Find the equation of the linear function represented by the table below in slope-intercept form.

x
0
1
2
3
4

y
2
7
12
17
22

Answer:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Step-by-step explanation:

Given:

Center of the ellipse is, [tex](h,k)=(-4,-3)[/tex]

Minor axis length is, [tex]2b=6[/tex]

A vertex of the ellipse is at (1, -3)

Now, distance between the center and the vertex is half of the length of the major axis.

Using distance formula for (-4, -3) and (1, -3), we get:

[tex]a=\sqrt{(1+4)^2+(-3+3)^2}=5[/tex]

Therefore, the value of half of major axis is, [tex]a=5[/tex]. Also,

[tex]2b=6\\b=\frac{6}{2}=3[/tex]

Now, equation of an ellipse with center [tex](h,k)[/tex] is given as:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Plug in [tex]h=-4,k=-3,a=5,b=3[/tex] and determine the equation.

[tex]\frac{(x-(-4))^2}{5^2}+\frac{(y-(-3))^2}{3^2}=1\\\\\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Therefore, the equation of the ellipse is:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Answer:

Yes ,we can prove the two triangles are similar by angle angle test.

Step-by-step explanation:

Given:

∠ABE = 45°

∠EAB = 63° and

∠MNP= 72°

∠NMP = 63°

To Prove:

ΔABE  ~  ΔMPN

Proof:

In a Triangle sum of the angles of a triangle is 180°

In  ΔMPN

∴ ∠MNP +  ∠NMP  + ∠MPN = 180°

Substituting the given values we get,

[tex]72+63+\angle MPN = 180\\135 + \angle MPN = 180\\\angle MPN = 180-135\\\angle MPN = 45[/tex]

∠MPN = 45°  ..........................( 1 )

Now,for triangles to be similar

In  Δ ABE and Δ  MPN

∠ ABE ≅ ∠ MPN = 45°      ……….{From ( 1 ) and Given}

∠ EAB ≅ ∠ NMP = 63°     ………...{Given}

Δ ABE ~ Δ MPN ….{Angle-Angle test}

..........Proved

Answer:

see explanation

Step-by-step explanation:

Given

(bx + a)(ax + b) = (ax² + b)b ← distribute parenthesis on both sides

abx² + a²x + b²x + ab = abx² + b² ( subtract abx² from both sides )

a²x + b²x + ab = b² ( subtract ab from both sides )

a²x + b²x = b² - ab ← factor out x from each term on the left side

x(a² + b²) = b² - ab ← divide both sides by (a² + b²)

x = [tex]\frac{b^2-ab}{a^2+b^2}[/tex]

Answer:

x = -b/a

Step-by-step explanation:

(bx + a)(ax + b) = (ax^2 + b)(b) needs to be muliplied out as a first step to solving for x:

abx^2 + b^2 + a^2x + ab = abx^2 + b^2

Notice that abx^2 shows up on both sides of this equation, so we can cancel it out:

b^2 + a^2x + ab = b^2

Also, b^2 shows up on both sides, so we can also cancel the b^2 terms:

a^2x + ab = 0

Dividing both sides by a, we get ax + b = 0

and so ax = -b,

which means that x = -b/a

75100 > 34

75100 is greater than 34

Answer:

its <

Step-by-step explanation:

Answer:

Yes then no

Step-by-step explanation:

A linear function is of the form y=mx+b, where b and m are constants(not variables). Since the input is the radius, we make that x. The circumference is πd, or 2πr, so if we plug in 2π for m, circumference for y, and 0 for b, this works. The area is πr², which would mean that m would have to be πr. Since r is not a constant, this does not work.

Answer:

The number of textbooks of each type were sold is 134 math and 268 psychology books.

Step-by-step explanation:

Given:

Total number of math and psychology textbooks sold in a week is 402.

Now, let the number of math textbooks sold be [tex]x[/tex].

And, the number of psychology textbooks be [tex]2x[/tex].

According to question:

[tex]x+2x=402[/tex]

[tex]3x=402[/tex]

Dividing both sides by 3 we get:

[tex]x=134[/tex]

So, total number of math textbooks were 134 .

And, total number of psychology textbooks were [tex]2x=2\times 134[/tex]

                                                                                 [tex]=268[/tex].

Therefore, the number of textbooks of each type were sold is 134 math and 268 psychology books.

Step-by-step explanation:

For any function,any point in the domain has a unique image in the codomain.

For set [tex]A[/tex]:

[tex]f(8)=-5[/tex] from the point [tex](8,-5)[/tex]

[tex]f(8)=7[/tex] from the point [tex](8,7)[/tex]

For a same point [tex]8[/tex],there are two images.

So,[tex]A[/tex] does not represent a function.

For set [tex]B[/tex]:

[tex]f(7)=-4[/tex] from the point [tex](7,-4)[/tex]

[tex]f(7)=-2[/tex] from the point [tex](7,-2)[/tex]

For a same point [tex]7[/tex],there are two images.

So,[tex]B[/tex] does not represent a function.

Answer:

[tex]x-2x-6=8x+12-x-4\\-x-6=7x+8[/tex]

Step-by-step explanation:

Given:

The equation is;

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

Now we need to simplify this equation we get;

Step 1: We need to simplify all the terms which are in brackets we get,

[tex]x-2x-6=8x+12-x-4[/tex]

Step 2: Now we need to simplify all variable term and non variable term we get:

[tex]-x-6=7x+8[/tex]

Answer:

These two equivalent equations Katrina has used

[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]

Step-by-step explanation:

Given :

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

Applying distributive property that is [tex]A\times (B +C) = A\times B + A\times C[/tex] we get

[tex]x - 2x + 3\times -2 = 4\times 2x + 4\times 3 - x - 4\\[/tex]

[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]

Answer:

25:16 is the surface area of the cones.

Step-by-step explanation:

Given: The ratio of their radii and altitudes is 5:4.

Area of similar figures are proportional to the squares of their corresponding sides and this ratio is called scale factor.

Let z be the scale factor

∴z= [tex]\frac{5}{4}[/tex]

Now, let x be the surface area of the larger cone

     and let y be the surface are of smaller cone.

∴ [tex]z^{2} = \frac{x}{y}[/tex]

next substituting the value of z ,

⇒[tex](\frac{5}{4} )^{2} =\frac{x}{y}[/tex]

∴ [tex]\frac{x}{y} = \frac{25}{16}[/tex]

The ratio for the surface area of cones is 25:16

Answer:

The correct answer is 25:16

Step-by-step explanation:

If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.

Answer:

the answer is 8

Step-by-step explanation:

If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.

To evaluate f(x)=3x3+x2−5x−14  when x=−2, use synthetic division to divide the polynomial by -2 and find the resulting value.

To evaluate f(x) = 3x^3 + x^2 - 5x - 14 when x = -2, we can use synthetic division. First, set up the synthetic division table with -2 as the divisor and the coefficients of the polynomial as the dividend.

Perform the synthetic division by bringing down the first coefficient, multiplying it by the divisor and adding it to the next coefficient, then continuing the process until you reach the last coefficient. The result in the last row of the table will be the evaluated value of the polynomial.

In this case, the evaluated value of f(x) when x = -2 is 0.

Final answer:

To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, use synthetic division to divide the polynomial by x + 2.

Explanation:

To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, we can use synthetic division. First, write the coefficients of the polynomial in order: 3, 1, -5, -14. The divisor will be x - (-2), which simplifies to x + 2. Set up the synthetic division table and perform the division. The result will be the quotient and the remainder. In this case, the quotient is 3x^2 - 5x - 7 and the remainder is -20.

Answer:

There was 40% decrease in the mass of the pumpkin.

Step-by-step explanation:

Given:

Mass of pumpkin before carving = 6.5 kg

Mass of pumpkin after carving = 3.9 kg

Decrease in mass = Mass of pumpkin before carving - Mass of pumpkin after carving = 6.5 kg - 3.9 kg = 2.6 kg

Now to find the percentage decrease in mass we need to divide Decrease in mass with the total mass of pumpkin before carving and then multiply by 100

% Decrease in mass = [tex]\frac{\textrm{Decrese in mass}}{\textrm{Mass of Pumpkin before carving}}\times100 = 40\%[/tex]

Hence, there was 40% decrease in the mass of the pumpkin.

Answer:

40%

Step-by-step explanation:

I had this problem

Answer:

what is the question

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Given, f(x)=-4log2(x+3)-6

      So, for domain of f(x) ,we have to find the domain of log2(x+3) as all other things are just numbers which do not affect the domain.

For domain of f(x),    2(x+3) > 0

                    Thus,      x + 3 > 0

                                    x > -3.

So, all real numbers greater than -3 are in the domain of f(x).

Answer:

1/6, 1/2, 7/8, 1/6

Step-by-step explanation:

1/6= .1666666667

1/2=.5

7/8=.875

5/2=2.5

1/6 is the smallest number than 1/2 than 7/8 and 5/2 is the greastest number.

Answer:

The common denominator [tex]\frac{15}{20}[/tex] and [tex]\frac{8}{20}[/tex]

Step-by-step explanation:

To find the common denominator:

Here is the work:

LCD of [tex](4,5)[/tex] is [tex](4\times 5)=20[/tex].

So we will divide [tex]20[/tex] with [tex]4[/tex] and then with [tex]5[/tex] the quotient will further be put into the fraction.

So

[tex]\frac{20}{4}=5[/tex] will make the fraction [tex]\frac{3}{4}[/tex] as [tex]\frac{3\times 5}{4\times 5} =\frac{15}{20}[/tex].

Similarly

[tex]\frac{20}{5}=4[/tex] will make the fraction [tex]\frac{2}{5}[/tex] as [tex]\frac{2\times 4}{5\times 4} =\frac{8}{20}[/tex].

Hence with common denominators the fraction can be written as [tex](\frac{15}{20}),(\frac{8}{20})[/tex].

Answer:

3x - 20 = 250

Step-by-step explanation:

Given,

The cost of cookies per dozen = $ 3,

Let x be the number of dozen cookies sold,

So, the cost of x dozen of cookies = x × cost of cookies per dozen

= 3x

Now, the amount of rent = $ 20,

Thus, total earning = cost of x dozen of cookies - rent

= 3x - 20

If $ 250 is needed to raise,

Then total earning = $ 250

⇒ 3x - 20 = 250

Which is the required equation.

Answer:

multiply both 3.25 and 10 by 100

or

multiple 3.25 by 10 then multiply by 10

Answer:

The statement is false

Step-by-step explanation:

we know that

If a system of equations has two equations with the same slope and the same y-intercept, then both equations represent the same line

so

we have a consistent dependent system

The system has has an infinite number of solutions

therefore

The statement is false

Answer:

3x^2 + 7x - 5 + 2x^2

= 5x^2 + 7x - 5 (a=5, b=7, c=-5)

x = (-b+/- √(b^2 - 4ac))/2a

= (-7+/- √(49+100))/10

= (-7+√149)/10, (-7-√149)/10

Hope this helps!

Answer:

2x-2+3x

Step-by-step explanation:

2x-2+3x

combine like terms (2x + 3x = 5x)

So 2x-2+3x = 5x-2

Answer:

total sum is called perimwter

the perimeter will be the outer border, and in this case we have three semi-circles and one square, well, the semi-circles have a diameter of 7, we can just get the circumference of all 3 semi-circles add them and append the 7 ft at the bottom, Check picture below.

[tex]\bf \textit{circumference of a semicircle}\\\\ C=\cfrac{\pi d}{2}~~ \begin{cases} d = diameter\\[-0.5em] \hrulefill\\ d=7 \end{cases}\qquad \implies \stackrel{\textit{circumference of all 3 semi-circles}}{3\left( \cfrac{\pi 7}{2} \right)\implies \cfrac{21\pi }{2}} \\\\\\ \stackrel{\textit{sum of all borders}}{\cfrac{21\pi }{2}~~+~~7}~~\approx ~~32.99+7~~\approx~~ 39.99[/tex]

The contractor bought 2 small boxes and 6 large boxes of nails. This was determined by setting up and solving a system of equations based on the given conditions.

To solve the problem of determining the number of small and large boxes of nails purchased by the contractor, we can set up a system of equations based on the information given:

Let's denote the number of small boxes as S, and the number of large boxes as L. The equations then are:

Substituting the value of L from equation (1) into equation (2):

150S + 400(3S) = 2700

Solving for S:

150S + 1200S = 2700

1350S = 2700

S = 2

Then, substituting S = 2 into the first equation to find L:

L = 3(2) = 6

Therefore, the contractor bought 2 small boxes and 6 large boxes of nails.

The contractor bought 2 small boxes and 6 large boxes, totaling 2700 nails, with each small box containing 150 nails.

Let's denote:

- x as the number of small boxes purchased.

- y as the number of large boxes purchased.

We're given the following information:

1. Each small box contains 150 nails.

2. Each large box contains 400 nails.

3. The total number of nails purchased is 2700.

4. The contractor bought 3 times as many large boxes as small boxes, so y = 3x.

We can set up two equations to represent the given information:

1. Total number of nails equation:

150x + 400y = 2700

2. Relationship between the number of small and large boxes:

y = 3x

Now, let's substitute the value of y from the second equation into the first equation:

150x + 400(3x) = 2700

150x + 1200x = 2700

1350x = 2700

Now, let's solve for x:

[tex]\[ x = \frac{2700}{1350} \][/tex]

x = 2

So, the number of small boxes purchased [tex](\( x \))[/tex] is 2.

Now, let's find the number of large boxes [tex](\( y \))[/tex]:

y = 3x

y = 3(2)

y = 6

So, the number of large boxes purchased [tex](\( y \))[/tex] is 6.

To summarize:

- The contractor purchased 2 small boxes.

- The contractor purchased 6 large boxes.

