what is 21ax + 10by - 35ay - 6bx? ​

Answer:

128.52

Step-by-step explanation:

Find the area of the figure by splitting it into two shapes - a trapezoid and a semi-circle.

The area of a semi-circle is found using A = 1/2πr² where r = 6 since the diameter is 12. A = 1/2π(6)² = 56.52.

The area of the trapezoid is found using A = 1/2(a+b)h = 1/2(12 + 6)(8) = 72.

Together the area is 56.52 + 72 = 128.52.

Answer:

The solutions are

t=2.07 sec  and t=5.43 sec

Step-by-step explanation:

The question in English

The height h above ground level (in feet) of a toy rocket, t seconds after it is launched, is given by h = -16t2 + 120t. When will the rocket be 180 feet above the ground?

we have

[tex]h=-16t^{2}+120t[/tex] -----> equation A

[tex]h=180[/tex] -----> equation B

equate the equation A and equation B

[tex]180=-16t^{2}+120t[/tex] ------> equation C

we know that

The solution of the equation C is equal to the x-coordinate of the intersection point of the graph equation A and the graph of the equation B

so

using a graphing tool

The solutions are

t=2.07 sec  and t=5.43 sec

see the attached figure to better understand the problem

Answer:

The answer is 2

Step-by-step explanation:

To find this, follow the order of operations as laid out below.

120(2x - 2) = 240 ----> Divide both sides by 120

2x - 2 = 2 ----> Add 2 to both sides

2x = 4 ------> Divide both sides by 2

x = 2

Answer: x= 2

Step-by-step explanation:

120(2x - 2) = 240

open the bracket

240x - 240 = 240

collect like terms

240x = 240 + 240

240x = 480

Divide bothside by 240

240x/240 = 480/240

x= 2

Answer:

Step-by-step explanation:

To find the length of an arc,

Angle/360 * circumference

Length = 4

Angle = ?

circumference = 20

Angle/360 * 20 = 4

Rearrange to find the Angle.

Angle/360 = 4 / 20 = 0.2

Angle = 360 * 0.2

Answer:

It’s correct

Step-by-step explanation:

Thanks

Answer:

7 feet

Step-by-step explanation:

Convert 1 3/4 into an improper fraction:

1 3/4 = 7/4

if 1/4 is one foot/ then 7/4 is 7 feet

sorry if i didn't explain this well, hope it helps

A wall that measures [tex]1 \frac{3}{4}[/tex] inches on a blueprint with a scale of 1 / 4 inch equals 1 foot is 7 feet long in actual size after converting the measurements.

The question is about converting a measurement on a blueprint to the actual size in feet. To find out how many feet long a wall that measures [tex]1 \frac{3}{4}[/tex] inches on the blueprint is, we apply the given scale factor. The scale on the blueprint is

1 / 4 inch equals 1 foot. Therefore, to find the actual length in feet, we divide the measured length on the blueprint by the scale factor.

[tex]1 \frac{3}{4}[/tex] inches can be converted to a decimal which is 1.75 inches. Now, we divide 1.75 inches by the scale of 1 / 4 inch per foot:

1.75 inches / (1/4 inches/foot) = 1.75 inches X (4 feet/1 inch) = 7 feet

So, a wall that measures 1.75 inches on the blueprint is 7 feet long in actual size.

Answer:

The equation

f(x) = x^2 + 12*x + 26

can be rewritten as

y = x^2 + 12*x + 26

More information about this equation can be seen in the picture attached below.

Answer:

f(-4) = 10.636

Step-by-step explanation:

In this problem we need to substitute and add together the remaining terms

f(x)=6−2+2e−0.3x

If we simplify

f(x) = (6−2) +2e−0.3x

f(x) = (4) +2e − 0.3x

We substitute the value for e (Euler's number)

e = 2.718

f(x) = (4) +2(2.718) − 0.3x

f(x) = (4) + 5.436 − 0.3x

f(x) = 9.436 -0.3*x

We just need to substitute for x = -4  ,  to get f(-4)

f(-4) = 9.436 -0.3*(-4)

f(-4) = 9.436 + 1.2

f(-4) = 10.636

Answer: 1.3

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

Answer: your answer is 40%

Fraction Percent

1/5 20%

2/5 40%

3/5 60%

4/5 80%

Answer:

1) (9, 75+360n)

2) (−9, 255+360n)

Step-by-step explanation:

(9, 75) is same as (9, 75 + 360)

so it would be (9, 435)

It can also be expressed as (-9, 75 + 180 degrees)

so (-9,255) degrees

In general, (9,75+360 n) for n≥0 represents half of the possible ways of representing the point : (9,75)  

All the polar coordinates of point p = (9, 75°) are p(2.329, 8.693), p(-2.392, 8.693), p(-2.392, -8.693) and p(2.392, -8.693).

