Two consecutive odd integers have a sum of 40. Find the integers

The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).

It follows from the task content that the image point of the pair of coordinates given is to be determined.

Given point is; (-3, -2).

Hence, after a reflection over the x-axis; we have; (-3, 2).

Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).

Therefore, the image point is; (-(-3), -(2)).

The image point is therefore; (3, -2).

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Answer:

220.

Step-by-step explanation:

If you plug in 4 for L and 6 for W, you are left with 25(4) + 20(6), which is equivalent to 100+120 = $220

Answer:

220

Step-by-step explanation:

The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polygon,(1/3)b - 1/3

Take 1/3 as common in the whole polygon,

1/3(b - 1).

Since the terms 1/3 and (b - 1) both are in the multiplication of each other.

Hence "The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1)".

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The expanded form of  7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.

The expanding form can be used to indicate the value of each digit in a number in arithmetic. Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.

It is given that,

a) 7(7a + 4b) + 10a - 10b

b) 6(2x+6y) -

a)

[tex]=7(7a + 4b) + 10a - 10b \\\\ =49a+28b+10a-10b \\\\ =49a+10a+28b-10b \\\\ =59a+28b-10b \\\\ =59a+18b[/tex]

b)

= 6(2x+6y) -

=12x+12y

Thus, the expanded form of  7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.

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Answer:

Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0

The  total cost for the group of ten people after discount is 10 t - 0.5 t.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Discount = 5%

Total tickets= 10

We have t represents the cost of one ticket.

So, For 10 person the cost of the ticket = 10t

Now, after discount the price of tickets

= 5% of 10t

= 0.5 t

Hence, the total cost for the group of ten people after discount is 10 t - 0.5 t.

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Answer:

[tex]\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)[/tex]

[tex]\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3x^3-2x^2-11x+10[/tex]

If (x + 2) is a factor then:

[tex]\implies f(x)=(x+2)(ax^2+bx+c)[/tex]

Expand:

[tex]\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c[/tex]

[tex]\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c[/tex]

[tex]\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c[/tex]

To find a, compare the coefficients of x³:

[tex]\implies a=3[/tex]

To find b, substitute the found value of a into the coefficient for x² and compare:

[tex]\implies 2a+b=-2[/tex]

[tex]\implies 2(3)+b=-2[/tex]

[tex]\implies b=-8[/tex]

To find c, compare the constants:

[tex]\implies 2c=10[/tex]

[tex]\implies c=5[/tex]

Therefore:

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

Now factor (3x²-8x+5):

[tex]\implies 3x^2-3x-5x+5[/tex]

[tex]\implies 3x(x-1)-5(x-1)[/tex]

[tex]\implies (3x-5)(x-1)[/tex]

Therefore the factored function is:

[tex]\implies f(x)=(x+2)(3x-5)(x-1)[/tex]

Zero Product Property

[tex]\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}[/tex]

To find the zeros, set each factor equal to zero and solve for x:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies 3x-5=0 \implies x=\dfrac{5}{3}[/tex]

[tex]\implies x-1=0 \implies x=1[/tex]

Therefore, the zeros of the function are:

[tex]x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

The radius of the bigger sphere is 30cm.

Two spherical solids have masses of 15g and 405kg respectively

Mass is directly proportional to volume for same metal (Density)

Let Mass of Solid 1 be M₁ and Volume be V₁

Mass of Solid 2 be M₂ and Volume be V₂

Now  M₁/M₂ =  V₁/V₂

Volume of sphere is directly proportional to R³

So,  M₁/M₂ = V₁/V₂ = R₁³/R₂³​

15/405000 = 10³/x³

∛15/∛405000 = 10/x

2.466/73.986 = 10/x

2.466x = 73.986 x 10

x = 739.86/2.466

x = 30

Therefore, the radius of the bigger sphere is 30cm.

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The equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18

The statement is

3 times the sum of 4 and a number is 18

The equation is the the mathematical statement the represents the relationship between two expression or variables with an equal sign.

Consider the unknown number = n

Sum of 4 and the number = n + 4

3 times the sum of 4 and the number = 3(n + 4)

3 times the sum of 4 and a number is 18

3(n + 4) = 18

Hence, the equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18

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Answer:

25 percent.

Step-by-step explanation:

25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.

Hope it helps.

The total cans collected by both Elizabeth and Herman is 650 and the total amount of money realized is 1300 cents.

A rate is a ratio in which the two terms being compared have different unit's.For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The aluminum cans collected by Elizabeth from Monday to Fridays is 50× 5days = 250 cans

Herman collected double from Monday to Thursday and collected non on Friday, therefore the total cans collected by Herman = 50×2× 4 days= 400cans

the total cans collected = 250+ 400 cans = 650cans

therefore the total money realized since 1 can is with 2 cent is 650× 2= 1300cents

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Option A. The statement that can be said to be true for h is h(2) = 16

If we look at the domain and range, we can rule out some straight away.

For h - 3 = -1

this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25

When h is 13 = 18

This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11

When h is 8 = 21

there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19

Therefore on h(2) = 16

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Answer:

the answer is 6

Step-by-step explanation:

I hope I helped, if you have questions let me know. I'll try to answer.

