A rectangle has a height of 4x and a width of 3.+ 1.
Express the area of the entire rectangle.
Expression should be expanded
3.1
4r
Area​

Answer:

Corresponding angles of similar triangles are congruent.

The true statement is (c) one pair of congruent corresponding angles is sufficient to determine similar triangles

From the complete question (see attachment), we have:

∠

�

�

�

≅

∠

�

�

�

∠NOP≅∠NML

This means that:

Angles NOP and NML are congruent

When the corresponding angles of similar triangles are congruent, then the triangles can be assumed to be similar.

Answer:

-1/2.

Step-by-step explanation:

( - 3 + 2) / 2

= -1 / 2.

The midpoint of a line segment with endpoints -3 and 2 is -0.5. This is calculated by adding the endpoints and dividing by 2.

The midpoint of a line segment is the average of its endpoints. We can find it by adding the two endpoints and dividing by 2. So, for the line segment with endpoints -3 and 2, we would calculate

(-3 + 2) / 2

The answer to this calculation is -0.5. Therefore, the midpoint of the line segment with endpoints -3 and 2 is -0.5.

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Answer:

The maximum value of P is 32

Step-by-step explanation:

we have following constraints

[tex]x\geq 0[/tex] ----> constraint A

[tex]y\geq 0[/tex] ----> constraint B  

[tex]2x+2y\geq 4[/tex] ----> constraint C

[tex]x+y\leq 8[/tex] ----> constraint D

Solve the feasible region by graphing

using a graphing tool

The vertices of the feasible region are

(0,2),(0,8),(8,0),(2,0)

see the attached figure

To find out the maximum value of the objective function P, substitute the value of x and the value of y of each vertex of the feasible region in the objective function P and then compare the results

we have

[tex]P=3x+4y[/tex]

so

For (0,2) ---> [tex]P=3(0)+4(2)=8[/tex]

For (0,8) ---> [tex]P=3(0)+4(8)=32[/tex]

For (8,0) ---> [tex]P=3(8)+4(0)=24[/tex]

For (2,0) ---> [tex]P=3(2)+4(0)=6[/tex]

therefore

The maximum value of P is 32

Answer:

Graph the inequalities given by the set of constraints. Find points where the boundary lines intersect to form a polygon. Substitute the coordinates of each point into the objective function and find the one that results in the largest value.

Step-by-step explanation:

the sample answer

Answer: t = 6

Step-by-step explanation: First we solve for -9(t-2) and that comes out to be -9t + 18. Then we solve for 4(t-15) which comes out to be 4t - 60. So the new equation we have is -9t + 18 = 4t - 60. In order to solve for t, we need to get t on one side of the problem by itself. To do this we will first add 9t to both sides and it comes out to be 18 = 13t - 60. t is still not by itself so now we add 60 to both sides and that gives us 78 = 13t. t is still not by itself so now we need to divide each side by 13 so that variable t is by itself. When we divide both sides by 13 we get 6 = t.

Answer:

6

Step-by-step explanation:

-9t + 18 = 4(t-15)

-9 +18 = 4t - 60

-9t = 4t-60-18

-9t = 4t - 78

-9 - 4 = -78

-13 = -78t =

t = -78/-13

t = 6

The instantaneous velocity of the ball after 4 seconds is -0.4 m/s

Step-by-step explanation:

If f(x) is the function which represents the distance that a particle moves after x seconds, with velocity v and acceleration a, then

∵ A ball is thrown vertically from the top of a building

∵ The height of the ball after t seconds can be given by the

   function s(t)= -0.1(t -2)² + 10

- To find the function of the velocity differentiate s(t)

∵ s(t) = -0.1(t - 2)² + 10

- Solve the bracket

∵ (t - 2)² = t² - 4t + 4

∴ s(t) = -0.1(t² - 4t + 4) + 10

- Multiply the bracket by -0.1

∴ s(t) = -0.1t² + 0.4t - 0.4 + 10

- Add the like terms

∴ s(t) = -0.1 t² + 0.4t + 9.6

Now let us differentiate s(t)

∵ s'(t) = -0.1(2)t + 0.4(1)

∴ s'(t) = -0.2t + 0.4

- s'(t) is the function of velocity after time t seconds

∵ s'(t) = v(t)

∴ v(t) = -0.2t + 0.4

We need to find the instantaneous velocity of the ball after 4 seconds

Substitute t by 4

∴ v(4) = -0.2(4) + 0.4

∴ v(4) = -0.8 + 0.4

∴ v(4) = -0.4

∴ The v is -0.4 m/s ⇒ -ve means the velocity is downward

The instantaneous velocity of the ball after 4 seconds is -0.4 m/s

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Final answer:

To determine the estimated instantaneous velocity of the ball after 4 seconds, calculate the derivative of the height function s(t) and evaluate it at t = 4 seconds to find the velocity of -0.2 m/s.

Explanation:

The estimated instantaneous velocity of the ball after 4 seconds can be found by calculating the derivative of the height function s(t) with respect to time t, which gives the velocity function v(t) = -0.2(t - 2). Evaluating this at t = 4 seconds, we get a velocity of -0.2 m/s.

Hint:

Diameter(d)= 2 radius(r)

circumference= 2πr= πd

1. diameter= 19 × 2 = 38 inches

circumference= 3.18(38) = 119 inches (3 s.f.)

Note that I use 3.18 instead of π because the question states to use 3.14 for π.

Likewise, if you are given the diameter, divide it by 2 to find radius. Let's try a question which only gives you the diameter.

4. radius= 22 ÷ 2 = 11cm

circumference= 3.14(22) = 69.1cm (3 s.f.)

Answer:

x=4, y=-1. (4, -1).

Step-by-step explanation:

x-3y=7

3x+3y=9

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

x=3y+7

3(3y+7)+3y=9

9y+21+3y=9

12y+21=9

12y=9-21

12y=-12

y=-12/12

y=-1

x-3(-1)=7

x+3=7

x=7-3

x=4

Answer:

48  chicken wings in 12 minutes.

Step-by-step explanation:

Answer:

4 chicken wings per minute

Step-by-step explanation:

12/3=4

Answer:

Exact Form:

y  =  − 25 /8

Decimal Form:

y  = − 3.125

The cost of package is $14.20

Step-by-step explanation:

Given,

Cost per pound of groundless beef = $5.99

Weight of package bought = 2.37 lbs

Cost of package = Cost per pound of beef * Weight of package

Cost of package = 5.99 * 2.37

Cost of package = $14.1963

Rounding off to nearest cent

Cost of package = $14.20

The cost of package is $14.20

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Answer:

Use a spreadsheet.

Step-by-step explanation:

If you mean a household budget you could use a spreadsheet.

The columns would be  months and the rows would be  items of expenditure and income.

You use  formulae ( provided by the spreadsheet)  to  do additions, subtractions and so on.

The point (3, 2) is the solution to given system of equations

Solution:

Given that system of equations are:

[tex]x^2 + y^2 = 13[/tex]    ------ eqn 1

[tex]2x - y = 4[/tex]    ------- eqn 2

From eqn 2,

y = 2x - 4

Substitute y = 2x - 4 in eqn 1

[tex]x^2 + (2x - 4)^2 = 13\\\\x^2 + 4x^2 + 16 - 16x = 13\\\\5x^2 -16x + 3 = 0[/tex]

Let us solve the above equation by quadratic formula,

[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Using the Quadratic Formula for [tex]5x^2 -16x + 3 = 0[/tex] where  a = 5, b = -16, and c = 3

[tex]\begin{aligned}&x=\frac{-(-16) \pm \sqrt{(-16)^{2}-4(5)(3)}}{2 \times 5}\\\\&x=\frac{16 \pm \sqrt{256-60}}{10}\\\\&x=\frac{16 \pm \sqrt{196}}{10}\end{aligned}[/tex]

The discriminant [tex]b^2 - 4ac>0[/tex] so, there are two real roots.

[tex]\begin{aligned}&x=\frac{16 \pm \sqrt{196}}{10}=\frac{16 \pm 14}{10}\\\\&x=\frac{16+14}{10} \text { or } \frac{16-14}{10}\\\\&x=\frac{30}{10} \text { or } x=\frac{2}{10}\\\\&x=3 \text { or } x=0.2\end{aligned}[/tex]

Substitute for x = 0.2 and x = 3 in 2x - y = 4

when x = 3

2(3) - y = 4

6 - y = 4

y = 2

when x = 0.2

2(0.2) - y = 4

0.4 - y = 4

y = 0.4 - 4

y = -3.6

Thus Option D is correct The point is (3, 2)

Final answer:

The volume of cylinder P is twice the volume of cylinder Q because the height of cylinder P is twice that of cylinder Q, while the radii are equal.