Coordinate is basically point on a surface which shows the position of point on the surface. It is like (x,y) in which x is the point on x axis and y is the point on y axis?

We know that x coordinate is r cosΘ and y=r sin Θ. and we have to first find the x coordinates and y coordinates.

The polar coordinates of point p:

1. p(9cos75, 9sin75) = p(2.329, 8.693)

2. p(9cos(180i - 75), 9sin(180 - 75)) = p(-2.392, 8.693)

3. p(9(cos(180 + 75), 9sin(180 + 75)) = p(-2.392, -8.693)

4. p(9cos(360 - 75), 9sin(360 - 75)) = p(2.392, -8.693)

Hence all the polar coordinates of point p = (9, 75°) are p(2.329, 8.693), p(-2.392, 8.693), p(-2.392, -8.693) and p(2.392, -8.693).

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What you have to do: 150 + 150 = 300. 1000 - 300 = 700. So 700 either divide that by two or find the square root. It’s either way. Im not quite sure ask your teacher or say you are confused on whether to find the square root or subtract.

To find the unknown side length of a rectangle given the perimeter, subtract twice the known length from the perimeter, then divide the result by 2.

To find the unknown side length of a rectangle using the perimeter, you need to know that the perimeter (P) of a rectangle is calculated by the formula P = 2l + 2w, where l is the length and w is the width (or the unknown side length in this case). If you know the perimeter and one side length, you can rearrange the formula to solve for the unknown length. Here are the steps:

In mathematical form, it would be w = (P-2l)/2.

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Answer:

y=|x-0.5|

Step-by-step explanation:

right/left is always within the absolute value itself.

to the right is always negative.

Answer:

|x|-0.5

Step-by-step explanation:

To solve the inequality 2x - 4 ≤ 12, add 4 to both sides to get 2x ≤ 16, then divide both sides by 2, resulting in x ≤ 8. This means x can be any number less than or equal to 8.

To solve the inequality 2x − 4 ≤ 12, we first isolate the variable x by following algebraic steps. Here's a step-by-step approach:

The solution to the inequality tells us that x can be any number less than or equal to 8. This is true for any real number x that satisfies the condition outlined by the inequality.

Remember, when solving inequalities, it's crucial to maintain the balance of the equation by performing the same operations on both sides. Also, note that multiplying or dividing both sides of an inequality by a negative number requires flipping the direction of the inequality sign, which was not necessary in this case since we divided by a positive number (2).

Answer:

[tex]y = 2 sin (\frac{2x- 1}{16 \pi} ) - 1[/tex]

Step-by-step explanation:

We know that the standard form of equation for the sine function is given by:

[tex]y = Asin(Bx-C)[/tex] where [tex]A[/tex] is amplitude, period is [tex]\frac{2\pi }{B}[/tex] and the phase shift is equal to [tex]Bx-C[/tex] set to zero. [tex]C[/tex] is then obtained by this equation.

Here in this problem: A is equal to 2, period=2π/B=2π/2=π, where B is equal to 2 and the phase shift is equal to 2x - 1/16 pi = 0.

[tex] y = 2 sin (\frac { 2 x - 1 } { 16 \pi} ) - 1[/tex]

To construct the sine function y = 2 × sin(2(x + π/8)) + 3, you need to consider the given amplitude, period, phase shift, and vertical shift and substitute them into the general sine equation form.

Constructing the Sine Function

To write a sine function with a given amplitude, period, phase shift, and vertical shift, we use the general form of the sine equation:

y = A × sin(B(x - C)) + D

Given the data:

Amplitude (A): 2

Period: π

Phase Shift (C): -1/8 π

Vertical Shift (D): 3

First, determine B using the formula for the period: Period = 2π / B. Since the period is π:

π = 2π / B

Solving for B, we get:

B = 2

Next, substitute A, B, C, and D into the general form:

y = 2 × sin(2(x + 1/8π)) + 3

The phase shift is negative, indicating a shift to the left. Therefore, the equation becomes:

y = 2 × sin(2(x + π/8)) + 3

Now, you have the sine function with the specified characteristics.

