Suppose an airplane climbs 15 feet up for every 40 feet it moves forward. What is the slope of this airplanes ascent?

Answer:

x=0.73

Step-by-step explanation:

(+16) 2x^2+12x-16= -3(+16)

2x^2+12x=13/12

2x^2= 1.08/2

x^2=.54

sqrt x^2=.54

x=0.73

Answer:

[tex]x_1=-6.9\\x_2=0.9[/tex]

Step-by-step explanation:

The first step is to move all the terms from the right side to the left side of the equation and then add the like terms:

[tex]2x^2+12x-16=-3\\\\2x^2+12x-16+3=0\\\\2x^2+12x-13=0[/tex]

Now we can apply the Quadratic formula. This is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case we can identify that:

[tex]a=2\\b=12\\c=-13[/tex]

Finally, we must substitute these values into the Quadratic formula. Then we get:

[tex]x=\frac{-12\±\sqrt{((12)^2-4(2)(-13)}}{2(2)}[/tex]

[tex]x_1=-6.9\\x_2=0.9[/tex]

Answer: 28.27

Step-by-step explanation:

A=3.14r^2

A=3.14•3^2

A=3.14•9

A=28.27

Answer: a = 28.3 m²

Step-by-step explanation:

a = πr²

a = π3²

a = 28.3 m²

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Answer:

[-2, ⅑], [-1, ⅓], [0, 1], [1, 3], [2, 9]...

Step-by-step explanation:

You are simply creating an x-y value value chart and simply plugging in integers for "x" to get your "y".

Answer:

This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.

The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:

Case 1: c=2.

Hence we get

a(a+b)=122=2×61

Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.

Case 2: c≠2.

Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have

a(a+2)=120+c

Adding one to each side and factorising shows

(a+1)2=121+c

from which

c=(a+12)(a−10)

(if you are confused about this step think about difference of two squares factorisations).

But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.

Step-by-step explanation:

Answer:

1978

Step-by-step explanation:

This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.

The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:

Case 1: c=2.

Hence we get

a(a+b)=122=2×61

Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.

Case 2: c≠2.

Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have

a(a+2)=120+c

Adding one to each side and factorising shows

(a+1)2=121+c

from which

c=(a+12)(a−10)

(if you are confused about this step think about difference of two squares factorisations).

But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.

Answer:

9.47

Step-by-step explanation:

Answer:

f(-2)=3

Step-by-step explanation:

we know that

f(-2) is the value of the function f(x) for the value of x equal to -2

so

Observing the graph

For x=-2

f(-2)=3

The result is found by substituting -2 into the equation of the function. Using the provided line of best fit equation, we find f(-2) to be approximately -3207.324, but this is just an approximation.

To find f(-2) using the given equations, we first identify the equation associated with the given function, which in this case, is not explicitly provided in the given information. By convention, the general format for a linear function is y=f(x). The value is found by substituting the value of x into the equation and solving for y.

However, since the equation of the function isn't provided but we have details about the line of best fit, we could use that if it closely represents the graph of our function. In the case of the line of best fit given as ŷ = −3204 + 1.662x, we simply plug in -2 for x:

ŷ = -3204 + 1.662*(-2) = -3204 - 3.324 = -3207.324

So, if we were using this line of best fit as a representation for our function f(x), then f(-2) would be approximately -3207.324. Always remember though, that the line of best fit is an approximation and the real value might slightly differ based on the actual function.

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Answer:

5.545

Step-by-step explanation:

place them in order

3.44, 5.0, 6.09, 8.74

since there are four numbers you add the middle two together and divide in half.

5.545

Median means middle. You must find the middle of this set of data. To do this you must first order the data from least to greatest:

3.44, 5.0, 6.09, 8.74

Now on each "level" remove the largest and the smallest number until you get to the middle number(s)

3.44, 5.0, 6.09, 8.74

         5.0, 6.09

Since there isn't exactly one number in the middle you must take the mean (average) of the two numbers left. To do this you must add the remaining numbers, 5.0 and 6.09, together then divide by 2

5.0 + 6.09 = 11.09

11.09 ÷ 2 = 5.545

The mean of this data set is 5.545

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

hypotenuse is always opposite the right angle and it is always the longest side of the triangle

Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c² example 3, 4, 5).

volume occupies a three dimensional space. Distance is measured in one unit of length

Step-by-step explanation:

Answer:

y = -2x + 3

Step-by-step explanation:

The three is the y-intercept, so when x=0, y will equal 3. (0,3)

The slope is negative (-2x), because the minus is present infront of x. So the line's going down.

