Find the equation of the line that is perpendicular to y=-2/3x and contain the point (4,-8)

Answer:

x = - 7, x = 0 and x = 4

Step-by-step explanation:

Factor the polynomial and solve for x

Given

x³ + 3x² - 28x = 0 ← factor out x from each term

x(x² + 3x - 28) = 0 ← factor the quadratic

x(x + 7)(x - 4) = 0

Equate each factor to zero and solve for x

x = 0

x + 7 = 0 ⇒ x = - 7

x - 4 = 0 ⇒ x = 4

These are the 3 points where the graph crosses the x- axis

ANSWER

The correct answer is D.

EXPLANATION

If we express the monomial,

[tex]18 {x}^{2} y[/tex]

as product of primes, we obtain:

[tex]2 \times {3}^{2} \times {x}^{2}y [/tex]

If we express the monomial

[tex]27x {y}^{3} [/tex]

as product of primes we obtain:

[tex] = {3}^{3} \times x {y}^{3} [/tex]

The least common multiple of these two binomials is the product of the highest powers of the common factors.

The LCM is

[tex] = 2 \times {3}^{3} \times {x}^{2} {y}^{3} [/tex]

[tex] =54 {x}^{2} {y}^{3} [/tex]

Therefore the correct answer is D.

Answer:

The correct answer is option D.

18x2y, 27xy3

Step-by-step explanation:

To find the LCM

A).To find the Lcm of  (2xy, 27xy2)

LCM((2xy, 27xy2)  = 54xy^2

B).To find the  Lcm of  (3x2y3, 18x2y3)

LCM(3x2y3, 18x2y3)  = 18x^2y^4

C). To find the  Lcm of (6x2, 9y3)

LCM(6x2, 9y3)  = 18y^2y^

D). To find the  Lcm of (18x2y, 27xy3)

 LCM(18x2y, 27xy3) = 54x^2y^3

Therefore the correct answer is option D

18x2y, 27xy3

Answer:

option B) f(x)=x^3-6x^2+11x-6

Step-by-step explanation:

Zeros means the point at which a given function becomes zero for the value of input.

In given case, zeros of f(x) is required at points 1,2 and 3.

Graphically the point on x-axis where the function line intersects the x-axis is the zero of the function i.e. the function value is 0,

hence

f(x)=0 when x=1

x-1=0

f(x)=(x-1)

f(x)=0 when x=2

x-2=0

f(x)=(x-2)

f(x)=0 when x=3

x-3=0

f(x)=(x-3)

Thus f(x)=(x-1)(x-2)(x-3)

Writing the above polynomial in standard form:

f(x)=x^3-6x^2+11x-6 !

Answer: 8nⁿ⁴

Step-by-step explanation:

Because we use the Qualinto formula (Taught in 4th grade) to get 6. After that multiply 6 by 8^(9n + 0) to get 48n^ + 54. After this, use the squint formula (Taught in 6th grade). To get 8n + 54. Once this step is completed, use extramath/56's equivalent formula to finally get your answer: 8nⁿ⁴

Answer:

x=2

Step-by-step explanation:

Divide 49 by 7, and you get 7 which is a perfect square

Let's test it out!

7^x=49

7^(2)=49

49=49

It works out!

Answer:

[tex](x-4)^2+(y-3)^2=2^2[/tex]

Step-by-step explanation:

The given circle has equation; [tex]x^2+y^2-8x-6y+24=0[/tex]

Comparing to the general equation of the circle:  [tex]x^2+y^2+2ax+2by+c=0[/tex]

We have [tex]2a=-8\implies a=-4[/tex] and [tex]2b=-6\implies b=-3[/tex]

The center of this circle is (-a,-b)=(4,3).

The required circle has radius r=2 units.

The equation of a circle, given the center (h,k) and radius r, is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the values to obtain [tex](x-4)^2+(y-3)^2=2^2[/tex]

Answer:

the answer is C

Step-by-step explanation:

ANSWER

Domain: All real numbers

Range:

[tex][2, \infty )[/tex]

EXPLANATION

The given function is

[tex]y = 3 {x}^{2} - 6x + 5[/tex]

To find the domain and range of the given function, we complete the square.

[tex]y = 3 ({x}^{2} - 2x )+ 5[/tex]

[tex]y = 3 ({x}^{2} - 2x + 1) + 3( - 1)+ 5[/tex]

[tex]y = 3 ({x - 1)}^{2} - 3+ 5[/tex]

[tex]y = 3 ({x - 1)}^{2} + 2[/tex]

The vertex is at (1,2).

