The base of a right pyramid is a triangle with base and a height of 17cm. If the volume of the pyramid is 11120 cubic cm, find the slant height of the pyramid

The required value of the given antiderivative function is G(4) = -7+∫₂⁴f(t)dt which is the correct answer that would be an option (E).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The antiderivative of a function is a function that when differentiated gives the original function.

Since G(x) is an antiderivative for f(x), G'(x) = f(x).

If G(2) = -7, then we know that G(4) = G(2) + ∫₂⁴ f(t)dt.

So, G(4) = -7+∫₂⁴f(t)dt

Therefore, the answer is (E) -7+∫₂⁴f(t)dt.

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Answer:

Step-by-step explanation:

ur mom

First, we need to find the number of students that are freshmen: 3400 students x 3/8 = 1050 students

Next, we need to find the number of students that are in favor of forming a track team: 3/5 of the freshmen are in favor = 3/5 * 1050 = 630 students

To find the number of non-freshmen students: 3400 students - 1050 students = 2350 students

Now we need to find the number of non-freshmen students in favor of forming a track team: 1/5 of the non-freshmen students are in favor = 1/5 * 2350 = 470 students

Finally, to find the number of students opposed to the idea we need to subtract the number of students in favor from the total number of students: 3400 students - (630 students + 470 students) = 3400 - 1100 = 2300 students

So there are 2300 students at Central High School that are opposed to the idea of forming a track team.

The equation 1/2r = π/CB is true. Choose the second option

The circumference of a circle is the distance around the circle, or the length of the perimeter of the circle. It is given by the formula:

circumference = 2πr = πd

where r is the radius and d is the diameter

Note: d = 2r

Given: d2 = 2r and CB denotes the circumference of ⨀B

CB =  πd2  

CB =  2πr   (d2 = 2r)

Divide both sides by CB:

CB/CB =  2πr/CB

1 = 2πr/CB

Divide both sides by 2r:

1/2r = 2πr/2rCB

1/2r = π/CB

Thus, the second equation is true

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Answer:

8296/17 = 488

4590/34 = 135

4550/26 = 175

8132/38 = 214

5265/15 = 351

8760/24 = 365

5643/33 = 171

4403/37 = 119

2400/48 = 50

The third option C: -5∛2x is a like radical to the expression 6∛2x.

In mathematics, the symbol √ is used to represent or show that a number is a radical. Radical expression is defined as any expression containing a radical (√) symbol.

The expression 6∛2x can be expanded into two factors which bare 6 and ∛2x

Also for the third option C, the expression -5∛2x can be expanded into two factors which are -5 and ∛2x

By observation, we will notice the two expressions 6∛2x and -5∛2x have same factor ∛2x which make them like radical expressions.

In conclusion, the expression -5∛2x is a like radical expression to 6∛2x.

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The height of triangle A ABC is 4 units.

What is the triangle's height, h?

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Answer:

1440

Step-by-step explanation:

"Percent" means "out of 100"

5 "percent" means 5 out of 100

[tex]\frac{5}{100} =\frac{72}{x}[/tex]

We need to find the number that when multiplied by 5, equals 72.

72 / 5 = 14.4

Now, we need to multiply 100 by 14.4 to "scale" proportionately.

100 * 14.4 = 1440

We can check our work:

1440 * (0.05) = 72

(A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

What is the explicit formula?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

A. The data provided is modeling a geometric sequence.

This is because the common ratio between consecutive terms is a constant value, specifically in this case is the ratio between consecutive terms is multiplied by 2.

B. To find the time Aurora will complete station 5 using a recursive formula,

we can use the formula T(n) = T(n-1) * r,

where T(n) is the time at the nth station, T(n-1) is the time at the (n-1)th station, and r is the common ratio.

In this case T(5) = T(4) * 2

and T(4) = 24 (from the data provided)

Therefore, T(5) = 24 * 2 = 48 minutes

C. To find the time Aurora will complete the 9th station using an explicit formula,

we can use the formula T(n) = T(1) * r^(n-1)

In this case, T(9) = T(1) * 2^(9-1)

and T(1) = 3 (from the data provided)

Therefore, T(9) = 3 * 2^8 = 3 * 256 = 768 minutes

The explicit formula assumes that the first term of the sequence is T(1) and the common ratio of the consecutive term is r.

Hence, (A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

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On solving the provided question we can say that -  Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

On solving the provided question, we can say that the value of x = 5√3

values of x and y

Pythagorean theorem,

The trigonometric ratio: soh-cah-toa, and

According to the given question:

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]

Pythagorean Theorem

[tex]5²+x²=10²\\x²=100−25=75\\[/tex]

x=√75=√3×25=5√3

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The number of days that the skier would have to go skiing for the season pass to be less expensive than the daily passes would be 5 days.

