}[/tex]

Now using the pythagorean :

[tex]x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2[/tex]

derivate the equation so  we get :

[tex]x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\[/tex][tex]165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}[/tex]

[tex]\frac{dz}{dt} =25.387[/tex] m/s

So Rate of change = 25.387 m/s

Answer:

He paid $6,000 in taxes.

Step-by-step explanation:

His final amount after taxes is $24000.  In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%).  In other words if he was taxed 20% he took home 80% of what he was paid.  Therefore mathematically we have:

[tex]0.8A_{pre-tax}=A_{taxed}[/tex]

Since we know he was left with $24000 after taxes then:

[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]

So originally he had $30,000.  So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:

$30,000 - $24,000= $6,000 taxed

To solve for the number of zeros in the product of (6x5) x 10³, one should first multiply the whole numbers (6x5) to get 30. Then, append as many zeros as the power of 10, which in this case is 3. So, we append three 0's to 30 which yields 30000. This gives us four zeros in total.

The problem (6x5) x 10³ refers to a multiplication involving whole numbers and a power of ten. Our task is to find out how many zeros will be in the resulting product.

Step 1: Multiply the whole numbers. 6x5 equals 30.

Step 2: When multiplying by a power of ten, you add as many zeros to the end of the number as there are in the exponent of ten. So, in this case, as it is power of ten to the power of 3 (10³), we would add three 0's.

Final result: 30000.

So, the product (6x5) x 10³ will have four zeros.

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there are 60 minutes in 1 hr.

every 10 minutes the factory makes 15 bears.

so 10+10+10+10+10+10 is 1 hr, and is really 15+15+15+15+15+15 bears, namely 90 per hour.

every day, the factory does that for 8 hours straight, so namely they make 90 * 8 teddy bears, or 720 per day.

let's make a table of bears per day

1 day............................... 720(1)

2 days............................ 720(2)

3 days............................ 720(3)

4 days............................ 720(4)

x days............................ 720(x)

so the amount of bears they make say "A" is per day is A = 720x.

what would be the fewest days to make 5000?

well, whatever 720x is, it has to be either 5000 exactly OR more, not less, then

5000 ⩽ 720x.

and dividing both sides by 720 we get about 6.94 ⩽ x.

so we can conclude that whole days, it'll be 7, since 6.94 is about 7 days, but rounded up to whole days it'll be 7 days.

Answer:

[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]

Step-by-step explanation:

This question demands that we convert from a degree measure to a radian measure.

To convert from a degree measure to radians, multiply by [tex]\frac{\pi}{180\degree}[/tex].

That is [tex]-135\degree=-135\degree \times \frac{\pi}{180\degree}[/tex].

This can be simplified by canceling out the common factors to get,

[tex]-135\degree=-3\times45\degree \times \frac{\pi}{4\times 45\degree}[/tex].

This will give us,

[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]

Answer:

- 3pi over 4

Step-by-step explanation:

I would say B. The mean is a good measure of central tendency.

I hope this helps!

Answer:

x = .140741

Step-by-step explanation:

0.7(3x−0.2)=0.3(0.8−2x)

Distribute

.7 * 3x - .7*.2 = .3*.8 - .3 * 2x

2.1x - .14 = .24 - .6x

Add .6x to each side

2.1x +.6x -.14 = .24 -.6x+.6x

2.7x -.14 = .24

Add .14 to each side

2.7x -.14+.14 = .24+.14

2.7x = .38

Divide by 2.7 on each side

2.7x/2.7 = .38/2.7

x = .140741

Answer:

The given sequence is neither arithmetic not geometric.

Step-by-step explanation:

A sequence is in arithmetic if it has a common difference.

i.e., a sequence a, b, c is in arithmetic if

b - a = c - b

Let's check if the given sequence is in arithmetic.

[tex]\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}[/tex]

[tex]= \frac{8}{9}[/tex]

[tex]4-\frac{4}{3} =\frac{12-4}{3}[/tex]

[tex]=\frac{8}{3}[/tex]

So, [tex]\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}[/tex]

Hence, the given sequence is not arithmetic.

Let's check if the given sequence is in geometric.

A sequence is in geometric if it has a common ratio.

i.e., a sequence a, b, c is in geometric if

[tex]\frac{b}{a} =\frac{c}{b}[/tex]

[tex]\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )[/tex]

= 3

[tex]\frac{4}{4/3} =4(\frac{3}{4} )[/tex]

= 3

Clearly, [tex]\frac{12}{4} =\frac{36}{12} =3[/tex]

But, [tex]\frac{0}{36} =0[/tex]

Therefore, the given sequence is not in geometric.

