Yessenia simplified an expression as shown below:

The cyclist cover 200 kilometer in 5 hours and his speed in miles are  25 miles per hour.

According to the statement

We have to find that the speed of the cyclist.

So, For this purpose, we know that the

Speed is the time rate at which an object is moving along a path

From the given information:

A cyclist his bike at a speed of 40 kilometers per hour

Then

The distance he covered in 5 hours = 40*5

The distance he covered in 5 hours = 200.

And then

The speed in miles :

We have given that the  1 mile is equal to 1.6 kilometers

Then

If he covers a 40 kilometers in a hour then

in miles it becomes = 40/1.6

In other words,

Speed in miles = 40/1.6

Speed in miles = 25 miles per hour.

So, The cyclist cover 200 kilometer in 5 hours and his speed in miles are  25 miles per hour.

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The Rate of the change of position per second is 23 feet.

According to the statement

We have to find that the rate of the change of the position in the sea level.

So, For this purpose, we know that the

Rate of change is used to mathematically describe the percentage change in value over a defined period of time

From the given information:

She begins 133 feet below sea level.

After descending for 4 seconds, she's 225 feet below sea level.

Then

Rate of the change of position is = final position - initial position / time

Rate of the change of position is = 225 - 133 / 4

Rate of the change of position is = 92 / 4

Rate of the change of position is = 23.

So, The Rate of the change of position per second is 23 feet.

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There is a 'strike-through' root at -1 and a double root at 2, so the equation is of the form

[tex]y=a(x+1)^3 (x-2)^2[/tex]

Since the y-intercept is 4,

[tex]4=a(0+1)^3(0-2)^2 \implies 4a=4 \implies a=1 \\ \\ \therefore \boxed{y=(x+1)^3 (x-2)^2}[/tex]

Answer:

5

Step-by-step explanation:

Hop the spaces from 1 until you reach to 6 and you get 5 hops

The real number whose sum and product are both 12 area 1.101 and 11.899

Let first number be  " x "

Let other number be " 12 - x "

According to the question the product of two numbers is 12 which is given by         x(12 - x) = 12

                        12x - x² = 12

                         x²- 12x + 12 = 0

Using quadratic formula , we get

Put a = 1 , b = -12 , c = 12 in equation (1) , we get

                      [tex]\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)} }{2(1)} \\\\\frac{12\pm\sqrt{144-48} }{2} \\\\\frac{12\pm\sqrt{96} }{2} \\\\\frac{12\pm9.79 }{2} \\\\[/tex]

Two numbers are 12 + 9.79 / 2 = 1.10 and 12 - 9.79/2 = 10.89

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Answer:

7.5 batches

Step-by-step explanation:

if he uses 0.6kg of sugar per 2 batches, it's 0.3kg per batch.

2.25kg would let us make

2.25kg / 0.3kg = 2.25 / 0.3 = 7.5 batches

Answer:

Y=2x-1

Step-by-step explanation:

(0,-1) parallel to y=2x + 4

parallel means the slope is the same (i.e m=2)

general equation would be

y=2x+k

now (0,-1) belongs to line where x=0 and y= -1

-1 =2(0)+k

-1 = k

hence k is -1

the equation is y=2x-1

According to the model, Leo's initial deposit was $0

The model is given as

a = 18t + 5

When he makes his initial deposit, the value of t is

t = 0

i.e. this represents his balance before he starts saving on a weekly basis

Substitute 0 for t in the equation a = 18t + 5

So, we have

a = 18 * 0 + 5

Evaluate

a = 5

Hence, Leo's initial deposit was $0

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The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.

A function is defined as a expression containing one or more variables.

Technically speaking, a function is a means of linking a set of inputs to a set of outputs.

The height of the ball  at any time t is given by the function:

[tex]h(t)=-16t^2+38t+2[/tex]

Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.

Let us substitute the values:

[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]

This is in the form of a quadratic equation in t.

Solving by using the quadratic formula:

We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]

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

Therefore for the above quadratic equation:

[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]

Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.

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Answer:

2+[tex]x^{2}[/tex]

Step-by-step explanation:

Converted from word to standard form.

Answer: True :)

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

-28 + 28 = 0

The length of XY is 4, the length of ZW is 6 and the lengths are not congruent

The coordinates of the points are given as:

X, Y, Z, and W = -8, -4, 3, and 9,

The above means that

XY = |Y - X|

ZW = |W - Z|

So, we have

XY = |-4 + 8| = 4

ZW = |9 - 3| = 6

Hence, the length of XY is 4, the length of ZW is 6 and the lengths are not congruent

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Considering the definition of perpendicular line, you obtain:

1) the equation of perpendicular line is y= -5x + 7.

2) the equation of perpendicular line is y= 7x + 54.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  1/5. So:

1/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (1/5)

slope perpendicular line= -5

So, the perpendicular line has a form of: y= -5x + b

The line passes through the point (2,-3). Replacing in the expression for perpendicular line:

-3= -5× (2) + b

-3= -10 + b

-3 +10 = b

7= b

Finally, the equation of perpendicular line is y= -5x + 7.

