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What does how many hours did he rent the bike for?




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We can transform the mathematical sentence into the equation:

(2/3)*x - (2*y)^2 = 43

Here we have the sentence:

" Two thirds of a number decreased by the product of a number and two, squared, is 43"

First, we can define x as "the number"

Then:

" Two thirds of a number..." is:

(2/3)*x

Now we add the next part:

"... decreased by the product of a number and two, squared, is 43"

Assuming that this is another number, let's call it y, we have:

(2/3)*x - (2*y)^2 = 43

This is our two-variable equation.

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Answer:

The number of solutions is equal to the highest power exponent.

That is a cubic equation, so it has 3 solutions.

Step-by-step explanation:

Answer: A linear system of two equations with two variables is any system that can be written in the form. ... A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time. For the example above x=2 and y=−1 is a solution to the system

Step-by-step explanation:

The two joggers who are 21 miles apart travel at a speed 8 mph and 6 mph respectively and would meet after one and half hours.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let a represent the speed of the faster jogger and represent the speed of the other jogger. Hence:

a = b + 2 (1)

Also:

In one and half hour (1.5 h):

a = d₁/1.5

d₁ = 1.5a

b = d₂/1.5

d₂ = 1.5b

d₁+ d₂ = 21

1.5a + 1.5b = 21   (2)

From both equation 1 and 2:

a = 8, b = 6

The speed of the joggers is 8 mph and 6 mph respectively.

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Answer:

9.75$

Step-by-step explanation:

Answer:

9.75$

Step-by-step explanation:

The original price of the shirt is $15, and it's on sale for 35% off. What is the item's sale price?

First, convert the 35% to a real mathematical number. For percents, this is always done by dividing the 35% by 100%, or 35% / 100% = 0.350.

Second, find out what 35% of $15 is. This is the amount of the sale discount. This is always found by multiplying 0.350 by the item's cost $15, like this:

0.350 x $15 = $ 5.25.

So for this sale, you'll save $ 5.25 on this item.

This means, the cost of the item to you is

$15 - $ 5.25 = $ 9.75.

hello

30/42 = x /49

42 x = 1 470

x =  35

30 /42 =  40/ 40 + y

30 y + 1200 = 1 680

30 y = 1 680 - 1 200

30 y = 480

y =  16

Answer:

x = 35

y = 16

Step-by-step explanation:

Both the triangles are similar by AA test of similarity.

[tex] \implies \: \frac{30}{30 + 12} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{30}{42} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{5}{7} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{5}{7} = \frac{x}{49} \\ \\ \implies \: x = \frac{5 \times 49}{7} \\ \\ \implies \huge \red {\boxed{ \: x = 35}}\\ \\ \implies \: \frac{5}{7} = \frac{40}{40 + y} \\ \\ 5(40 + y) = 280 \\ \\ \implies \: 200 + 5y = 280 \\ \\ \implies \: 5y = 280 - 200 \\ \\ \implies \: 5y = 80 \\ \\ \implies \: y = \frac{80}{5} \\ \\ \implies \: \huge { \orange{ \boxed{ y = 16}}}[/tex]

[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and  [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]

In this question we must prove that a given parallelogram is a rhombus. A rhombus is quadrilateral with four sides of equal length and two pairs of angles of equal measure, different to each other. We must demonstrate that [tex]\overline {QR} \cong \overline {RS}[/tex] and [tex]m\angle R \neq 90^{\circ}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex] and [tex]m\angle R \neq 180^{\circ}[/tex] by geometric and algebraic definitions and theorems:

[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and  [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]

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Answer:

200*20

÷100 ,=100+56

29+63

Step-by-step explanation:

200×20 =40000

40000÷100 =

100

Answer:

Go with anything, and I mean ANYTHING that is in a numerical order with an outlier

LITERALLY 1,2,3,4,5,6,7,8,9,100

you will get a median of 5.5 but with the high outlier, you will get a mean of 14.5

Answer:

185 children and 35 adults

Step-by-step explanation:

first equation: 6x+4y=1250

second equation: x+y=220

work:

6x+4y=1250 (-1)

x+y=220 (6) we eliminate x, that's why I multiply each term by 6 and -1

-6x-4y=-1250

6x+6y=1320

2y=70

2y/2=70/2

y=35 (I used y for adults)

x+35=220

x=220-35

x=185 (and I used x for children)

hope this helps you^^

Answer:

3.125 U.S. cups

take how many cups are in one ounce and multiply it.

Answer:  5 + 3x ≤ 20;  5

Step-by-step explanation:

at most means not more than(less or equal to),which use the symbol ≤. Let x be the hour that Max rent.

