3(x-4)=12 solve for x

Answer:

G -8, -6, -4, -2

Step-by-step explanation:

integers are ...-2,-1,0,1,2,3 ... and so on but

whole numbers are 1,2,3,4,5,6 ... so on

so the only one thats right is the negative numbers

Answer:

x = 3

Step-by-step explanation:

The diagonals of a rhombus bisect each other at right angles, thus

BE = ED, that is

4x + 2 = 3x + 5 ( subtract 3x from both sides )

x + 2 = 5 ( subtract 2 from both sides )

x = 3

Since diagonals of rhombus bisect each other,

AC bisects BD into two equal parts

ie,

⇒BE=ED

⇒4x+2=3x+5

⇒4x-3x=5-2

⇒x=3

Answer:

[tex]\displaystyle y = \frac{1}{3}x[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 - 4}{9 - 12} = \frac{1}{3}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done much swiftly that way. It does not matter which ordered pair you choose:

−4 = ⅓[−12] + b

−4

[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]

_______________________________________________

−3 = ⅓[−9] + b

−3

[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]

**You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

Answer:

The answer is...

Step-by-step explanation:

y = 1/3x

--or--

y = x/3

Both forms of writing are equivalent, so either choice would be correct. I hope this helps!

The remainder when a cubic polynomial is divided by (x-2)(x-3) can be found using the given remainders with (x-2) and (x-3) separately, resulting in a = 3 and b = -2. Hence, the remainder is 3x - 2. Then, using the condition that f(1)=1 and f(x) is cubic with a leading coefficient of 1, we can determine the entire function and Q(x).

Given that a polynomial f(x) has remainders when divided by (x-2) and (x-3), we can establish that:

From these conditions, we derive two equations:

Solving these simultaneously gives us a = 3 and b = -2. Thus, the remainder when f(x) is divided by (x-2)(x-3) is 3x - 2.

Considering f(x) is cubic and the coefficient of x^3 is 1, f(x) = x^3 + px^2 + qx + r, and since f(1)=1, we can find out Q(x) by plugging the values a, b, and f(1) into the polynomial f(x) and comparing it with the standard cubic form. This will lead us to determine the function Q(x).

Answer:

[tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{m^2+7m+6}+\frac{m+3}{m^2+7m+6}= \frac{5}{m+6}\\[/tex]

Simplifying the above equation we get:

Step 1: Solving for common denominator term we get;

[tex]\frac{1+m+3}{m^2+7m+6}= \frac{5}{m+6}\\\\\frac{m+4}{m^2+7m+6}= \frac{5}{m+6}[/tex]

Step 2: Multiplying denominators on both side we get;

[tex](m+4)(m+6)=5(m^2+7m+6)\\m^2+6m+4m+24 = 5m^2+35m+30\\m^2+10m+24 = 5m^2+35m+30\\5m^2+35m+30-m^2-10m-24=0\\4m^2+25m+6=0[/tex]

Step 3: Now we need to find the factors of m.

[tex]4m^2+25m+6=0\\4m^2+m +24m+6=0\\m(4m+1)+6(4m+1)=0\\(4m+1)(m+6)=0[/tex]

Step 4: Solving for both terms we get;

[tex]4m+1=0\\4m =-1\\m= - \frac{1}{4}[/tex]

Also,

[tex]m+6=0\\m=-6[/tex]

Hence [tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]

5x + 9 = x - 23

move x to the other side

sign changes from +x to -x

5x-x+9= x-x-23 ( combine like terms)

5x-x+9= -23

4x+9= -23

move -9 to the other side

4x+9-9= -23-9

4x= -23-9

4x= -32

divide both sides by 4 to get x by itself

4x/4= -32/4

answer:

x= -8

Answer:

10 hats and 30 scarves

Step-by-step explanation:

Let h be the number of hats Kaelyn makes and s be the number of scarves she makes.

Kaelyn wants to make 3 times as many scarves as hats, so

s = 3h

Each hat uses 0.2 kilograms of yarn, then h hats use 0.2h kg of yarn.

Each scarf uses 0.1 kilograms of yarn, then s scarves use 0.1s kg of yarn.

Kaelyn wants to use 5 kilograms of yarn, thus

0.2h + 0.1s = 5

You get the system of two equations:

[tex]\left\{\begin{array}{l}s=3h\\ \\0.2h+0.1s=5\end{array}\right.[/tex]

Substitute the first equation into the second

[tex]0.2h+0.1\cdot 3h=5\\ \\0.2h+0.3h=5\\ \\0.5h=5\\ \\5h=50\\ \\h=10\\ \\s=3\cdot 10=30[/tex]

Answer:

s=3h

0.2h+0.1s=15

Step-by-step explanation:

Answer:

a) 1 time

b) 1.75%

Step-by-step explanation:

a) The given expression is 1,000(1.0175)^2

Here,

1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).

Since two means 2nd year, therefore, the interest is compounded every year. Hence, it is annual compounding interest.

If the interest rate is compounded annually, the interest will be paid one time each year or period.

b) From part a, if we break the expression,

1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).

Since the interest rate is to be compounded annually, the percentage will not affect.

(1.0175 = 1 + 0.0175) in this expression, one is added to the interest to make the future compounding value.

Therefore, 0.0175 is the interest rate. If we take it to the percentage -

0.0175 x 100 = 1.75%.

Answer:

a) 1 time

b) 1.75%

Step-by-step explanation:

yes

Answer:

x = 8

Step-by-step explanation:

x/x+4=2/3

3x = 2x + 8

x = 8

Answer:

B. She subtracted the end time from the start time and

D. She did not account for a.m. and p.m. in the start and end times.

Step-by-step explanation:

The school started at 8:05 a.m. and ended at 2:40 p.m.

And the length of the school day is calculated by Erica and it is shown in the attached photo.

See the attached photo.

Erica has done two errors which are  

B. She subtracted the end time from the start time and  

D. She did not account for a.m. and p.m. in the start and end times. (Answer)

Answer:

-3

Step-by-step explanation:

start at the y axis where x= 0, go over one and down till your reach the next intersection of the graph, this is over one down three, or -3 for every x over

Conditions of the binomial distribution include a fixed number of independent trials, each trial having two possible outcomes, and constant probabilities of success and failure. Experiments that do not meet these conditions do not follow a binomial distribution. For example, if the probability of success varies across trials, it's not a binomial distribution.

The binomial distribution has several key conditions, and a statistical experiment is classified as a binomial experiment if it meets these conditions. Some of these conditions include the following:

Therefore a circumstance not meeting these conditions would not fit the binomial distribution. For example, if the conditions for each trial are not consistent, such as the probability of success changes from trial to trial, then it would not be classified as a binomial distribution.

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Answer:

∠B = 130°

Step-by-step explanation:

The opposite angles of a parallelogram are congruent, thus

∠D = ∠B, that is

10x - 20 = 9x - 5 ( subtract 9x from both sides )

x - 20 = - 5 ( add 20 to both sides )

x = 15

Hence

∠B = 9x - 5 = (9 × 15) - 5 = 135 - 5 = 130°

Answer:

15

Step-by-step explanation:

9x-5=10x-20

X-20=-5

X=15

Answer: -16

Step-by-step explanation:

slope=rise/run

slope=2-(-4)/-3-(-2)=6/-1=-6

y=mx+b

2=(-6)-3+b

b=-16

Answer:

3_561938 you are your

Step-by-step explanation:

3AM said

Henry's balloon was farther from the town at the beginning, but Tasha's balloon traveled more quickly.

To determine which balloon was farther from the town at the beginning, we need to compare the initial distances of Henry's and Tasha's balloons from the town. Henry's balloon begins 30 miles from the town, while Tasha's balloon is represented by the function y = 8x + 20, where x is the time in hours. Plugging in x = 0 into the function, we can find that Tasha's balloon was 20 miles from the town at the beginning.

To determine which balloon traveled more quickly, we can compare their speeds. Henry's balloon travels at a constant speed of (48 miles - 30 miles) / 2 hours = 9 miles/hour. Tasha's balloon has a constant speed of 8 miles/hour since it follows the equation y = 8x + 20. Therefore, Henry's balloon traveled more quickly.

Therefore, the correct answer is OC. Henry's balloon was farther from the town at the beginning, but Tasha's balloon traveled more quickly.

Answer:

32760 ways

Step-by-step explanation:

Suppose we all want to play different games, so 4 different games. At the first game there are 15 choices, at the 2nd game there are 14, the 3rd one there are 13 selections, and at the last there are only 12 options to select from. Then the total number of ways you can choose the 4 games is

15*14*13*12 = 32760 ways

There are 1,365 ways to choose four games out of the 15 available games.

Step 1

To find the number of ways you can choose four games out of the 15 available games, we use the combination formula:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

Where  n is the total number of games (15) and  k is the number of games to choose (4).

Step 2

Plugging in the values:

[tex]\[ C(15, 4) = \frac{15!}{4!(15-4)!} \][/tex]

[tex]\[ = \frac{15!}{4! \times 11!} \][/tex]

[tex]\[ = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{32,760}{24} \][/tex]

[tex]\[ = 1,365 \][/tex]

You can choose the four games out of the 15 available games in 1,365 ways, calculated using the combination formula.

Answer:

The answer is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

Step-by-step explanation:

The given product is,

[tex]\frac {-4}{5} \times \frac{3}{5} \times \frac{-6}{7} \times \frac {5}{6}[/tex]

= [tex]\frac {12}{35}[/tex]

[tex]\simeq 0.3429[/tex] ---------------------(1)

Now, the first product to compare is,

[tex](-1) \times \frac {1}{4} \times (-1) \times (-1)[/tex]

= - 0.25 ----------------------------(2)

The second product to compare is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

= 0.5 ------------------------(3)

The 3rd product to compare is,

[tex]\frac {-4}{2} \times \frac {3}{2} \times \frac{-2}{5} \times \frac {5}{2}[/tex]

= 3 ----------------------------(4)

The 4th product to compare is,

[tex]\frac {-3}{4} \times \frac {-3}{4} \times \frac {-1}{5} \times \frac {1}{2}[/tex]

= [tex]\frac {-9}{160}[/tex]

= 0.05625 -----------------(5)

Comparing all the values , we get (3) is closest to (1).

Hence, we get, the answer is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

Answer:

1/4 of the brownies were eaten

there were 1 - 1/4 = 3/4 of brownies left

2/3 of the 3/4 were eat or: (2/3)(3/4) = 1/2 of the whole pan of brownies were eaten

the total of brownies eaten is: 1/4 + 1/2 = (1*1 + 2*1)/4 = 3/4 of the whole pan of brownies were eaten.Step-by-step explanation:

John ate half or 50% of the original whole pan of brownies. This is calculated by multiplying 3/4 (the remaining brownies after 1/4 had been eaten) by 2/3 (the fraction John ate of the remaining amount).

Firstly, the question pertains to the proportion of brownies that were consumed. Initially 1/4 of the brownies were eaten, implying that 3/4 of the brownies were left on the counter. John ate 2/3 of the remaining brownies, so we will calculate 2/3 of 3/4 to determine how much of the whole pan of brownies John ate:

Step 1: Convert 3/4 and 2/3 to decimal points (0.75 and 0.67 respectively).

Step 2: Multiply 0.75 (the remaining brownies) by 0.67 (the fraction that John consumed). This equals approximately 0.50.

Step 3: The result 0.50 implies that John consumed 50% or half of the original brownies amount.

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Answer: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.

Step-by-step explanation:

Answer:

his rang is 113 and amelis is 179

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

if x = 32 and y = 2, then you just have to substitute the numbers in:

[tex]\frac{32}{4 * 2}[/tex]

so,

[tex]\frac{32}{8}[/tex]

then you simplify

[tex]\frac{4}{1}[/tex]

so the answer is 4

Answer:

2

Step-by-step explanation:

Replace the variables with the real numbers

32/4 2

Multiply

4 x 3 = 12

Divide

32 / 12 = 2⅔

2⅔ ≈ 2

Answer: 2

Edit: Instead, go with D.) 4

The equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) is P = R - 10

The profit is $15 million when revenue is $25 million

Step-by-step explanation:

The formula of the profit is P = R - E, where

If a company’s expenses were $10 million, wee need to write an equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) and then find the profit when revenue is $25 million

∵ P is the profit in millions of dollars

∵ R is the revenue in millions of dollars

∵ The expenses E were $10 million

∵ Profit = Revenue - Expenses

∴ P = R - 10

The equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) is P = R - 10

∵ The revenue R = $25 million

∵ P = R - 10

- Substitute the value of R in the equation

∴ P = 25 - 10

∴ P = 15

∴ The profit is $15 million

The profit is $15 million when revenue is $25 million

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The center of the ellipse is (10 , -4) and its vertices are (17 , -4) , (3 , -4)

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h , k)  

and major axis parallel to x-axis is [tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1[/tex]  

∵ The equation of the ellipse is [tex]\frac{(x-10)^{2}}{49}+\frac{(y+4)^{2}}{4}=1[/tex]

- Compare it by the standard form of the equation of an ellipse

∴ h = 10 and k = -4

∴ a² = 49 and b² = 4

∵ The center of the ellipse is (h , k)

∴ The center of the ellipse is (10 , -4)

∵ Its vertices are (h + a , k) and (h - a , k)

∵ a² = 49

- Take square root for both sides

∴ a = 7

∵ h = 10 and k = -4

- Substitute the values of h , a , k in the vertices above

∴ Its vertices are (10 + 7 , -4) and (10 - 7 , -4)

∴ Its vertices are (17 , -4) and (3 , -4)

The center of the ellipse is (10 , -4) and its vertices are (17 , -4) ,

(3 , -4)

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Answer:

Step-by-step explanation:

[tex]_{\bold{METHOD\ 1}}\\\\\begin{array}{ccc}100\%&-&106\\\\84\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\100x=(84)(106)\\\\100x=8904\qquad\text{divide both sides by 100}\\\\\dfrac{100x}{100}=\dfrac{8904}{100}\\\\x=89.04[/tex]

[tex]_{\bold{METHOD\ 2}}\\\\p\%=\dfrac{p}{100}\to84\%=\dfrac{84}{100}=0.84\\\\84\%\ of\ 106=0.84\cdot106=89.04[/tex]

Answer:

In 20 weeks they will have the same amount of money.

Step-by-step explanation:

Answer:

The ladder is approx 14.21 feet long.

Step-by-step explanation:

The base of the ladder is 7 feet from the fence, which is 2 feet from the building, so it will be 9 feet from the building.

The top of the ladder will reach the window which is 11 feet from the ground.

In this way, we get a right triangle with the ladder as the hypotenuse, that we have to find.

Let the hypotenuse be x.

Using the Pythagorean Theorem, we get;

Hence, the ladder is approx 14.21 feet long.

Answer:

a)  The amount of edging needed = 7.54 meters

b)  Cost to edge the garden = $32.80

Step-by-step explanation:

a)

the amount of edging needed is basically the circumference (perimeter) of the circle. It has the formula:

[tex]C=2\pi r[/tex]

Where

C is the circumference

r is the radius

Given, diameter = 2.4, radius is HALF of it, so

r = 2.4/2 = 1.2

Now, finding circumference:

[tex]C=2\pi r\\C=2\pi (1.2)\\C=7.54[/tex]

The amount of edging needed = 7.54 meters

b)

$4.35 is needed to edge 1 meter, since we need 7.54 meters, we find the total cost by multiplying 4.35 with 7.54, so we have:

4.35*7.54 = $32.80

Cost to edge the garden = $32.80

Option A: SU, TU, ST is the right answer

Step-by-step explanation:

In a triangle

So using the above axioms we can observe the triangle.

So the sides in order from least to greatest are: SU, TU, ST

Hence,

Option A: SU, TU, ST is the right answer

Keywords: Geometry, Triangles

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Answer:

x = 2

Step-by-step explanation:

The 2 coordinate points have the same x- coordinate of 2

This indicates that the line passing through them is vertical with equation

x = c

Where c is the value of the x- coordinates the line passes through, thus

x = 2 ← equation of line

Answer:

10

Step-by-step explanation:

3 3/4=15/4

(15/4)/(3/8)=(15/4)(8/3)=30/3=10

Answer:

207,50

Step-by-step explanation:

1% = 2,5

2,5x25 = 62,5 250 - 62,5 = 187,5

2,5x8 = 20

187,5+20= 207,50