Hence, the given sequence is neither arithmetic not geometric.

[tex]-\dfrac{1}{2}x+4=x+1\qquad\text{multiply both sides by 2}\\\\-x+8=2x+2\qquad\text{subtract 8 from both sides}\\\\-x=2x-6\qquad\text{subtract 2x from both sides}\\\\-3x=-6\qquad\text{divide both sides by (-3)}\\\\\boxed{x=2}[/tex]

Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.

The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.

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Answer: -2,0,2,4,6

The solution of the inequality is x<1

Step-by-step explanation:

Answer:

x < 1

Step-by-step explanation:

2x < 2

Divide 2 on both sides

x < 1

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

Table: (I think)

-2 , 0 , 2 , 4 , 6

Answer: The length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]

Step-by-step explanation:

Since we have given that

Ratio of width to length of the united states flag is 10:19

So, Let the length of the united states flag be 10x

Let the width of the united states flag is 19x

As we have the width of the flag of Emerson's school = 4 feet.

According to question,

[tex]19x=4\\\\x=\frac{4}{19}[/tex]

So, our length of the united states flag will be

[tex]10x=10\times \frac{4}{19}\\\\=\frac{40}{19}\\\\=2\frac{2}{19}\ feet[/tex]

Hence, the length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]

Final answer:

To find the length of the flag, you can set up a proportion using the given ratio of width to length. Solve for the unknown length by cross-multiplying and dividing. The length in feet is found by multiplying the width of Emerson's School flag by the ratio and dividing by 10.

Explanation:

To find the length of the United States flag, you can set up a proportion using the given ratio of width to length. The ratio is 10:19, and the width of Emerson's School flag is 4 ft. First, write the proportion using the length as the unknown value: 10/19 = 4/L. To solve for L, cross-multiply and divide: 10L = 4 * 19. Divide both sides by 10 to find the length:

L = (4 * 19) / 10.

Multiply 4 and 19, then divide by 10 to get the length in feet.

L= 7.6

Answer:

She gave away 24 cards

Step-by-step explanation:

(36)*([tex]\frac{2}{3}[/tex])=24

use both points to find the slope

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-13-3}{9-(-3)}[/tex]

[tex]\frac{-16}{12} =\frac{-4}{3} =slope[/tex]

Now, to find b, plug in one of the points in y=mx+b

3=[tex]\frac{-4}{3}[/tex](-3)+b

3=4+b

b= -1

therefore, your final equation should be,

y=[tex]\frac{-4}{3}[/tex]x-1

Answer:

D) x ≤ -2

Step-by-step explanation:

The dot is at -2 = -2

the dot is filled in = ≤ or ≥ because its means equal too

think of ≤ or ≥ like arrows = it points left.  

so its x ≤ -2

Note on using the  ≤ or ≥  like pointing arrows

this only works if its written:

variable <   constant form,

which is the way they are usually seen, like x < 5

but it could be 5 > x which means the > points the opposite way

Hello! :)

Answer:

D. x≤-2

*The answer must have a negative sign and less than or equal to.*

Step-by-step explanation:

Lesson: It's about the graphing inequalities

An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).

The arrow points to the left. The circle is closed.

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thanks!

Answer:

The answer is $3277.48

Step-by-step explanation:

An Annual Percentage Rate or APR is calculated by taking into account the interest rate on a credit card (or another borrowed sum) and any other charges such as an annual fee or arrangement fee.

So the first step here is to calculate the 3.5% cash advance fee on cash advance of $2790.00.

$2790.00 × 3.5%

2790 × (3.5 ÷ 100)

2790 × 0.035

$97.65

Now APR is calculated on the sum of cash advance and cash advance fee, i.e.,

13.5% × (2790 + 97.65)

13.5% × 2887.65

( 13.5 ÷ 100 ) × 2887.65

0.135 × 2887.65

$389.83

The total amount due at the end of the month is sum of Cash advance, Cash advance fee and APR

$2790 + $97.65 +$389.83 = $3277.48

3.277.48

this a a short answear

Answer: The answer is 12 days

Step-by-step explanation: miles total=miles per day times number of days

3000=250 times days

divide both sides by 250

12=days

The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex]  is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.

Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.

Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]

This demonstrates that the original formula you asked about is accurate.

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Answer:

B

Step-by-step explanation:

For a relationship to be a function

Each value of x in the domain can only have 1 unique value of y in the range. That is, one-to-one correspondence.

The only relation which meets this criteria is B

Answer:

The answer is option B: {(1,3);(-1,5);(2,7);(-2,7);(3,5);(-3,3)}

Step-by-step explanation:

Each element is composed of a first and second point, or by an 'x' and 'y' coordinates, respectively.  In this way, all x coordinate from the set of elements constitute the 'domain', and all y coordinates of the set of elements constitute the 'image'.

So, for a set of elements be a function, each point of the domain have to have one an only one image. In other words, two elements with the same image have to have a distinct x's coordinate.

If we take a look at the set of elements in the different options, we find different elements which repeat image:

1) The pairs (1,0) and (1,-1) in the set of point of option A

2) The pairs (-2,-1) and (-2,-2) in the set of point of option C

3) The pairs (1,3) and (1,3) in the set of point of option  

In the set of elements of B option, all the elements with the same y coordinate have different x's coordinates.

30/2 =15. So 182 times 15 is 2730, or D.

Answer: The statement is false because 1.2 is calculating 120% of the cost of pizza. The expression should be .2p.

Step-by-step explanation:

The expression 1.2p correctly represents the total bill for a pizza including a 20% tip, with p representing the price of the pizza. To determine the total cost, you multiply the price by 1.20.

The expression 1.2p does indeed represent the total bill including a 20% tip for the delivery of a pizza where p is the cost of the pizza. When you give a tip of 20%, you are adding 20% of the cost of the pizza to the original price. This is calculated by multiplying the price by 1.20 (which is equivalent to 100% + 20%).

Example Calculation:

If the cost of the pizza is $10 (p = $10), then the total bill with a tip would be 1.2 × $10 = $12. The 20% tip on $10 is $2, so the total bill equals $10 + $2 = $12.

The distributive property: a(b + c) = ab + ac

Answer:

c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)

Step-by-step explanation:

I don't know if this is the equation you need. But here it is.

Y - 4 = -2 (x + 1)

Answer:

Step-by-step explanation:

35 x .08 = $2.80

35 + 2.80 = 37.80

Answer:

T = 0.08 × 35

Step-by-step explanation:

The cost of a jacket = $35

The tax rate on the jacket = 8% =  [tex]\frac{8}{100}[/tex]

                                           = 0.08

The expression to find the cost of the tax on the jacket would be

T = 0.08 × 35

Answer:

You are correct

Step-by-step explanation:

Start with 1 1/2. This can be made into an improper fraction which is 3/2

Now multiply both top and bottom of 3/2 by 5

(3*5)/(2 * 5) = 15 / 10

16/10 is just slightly bigger than 15/10

The fraction is grather than 1 if the numerator is greater than denominator.

The fraction is less than 1 if the numerator is less than denominator.

The fraction is equal 1 if the numerator is equal the denominator.

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[tex]a.\ \text{greater than 1:}\ \dfrac{4}{3},\ \dfrac{7}{5};\ \dfrac{16}{10}\\\\b.\ \text{less than 1:}\ \dfrac{1}{3};\ \dfrac{12}{15};\ \dfrac{3}{10};\ \dfrac{3}{5}\\\\c.\ \text{equal to 1:}\ \dfrac{3}{3}[/tex]

[tex]\dfrac{16}{10}=\dfrac{10+6}{10}=\dfrac{10}{10}+\dfrac{6}{10}=1+\dfrac{6}{10}=1\dfrac{6}{10}=1\dfrac{6:2}{10:2}=1\dfrac{3}{5}\\\\3\text{ is greater than half of 5.}\ \text{Therefore}\ \dfrac{3}{5}>\dfrac{1}{2}.\\\\\text{Therefore}\ \dfrac{16}{10}>1\dfrac{1}{2}.\\\\OTHER:\\\\\dfrac{16}{10}=1\dfrac{6}{10}\\\\1\dfrac{1}{2}=1\dfrac{1\cdot5}{2\cdot5}=1\dfrac{5}{10}<1\dfrac{6}{10}\\\\OTHER\\\\\dfrac{16}{10}=1\dfrac{6}{10}=1.6\\\\1\dfrac{1}{2}=1.5\\\\1.6>1.5\Rightarrow\dfrac{16}{10}>1\dfrac{1}{2}[/tex]