What is the solution of the pair of equations y 0 and y =- 3?

[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]

notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.

The basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, section, and segment.

the surface or circumference of a circle, ball, and other object measured in a straight line The radius and diameter of a circle are equal. The length of such a line. whatever radiating or radial component. A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.

Here,

given

The letter "C" should be in the center.

radius=r=AC=CB

Diameter=d=2r=AB.

Therefore , the solution to the given problem of circle comes out to be ,the basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, sector, and segment.

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The sales team must sell 8 more computers than they sold last month to receive the bonus.

Last month the sales team of Electronic Mania sold 27 computers.

If they sold 30% more computer than they sold last month, they would get a bonus.

First we find the 30 percent if 27

27 × 30/100

= 8.1

Let m be the total number of computers sold.

So, the total number of computers sold would be,

m = 27 + 8.1

m = 35.1

m ≈ 35

Therefore, they need to sell 35 computers in total.

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The subtraction of the given number would be = 386

Subtraction is defined as one of the major arithmetic operations that is used to remove a value from another given values.

The subtraction of the value 340 from 726 would be = 386.

That is; 726 - 340 = 386

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

SQR-PRQ-SRP

SP/RP=RP/PQ

QP/QR=RQ/SQ

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

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Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

The probability that Sabreena is going to lose is given as 0.5833

Probability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.

A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.

If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7

In this case, the odds of Sabreena winning are 5:7,

so the probability of winning is 5/(5+7)

the probability of not winning is 1 -  5/12

The probability of not winning is approximately 0.5833

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Answer:

x = - 7

Step-by-step explanation:

given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then

x + 16 = 9 ( subtract 16 from both sides )

x = - 7

Answer:

x=-7

Step-by-step explanation:

The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.

-12+16=4   This addition problem does not equal to 9 so it is not correct.

-7+16=9     This is correct because -7+16 or 16-7 = 9.

-9+16=7    This addition problem does not equal to 9 so it is not correct.

-11+16=5    This addition problem does not equal to 9 so it is not correct.

So, x = -7.

Answer:

3, 2

Step-by-step explanation:

In order for the equation to be equal to zero, the following must be true:

x-3 = 0   or,

x-2 = 0

Therefore the 2 solutions are x=3, x=2

The equation for the linear model in the scatter plot is Y = -2x + 56.

To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.

The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.

The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.

Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.

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There are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

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

The factorial 4! is 24

Factorial value of 3!=6

Factorial value 2!=2

Factorial value 1!=1

4! x 3! x 2! x 1! =24×6×2×1=288

288 can be written as a product 2 and 144 which are perfect squares.

So 2 and 144 are the divisors of 4! x 3! x 2! x 1!

Hence, there are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

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The solution to the system of equations is x = 4 and y = 2.

We would use the elimination method to solve the system of equations:

Let's eliminate the variable y by adding equations 1 and 2:

4x + 8y = 24

2x + y = 19

.

.

.,

6x + 9y = 43

Now we can eliminate the variable x by subtracting equation 3 from the above equation:

6x + 9y = 43

3x + y = 15

.

.

.

3x + 8y = 28

We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:

x = (28 - 8y) / 3

Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:

4x + 2y = 12

Substituting x = (28 - 8y) / 3:

4((28 - 8y) / 3) + 2y = 12

If we simplify:

Finally, we can use this value of y to find x by plugging it into the expression we found earlier:

x = (28 - 8(2)) / 3

x = (28 - 16) / 3

x = 12 / 3

x = 4.

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(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then

the intensity level of sound, L, is 98.062 dB.

(b) If a rock concert has an intensity level of 112 dB, then the sound intensity, S, is [tex]10^{-0.8}\ Wm^{-2[/tex].

Sound intensity, also known as acoustic intensity, is defined as the dominion ferried by sound waves per unit area in a direction perpendicular to that area.

Given that the intensity level of sound, L, measured in decibels (dB), is a function of the sound intensity, S, watts per square meter ([tex]Wm^{-2[/tex]) as

[tex]L = 10log_{10}(S\times10^1^2), S\geq 0[/tex]

(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then

the intensity level of sound,

[tex]L = 10log_{10}(6.4\times10^{-3}\times10^1^2)[/tex]

   [tex]= 10log_{10}(6.4\times10^9)\\= 10(log_{10}6.4\ +\ log_{10}10^9 )\\= 10(0.8062\ +\ 9)\\=10 \times 9.8062\\= 98.062\ dB[/tex]

(b) If a rock concert has an intensity level of 112 dB, then

[tex]112 = 10log_{10}(S\times10^1^2)\\log_{10}(S\times10^1^2) = \frac{112}{10}\\log_{10}(S\times10^1^2)= 11.2\\S\times10^1^2 = 10^{11.2}\\S = \dfrac{10^{11.2}}{10^1^2} \\S = 10^{-0.8}\ Wm^{-2[/tex]

The sound intensity is [tex]10^{-0.8} Wm^{-2[/tex].

Hence, (a) L = 98.062 dB and (b) S [tex]= 10^{-0.8}\ Wm^{-2[/tex].

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The option 1 "Simple random sampling, because the people in the sample are accessible and available" is correct for the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

In the given question, we have to find which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

As we know that, you must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is known as a sampling method.