And we can confirm that it's the function

y = -2x + 3 by letting one point in the line from the graph enter the function.

For example (1,1)

1 = -2x + 3. (let y = 1.)

1 = -2(1) + 3 (let x = 1)

1 = 1

so we can see when we let 1 = -2(1) + 3 it equals the y value on the line.

Answer:

Step-by-step explanation:

y= -2x + 3

Answer:

There is no number when substituted for x that will make the statement true.

Step-by-step explanation:

First you would simplify the left side:

6x + 8x= 14x

14x=10x

This statement isnt true no matter what you plug in the sides will never be equal

Answer: If you substitute the number 2 for x in the problem, you’ll make it true.

6x + 8x = 10x

62 + 82 = 102

36 + 64 = 100

100 = 100

Step-by-step explanation

pennfoster

Not enough information, please attach a photo next time.

Answer:

3:1

Step-by-step explanation:

The probability of winning is

P(win) = 1/4 = winning/ total

1 win

4 total

total - wins = losses

4-1 = 3

There are 3 losses

To find the odds against winning is finding the odds of losing

We need to compare losing to not losing

3:1

Answer:

-51a^7

Step-by-step explanation:

-26a^7+(-25a^7) may be re-written as a^7(-26 - 25), or -51a^7

1 represents they are scheduled to work the 9am-3pm shift

2 represents they are scheduled to work the 3pm - 9pm shift

0 represents they are not scheduled to work that day

[tex]\begin{array}{c||c|c|c|c|c|c|c}&Mon&Tue&Wed&Thu&Fri&Sat&Sun\\Employee\ 1&1&1&1&1&0&0&1\\Employee\ 2&0&2&2&2&2&2&0\\Employee\ 3&2&0&0&0&1&1&2\end{array}[/tex]

Employees 1 & 2 will work 30 hours and have 2 days off in a row

Employee 3 will work 24 hours and have 3 days off in a row

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]lef=12ft,\ leg=35ft,\ hypotenuse=AB[/tex]

Substitute:

[tex]AB^2=12^2+35^2\\\\AB^2=144+1225\\\\AB^2=1369\to AB=\sqrt{1369}\\\\AB=37[/tex]

Answer:

8 candy bars

Step-by-step explanation:

Transform the question to an equation:

3 + 2x = 19

Solve:

2x = 16

x = 8

Check the answer:

3 + 2 (8) = 19

3 + 16 = 19

True

Hello There!

A magazine costs $3 and some candy bars. Let’s represent the number of candy bars as “X”

19-3=16 so that’s how much money is spent on candy bars.

If $16 is spent on candy bars then 8 candy bars were bought.

Answer:

532

Step-by-step explanation:

To make the right hand side as large as possible, the numerator must be as large as possible and the denominator must be as small as possible.  But we can only use each digit once.

Through trial and error:

(9 × 8 + 4) / (1 − 6 ÷ 7) = 532

532 is the largest possible three digit that can be obtained on the right side of equation.

What is PEMDAS?

PEMDAS is short form of parentheses, exponents, multiplication , division, addition and subtraction.

To get the the largest possible three digit from given condition, we have to make the denominator as small as possible by using subtraction and division. And we can increase the numerator.

Now, through trial and error method

we have (9 * 8 + 4) / ( 1 - 6 / 7 ) = 76 * 7 = 532

Hence 532 is the largest possible three digit that can be obtained on the right side of equation.

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Answer:

d) 6

Step-by-step explanation:

you multiply 3 by 6 because the reciprocal of 1/6 is 6/1

Answer: Last option.

Step-by-step explanation:

When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.

To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.

Then, the reciprocal of the fraction [tex]\frac{1}{6}[/tex] is:

 [tex]\frac{6}{1}=6[/tex]

Therefore, you can find the quotient of [tex]3[/tex]÷[tex]\frac{1}{6}[/tex]  by multiplying 3 by 6:

[tex]3[/tex]÷[tex]\frac{1}{6}=3*6=18[/tex]

Answer:

Inverse property of addition.