In this case, the line is x +7y -12= 0. Expressed in the form y = mx + b, you get:

7y= -x +12

y= (-x + 12)÷ 7

y= -1/7x +12/7

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -1/7. So:

-1/7× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-1/7)

slope perpendicular line= 7

So, the perpendicular line has a form of: y= 7x + b

The line passes through the point (5,-9). Replacing in the expression for perpendicular line:

-9= 7× (-9) + b

-9= -63 + b

-9 + 63 = b

54= b

Finally, the equation of perpendicular line is y= 7x + 54.

In summary, you obtain:

1) the equation of perpendicular line is y= -5x + 7.

2) the equation of perpendicular line is y= 7x + 54.

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Answer:

. Onusko made 60 cookies for a bake sale. She sold 2/3 of them and gave 3/4 of the remaining cookies to the students working at the sale. How many

Step-by-step explanation:

you mean the slope of the line between (8, 9) and (23, 9).

we can see that right away, as the y value does not change. it means it is a flat line, and that means the slope is 0.

now, formally :

the slope of a line is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction does not matter, but once we pick one for the comparison of one coordinate, we have to use the same direction also for the other.

I prefer to go from left to right.

so, from (8, 9) to (23, 9).

x changes by +15 (from 8 to 23).

y changes by 0 (from 9 to 9).

the slope is therefore 0/+15 = 0.

Answer: 6.83

Step-by-step explanation: 34.18 - 6.86 = 27.32 /4 = 6.83

Answer:

Its answer is -4..............

Answer:

Your answer is -4

Step-by-step explanation:

[tex]5 - (x - 2) { \\ }^{2} [/tex]

where x = -1

Therefore, p(-1) = 5 - ( (-1) - 2 )²

= 5 - (-3)²

= 5 - 9

= -4

A straight line that divides a given angle between two equal angles is referred to as an angle bisector. The following are the steps to constructing a bisector of angle BAC:

Construction with a straightedge and a set of compasses is a method for constructing lengths, angles, and other geometrical figures. It is also known as ruler-and-compass construction or classical construction.

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Answer: $0.33 per cup

15.84/3 to find the price per 1 gallon.

15.84/3 = 5.28 per gallon

There are 16 cups in a gallon, so divide the price of a single gallon by 16.

5.28/16 = price per cup

5.28/16 = .33

The price for each cup of bleach is $0.33.

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Answer:

about 3103

Step-by-step explanation:

Answer:

n = 7

Step-by-step explanation:

You will want to add all common factors with each other.

So that would be n + 3n + 5n which would be 9n.

Then -8 + 1 would be -7. So now it should be 9n - 7.

You are going to set 56 equal to 9n - 7, so that would be 9n - 7 = 56.

After that, you will have to leave 9n alone by itself, so you would have to add 7 to both sides. Your final equation should be 9n = 63.

After that, you should divide both sides by 9 since you want n alone.

So 63 ÷ 9 would be 7. So at the end, n = 7.

Step-by-step explanation:

(e)

because BCDF is a parallelogram, it means that F D = B C = 4.

and F B = D C = 6.

because EDCF is a parallelogram, it means that D C = E F = 6.

that means that E F = F B = 6, so the diagonal E B of ABDE is intersected by the other diagonal A D in the middle at F.

because ABCF is a parallelogram, it means that A F = B C = 4.

that means that A F = F D = 4, so, also the diagonal A D of ABDE is intersected by the other diagonal E B in the middle at F.

when 2 line segments E B and A D intersect each other that way, that makes them the diagonals of a parallelogram.

therefore, ABDE is a parallelogram.

Answer:

Ashleys age is 28.

Step-by-step explanation:

When finding numbers that are consecutive, I like to divide the sum in this case, 100 by the number of people or things, in this case, the 4 siblings. The sum is 100 and there are 4 of them so we divide them first.

100÷4=25 so our answer must be around there. The question states that the ages must be even. So the even numbers in the range of lets say 20-30 are 20, 22, 24, 26, 28 and 30. Closest four numbers to 25 are 22, 24, 26 and 28. We must have two numbers below 25 and two numbers above 25.  So we will keep 22,24,26 and 28. If you add them together, then you'll get 100! Since we are looking for Ashley's age which is the oldest, her age will be 28 as 28 is the highest number out the four numbers (22,24,26,28)

Good Luck and hope this helped! <33

Step-by-step explanation:

ok, let's try this again. we need to explain congruence then in its details as an implicit part of the proof, as everything boils down to that.

due to AE = FC we also know that ED = BF.

because as ABCD is a parallelogram, it means AD = BC (and AB = DC).

and AD || BC, AB || DC.

as AD = AE + ED and BC = BF + FC, it means that

AE + ED = BF + FC

with AE = FC we can then simplify to

ED = BF.

as AD || BC, so is also ED || BF.

since the distance from E to D is the same as for B to F, it means that EB and DF must be equidistant to each other, and that means they are parallel.

and because ED || BF, that also means that both line segments are equidistant from each other, and that means that the connections between their end points (EB and DF) must have the same lengths.

therefore, the shape is a quadrilateral with 2 pairs of parallel and equally long line segments. and that is the definition of a parallelogram.

so, BEDF is a parallelogram.

Answer:

9 9 years 9999999999999