Arianne is taking a geometry course and is working with the area of triangles. She knows the area and the height but needs to find the base. Rearrange the following equation for b, where A is the area, b is the base, and h is the height of the triangle.
A = one half b times h

A.b = 2A − h
B.b equals two times A over h
C.b = 2A + h
D.b = 2Ah

Answer:

2

Step-by-step explanation:

Center: (−4,3)

Radius: 2

Answer:

radius = 2

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

Given

x² + y² + 8x - 6y + 21 = 0

Use the method of completing the square to obtain standard form

Collect the x- terms and y- terms together and subtract 21 from both sides

x² + 8x + y² - 6y = - 21

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9

(x + 4)² + (y - 3)² = 4 ← in standard form

with centre (- 4, 3) and radius = [tex]\sqrt{4}[/tex] = 2

Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (3, 4)

m = [tex]\frac{4-2}{3+2}[/tex] = [tex]\frac{2}{5}[/tex]

[tex]\textbf{Answer:}[/tex]

[tex]\frac{-1}{4}[/tex]

[tex]\textbf{Step-by-step explanation:}[/tex]

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

[tex]\textrm{Use the formula above to determine the rate of change}[/tex]

[tex]\frac{1 - 2}{4 - 0} \rightarrow\frac{-1}{4}[/tex]

[tex]\textrm{The rate of change of this line is }[/tex] [tex]\frac{-1}{4}[/tex]

recall that all we need is two points off a straight line to get its slope, so... hmmm this one passes through (0 , 2) and (4 , 1), so let's use those

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{4-0}\implies -\cfrac{1}{4}[/tex]

Answer:

cos46°

Step-by-step explanation:

Using the co function identity

sin x° = cos(90 - x)°, hence

sin44° = cos(90 - 44)° = cos46°

Answer:  The correct option is (b) cos 46°.

Step-by-step explanation:  Given that when solving for x, the sine of 44º is used.

We are to select the other angle and trigonometric function that could be used to solve for x.

We know that,

the sine of any acute angle is equal to the cosine of its complement.

That is,

if y denotes the measure of any acute angle, then we have

[tex]\sin y=\cos(90^\circ-y).[/tex]

Therefore, if y = 44°, then we get

[tex]\sin 44^\circ=\cos(90^\circ-44^\circ)=\cos 46^\circ.[/tex]

Thus, the other angle and the  trigonometric function that could be used to solve for x is cos 46°.

Option (b) is CORRECT.

Answer:

205/6

Step-by-step explanation:

The question simply asks us to plug in 45 minutes into the given equation. In the graph, we see that y-axis is defined to be time. Therefore we set y=45 and solve for x.

45=-6/5x+86

-41=-6/5x (subtract 86 from both sides)

-41*(-5)=-6/5x*(-5) (multiply both sides by -5)

205=6x (divide both sides by 6)

205/6=x

Answer:

two ten-thousandths

Step-by-step explanation:

You would write 0.0002 as two ten-thousandths. However some people say it the easy way, zero point zero zero zero two.

Hope this helps!

Answer:

It would be 2 ten thousandths.

Step-by-step explanation:

It goes tenths, hundredths, thousands, 10 thousands in order as you move right 1 place value.  

The set of coordinates which paired with (-3,-2) and (-5,-2) are (-4,0) and (-4,0).

The coordinates are the points with the help of which we can draw any figure on the graph.

We know that all the sides of a square are equal to each other.

Let ABCD be a square.

Coordinates of A(-3,-3) and C be(-5,-2)

Let the coordinates of B and D be (x1,y1) and (x2,y2)

To be a square AB=CD=BC=AD

AB=BC

[tex]\sqrt{(x1+3)^{2}+(y1+2)^{2} }[/tex]=[tex]\sqrt{(-5-x1)^{2} +(-2-y1)^{2} }[/tex]

solving this we will find

x1=-4

because y1 is not in the solution so y1 be equal to 0.

AD=DC

[tex]\sqrt{(-5-x2)^{2} +(-2-y2)^{2} }[/tex]=[tex]\sqrt{(x2+3)^{2} +(y2+2)^{2} }[/tex]

solving this we will find x2=-4 and y2=0

Hence the coordinates are (-4,0),(-4,0)

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Final answer:

The coordinates that form a square when paired with (-3, -2) and (-5, -2) are (-3, 0) and (-5, 0). The sides of the square are 2 units long, and by moving perpendicularly up by 2 units from each given point, we find the other two vertices of the square.

