Pablo wants to save $800 to buy a TV. He saves $19 each week. The amount, A (in dollars), that he still needs after
weeks is given by the following function.
A(w) = 800-19 w
Answer the following questions.
(a) How much money does Pablo still need after 6 weeks?
si )3
(b) If Pablo still needs $477, how many weeks has he been saving?
I weeks​

Answer: 34.93 units

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=Bh[/tex]

Where "V" is the volume, "B" is the base area and "h" is the height.

Since we need to find the height, we must solve for "h":

[tex]h=\frac{V}{B}[/tex]

We know that the volume of that wooden chest (which is in the shape of a rectangular prism) is 524 cubic units and the base area is 15 square units. Then:

[tex]V=524units^3\\B=15units^2[/tex]

Subsitituting these values into [tex]h=\frac{B}{V}[/tex], we get that the height of the chest is:

 [tex]h=\frac{524units^3}{15units^2}=34.93units[/tex]

Answer:

B) -7m - 8 = m - 4

D) m - 4 = -7m - 8

E) -8 - 7m = -4 + m

Step-by-step explanation:

Solve all of the equations to see if they end up with the same result. Start with the original:

-2m - 5m - 8 = 3 + (-7) + m

-7m - 8 = -4 + m (now we know B and D and E are correct)

-7m - m - 8 = -4 + m - m

-8m - 8 = -4

-8m - 8 + 8= -4 + 8

-8m = 4

Answer:

-7m - 8 = m - 4

m - 4 = -7m - 8

-8 - 7m = -4 + m

Step-by-step explanation:

Given equation,

-2m - 5m - 8 = 3 + (-7) + m,

Combining like terms,

-7m - 8 =-4 + m

Subtract m from both sides,

-8m - 8 = -4

Add 8 on both sides,

-8m = 4

Divide both sides by -8,

m = [tex]-\frac{1}{2}[/tex]

(i)  -15m = -4m  ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0

(ii) -7m - 8 = m - 4  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(iii) -3m - 8 = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

(iv) m - 4 = -7m - 8  ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(v) -8 - 7m = -4 + m  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(vi) -8 - 3m = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

Answer:

Part 1) The exact value of the arc length is [tex]\frac{25}{6}\pi \ in[/tex]

Part 2) The approximate value of the arc length is [tex]13.1\ in[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

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

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

[tex]\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in[/tex]

step 3

Find the approximate value of the arc length

To find the approximate value, assume

[tex]\pi =3.14[/tex]

substitute

[tex]\frac{25}{6}(3.14)=13.1\ in[/tex]

Answer:

13.1 (rounded to tenths)

Step-by-step explanation:

150 ° into radian is 5/6.

150°/1 (π/180) =5π/6.

Then multiply the radian angle by the radius.

5π/6 (5) = 25π/6

25π/6 = 13.1 (rounded to tenths)

Which of the following lists the angles from smallest to largest?

Answer:

T, R, S

Answer:

The answer is B

Step-by-step explanation:

happy cheating

Answer:

The answer is B

Step-by-step explanation:

And it's not cheating just trying to make it through high school.

Answer: 2X+5Y≥ 90

Step-by-step explanation:

since you get two points per/ each (key word of multiplication) true & false question, this will be represented by 2X

since you get five points per/ each multiple choice question, this will be represented by 5Y

he needs at least 90 points in total to get an A in his class

Answer:

The third term is [tex]24x^2y^2[/tex]

Step-by-step explanation:

The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem

The Binomial Theorem is:

[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]

In the given question x = 2x

a = y

n = 4

We have to find the third term, so value of k will be 2 as k starts from 0

Putting the values in the Binomial Theorem

[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]

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

Putting the values:

[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]

So, the third term is [tex]24x^2y^2[/tex]

The prism's base perimeter is 28 units, calculated by summing the lengths of its sides or using the rectangle perimeter formula.

Step 1: Identify the Prism and Its Base

Given a triangular prism, focus on the rectangular base formed by sides S1, S2, S3, and S4.

Step 2: Understand Perimeter Calculation

Recall that the perimeter of any shape is the sum of all its sides.