The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis between the ordered pairs (-7,0) and (-6,0), and between (-2,0) and (-1,0).

The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis at those x-values that make the function equal to zero. To find these, we solve for x in the equation 0.5x² + x - 9 = 0 using the quadratic formula x = -b ± √(b² - 4ac) / 2a.

Here, a = 0.5, b = 1 and c = -9. Substituting these into the formula gives x = -1 ± √(1 + 36) / 1 = -1 ± √(37) / 1. The two possible solutions are approximately -7.06 and +5.06. Therefore, the ranges of x-values crossing the negative x-axis are between the ordered pairs (-7,0) and (-6,0), as well as between (-2,0) and (-1,0).

https://brainly.com/question/35505962

#SPJ12

The function f(x) = one-halfx2 + x - 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0) when solved using the quadratic formula.

The question concerned is a quadratic function, specifically, it wants to know where f(x) = one-halfx2 + x – 9 intersects with the negative x-axis. The x-axis is the line where y = 0, so we need to solve the equation 0.5x² + x - 9 = 0 to locate the roots. By applying the quadratic formula, x = [-b ± sqrt(b² - 4ac)] / (2a), we substitute our coefficients into the equation to get: x = [-1 ± sqrt((1)² - 4*0.5*(-9))] / (2*0.5). This will lead to two solutions, x = -2 and x = -3. Hence, the function f(x) = one-halfx2 + x – 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0).

https://brainly.com/question/12973784

#SPJ3

Answer:

The number of student's tickets sold was 7

Step-by-step explanation:

Let

x ----> number of adult's tickets sold

y ----> number of student's tickets sold

we know that

[tex]x+y=23[/tex] ----> [tex]x=23-y[/tex] ---> equation A

[tex]13x+9y=271[/tex] ----> equation B

solve the system by substitution

substitute equation A in equation B

[tex]13(23-y)+9y=271[/tex]

solve for y

[tex]299-13y+9y=271[/tex]

[tex]13y-9y=299-271[/tex]

[tex]4y=28[/tex]

[tex]y=7[/tex]

therefore

The number of student's tickets sold was 7

Answer:

There will be [tex]243[/tex] billion messages sent or received in November.

Step-by-step explanation:

Given.

Number of text messages sent or received [tex]=215[/tex] billion.

Increment on the very next month [tex]=13\%=\frac{13}{100}=0.13[/tex]

Lets find what is [tex]13\%\ of\ 215[/tex]

 ⇒[tex]13\%\ of\ 215[/tex]

 ⇒[tex]0.13\times 215=27.95[/tex]

So we will add this value to our previous months data.

Now

Number of text messages sent in the month of November [tex]=(27.5+215)=242.95[/tex] billion.

Rounding to the nearest tenth the answer will be [tex]243[/tex] billion.

So [tex]243[/tex] billion text messages were sent or received in November.

Answer:

709

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The simple interest per year is 3% times $5000 which is 150 dollars.

Now, we have the equation 150x = 600.

We solve and get x = 4

Answer:

September 17th will be the first date that she has to choose between cheerleading and play practice.

Step-by-step explanation:

Least Common Multiple for 4 and 6 is 12 that is LCM(4, 6) = 12

12 days after September 5th is September 17th

Patsy would need to choose between cheerleading and play practice on September 29th, as this is the next date when both practices fall on the same day, calculated by finding the least common multiple of the practice schedules.

To determine when Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of the two practice schedules, since she has cheerleading every fourth day and play practice every sixth day.

First, list the multiples of both 4 and 6 until we find a common one:

The lowest common multiple of 4 and 6 is 12, but since our sequence started on September 5th and 12 is not a multiple of both 4 and 6, we need to keep going. Continuing our list, 24 is the next common multiple but still not satisfying both conditions. At 24 days, the cycle would repeat itself, and Patsy would again have both practices on the same day.

If these practices both start on September 5th, to find the next date she has both practices, we add 24 days to September 5th. Because September has 30 days, adding 24 days to September 5th results in September 29th. Hence, Patsy would need to choose between cheerleading and play practice on September 29th.

Answer:

B. 10.2

Step-by-step explanation:

Answer : The value of chord XY is, 10.2 units

Step-by-step explanation :

As we are given that, XY and YZ are congruent.

XY and YZ are congruent by SSA.

The ΔXOY and ΔZOY are congruent triangles.

Side OX = Side OZ           (side)

Side OY = Side OY     (common side)

∠XOY = ∠ZOY                   (angle)

That means, in this two sides and one angle of a triangle are equal to another triangle then the triangles are congruent.

So, Side XY = Side YZ

As we are given :

Chord YZ = 10.2

So, Chord YZ = Chord XY = 10.2

Hence, the value of chord XY is, 10.2 units