Explanation:

The question is asking how many times larger the volume of cylinder P is as compared to cylinder Q, given that cylinder P has twice the height of cylinder Q but both have equal radii. To find the volume of a cylinder, we use the formula V = πr²h, where V is the volume, π is the constant pi (approximately 3.14159), r is the radius, and h is the height of the cylinder.

Since both cylinders have equal radii, the ratio of their volumes will only depend on the ratio of their heights. If we let the height of cylinder Q be h, then the height of cylinder P is 2h. Using the volume formula:

Volume of cylinder P, VP = πr²(2h) = 2πr²h.

By dividing the volume of P by the volume of Q, we get:

VP / VQ = (2πr²h) / (πr²h) = 2.

Therefore, the volume of cylinder P is twice the volume of cylinder Q.

Answer: 12 1/3

Step-by-step explanation:

First, you need to add up 11/4 and

6 1/2

11/ 4 + 6 1/2 = 11/4 + 13/2 = 37 / 4

To find how many 3/4 we have in 37/4, we simply dividw 37/4 by 3/4

37/4 ÷ 3/4

= 37/4 × 4/3 (4 will cancel out 4)

= 37/3

=12 1/3

The number of groups of 3/4 that are in 11/4 and 6 1/2 is 3 2/3 and 8 2/3 respectively.

= 11/4 ÷ 3/4

= 11/4 × 4/3

= 11/3

= 3 2/3

= 6 1/2 ÷ 3/4

= 13/2 ÷ 3/4

= 13/2 × 4/3

= 8 2/3

Therefore, the number of groups of 3/4 that are in 11/4 and 6 1/2 are 3 2/3 and 8 2/3 respectively.

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The number of hours the diesel train traveled  before the cattle train caught up is 15 hours

Solution:

Let t = travel time of the diesel train

Then  (t - 2) is the travel time of the cattle train (Left 2 hrs later)

Average speed of diesel train = 52 mph

Average speed of cattle train = 60 mph

To find: number of hours the diesel train traveled  before the cattle train caught up

Distance = speed x time

Distance traveled by diesel train:

Distance = 52 x t = 52t

Distance traveled by cattle train:

Distance = 60 x (t - 2) = 60t - 120

When the cattle train catches the diesel, they will have traveled the

same distance

Distance traveled by diesel train = Distance traveled by cattle train

52t = 60t - 120

60t - 52t = 120

8t = 120

t = 15

Thus the number of hours the diesel train traveled  before the cattle train caught up is 15 hours

Answer:

1- false; 2- true; 3- true; 4-false

Final answer:

The statements about drawing a card higher than 6 and certain to draw an even or odd number are true. It's false that drawing a multiple of 3 is unlikely and that drawing a card less than 8 is unlikely.

Explanation:

The question involves determining the likelihood of drawing a specific card from a shuffled deck of 10 cards numbered 1-10. Let's assess each of the four statements provided.

Card greater than 6: There are 4 cards greater than 6 (7, 8, 9, 10), so the probability is 4 out of 10 or 0.4. This means it is likely, making the statement true.

Multiple of 3: There are 3 multiples of 3 (3, 6, 9), so the probability is 3 out of 10 or 0.3. This is less than half, but not very small, so the statement is subjective; however, we would not generally describe a 30% chance as 'unlikely', hence the statement might be considered false.

Even or odd number: Every card is either even or odd, so it is certain that an even or odd card will be drawn, making the statement true.

Number less than 8: There are 7 cards less than 8 (1 through 7), so the probability is 7 out of 10 or 0.7. This means it's more likely to draw a card less than 8, which means the statement is false.

Answer:

The quantity of cherries bought is 1.67 lb

The quantity of grapes bought is 3.33 lb

Step-by-step explanation:

Given as :

The cost of cherries = $4 per lb

The cost of grapes = $2.50 per lb

Total money spend on fruits = $15

The quantity of both fruits to bought = 5  lb

Let The quantity of cherries bought = c  lb

Let The quantity of grapes bought = g    lb

Now, According to question

quantity of both fruits to bought = quantity of cherries bought + quantity of grapes bought

i.e c + g = 5 lb              ........1

And

Total money spend on fruits = cost of cherries × quantity of cherries bought + cost of grapes × quantity of grapes bought

Or , c   lb ×  $4 per lb +  g  lb  ×  $2.50 per lb = $15

Or, 4 c + 2.50 g = 15           .......2

Now, Solving equation 1 and 2

So, (4 c + 2.50 g) - 2.50 × (c + g) = 15 - 5 × 2.50

Or, (4 c - 2.50 c) + (2.50 g - 2.50 g) = 15 - 12.50

Or, 1.5 c + 0 = 2.5

∴ c = [tex]\dfrac{2.5}{1.5}[/tex]

I.e c = 1.67  lb

So, The quantity of cherries bought = c  = 1.67 lb

Putting the value of c in eq 1

Since , c + g = 5  lb

Or, g = 5  lb - c

Or, g = 5  lb - 1.67  lb

i.e  g = 3.33  lb

So, The quantity of grapes bought = g  = 3.33 lb

Hence, The quantity of cherries bought is 1.67 lb

and The quantity of grapes bought is 3.33 lb   Answer

Answer:

The cost of 5 gallons of fuel would be 5x assuming the cost of 1 gallon to be x.

Step-by-step explanation:

An old truck has a fuel efficiency rating of 12 mpg.

We have to find the cost of gasoline that will be used up after we drive 60 miles.

To drive 60 miles , it uses 5 gallons.

let the cost of 1 gallon of fuel be x.

We have to find the cost of 5 gallons of fuel.

So the cost of 5 gallons of fuel = 5[tex]\times coat of 1 gallon of fuel[/tex]

                                                      = 5x

The cost per ticket is $0.75 if Clayton purchases the package.

Step-by-step explanation:

Given,

Cost of package = $18.75

Tickets in package = 25 tickets

To determine the cost of one ticket, we will divide the cost of package with number of tickets in package.

Cost per ticket = [tex]\frac{18.75}{25}[/tex]

Cost per ticket = $0.75

The cost per ticket is $0.75 if Clayton purchases the package.

Keywords: division, unit rate

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Answer:

91.6

Step-by-step explanation:

Answer:91.6

Step-by-step explanation:

Answer: The maximum revenue is $7482 . To get a maximum yield , The number of trees per acre needed is 43.

Step-by-step explanation:

Solution:

Let x represent the extra tree

So for an additional tree the yield of each tree will decrease by 4 bushels.

(80 +x)(26-4x) by expanding

2080 - 320x +26x -4x^2

Using x= -b/2a

X= 294/ -8

X= - 36.75

So apparently he currently has far too many trees per acre. To get the maximum yield , she needs to reduce the number of trees per acre by 36.75

So the number of trees per acre for maximum yield is

80-36.75

=43.25

Approximately x=43

So by reducing he get extra bushel in the tune of 174.

Total revenue= 174 ×43× 1$

=$7482

Option A: 6x^2+75x+200 is the correct answer

Step-by-step explanation:

The profit is obtained by subtracting the cost from the revenue.

Given

[tex]R(x) = 6x^2+100x+300\\C(x) = 25x+100[/tex]

The Profit function will be obtained by subtracting the cost function from the revenue function

So,

[tex]P(x) = R(x) - C(x)\\= (6x^2+100x+300)-(25x+100)\\=6x^2+100x+300-25x-100\\=6x^2+100x-25x+300-100\\P(x)=6x^2+75x+200[/tex]

Hence,

Option A: 6x^2+75x+200 is the correct answer

Keywords: Functions, function operations

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Answer:

Explained.

Step-by-step explanation:

The graph of a line on the coordinate system represents the points that are on the graph that will satisfy the equation of the line.

Now, if two lines on the coordinate plane are graphed and they pass through the same point (h,k) that means the point satisfies both the equations of the lines.

Let us have two curve equations [tex]y = 2^{(- x)}[/tex] and [tex]y = 4^{x} + 3[/tex] and they pass through the same point (h,k) on the coordinate plane.

Then we can write [tex]k = 2^{(- h)}[/tex] ......... (1) and  

[tex]k = 4^{h} + 3[/tex] .......... (2)

Now, solving equations (1) and (2) we get

[tex]2^{(- h)} = 4^{h} + 3[/tex] ........... (3)

Therefore, we have to solve the above equation (3) to get the value of h i.e. the x-coordinate of the point/s where the graph of the equations (1) and (2) intersect.

