Logan can read at a rate of 2/3 page per minute. At that rate, how many pages can he read in 2 hours?

Let [tex]x[/tex] be the length of the shorter leg.

The other leg is 1m longer, so its length is [tex]x+1[/tex]

The hypothenuse is 9m longer, so its length is [tex]x+9[/tex]

The pythagorean theorem states that the sum of the squares of the legs is the square of the hypothenuse, so we have

[tex]x^2+(x+1)^2=(x+9)^2[/tex]

Expanding the squares gives

[tex]x^2+x^2+2x+1=x^2+18x+81[/tex]

Move all to the left hand side:

[tex]x^2-16x-80=0[/tex]

This equation has solutions [tex]x=-4[/tex] and [tex]x=20[/tex]

We can't accept the first solution, because it would lead to the side lengths

[tex]x=-4,\quad x+1=-3,\quad x+9=5[/tex]

And we can't have negative side lengths.

The other solution is fine, because it leads to the side lengths

[tex]x=20,\quad x+1=21,\quad x+9=29[/tex]

So, the side lengths are 20 (shorter leg), 21 (longer leg), 29 (hypothenuse)

Answer:

20 m , 21 m and 29 m.

Step-by-step explanation:

Let the length of the shorter leg be x m. Then the longer leg = x + 1 m and the hypotenuse =  x + 9 m. So, by Pythagoras:

(x + 9)^2 = x^2 + (x + 1)^2

x^2 + 18x + 81  = x^2 + x^2 + 2x + 1

18x + 81 = x^2 + 2x + 1

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

x = 20, -4  (as we are dealing with lengths of sides we ignore the negative root).

So the sides have length 20, 21 and 29 (answer).

25 I think I hope I’m right

.5 and 4 I think there should be a abcd questions

Answer:

(7.5, 1.2) and (7.5, –2.3)

Step-by-step explanation:

Hope this helps

Answer:

Because we knew that the function rule for the input/output table is to multiply by 6, just multiply 7 by 6 and we get y = 42

For the second question, we also knew that the function rule for the input/output table is to divide by 3, just divide 6 by 3 and we get y = 2

Since we already knew that the charge for downloading a movie is $3, then we can also predict that x is number of movies downloaded, and the total fee for downloading x movies should be 3x, plus the monthly fee, we have the equation: y = 3x + 6.50

*I could be wrong though

I think your correct answer is C. Please don’t be mad if I am wrong!❤️❤️

Answer: n divided by 43

Step-by-step explanation: You always take the last number of the equation and divide it by the answer and you should get the first number.

Circumference = diameter x PI

Circumference = 3.14 x 68 yards = 213.52 yards.

Area = PI x r^2

r = 1/2 the diameter = 1/2 x 68 = 34 yards.

Area = 3.14 x 34^2 = 3.14 x 1156 = 3629.84 yards^2

ANSWER

D) sin Y

EXPLANATION

The given triangle is a right triangle.

This implies that that:

[tex]x + y = 90 \degree[/tex]

Then we have

[tex]y= 90 - x[/tex]

Recall that

[tex] \cos(x) = \sin(90 - x) [/tex]

But

[tex]90 - x = y[/tex]

When we do the substitution, we get,

[tex] \cos(x) = \sin(y) [/tex]

Therefore cos(x) is a equivalent to sin(y).

The correct answer is D.

Answer:

-5cd

Step-by-step explanation:

-3cd-d(2c-4)-4d

Distribute the -d

-3cd-d2c-+d4-4d

-3cd -2cd +4d-4d

Combine like terms

-5cd

Answer:

4z-(3z) z

Step-by-step explanation:

I hope that helps

Answer:

Step-by-step explanation:First of all you don't have anything to solve and the formal of a rhombus is base times height.

Okay so like maybe next time try to include a picture so we can see it, because we cant solve anything

the answer would be 36

Answer:

36

Step-by-step explanation:

Cross a number out once on each side. That is, cross out 10 and 78, then 15 and 56, on and on until you get the last number that isn't crossed out. In this case, 36.

