If a = 5i - 6j and b = -2i + 4j , find -3a + 2b

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:

0.04

Step-by-step explanation:

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:

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

Answer:

$375

Step-by-step explanation:

subtract 9,000 from the 12,000, then divide the 3,000 by 8 and you get 375.

She needs to save $375 each month. This is because the total she needed was $12,000 but her mom paid $9,000 which leaves $3,000 and she has eight months and 3,000 divided by 8 = $375

Hope this helps.

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:

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.

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:

A) The worker is paid S= $ 1110 for producing 18 units.

B) The worker is paid $3,330 for producing x= 50 units.

Step-by-step explanation:

a) given x = 18 units

Time required T(x) = 4x+2

                               = 4(18)+2

                               = 72 +2

                               = 74 hrs

Amount paid S(T) = 15 T

                             = 15 ( 74) = $ 1110

b) Since S is given, S= $3,030

     S(T)= 15 (T)

     3030 /15= T

     202 hrs= T

Now, we can find x:

  T(x) = 4(x) +2

  202 = 4x + 2

  202-2 = 4x

  200 / 4 =x

  50 = x

so, worker produces 50 units.

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

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:

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

2 dive by 1/4= 8

6 dive by 1/3 = 18

2 dive by 1/3 = 6

5 dive by 1/2= 10

1/6 dive by 2= 1/12

1/3 dive by 6= 1/18

3 dive by 1/4= 12

1/2 dive by 5= 1/10

Answer:

Step-by-step explanation:

0.01041666666

Answer:

x = 140

Step-by-step explanation:

The figure is a quadrilateral. That means it has 4 sides and more importantly for this question 4 angles. All quadrilaterals have 4 angles that add up to 360o.

You know 3 of the angles. The fourth one is x.

90 + 90 + 40 + x = 360                    Combine like terms on the left

220 + x  = 360                                  Subtract 220 from both sides.

220 - 220 + x = 360 - 220               Combine all like terms

x = 140

Answer:

Step-by-step explanation:

y-intercept is for r = 0.

We have the equation y = -3 - 7r.

Substitute r = 0:

y = -3 - 7(0) = -3 - 0 = -3

Other way.

The slope-intercept form of an equation of a line:

y = mx + b (y = mr + b).

m - slope

b - y-intercept

We have the equation y = -3 - 7r = -7r - 3. Therefore m = -7 and b = -3.

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

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: your answer is 40%

Fraction Percent

1/5 20%

2/5 40%

3/5 60%

4/5 80%

Answer:

C

140

Step-by-step explanation:

Answer:

C. 140

Step-by-step explanation:

133 + 147 = 280
280 / 2 = 140

Edge 2022. Trust

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.

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).

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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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:

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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Answer:

0.000111

Step-by-step explanation:

0.0015 is a decimal between 0.001 and 0.002.

A number system is defined as a system of writing to express numbers.

To find a decimal between 0.001 and 0.002, you can take the average of the two numbers.

The average of 0.001 and 0.002 is:

(0.001 + 0.002) / 2

= 0.003 / 2

= 0.0015

Therefore, 0.0015 is a decimal between 0.001 and 0.002.

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Answer:

The volume of the rectangular one-story house is [tex]18,000\ ft^{3}[/tex]

Step-by-step explanation:

we know that

To find the volume, multiply the area of the base by the height

so

[tex]V=1,800*(10)=18,000\ ft^{3}[/tex]

Answer:

the sea level

Step-by-step explanation:

i can draw a picture

0-----------------------------------------------------------------------------------------------sea lvl

-1-----------------------------------------------------------------------------------------------1ft below

-2----------------------------------------------------------------------------------------2ft below

-3----------------------------------------------------------------------------3ft below

-4-------------------------------------------------------------------4ft below

-5-------------------------------------------------------------------------------5ft below

-6---------------------------------------------o-m----------------------------------6 ft below

                                                         ^

                                                    thats a turtle

Answer:

A)−3(y + z = 4)

Step-by-step explanation:

Equation P: y + z = 4  

Equation Q: 3y + 7z = 15  

To eliminate the y term,  The equations have to have the coefficients on y equal and opposite.

Equation Q has 3y, so Equation P needs -3y

Multiply equation P by -3

−3(y + z = 4)

Answer:

A

Step-by-step explanation: