If f(x) = -x^2 – 1, and
g(x) = x + 5, then
g(f (x)) = -x^2+[ ?]x + [ ?]

Answer:

x = -16

Step-by-step explanation:

subtract the two over first so x/4 = -4

multiply both sides by 4

x = -16

Answer:

x = -16

Step-by-step explanation:

First subtract -2 on both sides. Then you will get x/4 = -4

Then multiply 4 on both sides. This will then give you x = -16 because -4*4 = 16

To find the fraction of cupcakes with chocolate sprinkles, we multiply 5/7 (chocolate cupcakes) by 1/5 (those with sprinkles), resulting in 1/7 of all cupcakes having chocolate sprinkles.

The student's question is about calculating the fraction of cupcakes with chocolate sprinkles from the total number of cupcakes bought for a party. To find the answer, we can use a two-step process involving fractions. Since 5/7 of the cupcakes are chocolate and of those, 1/5 have chocolate sprinkles, we multiply these two fractions to find the fraction of all cupcakes that have chocolate sprinkles.

The calculation is as follows: (5/7) × (1/5) = 5/35 = 1/7. Thus, 1/7 of the cupcakes have chocolate sprinkles. This approach to solving the problem demonstrates the basic principle of multiplying fractions to determine a portion of a subset.

The problem involves finding the surface area and volume of a cylinder with a height of 18 ft and a diameter of 11 ft. Using the formulas for a cylinder's surface area and volume, appropriate calculations can be performed to determine the cylinder's surface area and volume.

To find the surface area and volume of a given figure, we need to identify the shape of the object. The question does not specify the shape, but the provided formulas suggest that we might be dealing with a cylinder. For a cylinder:

If the cylinder has a height (h) of 18 ft and a diameter of 11 ft (radius is half of the diameter, so r = 5.5 ft), we can calculate its surface area and volume using the following formulas:

Plugging in the values:

Now, you can substitute π with approximately 3.1416 to find the numeric answers. Remember to use the unit ft² for surface area and ft³ for volume.

Answer:

Well isn't anyone able to write?

Answer:

What?

Step-by-step explanation:

Answer:

1.2^n

Step-by-step explanation:

since a single dot brings about an increment by 20%, the total magnification becomes 120% after the click. The common ratio = 120 / 100 = 1.2

the formula  becomes 1.2^n  

The formula for the nth term of the geometric sequence that represents the magnification of each zoom level is an = (1.2)n-1.

In this problem, you are looking at a geometric sequence that represents the magnification of each zoom level on a map. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

In this case, the common ratio is 1 + 0.2 = 1.2 because the magnification increases by 20% (or 0.2 in decimal form) each time. We can denote the nth termed 'an'. The general formula for the nth term in a geometric sequence is: an = a1 * rn-1.

Since the initial magnification doesn't specify a specific value, we will take a1 as 1 for this case. Substituting these values into the formula yields: an = 1 * (1.2)n-1, or just an = (1.2)n-1.

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Answer:

 52

Step-by-step explanation:

Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...

  x + (x+2) +(x+4) = 162

  3x = 156 . . . . . . . . . . . .subtract 6

  x = 156/3 = 52

The smallest of the three numbers is 52.

___

I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.

Answer:

76 centimeters squared

Step-by-step explanation:

The formula for the surface area of a rectangular prism is simply 2lw+2lh+2wh. In this case, that is 2(5)(4)+2(5)(2)+2(4)(2)=40+20+16=76 square centimeters. Hope this helps!

The minimum amount of cardboard used for the wrapper will be 76 square cm. Thus, the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as,

SA = 2(LW + WH + HL)

A rectangular prism with a length of 5 centimeters, width of 4 centimeters, and height of 2 centimeters.

The minimum amount of cardboard used for the wrapper is calculated as,

SA = 2(5 x 4 + 4 x 2 + 2 x 5)

SA = 2(20 + 8 + 10)

SA = 2 x 38

SA = 76 square cm

Thus, the correct option is C.