The season ski pass would cost $ 350 while a pass a day would cost $ 79. The skier would then rent skis with either of the passes for the same price of $ 20 per day, which means that this factor is irrelevant in calculating the number of days till the season pass is less expensive.

The number of days till the season pass is less expensive is therefore:

= Cost of season pass / Cost of daily ski pass

= 350 / 79

= 4. 43

= 5 days

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On solving the provided question we can say that - the value of the equation x = y^2 -5 from the graph will be 59.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here, the equation from the graphs is

[tex]x = y^2 -5[/tex]

and y = 8

x = 59

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The coordinates for graph are (4, -3)(-8, 6)(8, -6)(-4, 3)(0, 0).

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

Given, equation

2/3y = -1/2x

according to option

when x = 0

y = 0

(0, 0)

when x = 4

2/3y = -1/2(4)

y = -3

(4, -3) and similarly (-4, 3)

when x = 8

2/3y = -1/2(8)

2/3y = -4

y = -6

(8, -6) similarly (-8, 6)

Hence the coordinates for equation are  (4, -3)(-8, 6)(8, -6)(-4, 3)(0, 0).

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The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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On solving the provided question, we can say that - the value of the quadratic equation will is 3X1 + 18 X 2 = 39.

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

the quadratic equation we have is -

[tex]3x^2 + 16y[/tex]

and x= 1

and y = 2

so,  3X1 + 18 X 2 = 39

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3.64 x [tex]10^8[/tex] divided by 3.3 x [tex]10^4[/tex] is equal to 110.12121212121212.

The division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into a number of equal parts. The symbol for division is typically a forward slash (/) or a horizontal line. For example, if you have 10 apples and you want to divide them equally among 5 people, each person would receive 2 apples (10 ÷ 5 = 2). The result of division is called the quotient.

Here is one way to divide 3.64 x 10^8 by 3.3 x 10^4 step by step:

Write the numbers as decimal numbers: 3.64 x 10^8 is equal to 364000000 and 3.3 x 10^4 is equal to 33000.

Divide the decimal numbers: 364000000 ÷ 33000 = 11006.06

The result is 11006.06.

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Answer;

-2

Step-by-step explanation;

Well take the last numbers in these points and subtract them

4 - (-8)

4+8

12

You've got the upper part of the slope fraction now subtract the first two numbers.

-4-2

-6

Put this fun together, 12/-6 = -2

hence, slope=-2 .

Answer:

Step-by-step explanation:

-2

Answer: If 2 melons cost Php190.50, then 4 melons cost 381 .

If 1 kg of Bangus costs Php167.35, then 3.5 kgs of Bangus cost 585.725

Step-by-step explanation:

2x2=4

190.50x2=381

1x3.5=3.5

167.35x3.5=585.725

The ratio of the amount Peter spent to that of John is 2:3, so:

(a) If Peter spent 500 dollars, then John spent 75p dollars

(b) If John spent 600 dollars, then they spend altogether 1000 dollars.

(c) If both boys spent 2000 dollars altogether, then John spent 1200 dollars and Peter spent 800 dollars.

(d) If John spent 100 dollars more than Peter, then they both spent 500 dollars as Peter will spend 200 dollars while John spends 300 dollars.

Let us represent the amount of money spent for Peter and John with P and J respectively.

Using the ratio 2:3 for the amount Peter spent to that of John;

If Peter spent 500 dollars, then;

2/3 = $500/J {cross multiply}

J = (3 × $500)/2

J = $1500/2

J = $750

If John spent 600 dollars, then;

2/3 = P/$600 {cross multiply}

P = (2 × $600)/3

P = $1200/3

P = $ 400

Peter and John spent altogether = $1000

If both boys spent 2000 dollars altogether, then;

their total ratio = 5

unit amount = $2000/5

unit amount = $400

Peter spent = 2 × $400 = $800

John spent = 3 × $400 = $1200

If John spent 100 dollars more than Peter, then;

2/3 = P/(P + $100) {cross multiply}

3P = 2(P + $100)

3P = 2P + $200 {collect like terms}

3P - 2P = $200

P = $200.

Peter spent = $200

John spent = $300.

In conclusion, using the ratio 2:3 for the amount of money spent by Peter and John respectively, we have the answers: $750, $1000, $800 for Peter and $1200 for John, and $200 for Peter and $300 for John for the questions lettered (a), (b), (c), and (d) respectively.

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The final answer of the corrected expression is  (-22, -26).

What is the solution to the linear equation?

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

We have given:

 y = x - 4

-2x + y = 18

---------------------

-2x + (x - 4) = 18

-x - 4 = 18

x = 22

y = 22 - 4

y = 18

Solution: (22, 18)

The error is in lines 3, 4, and 5.

It should have,

 y = x - 4

-2x + y = 18

---------------------

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22

x = -22

y = -22 - 4

y = -26

Solution: (-22, -26)

Hence, the final answer of the corrected expression is  (-22, -26).

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Answer:

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

y = –1 2 x + 3 and y = 1 2 x - 1, the systems of linear equations.

from the graph , we have,

the solution set to this system of equations is,

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

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Answer: D

Step-by-step explanation:

Answer:

Yes, the tank is more than half full of gasoline after 3.5 hours.

Step-by-step explanation:

To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!

Answer:

The average rate of change is −10.

Step-by-step explanation:

The average rate of change of f(x) on the interval [a,b] is f(b) − f(a) / b−a.

We have, a=3, b=5, f(x) = -1x^2 − 2x + 2.

Thus, f(b) − f(a) = −(5)^2 −2(5) + 2 − [−(3)^2 −2(3) + 2]

= -25 - 10 + 2 - ( -9 - 6 + 2 )

= -33 - 13

= - 20

Then, b−a = 5 - 3 = 2

f(b) − f(a) / b−a = - 20 / 2 = −10

Answer: the average rate of change is −10.

The function that best shows the relationship between n and f(n) is;

f(n) = 24(0.5)ⁿ⁻¹

The function table that shows the amount of chlorine is given as;

n    1        2      3     5

f(n)  24     12      6    3

Where;

f(n) is the amount of chlorine in ounces, that was left in the pool after n weeks:

We can see that the value of f(n) is decreasing as n increases from the table.

Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

Using the formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

Where;

a represents the first term = 24

r represents the common ratio = 0.5

Thus, the equation of the function is;

f(n) = 24(0.5)ⁿ⁻¹

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The percentage of the cookies were gingerbread is 60%.

Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"

Here, Difference =55-22

=3

Percentage =33/55 ×100

= 0.6 ×10

= 60%

Therefore, the percentage of the cookies were gingerbread is 60%.

Answer:

Step-by-step explanation:

 cccccc

Answer:

No solution

Step-by-step explanation:

When you solve it, it ends up as 0=-7 which isn't true.

Answer:

No solution!

Step-by-step explanation:

Answer:

$25,900 initially

$8,128 after 11 years

Step-by-step explanation:

One thing to note, is I'm assuming you meant: [tex]v(t)=25,900(0.90)^t[/tex] and not  [tex]v(t)=25,900(0.90)^2[/tex], otherwise that would just be a constant function and not an exponential function.

There are a couple key features of exponential functions we can derive from simply analyzing the equation.

For now I will be using the form: [tex]y=a(b)^x\text{ where b} > 0, \text{b}\ne 1[/tex]

The y-intercept, is just the "a" value, which is because the y-intercept is simply when x=0, and if we raise a number to the power of zero, we get one (excluding zero as a base), so we get the form: [tex]y=a[/tex], so "a" is our y-intercept.

there's actually two type of exponential functions: exponential growth and exponential decay.

Exponential Decay:

Exponential decay, as the name implies, is when a function is decaying or decreasing. This occurs when [tex]0 < b < 1[/tex].

The decay rate can be represented as "r" in decimal form, where: [tex]b=1-r[/tex].

The reason for this is because "1" can be thought of as 100% and "r" is r%, so you're taking away r% or decaying the value by r%, also known as a decay rate.

Exponential Growth:

Exponential growth as the name implies, is when a function is growing or increasing. This occurs when b > 1

The growth rate can be represented as "r" in decimal form where: [tex]b=1+r[/tex]

The reason for this is similar to decay rate except instead of taking away r% or decaying, it's "giving r%" or growing.

The question doesn't actually require finding exponential growth or decay, but it's still an important key feature.

In this case, we really just need to find the y-intercept and plug in t=11.

The y-intercept in many graphs, not just exponential graphs, represents some sort of initial value, which in this case, is the initial value of the car. As stated above, this y-intercept is just the value in front, which is 25,900.

As for the value after 11 years, we simply need to plug in t=11 to get the following: [tex]v(11)=25,900(0.90)^{11}[/tex], from here we can use a calculator to simplify this: [tex]v(11)\approx25,900(0.31381059609)\approx 8,127.694438731[/tex], which rounds to 8,128

The statement that "the midpoint of a line is found by subtracting two coordinates and dividing the answers by two" is false

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula midpoint involves addition two coordinates instead of subtraction, and dividing by two.

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