6. A.APR. 6 Perform the indicated operation:
x^3+ 2x² -5x-6
X-2
a. x² + x-3
b. x-5 R4
c. X4-9x?-16x +12
d. ** + 4x +3

She can make 3 shorts

Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

The total amount of fabric = 3 7/8 yards = 31/8 yards.

Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.

The number of shorts that can be made = 31/8 ÷ 5/4

⇒ 3.1 so it will be 3 because no relevance of decimal shorts.

Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".

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The given fraction can be converted into  whole  number as

16/5 +52/9 =9

99/7 -15/2=7

13/8+ 27/5=7

41/4-26/15=9

27/10+44/9=8

We can see that all the expression was given as a fraction the to convert to whole number we will need to solve them by performing the neccessary addition as well as substraction operations then it will converted to whole number.

16/5 +52/9

=404/45.

=8.977

=9

99/7 -15/2=

= 93/14

=6.643

7

13/8+ 27/5

= 281/40

=7.025

7

41/4-26/15

=511/60

=8.52

=9

27/10+44/9

= 683/90

=7.59

=8

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No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

53*_4_ hopes that you are not feeling

Answer:

\(\large\boxed{\tt x = 23^{\circ}}\)

Step-by-step explanation:

\(\textsf{We are given 2 \underline{Linear Pairs}. We are asked to form an equation, and to solve for x.}\)

\(\large\underline{\textsf{What are Linear Pairs?}}\)

\(\textsf{Linear Pairs are 2 Adjacent Angles that form a 180}^{\circ} \ \textsf{angle, or add up to 180}^{\circ}.\)

\(\textsf{For our problem, these 2 angles given to us are Linear Pairs, which equal 180}^{\circ}\)

\(\textsf{when added together. Let's create an equation to find x.}\)

\(\large\boxed{\tt 180^{\circ}=93^{\circ} + (3x+18)^{\circ}}\)

\(\textsf{Now, let's solve for x by using the \underline{Properties of Equality}.}\)

\(\large\underline{\textsf{What are the Properties of Equality?}}\)

\(\textsf{The Properties of Equality are Properties that allow us to manipulate equations.}\)

\(\textsf{There are 9 properties of equality that we can use, each allowing us to simplify}\)

\(\textsf{one side of an equation. These properties are mainly used to find missing variables.}\)

\(\textsf{Let's solve for x by using the Properties of Equality.}\)

\(\large\underline{\textsf{Solving for x;}}\)

\(\tt 180^{\circ} = 93^{\circ} + 3x^{\circ}+18^{\circ}.\)

\(\textsf{Let's first Combine Like Terms.}\)

\(\tt 180^{\circ} = \boxed{\tt 93^{\circ}} + 3x^{\circ}+\boxed{\tt 18^{\circ}}\)

\(\tt 180^{\circ} = 111^{\circ} + 3x^{\circ}\)

\(\textsf{Now, let's use the Subtraction Property of Equality which states that if 2 same}\)

\(\textsf{numbers are subtracted from both sides of the equation, then both expressions}\)

\(\textsf{still equal each other. Let's subtract 111 from both sides of the equation.}\)

\(\tt 180^{\circ} - 111^{\circ} = 111^{\circ} - 111^{\circ} + 3x^{\circ}\)

\(\tt 69^{\circ} = 3x^{\circ}\)

\(\textsf{Let's use the Division Property of Equality, which is similar to subtraction but it's}\)

\(\textsf{for division. Divide each side of the equation by 3.}\)

\(\tt \frac{69^{\circ}}{3} = \frac{3x^{\circ}}{3}\)

\(\large\boxed{\tt x = 23^{\circ}}\)

Answer:

315/32

Step-by-step explanation:

The answer given is an improper fraction.

Therefore, the perimeter of the polygon formed by connecting the points A(3,4), B(3,1), C(8,1), and D(8,4) is 12 units.

Perimeter is the total distance around the boundary or the outside of a two-dimensional shape such as a polygon. It is the sum of the lengths of all the sides of the shape. The perimeter is typically measured in units of length, such as meters, centimeters, feet, or inches. The concept of perimeter is used in many areas of geometry and mathematics, as well as in other fields such as architecture, engineering, and construction.