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Answer:

12x484=5808

Take 484x12 should be answer

Miss Tate travels a total of 5,808 miles each year making round trip journeys from St. Louis to Indianapolis and back 12 times.

Miss Tate travels from St. Louis to Indianapolis and back, comprising a distance of 484 miles for each round trip. She does these trips 12 times a year. To find the total number of miles Miss Tate travels each year, we simply multiply the round-trip distance by the number of trips she makes. Therefore, when calculated, the total number of miles traveled by Miss Tate from St. Louis to Indianapolis and back each year is 484 miles * 12 = 5,808 miles.

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Answer:

I think It would be C or B

Step-by-step explanation:

Depending on the value of the car at first purchase.

Answer:

C

Step-by-step explanation:

23,490/29000=0.81

0.81*23,490=19026.90

Answer:

A; The approximate area of the shaded sector is 283[tex]cm^{2}[/tex]

Step-by-step explanation:

In this question, we are tasked with calculating the area of the sector of a circle that subtends a particular angle at the center of the circle

To calculate this, we use the formula for the area of a sector.

Mathematically,

Area of the shaded sector = θ/360 × π × [tex]r^{2}[/tex]

In this question, The angle subtended by the sector ;θ = 100° and radius of the circle r = 18 cm

Area = 100/360 × 22/7 × [tex]18^{2}[/tex] = 712,800/2520 = 282.86 which is approximately 283[tex]cm^{2}[/tex]

Answer:

[tex]A \approx 282.743\,cm^{2}[/tex]

Step-by-step explanation:

The approximate area of the shaded sector is:

[tex]A = \frac{100}{360}\cdot \pi\cdot (18\,cm)^{2}[/tex]

[tex]A \approx 282.743\,cm^{2}[/tex]

Answer:

the answer would be 60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

The answer is 60 because you have to multiply 5 times 12 which equals 60.

Answer:

the probability of P given K is 0.86

Step-by-step explanation:

Conditional probability is defined as the probability that an event would happen based on the occurrence of an event that has already happened. It is calculated by multiplying the probability of the both the preceding event and the succeeding event together. It is given by the formula:

[tex]P(B/A)=\frac{P(A nB)}{P(A)}[/tex]

Given that:

Probability of members in the key club P(K) = 7.8% = 0.078

Probability of members enrolled in AP physics P(P)  = 8.6% = 0.086

Probability of members in both P(P n K) = 6.7% = 0.067

Therefore:

[tex]P(P/K)=\frac{P(PnK)}{P(K)} =\frac{0.067}{0.078} = 0. 86[/tex]

the probability of P given K is 0.86

Answer:

106/2

Step-by-step explanation:

53  1/2 =  106/2

Answer:

Part a) The railroad ties are parallel

Part b) One railroad tie is perpendicular to both rails

Step-by-step explanation:

Part a) The railroad ties are each perpendicular to one rail

we know that

if one line is perpendicular to several other lines, then the other lines are parallel

Conclusion:

If the railroad ties are each perpendicular to one rail then the railroad ties are parallel

That means----> The slopes of the railroad ties are equal and they are opposite reciprocal to the slope of the rail

Part b) The rails are parallel. One railroad tie is perpendicular to one rail

we know that

if two lines are parallel and another line is perpendicular to one of them, then this line is perpendicular to both lines

Conclusion:

If One railroad tie is perpendicular to one rail, then one railroad tie is perpendicular to both rails

That means ---> The slopes of the railroad ties are opposite reciprocal to the slope of the rail

Final answer:

The railroad ties are perpendicular to both rails, and the rails are parallel to each other, reflecting principles of linear perspective in geometry.

Explanation:

The student's questions relate to geometry, specifically the properties of lines and angles about railroad tracks and railroad ties. When analyzing these geometric structures, we draw on concepts such as parallel lines, and perpendicular lines, and the characteristics of their interaction.

Analysis of Statements

Therefore, we can conclude that the railroad ties are perpendicular to both rails and that the rails are parallel to each other. This aligns with linear perspective and the visual effect of perpendicular lines (orthogonal) converging at a vanishing point as they recede into the distance.

Answer:

Step-by-step explanation:

let n be the total number of notebooks.

let p be the total number of pens.

according to the question total number of pen and notebook is 8.

Therefore mathematically

n+p = 8 ---------------------equation A

______________________________________________

cost of one notebook = $2.50

number of notebook = n

therefore total cost of n notebook = n* 2.50 = 2.5n

cost of one pen = $2.00

number of pen = p

therefore total cost of p pen = p* 2.00 = 2p

according to the question total c cost of pen and notebook is $19.00.

Therefore mathematically

2.5n + 2p = 19 ---------------------equation B

______________________________________________

Set of equation as required by question are

Answer:

6,2

Step-by-step explanation:

(looked at in desmos)

Answer:

The Inequality  to determine the number of tickets the committee could sell to pay this years dance [tex]72+4t\geq 400[/tex].

The committee need to sell more than 82 tickets to have money left over after they pay this years dance.

Step-by-step explanation:

Given:

Cost of the Dance  =$400

Money earn from bake sale =$72

Cost of each ticket = $4

We need write the inequality to determine the number of tickets the committee could sell to pay this years dance.

Solution:

Let the number of tickets to be sell be 't'.

So we can say that;

Money earn from bake sale plus Cost of each ticket multiplied by  number of tickets should be greater than or equal to Cost of the Dance.

framing in equation form we get;

[tex]72+4t\geq 400[/tex]

Hence The Inequality  to determine the number of tickets the committee could sell to pay this years dance [tex]72+4t\geq 400[/tex].

On solving the above equation we get;

subtracting both side by 72 we get;

[tex]72+4t-72\geq 400-72\\\\4t\geq 328[/tex]

Dividing both side by 4 we get;

[tex]\frac{4t}{4}\geq \frac{328}{4}\\\\t\geq 82[/tex]

Hence The committee need to sell more than 82 tickets to have money left over after they pay this years dance.

Answer: f(x) = (x+6)^2 -25

vertex is (-6, -25)

Step-by-step explanation: complete the square, than use the binomial formula, then simplify and expand

Answer:

equation is y = (x+1)(x+11)

vertex: (-1,-11)

Step-by-step explanation:

y = x^2 + 12x + 11. The last value, the value 11 is how we can determine our values in the equation. First we need to find the factors of positive 11 which are: -11 * -1 and 1*11. now we will look at the second portion the 12x. As we can see the value is positive. Now we will add the two factors together and see which one gives us positive 12. The factors 1 and 11 make positive 12. Now we simply just need to add those values to x. When this is factored down or in other words vertex form, the equation is y = (x+1)(x+11). The vertex is what value would make the equation equal 0.  Since -1 + 1 equals 0 then that is one of the vertex and since -11 + 11 equal 0 that also makes that a vertex. This makes the vertex -1,-11.

Answer:

I see your profile everywhere, and the answer is Right scalene Pythagorean triangle.

Step-by-step explanation:

Answer:

-4 and -3

Step-by-step explanation:

-4 + -3 = -7

-4 times -3 = 12

Answer:

The answer is:

The domain consists of all the x-values

Step-by-step explanation:

The domain is the set of possible input values

The domain is the set of all possible values of the independent variable

In any ordered pair (x , y), x is the input (independent)

The domain is all values of x which make the function defined

The range is the set of possible output values

The range is the complete set of all possible resulting values of the dependent variable

In any ordered pair (x , y), y is the out put (dependent)

The range is all values of y which corresponding to x

The answer is:

The domain consists of all the x-values

Answer:

After 4 days, the number of people attending both conferences be the same.      

Step-by-step explanation:

We are given the following in the question:

Maths conference:

Number of people already signed = 7

Number of people who sign up each day = 2

Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:

 [tex]f(x) = 7+2x[/tex]

History conference:

Number of people already signed =11

Number of people who sign up each day = 1

Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:

 [tex]g(x) =11+x[/tex]

Both conference will have same number of people when

[tex]f(x) = g(x)\\\Rightarrow 7 + 2x = 11+x\\\Rightarrow x = 4[/tex]

Thus, after 4 days, the number of people attending both conferences be the same.