Answer: Option B

[tex]y = 0.75cos(2\phi)[/tex]

Step-by-step explanation:

The general cosine function has the following form  

[tex]y = Acos(b\phi) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum value of y is is 0.75 and the minimum is -0.75. Then the amplitude A is:  

[tex]A =\frac{0.75-(-0.75)}{2}\\\\A= 0.75[/tex]

Then [tex]k=0[/tex]

The cycle is repeated every [tex]\pi[/tex] units  

So the period is [tex]\pi[/tex]

Thus:

[tex]\frac{2\pi}{b}=\pi\\\\ b=\frac{2\pi}{\pi}\\\\ b=2[/tex]

The function is:

[tex]y = 0.75cos(2\phi)[/tex]

when [tex]\phi=0[/tex] y is maximum therefore [tex]y=0.75[/tex] As shown in the graph

Answer:

8

Step-by-step explanation:

hypotenuse = c = 17 feet

Height = a = 9 feet + 6 feet = 15 feet

Children's space = b

a^2 + b^2 = c^2

15^2 + b^2 = 17^2

225 + b^2 = 289                   Subtract 225 from both sides

225-225+b^2=289-225

b^2 = 64                                 Take the square root of both sides.

sqrt(b^2) = sqrt(64)

b = 8

Since each child takes up 1 foot, 8 children can sit on side b.  

Answer:

[tex]2x^3-3x^2-4x+3[/tex]

Step-by-step explanation:

Use FOILing to get the answer.  Distribute x into 2x^2, to get 2x^3, then into x to get - x^2, then into -3 to get -3x.  Then distribute the -1 into the 2x^2 to get -2x^2, then into the x to get -x, then into the -3 to get 3.  Combine like terms to get the solution above.

Answer:

2x^3-x^2-4x+3

Step-by-step explanation:

Answer:

1. Area of the land which can be ploughed daily is 50 hectares (and 70 hectares at higher rate)

2. Area of the field is 700 hectares

Step-by-step explanation:

Let x hectares be the number of hectares the farmers  normally ploughed in a day. At this rate, they will complete the work in 14 days, so they have to plough

[tex]14\cdot x=14x\ hectares.[/tex]  

Then x+20 hectares is the number of hectares the farmers ploughed in a day when they increased their productivity of work. At this rate, they will complete the work in 10 days, so they have to plough

[tex]10\cdot (x+20)=10(x+20)\ hectares.[/tex]

The work is the same, so

[tex]14x=10(x+20)\\ \\14x=10x+200\\ \\14x-10x=200\\ \\4x=200\\ \\x=50[/tex]

Ploughing 50 hectares each day 14 days in a row they will plough

[tex]14\cdot 50=700\ hectares[/tex]

Answer:

-5/12, -0.3, 4/5, 0.92

Step-by-step explanation:

because: -5/12 = -0.41666666666

                -0.3

                 4/5 = 0.8

                 0.92

and the negatives are always the least especially if it's a great number with a negative sign.

Answer:

24

Step-by-step explanation:

12 * 2 = 24

The value of x² is 144.

Just multiply an integer by itself to square it. For instance, "4 squared" equals 4 4 = 16. frequently displayed with a tiny 2 in the corner as follows: 42 = 16. "4 squared equals 16" is a common expression. The result of multiplying an integer (not a fraction) by itself is a square number.

Given

x = 12

x² = x * x = 12*12 = 144

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Answer:

25 minutes

Step-by-step explanation:

By using the rule of three we can solve this problem:

If a machine makes 312 bolts in 30 minutes, how much time it would take to produce 260 bolts?

312 bolts -----> 30 minutes

260 bolts ------>      X

X = (260*30)/312 = 25 minutes

312/30=10.4.

260/10.4=25

Answer:

D) y = 4x - 13

Step-by-step explanation:

Slope: the change in y over the change in x

In a equation in slope-intercept form is in y = mx + d, where m is the slope.

The slope can be found by its definition. As y goes up by 4, x goes up by 1, so the slope is 4/1 = 4.

The only option with 4 as the slope is D.

Answer:

Step-by-step explanation:

The center tells you how to handle the left side of a circle's equation.

(x - 2)^2 + (x - 1)^2 = r^2

The point (5,2) gives you enough information to find r^2

x = 5

y = 2

(5 - 2)^2 + (2 - 1)^2 = r^2

(3)^2 + 1^2 = r^2

9 + 1 = r^2

r^2 = 10

Complete equation

(x - 2)^2 + (y - 1)^2 = 10

Answer: (x-2)^2+(y-1)^2=10

Step-by-step explanation:

r=√(x-h)^2+(y-k)^2

r=√(5-2)^2+(2-1)^2

r=√3^2+1^2

r=√9+1

r=√10

X^2+y^2=r^2

(x-2)^2+(y-1)^2=(√10)^2

(x-2)^2+(y-1)^2=10

Answer:

114°

Step-by-step explanation:

The angle which represents 2/5 of a circle is 144 degree.