5 + 3x ≤ 20

     3x ≤ 15  [Subtract 5 from both sides.]

       x ≤ 5    [Divide 3 from both sides.]

Any value less than or equal to 5 will be satisfies the inequality.

Answer:

x = - 3

Step-by-step explanation:

given a parabola in standard form y = ax² + bx + c (a ≠ 0 )

then the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 6x - 9 ← is in standard form

with a = 1, b = 6 , then the equation of the axis of symmetry is

x = - [tex]\frac{6}{2}[/tex] = - 3 , that is x = - 3

Answer:

14

Step-by-step explanation:

3x-8y

(3*10)-(8*2)

30-16

14

Answer:

30-16

Step-by-step explanation:

Answer: The Egyptians, Babylonians, and Archimedes.

Step-by-step explanation: The Egyptians and Babylonians were the first known civilizations to use pi.  At the time, Egyptians devised the approximated value of pi as 3.1605.  Archimedes, however, did the first calculation of pi, with its approximate value of 3.141592 or 3.14 to make it shorter.  

Hopefully, this helps you!

Answer:

3.1

Step-by-step explanation:

When you round to the nearest tenth 4.35 is 4.4 and 1.27 is 1.3

Answer: 3.1

Step-by-step explanation: Round 4.35 and you get 4.4 round 1.27 you get 1.3 subtract them and you get 3.1

Answer:

0

Step-by-step explanation:

He loses it all in 2 hours

Answer:

-25 million

Step-by-step explanation:

Because after 2 hours you will lose all of your money and continue to go down into the negatives.

Answer:

87.50

Step-by-step explanation:

75,000 x 28% ÷ 12

She will budget $225 for her emergency savings for the month of March

We have:

Gross = $75,000 per year.

Payroll deductions = 28%

So, the net pay is:

Net = (1 - 28%) * $75,000

Evaluate

Net = $54000

The net income per month is:

Monthly = $54000/12

Evaluate

Monthly = $4500

5% of her net income goes to emergency.

So, we have:

Emergency = 5% * $4500

Evaluate

Emergency = $225

Hence, she will budget $225 for her emergency savings for the month of March

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Answer:

Step-by-step explanation:

Letter Grade Percentage Points Level

A+ 95-100                         4.00  Exceptional

A 90 to less than 95          3.75          Excellent

B+ 85 to less than 90          3.50    Superior

B 80 to less than 85          3.00     Very Good

C+ 75 to less than 80          2.50     Above Average

C 70 to less than 75          2.00      Good

D+​​ 65 to less than 70           1.50       High-Pass

D​ 60 to less than 65           1.00        Pass

F Less than 60                   0.00         Fail

Answer:

The answer is congruent

Answer:

10 pages

Step-by-step explanation:

386/42=9.1 pages

but you can not have .1 of a page so you add another page.

Answer:

2/3 or -5 is correct for all future users.

Step-by-step explanation:

The roots of the quadratic equations or the values of x are -5 and 2/3.

A quadratic equation is an algebraic equation of degree two. An algebraic equation of degree n has exactly n number of roots.

Given a quadratic equation 3x² + 13x = 10 which can be written as,

3x² + 13x - 10 = 0.

Now two numbers that add to 13 and multiplied to -30 are 15 and - 2.

3x² + 15x - 2x - 10 = 0.

3x(x + 5) - 2(x + 5) = 0.

(x+5)(3x-2) = 0.

x + 5 = 0 OR 3x -2 = 0.

x = -5 OR x = 2/3.

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Answer:

C

Step-by-step explanation:

The correct option is C because lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.

Pls rate.........

A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

A lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.

A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.

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The specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

If a polynomial p(x) can be written as:

[tex]p(x) = [f(x)]^2[/tex]

where f(x) is also a polynomial, then p(x) is called as perfect square polynomial

For the considered case, the polynomial specified is;

[tex]g(x) = 40x + 4x^2[/tex]

[tex]g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\[/tex]

Thus, the vertex form of the considered polynomial is [tex]g(x) = 4(x+5)^2 - 100[/tex]

Standard form of a quadratic polynomial is [tex]ax^2 + bx + c[/tex]

Thus, we get: the considered polynomial in standard form as:

[tex]g(x) = 4x^2 +40x[/tex]

[tex]g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)[/tex]

The considered polynomial has only two terms, therefore, its not a trinomial.

Thus,  the specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]

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Answer:

g(x)=4(x+5)^2-100

Step-by-step explanation:

Have the day you deserve :)