The given function is a polynomial and all polynomial functions are defined everywhere.

The domain is all real numbers.

The parabola opens upwards and have vertex at (1,2). Hence the minimum y-value is 2.

The range is

[tex][2, \infty )[/tex]

Answer:

A.

Step-by-step explanation:

Lucas put 1.30 in his coin bank.

Answer:

Any number times zero is zero.

Step-by-step explanation:

Simplify the following:

0 g f

Hint: | Any number times zero is zero.

0 g f = 0:

Answer:  0

Answer:

Volume=943 cm^3 Cross section area=79 cm^2

Step-by-step explanation:

volume of a cylinder is [tex]\pi r^{2} h[/tex]

so 10/2=5 5^2=25*12=300*pi is about 942.477 or 943 cm^3

to find the area of the cross section, on just needs to find the area of the face of the cylinder. so pi times 5^2=pi times 25=78.540 or 79 cm^2

Answer:

The answer to your question is C (27%)

Step-by-step explanation:

I looked up the answer for you but this was proven to be correct.

The computer is worth approximately $599.83 in 2009.

To find out how much the computer is worth in 2009, we need to determine the value after each year's decline. The computer's value declines by 7% each year, so we can calculate the worth of the computer in 2009 by multiplying the original value by (1 - 0.07) four times since there are four years between 2005 and 2009.

Year 1: $800 * (1 - 0.07) = $800 * 0.93 = $744

Year 2: $744 * (1 - 0.07) = $744 * 0.93 = $692.64

Year 3: $692.64 * (1 - 0.07) = $692.64 * 0.93 = $644.86

Year 4 (2009): $644.86 * (1 - 0.07) = $644.86 * 0.93 = $599.83

Therefore, the computer is worth approximately $599.83 in 2009.

Final answer:

To find the value of a computer in 2009 that Sally bought for $800 in 2005 with a 7% annual decline, we use the exponential decay formula. The computer would be worth approximately $598.48 in 2009.

Explanation:

The question asks to calculate the value of a computer after a specific period of time, considering a yearly depreciation. Sally bought a computer for $800 in 2005, and its value declines by 7% yearly. To find its value in 2009, we can use the formula for exponential decay:

Value = Initial Value × [tex](1 - Decline \ Rate)^{Years}[/tex]

Plugging in the values:

Value = $800 × [tex](1 - 0.07)^4[/tex]

Value = $800 ×  [tex](0.93)^4[/tex]

Value = $800 × 0.7481

Value = $598.48

Therefore, the value of the computer in 2009 is approximately $598.48.

The answer is:

The first option,

[tex]f^{-1}(x)=\frac{x-2}{4}[/tex]

To find the inverse of a function, we need to rewrite the variable "x" with "y" and the variable "y" with "x", and then, isolate "y".

We are given the function:

[tex]f(x)=4x+2[/tex]

Write "f(x)" is equal to write "y", so:

[tex]y=4x+2[/tex]

Now, finding the inverse, we have:

[tex]y=4x+2\\x=4y+2\\x-2=4y\\y=\frac{x-2}{4}[/tex]

Hence, we have that the answer is the first option,

[tex]f^{-1}(x)=\frac{x-2}{4}[/tex]

Have a nice day!

ANSWER

[tex]{f}^{ - 1} (x) = \frac{x - 2}{4} [/tex]

EXPLANATION

The given function is

f(x)=4x+2

To find the inverse, we let

y=4x+2

Then, interchange x and y.

x=4y+2

Solve for y,

x-2=4y.

Divide both sides by 4

[tex]y = \frac{x - 2}{4} [/tex]

Hence, the inverse is:

[tex] {f}^{ - 1} (x) = \frac{x - 2}{4} [/tex]

Answer:

8/35

Step-by-step explanation:

1 1/4 = 5/4

3 1/2 = 7/2

5/4 × 7/2

Find the reciprocal. (flip numerator and denomimator)

4/5 × 2/7 = 8/35

Answer:

8/35                                                                                                                                          This is your answer in simplest form.

One way is to find the area of the shape as if it was a whole square instead of an H shape.

That is (125+75+125) x (345), which is 112125 ft^2.

From this, let's subtract the areas of the cut-outs.