Explanation:

The student has asked which set of coordinates, when paired with (-3, -2) and (-5, -2), would result in a square. To find the coordinates that complete the square, we need to consider that the diagonals of a square are equal in length and bisect each other at right angles. The two given points (-3, -2) and (-5, -2) form a side of the square that is parallel to the x-axis and 2 units long. Since a square has all sides equal, the other two vertices of the square will be 2 units away from these points but in a perpendicular direction.

Here's how we calculate it step by step:

First, we determine the length of the side of the square by calculating the distance between the points (-3, -2) and (-5, -2), which is 2 units.

Next, we move 2 units perpendicularly from each point which can be done by either keeping the x-coordinate constant and changing the y-coordinate or vice versa. Since we want to be perpendicular to the x-axis, we change the y-coordinate.

The change in the y-coordinate could be either upwards (+2) or downwards (-2). Considering the y-value of the given points, one possible set of coordinates for the other two vertices are (-3, 0) and (-5, 0).

Therefore, the coordinates (-3, 0) and (-5, 0), when paired with (-3, -2) and (-5, -2), form a square.

Answer:

11

Step-by-step explanation:

arrange from smallest to greatest:

2,2,5,10,12,13,18,24

The median is the middle name.

If you have two middles, the median is the average of them.

So you have 2 middles, 10 and 12.

The average of 10 and 12 is given by (10+12)/2=11

Hello There!

The median is the middle number of the data set so let’s find it!

Step 1. Order your numbers from least to greatest so after we have done that, our numbers would be 2,2,5,10,12,13,18,24

Step 2. We want to cross of a number at the beginning so Starting with 2 and the last number 18 and do that either until we get to one number in the middle or two numbers.

Step 3. There is no one number in the middle but we have the numbers 10 and 12 so we add them together which gives us a sum of 22 and then divide 22 by 2 and we get a quotient of 11.

Our median is 11.

Answer:

answer for question 1 is A and question 2 is B

Step-by-step explanation:

i literally just took the assignment

[tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y in exponential form [tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex].

The correct option is (A)

power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and

exponent denotes the number of times the same base number is multiplied.

Given function is:

[tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y

Now, using rules of exponents and power

=[tex]x^{2/3} y^{3/3}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex] [(a²)³= [tex]a^{6}[/tex]]

=[tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex]

Hence, [tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y= =[tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex]

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Answer:

f(x)^-1 = 1/3x - 2

Step-by-step explanation:

Replace f(x) with y and solve:

y = 3x + 6

Swap x and y

x = 3y + 6

Now isolate y

x/3 = 3y/3 + 6/3

1/3 x = y + 2

1/3 x - 2 = y + 2 - 2

y = 1/3x - 2 or f(x)^-1 = 1/3x - 2

For this case we have the following function:

[tex]f (x) = 3x + 6[/tex]

We must find the inverse of the function, then:

Replace f (x) with y:[tex]y = 3x + 6[/tex]

We exchange the variables:

[tex]x = 3y + 6[/tex]

We solve for "y":

Subtracting 6 on both sides of the equation:

[tex]x-6 = 3y[/tex]

Dividing between 3 on both sides of the equation:

[tex]y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2[/tex]

We change y by [tex]f ^ {- 1} (x)[/tex], and finally we have:

[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]

ANswer:

[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]

Answer:

x = 0; x = 5

Step-by-step explanation:

2x² = 10x

2x² - 10x = 0

2x(x - 5) = 0

x = 0; x = 5

Answer:

The values of x for which it is true that  [tex]2x^2=10x[/tex]  are:

[tex]x = 0[/tex] and [tex]x = 5[/tex]

Step-by-step explanation:

We have the following equation

[tex]2x^2=10x[/tex]

To solve the equation subtract 10x on both sides of the equation

[tex]2x^2-10x=10x-10x[/tex]

[tex]2x^2-10x=0[/tex]

Now take the variable x as a common factor

[tex]2x(x-5)=0[/tex]

Then the equation is equal to 0 when x = 0 or when x = 5

[tex]x = 0[/tex] and [tex]x = 5[/tex]

Answer:

B.2 1/41

Step-by-step explanation:

In a perfect square trinomial of the form ax+bx+c where a, b and c are constants, the value of (b/2)²=ac

In the provided equation the value of a=1, b=-3 c=?

Therefore, (-3/2)²=c since a-the coefficient of x²=1 and 1×c=c

c=2.25= 2 1/4

Thus the trinomial x² - 3x + 2 1/4 is a perfect square.

To find out the difference between her highest score and lowest score, we can deduct the amount of highest score by lowest score.

Her highest score: 135

Her lowest score: 98

Her highest score is higher than the lowest score by:

135 - 98

=37

Therefore, her highest score is 38 more than her Lowest score.

Hope it helps!

Hello

Good Luck

Goodbye ♥

Answer:

B) 5.4 cm 2

Step-by-step explanation:

A==1/2 bh

5.4*2=10.8

10.8/2=5.4

[tex]\displaystyle\\\sum_{n=2}^6\dfrac{(n-1)!}{2}=\dfrac{(2-1)!}{2}+\dfrac{(3-1)!}{2}+\dfrac{(4-1)!}{2}+\dfrac{(5-1)!}{2}+\dfrac{(6-1)!}{2}=\\\\=\dfrac{1}{2}+\dfrac{2}{2}+\dfrac{6}{2}+\dfrac{24}{2}+\dfrac{120}{2}=0.5+1+3+12+60=76.5[/tex]

Answer:

D. 76.5

Step-by-step explanation:

The summation sign means that it is the sum of the expression for all values of n upto 6.

n = 2 below the summation sign means that n starts from 2.

∑(n-1)!/2 from n= 2 to n=6

= (2-1)!/2 + (3-1)!/2 + (4-1)!/2 + (5-1)!/2 + (6-1)!/2

= 1!/2 + 2!/2 + 3!/2 + 4!/2 + 5!/2

= 1/2 + 2*1/2 + 3*2/2 + 4*3*2/2 + 5*4*3*2/2

= 1/2 + 2/2 + 6/2 + 24/2 + 120/2

= 0.5 + 1 + 3 + 12 + 60

= 76.5

Answer:

x=-2 x=-8

Step-by-step explanation:

x2 + 10x + 16 = 0

(x + 2)(x + 8) = 0

x + 2 = 0 or x + 8 = 0

x = and x =

x=-2 x=-8

Answer: X+5

Step-by-step explanation:

When you take out the 9 it should be 9(x+5) and when you take out the 9x on the bottom it gives you (x+5)+20 therefore x+5 is your GCF.

I hope this helps :)

The greatest common factor (GCF) of the numerator 9x+45 and the denominator x^2 +9x+20 of the provided rational expression is x+5.

The greatest common factor (GCF) is found by factoring both the numerator and the denominator and then identifying the largest factor that appears in both. For the provided rational expression 9x+45 over x2 +9x+20, let's factor both parts:

Comparing both factored forms, we can see that x+5 appears in both the numerator and the denominator, and it is the largest factor common to both. Therefore, the GCF of the numerator and the denominator is x+5.

Answer:

$0.20

Step-by-step explanation:

A dozen of pencils = $2.40

1 pencil = $2.40 ÷ 12 = $0.20

PLEASE DO MARK ME AS BRAINLIEST UWU

ALSO, DO HAVE A GREAT DAY ;)

The unit price per pencil is determined by dividing the total cost of the pencils ($2.40) by the total number of pencils (12), giving a result of $0.20 per pencil.

To find the unit price per pencil, you would divide the total cost by the total number of items.

In this case, the total cost is $2.40 and there are twelve pencils, so the calculation is $2.40 ÷ 12.

This will give you the unit price per pencil.

Using the numbers provided, $2.40 (the total cost) divided by 12 (the total number of pencils) equals $0.20.

So, the unit price of a pencil is $0.20.

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Answer:

B and C

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

solve

3x² - 75 = 0 ( add 75 to both sides )

3x² = 75 ( divide both sides by 3 )

x² = 25 ( take the square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5 → B and C

Answer:

The airplane gains speed when it takes off. Then it begins to lose speed at the same rate. The plane then stays at the same speed the rest of the time.

Answer:

Frequency = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We are given the following function and we are to find its frequency:

[tex]f (x) = 3 cos (\pi x) -2[/tex]

We know that the standard form of cosine function is [tex]y=Acos (Bx)+c[/tex]

where [tex]A[/tex] is the amplitude, [tex]B=\frac{2\pi}{\text{Period}}[/tex] while [tex]c[/tex] is the mid line.

Frequency is given by:

[tex]F=\frac{1}{P}[/tex] where [tex]F[/tex] is frequency and [tex]P[/tex] is the period.

Finding period by comparing the given function:

[tex]y=3cos(\pi x)-2[/tex]

[tex]Period - B = \pi[/tex]

Substituting B to get:

[tex]\pi =\frac{2\pi}{\text{Period}}[/tex]

[tex]\text{Period}=\frac{2\pi}{\pi}=2[/tex]

So, Period = 2.

Since frequency is [tex]\frac{1}{P}[/tex], therefore

Frequency = [tex]\frac{1}{2}[/tex]

The frequency is T / (2π).

To find the frequency of the function f(x) = 3 cos(T x) – 2, start by recognizing the standard form of a cosine function, which is f(x) = A cos(Bx + C) + D. Here, A, B, C, and D are constants with specific roles.

        f = ω / (2π)

        f = T / (2π)

Therefore, the frequency of the function f(x) = 3 cos(Tx) – 2 is T / (2π).

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{4}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\ (x-4)^2+(y-1)^2=2^2\implies (x-4)^2+(y-1)^2=4[/tex]

Answer:

18

Step-by-step explanation:

2(15) - 3(4)

= 30 - 12

= 18

Answer:

Slope = -3

Step-by-step explanation:

Slope of a straight line graph is given by; change in y ÷ change in x

Slope = [tex]\frac{-3 - 6}{2 - -1}[/tex] = [tex]\frac{-9}{3}[/tex] = -3

[tex]\text{Hey there!}[/tex]

[tex]\text{The formula should look like: m =\ }\bf{\frac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\text{y}_2=-3\\\\\text{y}_1=6\\\\\text{x}_2=2\\\\\text{x}_1=-1[/tex]

[tex]\frac{-3-6}{2-(-1)}[/tex]

[tex]\text{-3 - 6 = -9}[/tex]

[tex]\frac{-9}{2-(-1)}[/tex]

[tex]\text{2-(-1)=2 + 1 = 3}[/tex]

[tex]\frac{-9}{3}=-9\div3=-3[/tex]

[tex]\boxed{\boxed{\text{Thus your answer/ slope is: -3}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

.0075 (hope this help; let me know if not)

Step-by-step explanation:

The operation is + and the signs of the numbers are opposite so we have to subtract. The bigger number has positive sign in front if so we do 1.2-1.125=1.200-1.125

I'm going to line up

1.200

-1.125

---------

If you have 200 and you take about 125... 75 should beleft

so

1.200

-1.125

---------

0.075

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-7]^2+[-9-(-1)]^2}\implies d=\sqrt{(-8-7)^2+(-9+1)^2} \\\\\\ d=\sqrt{225+64}\implies d=\sqrt{289}\implies d=17[/tex]

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

According to the data we have:

[tex](x_ {1}, y_ {1}) :( 7, -1)\\(x_ {2}, y_ {2}): (- 8, -9)[/tex]

Substituting:

[tex]d = \sqrt {(- 8-7) ^ 2 + (- 9 - (- 1)) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 9 + 1) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 8) ^ 2}\\d = \sqrt {225 + 64}\\d = \sqrt {289}\\d = 17[/tex]

Thus, the difference or distance between the points is 17

Answer:

[tex]d = 17[/tex]

The second option is the best representation of the question.

Fractions represent equal parts of a whole or a collection.

Explanation:

The whole quantity = 1

Divide this whole by 4 and separate it into four equal parts of 1 / 4

Combine two of these four parts to make 1 / 2

Hence, the second option is the best representation of the given question.

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Answer:

13 is the answer.

Step-by-step explanation:

In this question the given fraction is

Now we have to simplify the fraction to the nearest integer.

Since the integers are whole number not in fraction therefore 12.5 can be written as 13 as the nearest integer.

Step-by-step explanation:

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To find 1,242 divided by 99 and rounded to the nearest integer, we do the division and then round the result. The result of the division is 12.545..., and when rounded to the nearest integer, we get 13.

The question is asking us to divide 1,242 by 99 and round the result to the nearest integer. First, we do the division: 1,242 ÷ 99 = 12.545454545.... Since we need to round to the nearest integer, we look at the digits following the decimal point. Because the digit immediately after the decimal point is 5 or more, we round up the integer part. So, 1,242 ÷ 99 rounded to the nearest integer is 13.

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