Answer:

KC=54

Step-by-step explanation:

You have the number for MU=78, HU=96

so that you can find HM=HU-MU=96-78=18

and then JH=22, JK=82 and we got HM=18

so that you can find MK=JK-JH-HM=82-22-18=42

And then MU=78,

so KU=MU-MK=78-42=36

And then CN=51, KN=105 and we just got KU=36,

so UC=KN-CN-KU=105-51-36=18

And you want to find out what's the length of KC,

KC=KU+UC=36+18=54

So your final answer is KC=54.

Answer:

The correct answer is KC = 54

Step-by-step explanation:

From the given figure we can see that,

total length JN =  82 + 105 = 187

To find the length KC

From figure we can write,

KC = Total length - (JK + CN) = JN - (JK + CN)

JN = 187

JK =82 and CN = 51

Therefore KC = 187 - (82 + 51) = 187 - 133 = 54

The correct answer is KC = 54

Answer:

Step-by-step explanation:

the answer would be 7.5

Answer:

15.59 inches²

Step-by-step explanation:

Area of a triangle = [tex]\frac{1}{2}[/tex] (base) × (height)

Base of the triangle = 6 inches = BC

so BD = CD = 3 inches

Now height h = AD = [tex]\sqrt{6^{2}- 3^{2} }[/tex] [ By Pythagoras theorem ]

h = [tex]\sqrt{36-9}[/tex]

= [tex]\sqrt{27}[/tex]

= [tex]\sqrt[3]{3}[/tex]

Now area of equilateral triangle ABC

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

= 3 ×  ([tex]\sqrt[3]{3}[/tex])

=  [tex]\sqrt[9]{3}[/tex] inches²

≈ 15.59 inches²

Answer:

D) 2/3

Step-by-step explanation:

Let x represent the number of boys at the high school.

1/8x total tried out for football.

1/6 total tried out for baseball.

If we were to draw a Venn diagram, the intersection of the two circles would be the 1/12 of the students that tried out for both, or 1/12x.

Taking this away from the total of 1/8x for football,

1/8x - 1/12x

3/24x - 2/24x

1/24x tried out for just football.

Taking the 1/12x away from the 1/6x that tried out for just baseball,

1/6x - 1/12x

4/24x - 2/24x

2/24x = 1/12x tried out for just baseball.

Looking at those that tried out for football, 2/24 tried out for both and 3/24 total tried out for football.  This means 2 out of 3, or 2/3, of the football try outs also tried out for baseball.

2 / 3 are the required fraction of the boys who tried out for football and also tried out for baseball. OPtion D) is correct.

Given that,
1/8 of the boys at a high school tried out for the football team,
1/6 tried out for the baseball team, and 1 /12 tried out for the football team and baseball team.
What fraction of those who tried out for football also tried out for baseball is to be determined.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The fraction of boys that tried out for football also tried out for baseball.
= (1 / 6 - 1 / 12) / 1 / 8
= 2 / 24 * 8 / 1
= 2 / 3

Thus, 2 / 3 are the required fraction of the boys who tried out for football and also tried out for baseball. Option D) is correct.

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The coordinates for the origin of the coordinate plane is (0,0).

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

The coordinate plane consists of two axes which are the two mutually perpendicular lines, the X-axis and the Y-axis respectively.

The point of intersection of these two axes is known as the origin of the coordinate plane.

For the frame of reference, we take the origin of the coordinate plane as (0,0).

Therefore, the coordinates for the origin of the coordinate plane is (0,0).

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Answer:

Smallest x  -14

Larger x   0

Step-by-step explanation:

(x+7)^2 -49=0

Add 49 to each side

(x+7)^2 -49+49=0+49

(x+7)^2 = 49

Take the square root of each side

sqrt((x+7)^2) = ±sqrt(49)

x+7 = ±7

Subtract 7 from each side

x+7-7 = -7±7

x = -7±7

x = -7 -7       x = -7+7

x = -14             x =0

Smallest x  -14

Larger x   0

Answer:

Smaller [tex]x=-14[/tex]

Larger [tex]x=0[/tex]

Step-by-step explanation:

[tex](x+7)^2-49=0[/tex]

[tex](x+7)^2=49[/tex] (add 49 to both sides)

[tex]\sqrt{(x+7)^2} =\sqrt{49}[/tex]

Knowing that [tex]7*7=49[/tex] and [tex]-7*-7=49[/tex]

[tex]x+7=7[/tex] or [tex]x+7=-7[/tex]

Solving for [tex]x+7=7[/tex] first...