The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.

According to the question,

We have the following information:

The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.

And h represents the number of hours.

So, we have the following expression to find the total cost:

150+25h

Now, it is given that the total rental cost should not exceed $300.

So, we have the following inequality:

150+25h ≤300

Hence, the correct option is C.

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The slope of given line is 43

The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.

The formula of finding the slope of line with two given points is as follows,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1

It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43

Hence,the slope of the give line is 43

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The first step to find the quotient of a long division problem is to Divide the terms with highest degreee

A quotient is a quantity produced by the division of two numbers. For example 16/4 ,the number that is being divided (in this case, 16) is called the dividend, and the number that it is being divided by (in this case, 4) is called the divisor. The result of the division(5) is the quotient.

The step that is needed to find a quotient of a division are

1.Divide the terms with the highest degree

2.Multiply terms by the divisor

3.Place the result in the quotient

4. Subtract the product from the dividend

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Answer:

Step-by-step explanation:

The length of material needed for the border is the perimeter of the backyard play area

How to calculate the length of material needed

The area of the play area is given as:

The area of a trapezoid is calculated using:

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

Using the assumed values, the length of material needed for the border is 74.4 feet

The piece of information does he need is  ∠F ≅ ∠J.

What is triangle?

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.

Properties of triangle?

Given,

ΔFGH = ΔJKL

By SAS property of triangle;

[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex],     FG ≅ JK

third property ,

                         ∠F = ∠J

By SAS property at least two side their ratio must be equal and one angle.

[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]

∠F = ∠J

So, option A is correct.

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The total number of degrees the temperature changed in the 6 hours is 12°F

Here,

The temperature dropped 2°F every hour for 6 hours.

We have to find,

The total number of degrees the temperature changed in the 6 hours.

Fahrenheit is a scale for measuring temperature, in which water freezes at 32 degrees and boils at 212 degrees. It is represented by the symbol ° F.

Now,

The temperature dropped 2°F every hour for 6 hours.

1 hour =  2°F

6 hour = 6 x 2 = 12°F

Hence, The total number of degrees the temperature changed in the 6 hours is 12°F.

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Answer:

I believe... f(x)=1400+4x

The proportion of selling times is 0.35

From the question, we have

Selling Time___ Frequency

0 10____________3

10 20__________ 4

20 30__________ 6

30 40__________ 4

40 50__________ 3

Proportion of selling times in sample above that are less than 20 days :

total frequency = (3 + 4 + 6 + 4 + 3) = 20

Selling time which is less Than 20 days :

(0 - 10) = 3

(10 - 20) = 4

Total = (3 + 4) = 7

Proportion = selling time less Than 20 days / total frequency

= 7 / 20

= 0.35

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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Answer:

yup

Step-by-step explanation:

so to find the amount of plates he has we :

30*9 = 270

How many guests :

250

Hank has 20 extra plates,

hope this helps :)

An equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

Given that, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

We know that, the slope of a line parallel to given line is m1=m2.

Here, x−2y=6

⇒ 2y=x-6

⇒ y=x/2-3

So, slope = 1/2

The slope of a line parallel to the given line = 1/2

Now, put m=1/2 and (x, y)=(-6, -8) in y=mx+c and solve for c

-8=1/2(-6)+c

⇒ c=-8+3

⇒ c=-5

Thus, y=x/2-5

Therefore, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

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During the first 3 months students club has raised fund of  $1680.

Given that, The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

After 3 months, it reaches 42% of its goal.

The fund raised during the first 3 months is

42% of 4000

= 42/100 × 4000

= 42×40

= $1680

Therefore, during the first 3 months students club has raised fund of  $1680.

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Answer:

$1,680

Step-by-step explanation:

The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB

A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.

The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²

Converting the unit of the sound intensity to Watts/m² gives;

1 cm² = 0.0001 m²

10,000 cm² = 1 m²

2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²

The equation for the decibel from the power of sound is presented as follows;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]

Where;

I₀ = 10⁻¹² W/m²

Which gives;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]

The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels

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The mean of the data is 3.85 using the stem-and-leaf plot.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.

Given the stem-and-leaf plot, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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(a) The shape of the distribution of donations is rectangular.

(b) The proportion of donations are at least 75 cents id 0.24

(a)The density curve is rectangular in shape.

This indicates that donations are distributed uniformly.

(b) From the question, we have

The probability of donations at least 75 cents as follows:

[tex]P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\[/tex]

Substituting the limits,  we get

[tex]P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24[/tex]

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of even numbers in a deck of cards.

= 5 x 4

= 20

The number of diamonds in a deck of cards.

= 4

Now,

The probability of drawing an even number from a deck of cards.

= 20 / 52

= 10/26

= 5/13

Now,

The remaining cards.

= 52 - 20

= 32

The probability of drawing diamonds after drawing the even numbers.

= Number of diamonds / remaining cards

= 4 / 32

= 1/8

Thus,

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

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Answer:

Step-by-step explanation:

457-235= 222

222-125=97

97÷2= 48.5

≈49 pairs of pants and shoes