A figure known as an angle is created when two rays, referred to as the angle's sides and vertices, share a single terminal. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given:

Shaded portion= 2/5

and, the complete angle= 360

So, the 2/5 portion of the angle

= 360 x 2/5

= 720/5

= 144

Hence, the angle of portion 2/8 is 144 degree.

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Answer:

The slope is -2

Step-by-step explanation:

To find the slope of a line when we have 2 points, we use the formula

m = (y2-y1)/(x2-x1)

    = (3-9)/(4-1)

     = -6/3

   -2

The slope of the line is -2

To find the slope of a line using two points, there are many formulas, however the easiest one to use is (rise/run)

The rise is the difference in the Y value and the run is the difference in the X value

(9-3)/(1-4) = (6/-3) = -6/3, which can be simplified to -2

en un año gano 55 $ locual es un dato clave

Step-by-step explanation:

Answer:

Width = x-1

Step-by-step explanation:

Given

Area of rectangle=A= x^4+4x^3+3x^2-4x-4

Length of Rectangle=L= x^3+5x^2+8x+4

We have to find width

Width of rectangle=W= ?

We know that the formula for the area of triangle is:

Area of Rectangle=Length*Width

A=L*W

Since we need the value of width, length will be moved to the left of equals to.

A/L=W

W= (x^4+4x^3+3x^2-4x-4)/(x^3+5x^2+8x+4)

After long division, we will get

Width=W=x-1

Answer:nise xdxxxxdddd

Step-by-step explanation:

Conociendo los porcentajes de cada componente y usando algebra simple, veremos que el porcentaje de la nueva mezcla que es maiz morado es el 49%.

Asumamos que comenzamos con una cantidad A de chicha morada.

Sabemos que:

Ahora mezclamos eso.

Ana se bebe el 30% de la chicha morada, es decir, la cantidad restante de chicha morada es:

0.7*A

Conociendo las proporciones con las que esto se preparo, podemos ver que la cantidad de agua restante es:

0.3*0.7*A

Y la cantidad de maiz restante es:

0.7*0.7*A

Ahora reemplaza el 0.3*A faltante con agua, es decir, la cantidad total de agua será:

0.3*0.7*A + 0.3*A

(0.3*0.7 + 0.3)*A

0.51*A

Es decir, en la nueva mezcla un 51% es agua.

Entonces el porcentaje de la nueva mezcla que es maiz morado es el 49% restante.

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what's the equation to find x

First, we have to find the ratio of quarters to the ratio of total coins:

15/15+8+27 = 15/50

Then, multiply the ratios:

15/50 * 14/49

(14/49 since one quarter has already been removed)

210/2450

21/245 = 0.0857

The probability is about 9 percent.

The insufficient evidence found in your test indicates that there's not ample proof to reject the claim regarding the standard deviation of time women spend washing their hair in the morning being 15 seconds.

In the realm of statistics, we are testing a claim about the standard deviation. In this case, you've tested a claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds. If your test does not reject the null hypothesis, that means you've found insufficient evidence to say the standard deviation differs from your claim. Thus, your final conclusion in this instance would be: 'There is not sufficient evidence to reject the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds.'

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The final conclusion is: There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.

The final conclusion is: There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds. When the initial test fails to reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis. In this case, it suggests that there is not enough evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.

To reach this conclusion, you would have conducted a hypothesis test using a significance level (alpha). If the p-value from the test is greater than alpha, you would fail to reject the null hypothesis. This means there is not enough evidence to support the alternative hypothesis, which implies that the claim of the standard deviation not being 15 seconds is not supported.

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Answer:

Given in the question an expression,

y = 3x/(8+x)

Step1

interchange the variables

x = 3y/(8+y)

Step 2

x(8+y) = 3y

Step 3

8x + xy = 3y

Step 4

8x = 3y - xy

Step 5

8x = y(3 - x)

Step 6

8x = y(3 - x)

Step 7

y = 8x/(3-x)

Step 8

y = f(x^-1) = 8x/(3-x)

So the inverse of  f(x)= 3x/(8+x) is f(x^-1) = 8x/(3-x)

It is false because they could be at the end of a number