Here,

To find the perimeter of the polygon formed by connecting the points A(3,4), B(3,1), C(8,1), and D(8,4), we need to calculate the distance between each pair of adjacent points and then add up these distances.

We can use the distance formula to find the distance between two points:

distance = √[(x2 - x1)² + (y2 - y1)²]

So, the distance between points A and B is:

AB = √[(1 - 4)² + (3 - 3)²]

= √[(-3)² + 0²]

= √9

= 3

The distance between points B and C is:

BC = √[(1 - 1)² + (8 - 3)²]

= √[0² + 5²]

= √25

= 5

The distance between points C and D is:

CD = √[(4 - 1)² + (8 - 8)²]

= √[3² + 0²]

= √9

= 3

The distance between points D and A is:

DA = √[(4 - 4)² + (3 - 3)²]

= √[0² + 1²]

= √1

= 1

Now we can add up these distances to find the perimeter:

perimeter = AB + BC + CD + DA

= 3 + 5 + 3 + 1

= 12

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Answer:

the answer is 400$

Step-by-step explanation:

Answer: A side of a square for the area given 100/9 square meters, then length = 3.33 meters .

Step-by-step explanation:

The area of a square is (100/9) cm.

So, find out the length of the square?

Then,

Define Square:

A square is closed, two-dimensional shape with 4 equal sides. A square is a quadrilateral. We can find the shape of a square in a game board or chess board, a wall clock and in a slice of bread, around us.

The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.

Define Area of Square:

Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units with the standard unit being square meters (m²).                    

The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.    

Area of a Square = Side ×  Side

Therefore, the area of square = side²  square units                          

                                              A = s²

Means,       A= area of square

You have the area so you need to find the side length that when multiplied by itself equals that area. If you don’t know what number squared is (100/9) you can plug and chug or use a calculator with square roots.

Replace with A=(100/9) values,

We can write,

                        A = s²

               (100/9) = s²

Then we can solve it,

               \(\sqrt{100/9}\) = s

                 \(\sqrt{\frac{(10^{2}) }{3^{2} } }\) = s

We can write, \(\sqrt{10^{2} }\) = 10 , and \(\sqrt{3^{2} }\) = 3

Then,  

                    (10/3) = s

Therefore,   s = (10/3)

                    s = 3.33 meters

So, length = 3.33 meters

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Answer:

I cant see it its too small

Step-by-step explanation:

In the  word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.

Let  S = number of small pizzas delivered

Let M = number of medium pizzas delivered

Let L = number of large pizzas delivered

We'll start by solving equation 1 for one variable and substituting it into the other equations.

S + M + L = 12

We can rewrite this equation as -

S = 12 - M - L

Now, substitute this value of S in equations 2 and 3 -

4S + 10M + 15L = 109

4(12 - M - L) + 10M + 15L = 109

48 - 4M - 4L + 10M + 15L = 109

6M + 11L = 61

2S + 4M + 13L = 81

2(12 - M - L) + 4M + 13L = 81

24 - 2M - 2L + 4M + 13L = 81

2M + 11L = 57

Now we have a system of two equations with two variables -

6M + 11L = 61 ...(4)

2M + 11L = 57 ...(5)

Subtract  equation   (5)from equation (4) -

(6M +   11L) - (2M +11L) = 61 - 57

4M = 4

M = 1

Substitute the value of M into equation (5) -

2(1) + 11L = 57

2 + 11L = 57

11L = 55

L = 5

Now substitute the values of M and L into equation (1) -

S + 1 + 5 = 12

S + 6 = 12

S = 6 - 6

S = 0

Therefore, the solution is -

S = 0 (no small pizzas)

M = 1 (1 medium pizza)

L = 5 (5 large pizzas)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?

Using multipliers, the expression is given by:

\(y = 0.9875x\)

-------------------

The decimal multiplier for a decrease of x% is given by:

\(M = \frac{100 - b}{100}\)

In this problem, decrease of 1.25%, thus:

\(M = \frac{100 - 1.25}{100} = \frac{98.75}{100} = 0.9875\)

Alex's net proceeds is then of 98.75% = 0.9875 of y, removing the broker proceedings, thus, the expression is:

\(y = 0.9875x\)

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Answer:

adsfasdfadfadsfasdfasdfasdfasfasdf

Step-by-step explanation:

asdfasdfadsfasdfasdfadsfasfsdfdas 69 69 69 69 69 69 696 96 69 69 69 69 6

a) The Prοgressiοn rule for this situation will be, \(\rm a_{n}=a_{1}+(n-1)(-8)\).

b) The price of the shoes after 8th months is a₈ = $24.