Now, converting h to x we will get the same result. (Answer)

Inconsistent

Step-by-step explanation:

When you graph a system of equations then ;

They are consistent and independent, they have exactly one solution

If they are consistent and dependent, they have infinite number of solutions

If they there is no solution, the system is inconsistent

In this case, the lines are parallel, no intersecting for a solution.

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Answer:

inconsistent

Step-by-step explanation:

because they dont cross eachother

Answer:

10,93,500.

Step-by-step explanation:

On first February total number of rabbits were 500.

Now it is given that after each month rabbit population will become triple of initial.

So, after one month rabbits will become 3×500.

After two months they will become [tex]3^{2}[/tex]×500.

Thus , after m months total number of rabbits will become [tex]3^{m}[/tex]×500.

Now,

On August 1 , 7 months will get passed from February 1 so putting m = 7 in the equation we get ,

Total number of rabbits = [tex]3^{7}[/tex]×500 = 10,93,500.

The function that represents the number of rabbits is f(m) = 500 * 3^m. Replacing m with 6, which represents the 6 months from February 1st to August 1st, we get that there would be 145800 rabbits in Lancaster on August 1st.

This question is about an exponential function, specifically a geometric sequence, where each term is tripled to get the next. The general form of an exponential function is f(m) = ab^m, where a is the initial amount, b is the rate of growth, and m is the time period.

In this case, the initial amount (a) of rabbits is 500, the rate of growth (b) is 3 (as the population triples every month), and m represents the months passed. Hence, the function relating to the rabbit population becomes f(m) = 500 * 3^m.

For the rabbit population on August 1st, we have to consider that February 1st to August 1st is 6 months. Thus, replacing m with 6 in our function: f(6) = 500 * 3^6, which equals 145800, so there would be 145800 rabbits in Lancaster on August 1st.

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The domain of a relation is the set of all the x-terms of the relation.

Let's look at an example.

In the image provided I have attached a relation and we want to list the domain.

So, I will list all the x-terms. Notice however that I listed 7 once even though it appears twice in the relation. When listing the domain, you don't repeat the x-terms.

Answer:

Here's what I get.

Step-by-step explanation:

When you dilate an object by a scale factor, you multiply its coordinates by the same number.

If the scale factor is 4, the rule is (x, y) ⟶ (4x, 4y)

Your table then becomes

[tex]\begin{array}{lcl}\textbf{Vertices of}& \, & \textbf{Vertices of}\\\textbf{VWXY}& \, & \textbf{V'W'X'Y'}\\V(-1 ,1) & \quad & V'(-4, 4)\\W(-1, 2) & \quad & W'(-4, 8)\\X(2, -1) & \quad & X'(8 ,-4)\\Y(2, 2) & \quad & Y'(8, 8)\\\end{array}[/tex]

The diagram below shows figure VVXY as a green bow-tie and its image V'W'X'Y' in orange.

The scale factor is greater than one, so the dilation is an enlargement.

Answer

Tina is 21, t-3

Step-by-step explanation:

Cole is 18, we don't really need that so just ignore it. Cole is 3 years younger than Tina. Therefore T which is Tina's age, minus 3 would equal Cole's age of 18.

Answer:

a

Step-by-step explanation:

The correct function to express the area of the rectangular corral as a function of its width, given a fixed amount of fencing, is A(x) = x(70 - x).

The student is asking about expressing the area of a rectangular corral as a function of its width when a fixed amount of fencing is used. Given that Farmer Jones has 140 feet of fencing to construct the corral and the width is represented by x, the perimeter of the rectangle is twice the sum of its width and length.

Therefore, if x is the width, the length will be (140 - 2x)/2 or 70 - x. We can then express the area A as a function of x by multiplying the width by the length, leading to the function A(x) = x(70 - x).

Answer with Step-by-step explanation:

Jamel' spend on apples

= Jamel' spend on Green apples + on Red apples

= Cost per pound of apples *( Pounds of green apples + Pounds of red apples)

= 1.65*(2+3.2)

= 1.65*5.2

= $8.58

Answer: $8.58 is Jamel' total spend on apples.