Answer: A

Step-by-step explanation:

The devil is trying to see how and why Robert is negative with his view of numbers. He pokes Robert so he can see how negative Robert is about it.

Answer: A

Step-by-step explanation:

Answer: he invested $8600 in bonds.

Step-by-step explanation:

Let x represent the part of his money that he invested in stocks.

Let y represent the part of his money that he invested in bonds.

Ben invested part of his $15,000 savings in stocks paying 4.25% simple interest annually. He invested the rest in bonds paying 3.75% simple interest annually. It means that

x + y = 15000

The interest that he would earn on the amount invested in stocks after 1 year is

4.25/100 × x = 0.0425x

The interest that he would earn on the amount invested in bonds after 1 year is

3.75/100 × y = 0.0375y

If Ben earned $594.50 in interest after one year, it means that

0.0425x + 0.0375y = 594.5- - - - - - 1

Substituting x = 15000 - y into equation 1, it becomes

0.0425(15000 - y) + 0.0375y = 594.5

637.5 - 0.0425y + 0.0375y = 594.5

- 0.0425y + 0.0375y = 594.5 - 637.5

- 0.005y = - 43

y = - 43/- 0.005

y = $8600

x = 15000 - 8600

x = $6400

Answer:

38.6 m/s

Step-by-step explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction  

Therefore we have to analyze the horizontal and vertical motion separately.

Along the horizontal direction, the velocity is constant during the motion, since there are no forces acting in this direction. So the horizontal velocity 3 seconds after the launch will be the same as the velocity at the launch:

[tex]v_x = v_0 = 25 m/s[/tex]

The vertical velocity instead changes according to the suvat equation:

[tex]v_y = u_y - gt[/tex]

where

[tex]u_y=0[/tex] is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

t is the time

Therefore, after t = 3 s,

[tex]v_y=0-(9.8)(3)=-29.4 m/s[/tex]

So the velocity after 3 seconds is < 25, -29.4 > m/s. The magnitude of the velocity is

[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{25^2+(-29.4)^2}=38.6 m/s[/tex]

The statement is true regarding the horizontal component but contains a typo in the vertical component. A ball thrown horizontally from a 150m building will maintain its horizontal velocity but the vertical velocity will be -29.4 m/s after 3 seconds. The total speed will be 38.6 m/s, not 46.493 m/s.

The statement is True. To analyze the velocity and speed of a ball thrown horizontally, we will consider two components of the motion separately: the horizontal component, which remains constant due to the absence of horizontal forces when air resistance is ignored, and the vertical component, which changes due to gravity.

Horizontally, the velocity remains at the initial value of 25 m/s because no horizontal forces are acting on the ball (assuming air resistance is negligible).

Vertically, the acceleration due to gravity (g) is 9.8 m/s2. The vertical velocity (Vy) at a time t after release can be calculated using the equation Vy = g × t, which after 3 seconds gives us Vy = 9.8 m/s² × 3 s = 29.4 m/s.

Since the question states a vertical velocity of -39.2 m/s, there might be a typo, as the correct vertical velocity should be -29.4 m/s (negative sign indicates downward direction).

Now, to find the overall speed, we use the Pythagorean theorem: speed = \/(Vx² + Vy²). Substituting Vx = 25 m/s and Vy = -29.4 m/s, we get the speed as 38.6 m/s (approximately).

Therefore, the provided velocity and speed are incorrect; the corrected velocity after 3 seconds is <25, -29.4> and the speed is approximately 38.6 m/s.

Answer:

 (7, 0), (-3, 0)

Step-by-step explanation:

The x-intercepts are the values of x that make the factors zero. A zero factor makes the value of the function be zero.

  x - 7 = 0   ⇒   x = 7

  x + 3 = 0   ⇒   x = -3

The corresponding (x, y) coordinates are ...

  (7, 0), (-3, 0)

The x-intercepts of the quadratic function f(x) = (x-7)(x+3) are (7, 0) and (-3, 0).