The cutouts are squares and both the same size. One side of it is 112 feet, so the area of one is 112x112=12544. So, the two squares have an area of 25088.

Now subtract that from the original total. 112125-25088=87037. <<that is the area.

You might want to double check my work.

Answer:

[tex]6z^{4}[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{ (2z^5)(12z^3)}{4z^4}[/tex]

Step 1

Apply exponential "product rule"

[tex]x^{m}x^{n}=x^{m+n}[/tex]

[tex]\frac{ 12(2)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ (24)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ 24(z^{(5+3)})}{4z^4}[/tex]

[tex]\frac{ 24(z^{8})}{4z^4}[/tex]

Step 2

Apply exponential " divide rule"

[tex]\frac{x^{m}}{x^{n}}=x^{m-n}[/tex]

[tex]\frac{24/4(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8-4})}{1}[/tex]

[tex]6z^{4}[/tex]

It’s the fourth one

Answer:

None of these

Step-by-step explanation:

This is because the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.

Answer:

Step-by-step explanation:

Answer alternate interior

I believe

Answer:

alternate interior

Step-by-step explanation:

it should be this not sure though

I’ll help you, but what’s “Number 9”?

The initial hight was 5

Approximately after 2second the disc with hit the ground

The formula for the absolute value function that has its vertex at point (0,6) and passes through the point (-1,-2) is y = -1/8|x| + 6.

To find the formula of an absolute value function, we need to use the formula |x - h| = a(y - k), where (h, k) is the vertex of the graph. In this case, the vertex is at point (0,6), so h = 0 and k = 6. The other point given is (-1,-2). We can substitute these values into the formula to find the value of 'a'. So, |-1 - 0| = a(-2 - 6) which simplifies to 1 = -8a. Solving this equation gives us a = -1/8. So, the formula for the absolute value function in this case is y = -1/8|x - 0| + 6 or just y = -1/8|x| + 6.

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The formula for the absolute value function with a vertex at (0,6) and passing through the point (-1,-2) is y = -8|x| + 6.

The formula for the absolute value function with a vertex at (0,6) and passing through the point (-1,-2) can be determined by considering how the graph of an absolute value function is shifted and stretched. In general, the formula for an absolute value function with a vertex at (h,k) can be written as y = a|x-h| + k. Using the given information, we can substitute the values h=0 and k=6 into the formula, and use the point (-1,-2) to solve for the value of a:

-2 = a|(-1)-0| + 6

-2 = a|-1| + 6

-2 = a + 6

a = -8

Therefore, the formula for the absolute value function is y = -8|x-0| + 6, which simplifies to y = -8|x| + 6.

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Answer:

(2/5, 9/6)

Step-by-step explanation:

6y = 10x + 5 | 6y = 5x + 7

Set them equal to each other because 6y = 6y.

10x +5 = 5x + 7

5x = 2

x = 2/5

6y = 5*2/5 + 7

6y = 2 + 7

y = 9/6

The given data set is:

37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61

We arrange the data set in ascending order of magnitude {4,5,6,25,37,42,48,53,61,65,78,79}

The median is 45.

The lower half of the data set is

{4,5,6,25,37,42}

The first quartile is the median of the lower half set;

[tex]Q_1=15.5[/tex]

The upper half of the data set is:

{48,53,61,65,78,79}

The median of the upper half is [tex]Q_3=63[/tex].

The inter-quartile range  [tex]Q_3-Q_1=63-15.5=47.5[/tex]

8. The given data set is 112, 149, 112, 148, 139, 121, 116, 134, 148.

The mean of the data set is [tex]\bar X =\frac{\sum x}{n}[/tex]

[tex]\bar X =\frac{112+149+112+148+139+121+116+134+148}{9}[/tex]

[tex]\bar X =\frac{179}{9}=131[/tex]

The standard deviation is given by:

[tex]s=\sqrt{\frac{\sum (x-\bar X)^2}{n} }[/tex]

[tex]s=\sqrt{\frac{(-19)^2+(18)^2+(-19)^2+(17)^2+(8)^2+(-10)^2+(-15)^2+(3)^2+(18)^2}{9} }[/tex]

[tex]s={\frac{\sqrt{2022}}{3}=14.98888477[/tex]

The standard deviation is 15.0 to the nearest tenth.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope m = -2 and the y-intercept b = 8. Substitute:

[tex]y=-2x+8[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]y=-2x+8[/tex]              add 2x to both sides

[tex]2x+y=8[/tex]              subtract 8 from both sides

[tex]2x+y-8=0[/tex]

Answer:

1. Given

2, Exterior sides on opposite rays

3. Definition of supplementary angles

4. If lines are ||, corresponding angles are equal

5. Substitution

Step-by-step explanation:

For the first one, it is given as shown in the problem. Also in the figure you can see that line s is parallel to line t.

2. ∠5 and ∠7 are adjacent, they share a common side. Their non-common side are rays that go in a direction opposite of each other. Also you can see that they form a straight line, which means that they are supplementary.

3. Supplementary angles simply put are angles that sum up to 180°. You know this for sure because of proof 2, specifically the part that they form a straight line. The measure of a straight line is 180°.

4. Corresponding angles are congruent. These are angles that have the same relative position when a line is intersected by parallel lines. You have other example in the figure like ∠2 and ∠6; ∠3 and ∠7.

5. This is substitution because ∠1 substituted ∠5 in this case. Since ∠1 is equal to ∠5, then it can substitute it in the equation given in step 3. This means that ∠1 and ∠7 are supplementary as well.

the like terms are 9x and 7x, if you are told to simplify, you write, "12y+16x"

12y + 9x + 7x

The like terms are 9x and 7x. This is because they both have the x variables attached to the number. This means that you can add only 9x and 7x (not 12y because it isn't a like term) together like normal numbers (except with an x at the end so you would get: 12y + 16x

Hope this helped!

Answer:

A = $7,350.00

Step-by-step explanation:

Equation:

A = P(1 + rt)

First, converting R percent to r a decimal

r = R/100 = 9%/100 = 0.09 per year.

Putting time into years for simplicity,

30 months / 12 months/year = 2.5 years.

Solving our equation:

A = 6000(1 + (0.09 × 2.5)) = 7350

A = $7,350.00

The total amount accrued, principal plus interest, from simple interest on a principal of $6,000.00 at a rate of 9% per year for 2.5 years (30 months) is $7,350.00.

* Therefor, the answer is $7,350.00.

* Hopefully this helps:) Mark me the brainliest:)!!!

To find Dominick's monthly installment payments for a $6,000 loan at 9% simple interest over 30 months, you first calculate the total interest ($1,350), add it to the principal to get the total amount owed ($7,350), and then divide by the number of months (30) to find the monthly payment, which is approximately $245.

Calculating Monthly Installment Payments

Dominick borrowed $6,000 from a credit union at 9% simple interest for 30 months. To calculate the total amount of interest, we'll use the formula for simple interest, which is Interest (I) = Principal (P) × Rate (R) × Time (T). For this loan, the principal P is $6,000, the annual interest rate R is 9% (or 0.09 when expressed as a decimal), and the time T is 30 months (or 2.5 years). Plugging these values into the formula gives us:

I = $6,000 × 0.09 × 2.5 = $1,350

The total amount owed, including interest, is $6,000 + $1,350 = $7,350. To determine the monthly installment payments, we divide this total amount by the number of months over which the loan will be repaid, which is also 30 months.

Monthly Installment Payments = Total Amount / Number of Months

Monthly Installment Payments = $7,350 / 30 ≈ $245

So, Dominick's monthly installment payment is approximately $245 to the nearest whole cent.

Answer:

I believe the answer is 120

The value of x in the figure is 120° .

Since MN and NP are tangent to O, then the angle subtended at the center is twice angle m

Now we have :

O = 2 * 60

O = 120°

Therefore, angle O = 120°

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QUESTION 11

Given : [tex]\ln(3x-8)=\ln(x+6)[/tex]

We take antilogarithm of both sides to get:

[tex]3x-8=x+6[/tex]

Group similar terms to get:

[tex]3x-x=6+8[/tex]

Simplify both sides to get:

[tex]2x=14[/tex]

Divide both sides by 2 to obtain:

[tex]x=7[/tex]

12.  Given; [tex]\log_3(9x-2)=\log_3(4x+3)[/tex]

We take antilogarithm to obtain:

[tex](9x-2)=(4x+3)[/tex]

Group similar terms to get:

[tex]9x-4x=3+2[/tex]

[tex]5x=5[/tex]

We divide both sides by 5 to get:

[tex]x=1[/tex]