Every individual in the population has an equal chance of being chosen in a simple random sample. The entire population should be included in your sampling frame.

You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.

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The complete question is:

Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country?

(1) Simple random sampling, because the people in the sample are accessible and available

(2) Stratified sampling, because there are specific subgroups to investigate

(3) Systematic sampling, because of the ease in selecting every nth person

(4) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement

(5) All the above sampling methods

Given:

A length of a side of an equilateral triangle = 32 cm

Formula Used:

If in an equilateral triangle with side length 'a' then,

Area of an equilateral triangle = [(√3)/4] × a2 

Calculations:

Area of an equilateral triangle = [(√3)/4] × 322

⇒ (1024 × √3)/4

⇒ 256√3 cm2

The area of the front of the book after it has been enlarged would be = 121.5 in². That is option C.

A rectangle is defined as the type of quadrilateral which has two opposite sides that are equal and parallel and with four angles that are equal to 90°.

The length of the rectangular book= 6 inches

The width of the rectangular book = 9 inches

Using the scale factor of 1.5 the new length and width is thus:

length = 6 × 1.5 = 9 inches

9× 1.5 = 13.5

Therefore area of the book = l×W = 9 × 13.5 = 121.5 in².

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Answer:

x = -4 or x = -1

Step-by-step explanation:

Let's check

x = -4

(-4 + 4)(-4 + 1) = 0

(0)(-3) = 0

0 = 0

Let's check x = -1

(-1 + 4)(-1 + 1) = 0

(-3)(0) = 0

0 = 0

So, x = -4 or x = -1 is correct answer!

Answer: x= 23

Step-by-step explanation:

By using formula and solving we get the item is on sale for $76.

What is selling price?

The selling price is the amount of money that a seller asks for in exchange for a product or service. It is also known as the "list price" or "retail price" and it is the price at which an item is intended to be sold. Selling price is usually set by the manufacturer or the retailer, taking into account the cost of production, distribution, and marketing, as well as competition and market demand. The selling price is usually higher than the cost of production, which includes the cost of the materials, labor, and overhead expenses.

The formula to calculate the selling price of a product or service depends on the information available and the desired level of accuracy. However, there are a few common formulas used to calculate the selling price based on different factors.

Cost-plus pricing formula: This formula calculates the selling price by adding a markup percentage to the cost of the product or service.

The formula is: Selling price = Cost + (Cost x Markup percentage)

If the original price of an item was $95 and it is now on sale for 20% off, we can calculate the sale price using the following formula:

Sale price = Original price x (1 - Discount percentage)

In this case, the discount percentage is 20%, so we can express it as 0.2. Therefore, the formula becomes:

Sale price = $95 x (1 - 0.2)

To calculate the sale price, we need to multiply the original price by (1 - 0.2) which is (1-0.2) = 0.8

Sale price = $95 x 0.8

Sale price = $76

So, the item is on sale for $76.

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Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.

Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:

length of wood per birdhouse x number of birdhouses = total length of wood

So, in this case, we can substitute the given values in the formula:

58 yards x 12 birdhouses = 696 yards

This means Meri needs 696 yards of wood to make 12 birdhouses.

This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.

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If Dawson says that the expression [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] is equal to a whole number , then we can say that Dawson is correct .

The Mixed fraction expression is given as : [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] ;

first , we need to convert the mixed fraction in to simpler fractions ,

On converting ,

we get ;

the expression as : [tex](\frac{24}{10}+\frac{44}{5})-\frac{16}{5}[/tex] ;

taking the LCM of 10 and 5 as 50 ,

we get ;

⇒ [tex](\frac{24}{10}+\frac{88}{10})-\frac{16}{5}[/tex]

⇒ [tex](\frac{112}{10})-\frac{16}{5}[/tex]

Simplifying further ,

we have ;

⇒ [tex](\frac{112}{10})-\frac{32}{10}[/tex] ,

⇒ [tex]\frac{80}{10}[/tex]

= 8 , which is a whole number .

Therefore , we can agree with Dawson's statement that the expression [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] equals to a whole number "8" .

The given question is incomplete , the complete question is

Dawson says that the expression ([tex]2\frac{4}{10}[/tex] + [tex]8\frac{4}{5}[/tex]) - [tex]3\frac{1}{5}[/tex] is equal to a whole number .  Do you agree ? Explain .

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The expression represents a polynomial with three terms.

A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.

The expression represents a polynomial with three terms.

The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.

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The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.

This means,

3x + 5y = 15

5y = -3x + 15

y = (-3/5)x + 3

m(2) = (-3/5)

Now,

m(1) x m(2) = -1

m(1) = -1 / ((-3/5)

m(1) = 5/3

Now,

(3, 2) = (x, y)

y = m(1)x + c

2 = (5/3) x 3 + c

2 = 5 + c
c = 2 - 5

c = -3

Thus,

The equation of the line is y = (5/3)x - 3.

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When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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Answer:

-2 i think hope this helps

Step-by-step explanation:

Answer:

x = 40° , y = 140° z = 10°

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , then

x + 60° + 80° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle , then

y = 60° + 80° = 140°

x is also an exterior angle , then

30° + z = x

30° + z = 40° ( subtract 30° from both sides )

z = 10°