Simplify each expression by combining like terms. NO SPACES in your answer.

−5.2t+8.2−7.8t

What is the answer in simpelest form?

The fractions are rewritten as so that they have a common denominator as  107/100

A fraction can be described as the part of a whole element, variable or number.

The several types of fractions are;

From the information given, we have that;

13/25 and 11/20

To rewrite the fractions, we have to determine the lowest common multiple

13/25 + 11/20

52 + 55 /100

Add the numerators , we have;

107/100

Hence, the fraction is 107/100

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So, on solving the provided question, we can say that the range of the function =  [-9, 8]

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.

From the graph we have the following observations.

The endpoints of the graph have closed circles (this means that, the endpoints are inclusive of the range)

The endpoints on the y-axis =-9 and 8

So, the range of the function =  [-9, 8]

This can be rewritten as = -9≤y≤8

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A number cube is a 6 sided die, so the probability of rolling a 3 is 1/6.

Each coin flip is treated as a separate event because the outcome of one flip has no bearing on the outcome of any subsequent flips. List every outcome that each experiment could produce. A coin is flipped after rolling a regular number cube. Flipping four coins.

Okay, so the likelihood of rolling an even number is equal to half. Flipping tells is likewise half, as well. Thus, in its most basic form, this is the answer to the exercise and the likelihood of doing both will be 1/4. An event's probability is always between 0 and 1.

Given that both occurrences took place at the same time. As a result, when a coin is tossed and a cube is rolled, the likelihood of getting a tail and a six increases.

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The polynomial f(x) = 4x³ + 9x² - 3x - 10 divided by d(x) = x + 2 will give a quotient of 4x² + x - 5 and a remainder of 0 using the synthetic division.

Using the remainder theorem, f(-2) = 0.

d(x) is a factor of f(x).

f(x) = (x + 2)(4x² + x - 5) + 0.

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

We shall divide the polynomial 4x³ + 9x² - 3x - 10 by x + 2 as follows;

4x³ divided by x equals 4x²

x + 2 multiplied by 4x² equals 4x³ + 8x²

subtract 4x³ + 8x² from 4x³ + 9x² - 3x - 10 will result to x² - 3x - 10

x² divided by x equals x

x + 2 multiplied by x equals x² + 2x

subtract x² + 2x from x² - 3x - 10 will result to -5x - 10

-5x divided by x equals -5

x + 2 multiplied by -5 equals -5x - 10

subtract -5x - 10 from -5x - 10 will result to a remainder 0

The remainder theorem states that if a polynomial say f(x) is divided by x + a, then the remainder is f(-a)

f(-2) = 4(-2)³ + 9(-2)² - 3(-2) - 10

f(-2) = -32 + 36 + 6 - 10

f(-2) = 0

The factor theorem states that: if the polynomial f(x) is divisible by x + a if and only if f(-a)=0

d(x) is a factor of f(x) because f(x) is divisible by d(x)

Therefore, presenting the result from the synthetic division of the polynomial f(x) using the division algorithm, we have; f(x) = (x + 2)(4x² + x - 5) + 0

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The average change in the price per mp3 download was a decrease of $0.06 per year because 0.3/5 is 0.06

A division is a process of splitting a specific amount into equal parts.

Given that price per mp3 download 5 years ago was $0.99.

Now, each mp3 download costs $1.29.

We have to find the difference between cost 5 years back and now

1.29-0.99

Which is 0.3

The change is 0.3 for five years.

Now we have to find the change per year.

To find this we have to divide 0.3 by 5.

0.3/5

0.06

Hence, option C is correct. The average change in the price per mp3 download was a decrease of $0.06 per year because 0.3/5 is 0.06

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The equation similar to the sentence is 9x - 3 = 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The statement here is "Three less than the product of 9 and a number equals 2."

We have a unknown number here where the number 9 is multiplied. Let the unknown number be x.

3 less than the product of 9 and x is mathematically represented as 9x - 3.

Since this is equal to 2, we get, 9x - 3 = 2, which is a linear equation where the highest degree of the variable is 1.

Hence the equation related to the statement is 9x - 3 = 2.

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Answer: 100% more than 3026.9 is  6053.8

Step-by-step explanation:

If you have a calculator, you put 3026.9 plus 100%

Answer:

6053.8

Step-by-step explanation:

100% = 1.00

3026.9 + 3026.9(1.00) = 6053.8

Increasing a number by 100% is the same thing as doubling it

Answer:

Patrick = 19

Olivia= 35

Step-by-step explanation:

Olivia = 16 + Patrick (equation 1)

Patrick + Olivia= 54  (equation 2)

Replace Olivia from equation two with the value of Olivia from equation 1

Patrick + (16 + patrick) = 54

2 Patrick + 16 = 54

2 Patrick = 38

Patrick = 19

If patrick is 19, olivia is 19 + 16 = 35

Apply the indicated rule for each vertex of the polygon and then graph both the image and preimage.

See attached for both.

Answer:

Question 7:

Question 8:

Step-by-step explanation:

Given vertices of the pre-image:

Given transformation rule:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is dilated by a scale factor of ¹/₂ then the transformation rule is:

Therefore the vertices of the image are:

Answer:

50π

Step-by-step explanation:

The formula for the volume of a cylinder is  πr^2h

r=radius

h=height

The radius is half of the diameter. This means the radius is 5. 5 to the power of 2 is 25. 25 times 2 equals 50.

The percent of all trucks produced that are flat bed trucks for domestic use is 4%.

From the information, flat-bed trucks and tanker trucks are assembled in a plant in this country. OF these, 84% are for export only.

Those that are used for domestic purpose will be:

= 100 - 84

= 16%

Of those that are for domestic use, 25% are tanker trucks. The percent of all trucks produced that are flat bed trucks for domestic use is:

= 25% × 16%

= 4%

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The slope of the best-fit line, where y represents the overall number total ice cream purchases and x represents the typical daily temperatures, is 1.4.

The steepness at which a line slopes form LEFT to RIGHT is known as its slope. When calculating a line's slope, the rise, or vertically change, is divided by the run, or horizontally change. A line's slope is always consistent, regardless of your choice of two points on the line.

Here,

The points for with this issue are broken down as follows:

(56.1, 107), (60.3, 116), (64.2, 120), (66.4, 122), (71.3, 125), (73.9, 130), (74.2, 132), (75.2, 135), (80.2, 141), (84.8, 151). (84.8, 151). (84.8, 151).

These values are typed into a calculator to produce the equation, which is as follows:

y = 1.4x + 26.8.

Therefore, the function's slope is:

m = 1.4

The slope of the best fitting line where x represents the typical daily temperature and y represents the total amount of ice cream sales, is 1.4.

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Answer:

y = -1/3x - 11

Step-by-step explanation:

We need to find our y-intercept. Substitute the coordinate for the x and y in slope-intercept form (y=mx+b). Your x would be 3, and your y would be -12. The equation from that is -12=-1/3(3) + b. Multiply -1/3 and 3. You'll get -12=-1+b. Add the reciprocal of -1 ( positive 1) to -12. You'll get -11=b. Now that you have your b (y-intercept), you can write it in slope-intercept form. y= -1/3x - 11

Answer:

The first one

Step-by-step explanation:

1. 7 cones are required to make sphere and cylinder.

2. 4 cons are required to make one sphere.

3. 3 cones are required to make one cylinder.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.

Given that,

The height and radius are the same for the cone, cylinder and sphere.

Let height = radius = r.

Volume of the cone = 1/3πr²h = 1/3πr³.

Volume of cylinder = πr²h = πr³.

And volume of sphere = 4/3πr³.

1 .

Number of cones to make one cylinder along with sphere

Ratio of volume of cone to cylinder and sphere = 1/3πr³ : 4/3πr³+πr³

=πr³ : 7πr³

= 1 : 7

Hence, 7 cones are required to make sphere and cylinder.

2.

The ratio of volume of cones to spheres = 1/3πr³ : 4/3πr³ = 1 : 4.

Implies that, 4 cons are required to make one sphere.

3.

Ratio of volume of cone to cylinder = 1/3πr³ : πr³ = 1 : 3.

Hence, 3 cones are required to make one cylinder.

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The expression which can be simplified to find the slope of the trend line as required is; StartFraction 78 minus 87 Over 8 minus 2 EndFraction.

As evident in the task content; the two points which are to be considered to determine the slope of the trend line are; (2, 87) and (8, 78).

Recall from the slope formula that;

Slope, m = (y₂ - y₁) / (x₂ - x₁)

On this note, it can be inferred that upon substitution;

Slope, m = (78 - 87) / (8 - 2)

Ultimately, the required expression is; StartFraction 78 minus 87 Over 8 minus 2 EndFraction.

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The option that describes the end behavior of the graphed function is the second one.

f(x) → ∞ as x →-∞

f(x) →∞ as x →∞

For any function y = f(x), we define the end behavior as the behavior of the function as x tends to negative infinity and positive infinity.

If we look at the left side of the graph, we can see that the function goes upwards.

Then we can assume that as x tends to negative infinity, the function tends to infinity (because it keeps going up) this is written as:

f(x) → ∞ as x →-∞

On the right side we can see the same thing, then when x goes to infinity we can write:

f(x) →∞ as x →∞.

So the end behavior of the function is:

f(x) → ∞ as x →-∞

f(x) →∞ as x →∞.

So the correct option is the second one.

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Here are the shapes and dimensions of each garden space:

Rose Bush: rectangular, 3x + 1 and 2x + 7

Iris Orchid: rectangular, 4x + 2 and x + 5

Sonny Flower: square, 4x + 2

To find the area of each garden space, you will need to use the formula for the area of a rectangle (length x width) or the area of a square (side length x side length). Here is how you would find the area of each space:

Rose Bush: (3x + 1) * (2x + 7) = 6x^2 + 7x + 2x + 7 = 6x^2 + 9x + 7

Iris Orchid: (4x + 2) * (x + 5) = 4x^2 + 9x + 2x + 10 = 4x^2 + 11x + 10

Sonny Flower: (4x + 2) * (4x + 2) = 16x^2 + 32x + 16x + 4 = 16x^2 + 48x + 4

Therefore, the area of the garden space for Rose Bush is 6x^2 + 9x + 7, the area of the garden space for Iris Orchid is 4x^2 + 11x + 10, and the area of the garden space for Sonny Flower is 16x^2 + 48x + 4.

The linear equation that is perpendicular to 2x+3y=15 that we wanted to find can be written as:

y = (3/2)*x + 3/2

Remember that a general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if our line must be perpendicular to:

2x + 3y = 15

(we can rewrite that to get):

3y = 15 - 2x

y = (15 - 2x)/3

y = 5 - (2/3)*x

Then we must have that:

a*(-2/3) = -1

a = -1*(-3/2) = 3/2

So the perpendicular line is something like:

y = (3/2)*x + b

We know that our point passes through (1, 3), replacing the values on the equation we will get:

3 = (3/2)*1 + b

3 = 3/2 + b

3 - 3/2 = b

6/2 - 3/2 = b

3/2 = b

Then the linear equation is:

y = (3/2)*x + 3/2.

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The volume of the cone is  37.68 cm³.

The volume of a cone can be found as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore, let's find the height of the cone using Pythagoras's theorem.

The height of the cone and the radius of the cone are the two legs of the right angle triangle. The slant height of the cone is the hypotenuse of the right angle triangle.  

Hence,

h² = 5² - 3²

h² = 25 - 9

h = √16

h = 4 cm

Hence,

volume of the cone = 1 / 3 πr²h

h = 4 cm

r = 3 cm

Therefore,

volume of the cone = 1 / 3 × 3.14 × 3² × 4

volume of the cone = 1 / 3 × 3.14 × 9 × 4

volume of the cone = 113.04 / 3

volume of the cone = 37.68 cm³

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Answer: Choice (A)

Step-by-step explanation:

#Tip: Use the process of elimination when dealing with a multiple choice question-

What is a perpendicular line? Two distinct lines intersecting each other at 90°, or a right angle.

What is a parallel line? Lines in a plane that are always the same distance apart, and will never intersect.

Step 1: Identify the Given-

Step 2: Eliminate what does not apply to what you found-

Choice (A): True

Lines TU and MN are perpendicular. Lines MN and PQ are parallel

Choice (B): False

Lines PQ and TU are perpendicular. Lines PQ and RS are parallel

Choice (C): False

Lines MN and PQ are parallel. Lines UT and RS are perpendicular

Choice (D): False

Lines MN and RS perpendicular. Lines MN and PQ are perpendicular

To isolate the variable and solve the equation, shift all terms associated with X to the other side of the equation (i.e to the other side of =). The solution of  is: [tex]X-62= 123[/tex] is [tex]X=185[/tex]

To isolate the variable and solve the equation [tex]X-62=123[/tex] , shift all terms associated with X to the other side of the equation (i.e to the other side of =).

given: [tex]X-62=123[/tex]

in the given equation 62 is associated with X, now we shift -62 to the right side of the = sign . So it becomes +62 on another side.

∴ [tex]X = 123+62[/tex]

∴ [tex]X=185[/tex]

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Answer:

D: 9(x + 9)

Step-by-step explanation:

If you divide the equation 9x+81 by 9

you get x+9, making 9 your common factor.

9(x+9)

Answer:

Option D; 9(x + 9)

Step-by-step explanation:

Hope this helped! :D

We can simplify the given expression to get:

-11/|-11| = -1

Here we want to rewrite the expression below:

-11/|-11|

First, remember how the absolute value works.

|x| = x  if x  ≥0

|x| = -x if x < 0.

Then we can rewrite the denominator as:

|-11| = 11

Replacing that on the expression we will get:

-11/|-11| = -11/11 = -1

That is the expression simplfied.

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The new measurements for Ms. Melissa's garden are 27 ft by 6 ft

A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also opposite sides are parallel and of equal length.

Given that, Last year, Ms. Melissa's rectangular garden had a width of 3 feet and an area of 27 square feet. This year, Ms. Melissa wants her garden to be 3 times as long and twice as wide.

The area for a rectangular garden is = length × width

Solving for last year's length =

27 = 3 × length

length = 27 / 3 = 9 feet

Therefore, the length of the garden last year was 9 feet.

She wants her garden to be 3 times as long and twice as wide this year.

Therefore, new dimension should be =

Length = 3 × 9 = 27 feet

Width = 2 × 3 = 6 feet

Hence, the new dimension is 27 ft by 6 ft

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Answer:Answer: (i) The capacity of the bucket in litres = π × 30 × 30 × 0.4 = 113.04 litres.

(ii) The volume of water required to fill the tank in litres = π × 1.2 × 1.2 × 1.35 × 0.8 = 4.72 m3.

(iii) The number of buckets that must be drawn to fill the tank = 4.72 m3 / 113.04 litres = 41.76 = 42 buckets.

Step-by-step explanation:

The ratio 6/8 is larger than 5/8, option b is the best choice.

Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Explanation:

12/24=4x3/8x3

4/8 is less than 5/8, so it's incorrect.

B) 3/4

To make the denominator equal 8, multiply and divide it by 2 first.

3x2/4x2=6/8

Because 6/8 is larger than 5/8, option b is the best choice.

C) Since 15/24 equals 5/8, the solution is incorrect because 5/8 is equivalent to 15.

D)4/12=1/3 In addition, it is below 5/8.

The complete question is,

What ratio is higher than 5/8?

A)12/24

B)3/4

C)15/24

D)4/12.

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Step-by-step explanation:

The set of whole numbers between 2 and 8 is: {3, 4, 5, 6, 7}.

This set can be written as: {x|x is a whole number between 2 and 8} = {3, 4, 5, 6, 7}.

Answer:

omg you're so right!

Answer:

Step-by-step explanation:

putting the value of x in the equation then we simply get..

5×1+15 = 20