13.  [tex]\log(4x+1)=\log25[/tex]

We take antilogarithm to get:

[tex](4x+1)=25[/tex]

Group similar terms

[tex]4x=25-1[/tex]

[tex]4x=24[/tex]

Divide both sides by 4

[tex]x=6[/tex]

14. Given ; [tex]\log_6(5x+4)=2[/tex]

We take antilogarithm to get:

[tex](5x+4)=6^2[/tex]

Simplify:

[tex](5x+4)=36[/tex]

[tex]5x=36-4[/tex]

[tex]5x=32[/tex]

Divide both sides by 5

[tex]x=\frac{32}{5}[/tex]

Or

[tex]x=6\frac{2}{5}[/tex]

15. Given: [tex]\log(10x-7)=3[/tex]

We rewrite in the exponential form to get:

[tex](10x-7)=10^3[/tex]

[tex](10x-7)=1000[/tex]

[tex]10x=1000+7[/tex]

[tex]10x=1007[/tex]

Divide both sides by 10

[tex]x=\frac{1007}{10}[/tex]

16. Given:   [tex]\log_3(4x+2)=\log_3(6x)[/tex]

We take antilogarithm to obtain:

[tex](4x+2)=(6x)[/tex]

[tex]2=6x-4x[/tex]

Simplify

[tex]2=2x[/tex]

Divide both sides by 2

[tex]1=x[/tex]

17. Given [tex]\log_2(3x+12)=4[/tex].

We rewrite in exponential form:

[tex](3x+12)=2^4[/tex]

[tex](3x+12)=16[/tex]

[tex]3x=16-12[/tex]

[tex]3x=4[/tex]

Divide both sides by 3

[tex]x=\frac{4}{3}[/tex]

18. Given [tex]\log_3(3x+7)=\log_3(10x)[/tex]

We take antilogarithm to get:

[tex](3x+7)=(10x)[/tex]

Group similar terms:

[tex]7=10x-3x[/tex]

[tex]7=7x[/tex]

We divide both sides by 7

[tex]x=1[/tex]

19.  Given: [tex]\log_2x+\log_2(x-3)=2[/tex]

Apply the product rule to simplify the left hand side

[tex]\log_2x(x-3)=2[/tex]

We take antilogarithm to obtain:

[tex]x(x-3)=2^2[/tex]

[tex]x^2-3x=4[/tex]

[tex]x^2-3x-4=0[/tex]

[tex](x-4)(x+1)=0[/tex]

x=-1 or x=4

But x>0, therefore x=4

20. Given  [tex]\ln x+ \ln (x+4)=3[/tex]

Apply product rule to the LHS

[tex]\ln x(x+4)=3[/tex]

Rewrite in the exponential form to get:

[tex]x(x+4)=e^3[/tex]

[tex]x^2+4x=e^3[/tex]

[tex]x^2+4x-e^3=0[/tex]

This implies that:

[tex]x=-6.91[/tex] or [tex]x=2.91[/tex]

Answer: [tex]47,916\pi \ cm3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere. This is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

You know that the radius of the exercise ball is 33 centimeters, then, you must substitute the valueof this radius into the formula  [tex]V=\frac{4}{3}\pi r^3[/tex].

Therefore, the volume of the exercise ball is:

[tex]V=\frac{4}{3}\pi (33cm)^3[/tex]

[tex]V=47,916\pi \ cm3[/tex]

For this case we must solve the following equation:

[tex]-17+ \frac {n} {5} = 33[/tex]

Adding 17 to both sides of the equation we have:

[tex]\frac {n} {5} = 33 + 17\\\frac {n} {5} = 50[/tex]

Multiplying by 5 on both sides of the equation:

[tex]n = 50 * 5\\n = 250[/tex]

Thus, the value of n is 250

ANswer:

[tex]n = 250[/tex]

The solution to the equation -17 + n/5 = 33 is n = 250.

We have,

To solve the equation, we can start by isolating the variable term.

Here's the step-by-step solution:

-17 + n/5 = 33

First, let's get rid of the constant term (-17) by adding 17 to both sides of the equation:

-17 + 17 + n/5 = 33 + 17

Simplifying, we have:

n/5 = 50

To isolate n, we can multiply both sides of the equation by 5:

5 * (n/5) = 5 * 50

This simplifies to:

n = 250

Therefore,

The solution to the equation -17 + n/5 = 33 is n = 250.

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