The question is about finding the x-intercepts of the quadratic function f(x) = (x-7)(x+3). The x-intercepts occur where the function equals zero, so we set f(x) = 0 and solve for x. This gives us two solutions:

x - 7 = 0, which simplifies to x = 7

x + 3 = 0, which simplifies to x = -3

Therefore, the x-intercepts of the function are at (7, 0) and (-3, 0), with the one having the larger x-value being (7, 0).

All the given options are valid and correct.

If Karen boards the bus first, the possible outcomes for the event are those where the other three band members board the bus in various orders after Karen. Let's consider the options:

1. KHIJ: This represents Karen boarding first, and the remaining band members (Harry, Isabel, and Jose) boarding in the order H, I, J. This is a valid outcome.

2. KHIJ, KHJI: These arrangements represent Karen boarding first, and the remaining band members boarding in different orders (H, I, J and H, J, I). Both are valid outcomes.

3. KHIJ, KHJI, KJHI, KJIH: These arrangements include all possible orders of the remaining band members after Karen. All of them are valid outcomes.

4. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH: These arrangements cover all possible orders of the band members after Karen, including swapping the positions of Harry and Isabel. All are valid outcomes.

Therefore, the possible outcomes for this event are all of the given options.

The given question seems incomplete, but the complete question could be:

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?

A. KHIJ

B. KHIJ, KHJI

C. KHIJ, KHJI, KJHI, KJIH

D. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

The vertex of the parabola [tex]y=4x^2-8x-12[/tex] is (1, -16).

To find the coordinates of the vertex of the parabola [tex]y=4x^2-8x-12[/tex], we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 4 and b = -8.

Plugging these values into the formula, we get x = -(-8)/(2*4) = 1.

Now, we can substitute this value of x back into the equation to find the corresponding y-coordinate.

Plugging x = 1 into y = [tex]4x^2-8x-12[/tex], we get y = [tex]4*1^2 - 8*1 - 12 = -16[/tex].

Therefore, the vertex of the parabola is (1, -16).

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Final answer:

The vertex of the parabola [tex]y=4x^2-8x-12[/tex] is found by completing the square and transforming the equation into vertex form, resulting in the vertex coordinates at (1, -16).

Explanation:

To find the coordinates of the vertex of the parabola given by the equation [tex]y=4x^2-8x-12,[/tex] we use the fact that the vertex form of a parabola's equation is[tex]y=a(x-h)^2+k,[/tex]where (h, k) is the vertex of the parabola. In this case, we can complete the square to transform the given equation into vertex form. To do that, we can factor out the coefficient of [tex]x^2[/tex] from the first two terms:

[tex]y = 4(x^2 - 2x) - 12[/tex]

Now, we add and subtract the square of half the coefficient of x inside the parentheses, which is [tex](2/2)^2 = 1:[/tex]

[tex]y = 4(x^2 - 2x + 1 - 1) - 12[/tex]

[tex]y = 4((x - 1)^2 - 1) - 12[/tex]

[tex]y = 4(x - 1)^2 - 4 - 12[/tex]

[tex]y = 4(x - 1)^2 - 16[/tex]

Now that we have the equation in vertex form, we can see that the vertex of the parabola is at (1, -16).

Answer:

7

Step-by-step explanation:

2-(-5)

2 + 5 --- opposite

=7

The circumference of a circle with a radius of 9 meters, using pi as 3.142, is calculated as 56.6 meters when rounded to one decimal place.

The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius of the circle.

In this case, the radius of the circle is 9m. Let's substitute this value into the formula:

C = 2 × 3.142 × 9

C = 56.556m

Therefore, the circumference of the circle is 56.6 meters (rounded to 1 decimal place).Calculating the Circumference of a Circle

To calculate the circumference of a circle with a radius (r) of 9 meters and using π (pi) as 3.142, we use the formula C = 2πr. By plugging in the given values, we get C = 2 × 3.142 × 9m. Performing the multiplication, we find that the circumference is 56.556 meters. Since we need to give our answer with one decimal place, we round to 56.6 meters.

The step-by-step calculation involves: