1a, b/46 = 50/23 1b. 34/d = 68/44​

Answers

Answer 1

Answer:

1a. 100, 1b. 22

Step-by-step explanation:

1a. Given information from the question:

[tex] \frac{b}{46} = \frac{50}{23} \\ 23b = (50)(46) \: (cross \: multiply) \\ b = \frac{50 \times 46}{23} \\ = 50 \times 2 \\ = 100[/tex]

1b. Given information from the question:

[tex] \frac{34}{d} = \frac{68}{44} \\ 68d = (34)(44) \: (cross \: multiply)\\ \\ d = \frac{34 \times 44}{68} \\ d = \frac{44}{2} \\ = 22[/tex]

Answer 2

Answer:

• [tex]b = \bf 100[/tex]

• [tex]d = \bf 22[/tex]

Step-by-step explanation:

To solve these questions, we need to rearrange the equations to make the unknown variables the subject of the equations.

1a.

[tex]\frac{b}{46} = \frac{50}{23}[/tex]

⇒ [tex]b = \frac{50 \times 46}{23}[/tex]             [multiplying both sides by 46]

⇒ [tex]b = \bf 100[/tex]

1b.

[tex]\frac{34}{d} = \frac{68}{44}[/tex]

⇒ [tex]34 = \frac{68 \times d}{44}[/tex]               [multiplying both sides by d]

⇒ [tex]34 \times 44 = 68 \times d[/tex]    [multiplying both sides by 44]

⇒ [tex]\frac {34 \times 44}{68} = d[/tex]               [dividing both sides by 68]

⇒ [tex]d = \bf 22[/tex]


Related Questions

Find the absolute maximum and minimum values of f on the set d. f(x, y) = xy2 7, d = {(x, y) | x ≥ 0, y ≥ 0, x2 y2 ≤ 3}

Answers

Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain

[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]

we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.

There are no critical points elsewhere in the interior of [tex]D[/tex], since

[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]

Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then

[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]

Find the critical points of [tex]g[/tex].

[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]

[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]

[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]

In the first case, we get

[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]

where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].

In the second case, we get

[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex]  corresponding to [tex](1,\sqrt2)[/tex].

In the third case, we get

[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].

So, we find

[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]

(but really any point on either axis works)

[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]

whats the surface area of the rectangular prism

Answers

The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

What is the area of a rectangle?

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

How to calculate the area of the rectangular prism?

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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find the value of n:
[tex]\frac{10}{n} =\frac{15}{6}[/tex]

Answers

4. Cross multiply (10•6) (15•n) 15n=60 you do the opposite operation so instead of multiply 15•n you divided 15 from n. And what u do on one side u do on both. So divide 15 from 60 and u get 4.

Please help!
The graph shows a system of inequalities.
Which point is a solution to the system?
(0,-1)
(2,3)
(4,0)
(6,-6)

Answers

Check the picture below.

In the diagram below, if < ACD = 48 °, find the measure of < ABD.

Answers

Answer:

d

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , that is

∠ ABD + ∠ ACD = 180°

∠ ABD + 48° = 180° ( subtract 48° from both sides )

∠ ABD = 132°

What is the domain of the function y = X+ 6 -7?
x>-7
x>-6
x>6
x>7

Answers

The domain of the function y = √(x + 6) - 7 is x > -6

How to determine the domain of the function?

The equation of the function is given as

y = √(x + 6) - 7

Set the radical greater than 0

x + 6 > 0

Subtract 6 from both sides of the equation

x > -6

Hence, the domain of the function y = √(x + 6) - 7 is x > -6

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The domain of the function in discuss described as; y = √x+6 -7 is; x >= -6.

What is the domain of the function described as in the task content above?

According to the task content, it follows that the domain of.the function can be evaluated by means of the characteristics associated with the square root.

The function given is; y = √x+6 -7

Since, the square root of a negative number renders a complex number as it's results, it follows that; x+6 >= 0.

Hence, x >= -6.

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At the movie theatre, child admission is $6.80 and adult admission is $9.90. On Thursday, twice as many adult tickets as child tickets were sold, for a total sales
of $984.20. How many child tickets were sold that day?
Number of child tickets:0

Answers

Answer:

37 child tickets / 74 adult tickets

Step-by-step explanation:

I randomly picked a number and increased or decreased whether the solution was too high or low (guess and check)

The number of child tickets sold that day is 37.

We have,

Let's assume the number of child tickets sold is "C" and the number of adult tickets sold is "A."

The cost of a child ticket: $6.80

The cost of an adult ticket: $9.90

The total sales for the day: $984.20

The number of adult tickets sold is twice the number of child tickets sold:

A = 2C

To find the number of child tickets sold, set up an equation based on the total sales:

6.80C + 9.90A = 984.20

Substituting the value of A from equation 4:

6.80C + 9.90(2C) = 984.20

Simplifying the equation:

6.80C + 19.80C = 984.20

26.60C = 984.20

C = 984.20 / 26.60

C ≈ 37

Therefore,

37 child tickets were sold that day.

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Which of the equations below represents
this ellipse?

a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1

Answers

The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

What is the equation of the ellipse represented in the graph?

Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

(h, k) - Coordinates of the centera, b - Lengths of the semiaxes

Please notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

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Select the correct answer. emily wants to find the number that appears in the middle of a set of 25 numbers arranged in ascending order, in a spreadsheet. which statistical function will help her do so? a. mode b. rank c. median d. average

Answers

The correct answer is option (C) median.

The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

What is the mean, median and mode?

The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.

The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.

When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.

The number that appears most frequently in a set of numbers is called the mode.

So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

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A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?

Answers

The probability of event A and event B IS  15/91.

What is the probability?

Probability determines the odds that a random event would occur. The odds lie between 0 and 1.

The probability of event A  = number of brown marbles / total number of marbles

= 6/14

The probability of event B = number of orange marbles / total number of marbles -1

= 5/13

P(A and B) =6/14 x 5/13

                 = 30/182

                 = 15/91

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Answer:

B.) 5/13

Step-by-step explanation:

15/3=5

91/7=13

5/13

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What two nonnegative real numbers with a sum of have the largest possible​ product?.

Answers

The two non negative real numbers with a sum of 60 that have the largest possible​ product are 30 and 30.

What are non negative numbers?

Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.

An integer that is either positive or zero is considered a non-negative integer.

Let us assume the two non negative numbers are [tex]x[/tex] and [tex]y[/tex].

According to the question,

Sum of two non negative numbers = 60

⇒ [tex]x+y=60[/tex]

⇒ [tex]y=60-x[/tex]

Their product will be given as,

⇒ [tex]P=xy[/tex]

⇒ [tex]P=x(60-x)[/tex]

⇒ [tex]P=60x-x^2[/tex]

For the product to be largest [tex]P'(x)=0[/tex]

⇒ [tex]P'(x) = 60-2x[/tex]

⇒ [tex]60-2x=0[/tex]

⇒ [tex]2x=60[/tex]

⇒ [tex]x=30[/tex]

Now, for the value of [tex]y[/tex]

⇒ [tex]y=60-x[/tex]

⇒ [tex]y=60-30[/tex]

⇒ [tex]y=30[/tex]

Therefore, the two non negative numbers are 30, 30.

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Need this quick ! Correct answers appreciated

(Selected answer is not known to be correct it just won’t let me un select an answer)

Answers

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]

[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]

next,

g(f(-5)) represents value of y at x = f(-5) = 1

hence,

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\sf \:g(f( - 5)) = 5[/tex]

Given that a randomly chosen flight arrives in los angeles (lax), what is the probability that the carrier is american airlines (aa)?

Answers

Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).

What is probability?

A probability exists given by the number of expected outcomes divided by the number of total outcomes.

Over a large number of trials, a percentage can also define the probability of a single event.

In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in  American airlines.

There exists a 4.7% probability that it arrives on American airlines(aa).

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Answer: 2316/16924 = 0.137 = 13.7%

Step-by-step explanation:

(08.07 HC)
An expression is shown below:
f(x) = 2x²-3x - 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)

Answers

Answer:

Below in bold.

Step-by-step explanation:

Part A

At the x-intercepts  f(x) = 0, therefore:

2x^2 - 3x - 5 = 0

(2x - 5)(x + 1) = 0

x = 5/2, -1)

So the x intercepts are (-1, 0) and (5/2, 0).

Part B

The Coefficient  of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.

Convert f(x) to vertex form, by completing the square:

f(x) = 2x^2 - 3x - 5

= 2(x^2 - 3/2x) - 5

= 2[(x - 3/4)^2 - 9/16] - 5

= 2(x - 3/4)^2 -18/16 - 80/16

= 2(x - 3/4)^2 - 49/8

So the coordinates of the vertex are

(3/4, -49/8)  or

(0.75, -6.125) in decimal form.

Part C

To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.

The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).

You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.

Suggest   x = - 2  and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 =  11.

- that is the point (-2,11) and the other would be  x = 4,  f(x) = 15. (4, 15)

Once you have plotted these points draw a smooth u shaped curve through them.

A dairy farmer decides to sell three fifth of her 500 cows. How many cows will she be left with after the deal is complete?

Answers

Answer is 200 cows
Step by step
She is selling 3/5 of 500
Multiply across 3/5 x 500
1500/5 divide to get 300 sold
Now 500-300 sold = 200 cows left
Problem solved

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 − 3x x2

Answers

It looks like the limit is

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]

L'Hôpital's rule works in this case; applying it twice gives

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]

A 2-quart carton of non-dairy creamer costs $1.04. What is the price per cup?

Answers

Answer is $0.13 per cup

We know there are 4 cups per 1 quart, therefore we have 8 cups in a 2 quart container (4x2)

We will divide the 1.04 cost by 8 cups to get our price per cup

1.04 / 8 = .13
Problem solved

what expression is equivalent to 6+3(n-4)-8+2n

Answers

Answer:

Step-by-step explanation:

Comment

Begin by removing the brackets.

6+3(n-4)-8+2n

6 + 3n - 12 - 8 + 2n                 Collect like terms

3n + 2n + 6 - 12 - 8                 Combine

5n - 14

Answer

5n - 14

10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60

Answers

Answer:

C

Step-by-step explanation:

2/5 x1/5 = 2/25  If you divide 2 by 25, you get.08.  To change a decimal into a percent, you move the decimal two places to the right to get 8%

G.CO.5 △ABC undergoes a series of transformations to create △A'B'C'. Which of the following series of transformations will carry △ABC onto △A'B'C'?

Answers

Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.

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How do you determine the
solution to a system of equations
when graphing? Is it possible to
have more than 1 solution when
graphing? Is it possible to have no
solutions? How?

Answers

When graphing, the intersections of the graphs represent the solutions of the system.

How to determine the solutions of a system by graphing?

When graphing a system of equations, you just need to graph both equations in the same coordinate axis.

The solutions of the system are all the points where the graphs of the two equations intersect.

This means that if there is only one intersection, there is one solution.

But we can have more than one intersection, like in the case where at least one of the equations is a polynomial of degree 2 or more.

And there is also the case that the graphs never intersect, like in parallel lines, in these cases we have no solutions.

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In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________

Answers

For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

According to the statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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Which function is positive for the entire interval [-3, -2]?

Answers

Answer:

A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5.

Answer:

The second function (second graph and choice)

Step-by-step explanation:

If you look at the second function you will see that within the closed interval [-3,-2] the graph y  values are positive

First choice is incorrect since at x = -2  the y value is negative

Third choice incorrect since at x = -2, y value is negative

Fourth choice incorrect since y value is negative for x = -2



A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet. What is the angle of depression from the bird (B) to the
observer (0)?

Answers

Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

For this problem, we have that:

The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.

Hence, considering θ as the depression angle, we have that:

tan(θ) = 9000/6000

tan(θ) = 1.5

θ = arctan(1.5)

θ = 56.31º.

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Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point and its radius is
units.

Answers

The required answers are:

1) The center of the circle = (4, 8)

2) The radius of the circle = 2.5 units

3) The equation of the circle = (x - 4)² + (y - 8)² = 6.25

What is the equation of a circle?

The equation of the circle which has a center at (h, k) and a radius of 'r' units is (x - h)² + (y - k)² = r²

To calculate radius 'r', we have r = sqrt( (x1 - h)² + (y1 - k)²)

Where (x1, y1) is the point that lies on the circle.

Calculation:

Given that,

The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)

We know that the longest chord on a circle is nothing but the diameter of the circle.

So, the center is the midpoint of the diameter. I.e.,

(h, k) = ([tex]\frac{4+4}{2}[/tex], [tex]\frac{5.5+10.5}{2}[/tex])

⇒ (h, k) = (4, 8)

Therefore, the center of the circle is (4, 8)

Then, the radius is calculated by

r = sqrt( (x1 - h)² + (y1 - k)²)

⇒ r = [tex]\sqrt{(4-4)^2+(5.5-8)^2}[/tex]

⇒ r = 2.5 units

Thus, the radius of the circle is 2.5 units.

So, the equation of the circle with center (4, 8) and radius of 2.5 units is,

(x - h)² + (y - k)² = r²

⇒ (x - 4)² + (y - 8)² = 2.5²

⇒ (x - 4)² + (y - 8)² = 6.25

Thus, the equation of the circle is x - 4)² + (y - 8)² = 6.25.

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Perfect pizza has 16 toppings listed on their menu. how many ways could a customer choose a pizza that contains 5 different toppings?

Answers

Answer:

4368 ways

Step-by-step explanation:

Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

○ [tex]h = \frac{2A}{b}[/tex]  

Step-by-step explanation:

We are given:

[tex]A = \frac{1}{2} b h[/tex]

To solve for [tex]h[/tex], we have to rearrange the equation to make [tex]h[/tex] the subject:

[tex]A = \frac{1}{2} b h[/tex]

⇒ [tex]2A = bh[/tex]     [multiplying both sides by 2]

⇒ [tex]\frac{2A}{b} = h[/tex]       [dividing both sides by b]

⇒  [tex]h = \frac{2A}{b}[/tex]      [swapping sides]

What is the sum of this infinite geometric series?

Answers

[tex]\qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\stackrel{\textit{first term}}{\frac{1}{8}}\\ r=\stackrel{\textit{common ratio}}{\frac{2}{3}}\\ \qquad -1 < r < 1 \end{cases}[/tex]

[tex]\displaystyle\sum_{k=0}^{\infty} ~~ \underset{a_1}{\frac{1}{8}}\underset{r}{\left( \frac{2}{3} \right)}^k\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{1-\frac{2}{3}}\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{\frac{1}{3}}\implies S=\cfrac{3}{8}[/tex]

write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15

Answers

Answer:

[tex]y=-\dfrac{1}{3}x+4[/tex]

Step-by-step explanation:

Slope of line with given x and y intercepts

The x-intercept is when y = 0.  
Therefore, if the x-intercept is 5 ⇒ (5, 0).

The y-intercept is when x = 0.  
Therefore, the y-intercept is -15 ⇒ (0, -15).

Inputting these two points into the slope formula to find the slope of this line:

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]

Slope of function f(x)

If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.

[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]

Equation of f(x) in point-slope form

Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]

[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]

Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:

[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]

[tex]\implies y=-\dfrac{1}{3}x+4[/tex]

Learn more about linear equations here:

https://brainly.com/question/27317293

https://brainly.com/question/28062655

(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)

Answers

Answer:

8x³ - 2x² - 51x - 45

Step-by-step explanation:

(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL

= (x - 3)(8x² + 10x + 12x + 15)

= (x - 3)(8x² + 22x + 15)

multiply each term in the second factor by each term in the first factor.

x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis

= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms

= 8x³ - 2x²- 51x - 45

Expand first 2 bracket first to get:

2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.

2x^2 - 3x - 9 (4x + 5)

2x^2 x 4x = 8x^4

2x^2 x 5 = 10x^2

Repeat for the next two numbers next to the bracket.

You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45

Final simplified answer of:

8x^3 - 2x^2 - 51x - 45

Hope this helps!

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