Arithmetic Prοgressiοn (AP) is a sequence οf numbers in οrder, in which the difference between any twο cοnsecutive numbers is a cοnstant value. It is alsο called Arithmetic Sequence. Fοr example, the series οf natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Prοgressiοn, which has a cοmmοn difference between twο successive terms (say 1 and 2) equal tο 1 (2 -1). Even in the case οf οdd numbers and even numbers, we can see the cοmmοn difference between twο successive terms will be equal tο 2.

\(\rm a_{n}=a_{1}+(n-1)d\)

aₙ = the nᵗʰ term in the sequence

a₁ = the first term in the sequence

d = the common difference between terms

a) Here, the d = 2nd term - 1st term = 72 - 80 = -8

So the rule will be, \(\rm a_{n}=a_{1}+(n-1)(-8)\)

b) Apply the rule above and solve for 8th month:

\(\rm a_{n}=a_{1}+(n-1)(-8)\)

\(\rm a_{8}=80+(8-1)(-8)\)

\(\rm a_{8}=80+(7)(-8)\)

\(\rm a_{8}=80-56\)

a₈ = 24

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Well if Jorge's motion can be described by vectors then he first went +25 steps then -75 steps which means he did -50 steps in total. His position is thus 50 steps to the south of the original position.

Hope this helps.

Answer:

50

Step-by-step explanation:

The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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The complete question is: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

a. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

d. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

Answer:

Step-by-step explanation:

The additional information needed to prove the triangles are congruent by the SAS postulate:

If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent.

Answer:

x = 42

y = 21

Step-by-step explanation:

Since its a right triangle, we have:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

\(sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42\)

\(cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21\)

Answer:

The p-value is 0.0012.

Step-by-step explanation:

The hypothesis is:

H₀: µ = 72 vs. Hₐ: µ > 72

The information provided is:

\(n =16\\\bar x=75.8\\\sigma=5\)

Compute the test statistic value as follows:

\(z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}\)

  \(=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04\)

Compute the p-value as follows:

\(p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012\)

*Use a z-table.

Thus, the p-value is 0.0012.

The product of 83 and 4.5 \times 10^64.5×106 is expressed in scientific notation is 830*10^-12.

Scientific notation can be described as the representation of the large numbers or very small numbers in the standard form which can be seen in the final answer of this question , it do make the handling of numbers to be easier when making a calculation.

From the question, we are asked for the product of 83 and 4.5 \times 10^64.5×10^6,

Then we can multiply 10^6 * 4.5×10^6 which is (4.5*10^11)

Then 4.5/(4.5*10^11) = 10 *10^-12

Then we can found the product  expression as (83* 10 *10^-12) = 830*10^-12.

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Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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Answer:

Step-by-step explanation:

Using

Point A: x= 1 and y=3

And point B: x=-2 and y=-6

use equation of slope and substitute the values

Slope= YB-YA/Xb-Xa

= -6-3/-2-1

=3

Answer:

neither

Step-by-step explanation:

4x - 6y = -24                                           y = 2/3x + 4

-6y = -4x - 24

-6/-6y = -4/-6x -24/-6                              y =2/3x + 4

  y  = 2/3x +4

Same line

Answer:

we have for triangle

base:51m

height:18m

area of triangle: ½base*height=½(51*18)=459m²

height of prism:9m

Now

Volume of prism: area of base×height=459*9=

4131m³ is a required volume.

The volume of the given prism is 4131 cubic meters

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A triangular prism has a height of 9 meters,

We have to find the volume of the prism

According to the given dimension for the base,

The area of base is 1/2×51×18

Area of base =459 square meters

Volume of prism = Area of base × Height

=459×9

=4131 cubic meters

Hence, the volume of the given prism is 4131 cubic meters

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Answer:

0.042

Step-by-step explanation:

Answer:

0.042

Step-by-step explanation:

(C)

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

Answer:

x = 29

Step-by-step explanation:

(6x-1) = (5x+28)

or, 6x-1 = 5x+28

or, 6x-5x = 28+1

or, x = 29

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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