Step 3: Label the Sides of the Base

Define the sides of the rectangular base:

S1 = 4 + 5

S2 = 5

S3 = 4 + 5

S4 = 5

Step 4: Apply Perimeter Formula

Utilize the formula for the perimeter of a rectangle: P = 2 * (length + width).

For the rectangular base, length = S1 + S3 and width = S2.

Step 5: Calculate Perimeter

Substitute the values into the formula: P = 2 * (9 + 5) = 2 * 14 = 28 units.

Step 6: Verify Using Summation

Confirm the result by adding the individual sides: P = S1 + S2 + S3 + S4 = 9 + 5 + 9 + 5 = 28 units.

Answer: [tex]g(x)=2x^4+3[/tex]

Step-by-step explanation:

These are some transformations for a function f(x):

If [tex]f(x)+k[/tex], then the function is shifted up "k" units.

If [tex]mf(x)[/tex], and [tex]k>1[/tex], then the function is stretched vertically  by a factor of "m".

Knowing this transformation and knowing that the function [tex]f(x)=x^4[/tex] is stretched vertically by 2 and shifted up 3 spaces, then we can conclude that new function, which we can call g(x), is:

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

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

Answer:

x=a²+ab+b²/a+b , y=-ab/a+b

Step-by-step explanation:

The system of the given equation may b written as:

ax+by-a²=0

bx+ay-b²=0

Here,

a1=a,b1=b,c1= -a²

a2=b,b2=a and c2= -b²

By cross multiplication we get

x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b

x/-b³+a³ = -y/-ab²+a²b  = 1/a²-b²

Now

x/-b³+a³ = 1/a²-b²

x=a³-b³/a²-b²

x=(a-b)(a²+ab+b²)/(a-b)(a+b)

x=a²+ab+b²/a+b

And,

-y/-ab²+a²b = 1/a²-b²

-y=a²b -ab²/a²-b²

y=ab²-a²b/a²-b²

y=ab(b-a)/(a-b)(a+b)

y= -ab(a-b)/(a-b)(a+b)

y= -ab/a+b

Hence x=a²+ab+b²/a+b , y=-ab/a+b....

Answer:

[tex]\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Step-by-step explanation:

we know that

Te volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=(r/2)\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (r/2)^{2}h[/tex]

[tex]V=\frac{1}{12}\pi r^{2}h[/tex]

Te volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we know that

To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder

so

[tex]\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Answer:

the first one

Step-by-step explanation:

the number of mistakes went from 19 the first week of class to 0 the 20th week

Answer:

1/3 sin(3x)+C

Step-by-step explanation:

int (cos(3x) dx)

Let u=3x then du=3 dx so 1/3 du=dx

rewriting integral

int(1/3 cos(u) du)

now evaluating

1/3 sin(u)+C    since (sin(u))'=cos(u)

Replace u with 3x

Answer is 1/3 sin(3x)+C

Answer:

Step-by-step explanation:

Integral of cos3x = ⅓sin3x

So when integrating just simply multiply by reciprocal of the cooeffecient of the angle and the integral of that particular trig ratio, in this case it's the sinx.

The incorrect step and with error is subtract 3 from both sides. Option 3

We have that the equation is;

-3/8 (-8-16d) + 2d= 24

multiply the values, we get;

-24 + 48d + 2d = 24

add the like terms

-24 + 50d = 24

50d = 48

d = 48/50

The other steps are;

Subtract 3 from both sides (However, the instruction mentions subtracting 3, but there is no number 3 in the equation.

Divide both sides by the equation by -14

Answer:

I would say the third one ( 15x + 10 = 10 )

Step-by-step explanation:

I say this because, if we take 10 from both sides, 15x = 0. Even if you tried to divide by 15, x = 0. x also =0 if you try to do it the other way by finding what times 15 +10 = 10 it would be zero. The third one is your Answerr

Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

Equation of functions With only one solution

Equations With just one solution are knoWn to have a leading degree of one and Without a modulus sign

Fro the linear function 15x + 10  = 10

Check:

Subtract 10 from both sides

15x + 10 - 10 = 10 - 10
15x = 10 - 10
15x = 0

Dividde both sides by 15 to have:

15x/15 = 0/15
x = 0
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

-y=x+1

Find the y-intercept

For x=0

-y=0+1

y=-1

The y-intercept is the point (0,-1)

Find the x-intercept

For y=0

-0=x+1

x=-1

The x-intercept is the point (-1,0)

Find a third point

For x=1

-y=1+1

-y=2

y=-2

The third point is (1,-2)

Plot the three points to graph the linear equation

see the attached figure

Note Remember that to graph the linear equation is sufficient with two points

Answer:

(2,1) (0,-1) (-6,7)

Step-by-step explanation:

Answer:

(x+2) (x+4)

Step-by-step explanation:

x^2+6x+8

What 2 numbers multiply together to give us 8 and add together to give us 6

(2*4) =8

(2+4) = 6

(x+2) (x+4)

Answer:

(x + 4)(x+2)

Step-by-step explanation:

We must multiply 8 and 1, and find two numbers which add to 6:

8 * x(suppose x is 1) = 8

Two numbers which add to 6, but also multiply to 8:

4 and 2

4 * 2 = 8

4 + 2 = 6

Hence, the answer would be (x + 4)(x+2)

Answer: 33

if you add them all up,they are 33

Answer:

HL

Step-by-step explanation:

You have a the two hypotenuses from the two triangles are congruent.

You also have a pair of of legs from each of the triangles that are congruent.

So HL means hypotenuse-leg which is what you have in the pic!

Final answer:

To prove two 'A's are equivalent, methods such as direct proof, disjunctive syllogism, conditional proof, and indirect proof can be applied. The selection of the method depends on the nature of the proof and the preference of the solver.

Explanation:

To establish that both 'A's are equivalent in a given proof, one might utilize several methods including direct proof, disjunctive syllogism, conditional proof, or indirect proof. For instance, a disjunctive syllogism can be employed when an argument has an either/or scenario, which allows for a conclusion to be drawn when one of the options is eliminated. Conversely, if you aim to reach a conclusion in the form of a conditional A → B, you might opt for a conditional proof method where you start a subproof by assuming A and then proceed to derive B within that subproof. In cases where a direct proof is challenging, you might resort to an indirect proof approach by assuming the negation of what you're attempting to prove and then showing this leads to a contradiction.

Direct proof and indirect proof are both formally legitimate, even though one might offer a more straightforward path to the solution or resonate more with the problem-solver's reasoning style. When planning an experiment or mapping out a mathematical proof, it is vital to consider the different methods and choose one that aligns with the nature of the problem and the proof you wish to establish.

Answer:

D

Step-by-step explanation:

The system of equation will also have a solution of (2,0) are,

x + 4y = 2, 7x = 14.

Given that,

The solution to the system of equations shown is (2,0).

3x – 2y = 6 ,  x + 4y = 2

When the first equation is multiplied by 2, the sum of the two  equations is equivalent to 7x = 14.

We have to determine,

Which system of equations will also have a solution of (2,0).

According to the question,

To determine the system of the equation after applying all the given conditions in the steps, follow all the steps given below.

System of equations;  3x – 2y = 6 ,  x + 4y = 2.

                   [tex]2 \times (3x-2y) = 2 \times 6\\\\6x - 4y = 12[/tex]

                   [tex]6x - 4y + x + 4y = 12+ 2\\\\7x = 14\\\\x = \dfrac{14}{7}\\\\x = 2[/tex]

                      [tex]6(2) - 4y = 6\\\\12-4y = 6\\\\-4y = 6-12\\\\-4y == -6\\\\y = \dfrac{-6}{-4}\\\\y = \dfrac{3}{2}[/tex]

Hence, The required system of equation will also have a solution of (2,0) are, x + 4y = 2, 7x = 14.

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Answer:

I just know its formula 2 pie r square

Step-by-step explanation:

Answer: A = 12.56 cm

Step-by-step explanation:

A = 3.14 x r^2

A = 3.14 x 2^2

A = 3.14 x 4

A = 12.56 cm

Answer:

x = 8

Step-by-step explanat

Answer:

6

Step-by-step explanation:

Answer:

AB = 4 cm

Step-by-step explanation:

The tangent and secant are drawn from an external point to the circle.

Then the square of the measure of the tangent is equal to the product of the external part of the secant and the entire secant.

let AB = x, then

x(x + 5) = 6²

x² + 5x = 36 ( subtract 36 from both sides )

x² + 5x - 36 = 0 ← in standard form

(x + 9)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 4 = 0 ⇒ x = 4

However x > 0 ⇒ x = 4 ⇒ b = 4 CM

The question is missing the specific equation needed to estimate average annual snowfall for Columbia, South Carolina at 34 degrees north latitude. Factors like latitude and climate patterns influence snowfall levels, and based on Columbia's location, low snowfall would be expected.

The student is asking about an equation to estimate average annual snowfall for a specific location based on its latitude, in this case, Columbia, South Carolina, which is at 34 degrees north latitude. Unfortunately, the explicit equation needed to estimate the snowfall is not provided in the question or the contextual information. Generally, to estimate snowfall or precipitation levels using latitude, additional climatic data such as elevation, proximity to oceans or large bodies of water, and prevailing wind patterns are also necessary.

However, referring to the geographical regions mentioned, it's noted that certain latitudes often correspond with specific climate patterns. The comparison with other regions suggests that areas farther away from the equator, especially those close to either the Arctic Circle or the Antarctic Circle, experience more extreme temperatures and snowfall. Given the subtropical zone where Columbia, South Carolina, is located, the expected average snowfall would likely be relatively low compared to higher latitudes.

Answer:

14

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = 2x² + 3x + x - 2 = 2x² + 4x - 2

To evaluate (f + g)(2) substitute x = 2 into (f + g)(x)

(f + g)(2) = 2(2)² + 4(2) - 2 = 8 + 8 - 2 = 14

Answer:

14

Step-by-step explanation:

First find an algebraic formula for (f + g)(x).  To do this, combine like terms from f and g:  (f + g)(x) = 2x^2 + 4x -2

Next, substitute 2 for x:  (f + g)(2) = 2(2)^2 + 4(2) - 2 = 8 + 8 - 2 = 14

The answer you are looking for is 6y + 9.

In the equations (5y + 9) + y, you'd combine like terms to find the answer. You aren't distributing anything into the parenthesis, and 5y and 9 are not like terms (since the 9 doesn't have a "y" after it). That being said, you simply add "y" and 5y together to get 6y, and add the 9 to the end. Thus getting 6y + 9 as an answer.

I hope this helps!

Answer:

A. 6y+9

Step-by-step explanation:

Distributive property:

    ↓

[tex]A(B+C)=AB+AC[/tex]

First, you remove parenthesis.

5y+9+y

Group like terms:

   ↓

5y+y+9

Then,  you add by similar into elements.

5y+y=6y

6y+9 is the correct answer.

Answer:

y= 4x + (-16)

Step-by-step explanation:

The slope of the given lime is m=4

x-intercept of the parallel line: (4,0)

plug that into the equation y= mx+b to find that b= -16

since the slope stays the same for parallel lines, and we just found b, we have the new line equation

The equation of parallel line with x intercept of 4 will be : y= 4x + (-16)

Given,

x intercept : 4

Slope = 4

Now,

x-intercept of the parallel line: (4,0)

As the equation of line to be obtained is parallel . Thus both lines will have same slope .

Slope of parallel line = 4

Substitute the value to find y intercept,

y = mx + b

0 = 4(4)  + b
b = -16

So,

Equation of parallel line: y = 4x + (-16)

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Answer:

67

Step-by-step explanation:

you have to divide

Answer

Step-by-step explanation:$149.50 is the answer

Answer:

C is your answer I did this test before.

Step-by-step explanation:

good luck.

C is your answer

We have given that,

when using the rational root theorem, which of the following is a possible root of the polynomial function below

F(x)=3x^3-x^2+4x+5

The rational root theorem says, a rational zeros of a polynomial is of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

p/q=±a0/a1

from the given polynomial a1=3 and a0=5

p/q=±3/5

+3/5 is not in the option so the correct option -3/2

So the root of the given polynomial is -3/5

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