[tex]x=0[/tex] (subtract 7 from both sides)

Solving for [tex]x+7=-7[/tex]

[tex]x=-14[/tex] (subtract 7 from both sides)

Answer:

the equation thats equal to 26-17=x

Step-by-step explanation:

we can use fact families and do 26-17 is the missing number.if we were to solve it, the answer would be 9

x + y = 26 , 17 + y =26 , 26 - 17=y,26-17=9

y=9, x=17

4/8 simplifies to 1/2. Multiply 1/2 by 100 to get 50%. Thus, 4/8 expressed as a percent is 50%.

To express 4/8 as a percent without dividing, first, recognize that 4/8 simplifies to 1/2 by dividing both the numerator and denominator by their greatest common divisor, which is 4.

Then, to convert 1/2 to a percent:

1. Multiply 1/2 by 100 to express it as a percentage.

  (1/2) × 100 = 50.

So, 4/8 as a percent without dividing is 50%.

Steps:

1. Simplify 4/8 to 1/2.

2. Multiply 1/2 by 100 to convert to a percent.

  (1/2) × 100 = 50.

Therefore, 4/8 equals 50% without dividing.

Answer:

.28

Step-by-step explanation:

Answer:

.28

Step-by-step explanation:

because in the pie chart it shows:

28% of students who likes red.

34% of students who like green.

38% of students who like blue.

28

----- = .28

100

Answer:

[tex]4(2x^5+x^2-3)[/tex]

Step-by-step explanation:

The question is to factorize  [tex]8x^5+4x^2-12[/tex]

What is common from all 3 terms? It is the factor 4, so we take out 4 and write the remaining as "factorized form".

(Work shown below):

[tex]8x^5+4x^2-12\\=4(2x^5+x^2-3)[/tex]

First answer choice is right.

Answer:

4(2x^5+x^2−3)

Step-by-step explanation:

In other words the other guy above was correct. Picture below is the answer, also I do know that it's what you meant by this question.

For this case we must find the value of the variable "x" of the following expression:

[tex]17x> -17[/tex]

We must divide 17 on both sides of the inequality:[tex]\frac {17x} {17}> - \frac {17} {17}[/tex]

x> -1

Thus, the domain of the variable "x" is given by all the higher strict numbers than -1.

Answer:

x> -1

In the given inequation 17x [tex]>[/tex] -17, solved for x gives x [tex]>[/tex] -1.

An inequation, also known as an inequality, is a mathematical statement that compares two expressions or quantities using inequality symbols such as "[tex]<[/tex]" (less than), "[tex]>[/tex]" (greater than), "[tex]\leq[/tex]" (less than or equal to), "[tex]\geq[/tex]" (greater than or equal to), or "[tex]\neq[/tex]" (not equal to).

Inequations express relationships between values that may not be equal but have a specific order or comparison. The solution to an inequation is a range of values that satisfy the given inequality.

Given that

17x [tex]>[/tex] -17

which implies that

x  [tex]>[/tex] - [tex]\frac{17}{17}[/tex]

x [tex]>[/tex] -1.

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The volume of the rectangular prism is 138.48 cubic centimeters. It is calculated by multiplying the base area of 36 cm² with the height of 3 and 5/6 cm.

To find the volume of the rectangular prism, you need to multiply the area of the base by the height. The formula for the volume of a rectangular prism is:

Volume = Base Area × Height

Given:

Base Area = 36 cm²

Height = 3 and 5/6 cm

First, let's convert the height to an improper fraction:

3 and 5/6 = (6 × 3 + 5) / 6 = 23/6 cm

Now, plug in the values into the formula:

Volume = 36 cm² × 23/6 cm

To multiply, you can first simplify the fraction:

Volume = 36 cm² × 3.83 cm

Finally, calculate the volume:

Volume = 138.48 cm³

The volume of the rectangular prism is 138.48 cubic centimeters.

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Answer:

Step-by-step explanation:

The have to divide $4.55 by 7

$4.55/7

$0.65/1

The price for one Apple is $0.65.

7 divided 4.65 = 0.65 answer is each apple cost 0.65 cents

Answer:

C

140

Step-by-step explanation:

Answer:

C. 140

Step-by-step explanation:

133 + 147 = 280
280 / 2 = 140

Edge 2022. Trust

Answer:

The area of the circle depends of the square of the radius

The area of the circle D is [tex]324 \pi\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

In this problem we have

[tex]r=CD=18\ cm[/tex]

substitute

[tex]A=\pi (18)^{2}=324 \pi\ cm^{2}[/tex]

therefore

the statements that are true are

The area of the circle depends of the square of the radius

The area of the circle D is [tex]324 \pi\ cm^{2}[/tex]