Check the picture below.

The measure of XZ is 72

A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.

Given

θ = arc / 2

36 = arc/2

XZ= [tex]36*2[/tex]= 72

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Answer:

P(A given B) = 3/4

Step-by-step explanation:

As we know that it is conditional probability, where the probability of an event depends on the event that has certain probability of occurrence.

The formula for conditional probability is:

P(A given B) = P(A ∩B) / P(B)

Where a and B are events. The probability of event B is known and we also know probability of A∩B

So, putting the values in the formula:

[tex]P(A\ given\ B) = \frac{P(A and B)}{P(B)}\\= \frac{\frac{3}{10} }{\frac{2}{5} } \\=\frac{3}{10} *\frac{5}{2}\\=\frac{3}{4}[/tex]

So, the probability of A given B is 3/4 ..

Answer:

30:48

Step-by-step explanation:

because 30 divides into 10 and 48 divides into 16

Answer:

Option A is correct

30 to 48

Step-by-step explanation:

Given the ratio:

10 : 16

We have to find the ratios are equivalent to 10:16.

Option A.

30 to 48

⇒[tex]\frac{30}{48}[/tex]

Divide numerator and denominator by 3 we have;

⇒[tex]\frac{10}{16}[/tex]

Option B.

25:35

⇒[tex]\frac{25}{35}[/tex]

Divide numerator and denominator by 5 we have;

⇒[tex]\frac{5}{7}[/tex]

or

5 : 7

Option C:

8 : 32

⇒1 : 4

Option D:

5 to 15

⇒[tex]\frac{5}{15}[/tex]

Divide numerator and denominator by 5 we have;

⇒[tex]\frac{1}{3}[/tex]

or

1 : 3

Therefore, the ratio equivalent to 10:16 is, 30 to 48.

Answer:

The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared

Let

z ----> the scale factor

In this problem

z=2

therefore

z²=2²=4

The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism

Answer:

The surface area of the larger prism is 4 times the surface area of the smaller prism.

Step-by-step explanation:

Was right on edge

Answer:

Factors of the constant term

Step-by-step explanation:

A polynomial, P, has a leading coefficient of 1 and a constant term. The rational roots of P are all factors of the constant term.

The correct option is (2).

The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.

Given statement is:

A polynomial, P, has a leading coefficient of one and a constant term. The rational roots of P are all

We know by Rational Zeros Theorem states:

If P(x) is a polynomial with integer coefficients and if is a zero of P(x)

(P( ) = 0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

So, from the above statement it is clear that p is a factor of the constant term.

Hence,  The rational roots of P are all factors of the constant term.

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Step-by-step answer:

Percentage difference = (new value-old value)/old value*100%

=(56-45)/45*100%

=11/45%100%

= 24.4%

Answer: 24

Step-by-step explanation:

its just 24 have the same question ^^

Answer:

D. 1.25

Step-by-step explanation:

The values of the correlation coefficient must be between -1 and 1 (they can include -1 and 1)

The only value outside that range is 1.25

1.25 is not a possible correlation coefficient

Answer:

1648 are boys.

Step-by-step explanation:

You divide the 3708 by 9 and get 412. Then you multiply that by 4 and get 1648

To find how many boys are in the school, first calculate the number of girls by multiplying the total students, 3708, by 5/9, resulting in 2060 girls. Subtracting this from the total gives 1648 boys.

The question asks how many students are boys in a school if 5/9 of the students are girls, and the total number of students is 3708. To solve this, first, we need to calculate the number of girls by multiplying the total number of students (3708) by 5/9. Then, to find the number of boys, we subtract the number of girls from the total number of students.

Therefore, there are 1648 boys in the school.

Answer:

The pair of sneakers cost 80 dollars.

The sweatshirt costs 40 dollars.

Step-by-step explanation:

Let x represent the pair of sneakers

Let y represent the sweatshirt

x + y = 120

The sweatshirt costs one-half the price of sneakers, which is represented by:

y = 1/2(x)

Use the substitution method

x + y = 120

x + 1/2(x) = 120

Multiply the equation by 2

2x + x = 240

3x = 240

x = 80

The cost of the sneakers is 80 dollars

To determine the cost of the sweatshirt subtract 120 by 80/

120 - 80 = 40

The cost of the sweatshirt is 40 dollars