6. Rectangle GHIJ is enlarged to form
rectangle KLMN.
G 5cm H
2.5 cm
20 cm
10cml
Scale Factor:​

[tex]$x=\frac{3}{4}[/tex]

Solution:

Given expression is [tex]x^3=\frac{27}{64}[/tex].

To solve the expression and find the value of x.

[tex]$\Rightarrow x^3=\frac{27}{64}[/tex]

27 can be written as 3 × 3 × 3 = [tex]3^3[/tex]

64 can be written as 4 × 4 × 4 = [tex]4^3[/tex]

[tex]$\Rightarrow x^3=\frac{3^3}{4^3}[/tex]

Taking cube root on both sides of the function.

[tex]$\Rightarrow\sqrt[3]{x^3}=\sqrt[3]{\frac{3^3}{4^3}}[/tex]

Cube and cube roots are cancelled.

[tex]$\Rightarrow x=\frac{3}{4}[/tex]

Therefore, [tex]x=\frac{3}{4}[/tex].

Answer: Remember PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. But when trying to solve a problem with a variable, remember to go backwards.

Answer:

From 10 to 20 meters.

Step-by-step explanation:

1) If the sparrow has a parabolic trajectory then it must be actually:

[tex]y=-5\left ( x+6 \right )^{2}+10[/tex]

2) If the eagle is at 20 meters high, then we write:

[tex]y=20[/tex]

Since the exact x coordinate was not given.

But since it wants to get the sparrow

3) If we expand the equation we have:

[tex]-5x^{2}-60x-170=0\\\\X_{v}=\frac{-b}{2a}=\frac{60}{-10} = -6\\Y_{v}=\frac{-\Delta}{4a} =\frac{-200}{-20} =10[/tex]

Since the maximum point is equal to 10. The distance where the sparrow is flying ranges from 10 to 20 meters to the eagles spot.

[tex]10\leq d \leq20 \:or \:[10,20][/tex]

4) Since the x coordinate was not given then we can neither precisely calculate the distance where A is nor where B is located.

Answer:

3 meters

Step-by-step explanation:

Answer:

5817 Newtons.

Step-by-step explanation:

Total mass of the cage + the miners = 700 Kg which is a downward force of  700g N.

The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.

We  calculate the  acceleration of the cage by using an equation of motion:

Distance = ut + 1/2 a t^2     where u = initial velocity , t = time and a = acceleration:

75 = 0(t) + 1/2 a (10^2)

50a =  75

a = 1.5 m s-2.

So using Newtons second law of motion

Force = mass * acceleration:

700*9.81 - T = 700 * 1.5

T = 700 * 9.81 - 700*1.5

= 5817 N.

The force in the cable during the first 10 seconds is 7930N. This was determined using the formulas s = ut + 1/2at² (to calculate acceleration) and F = ma + mg (to calculate the force).

The subject of this question is Physics, specifically dealing with forces and acceleration. The total weight of the miners and the cage equals the sum of the miners' weight and the cage's weight, giving a total of 700kg, using the formula weight = mass x gravity (assumed to be 9.8m/s²). Therefore, the total weight is 700kg x 9.8m/s² = 6860N.

Then, we'd calculate the acceleration. The formula used is s = ut + 1/2at², where s is distance, u is initial velocity, a is acceleration, and t is time. Given that initial velocity is 0, the formula is simplified to s = 1/2at². After rearranging, we get acceleration (a) = 2s/t² = 2*75/10² = 1.5m/s².

Finally, we can determine the force on the cable using the formula F = ma + mg (F = force, m = mass, a = acceleration, g = gravity). Substituting, we get F = 700kg x 1.5m/s² + 700kg x 9.8m/s² = 7930N. Therefore, the force in the cable during the first 10 seconds is 7930N.

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Answer:

Since this dude got a Bird Brain I got ya'll

Step-by-step explanation:

Whats in Bold is what you put in the drop down menu. :)

So, f(3) = 26. This means that after 3 months, the number of products sold were 26,000.

If f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Finding profit, populations, and distance traveled are some applications of functions. By entering a number into the formula, locating the independent variable on a table or graph, and then computing the resulting dependent variable, functions are employed.

It is given that,

f(t)=5t+11

So for the given condition after three months,

Substitute the value of t as 3,

f(3)=5(3)+11

f(3)=15+11

f(3)=26

Thus, if f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.

Learn more about the function here:

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Answer:

0.8 hours

Step-by-step explanation:

From the question;

We need to determine the time he takes to cover the distance given;

We need to know that;

Speed = Distance ÷ time

Rearranging the formula;

time = Distance ÷ speed

Thus;

Time = 21 miles ÷ 27 miles per hour

        = 7/9 hours

        = 0.8 hours

Thus, he took 0.8 hours to cover the distance covered

Answer:

A: The data are so varied that there is almost no discernible trend whatsoever.

Step-by-step explanation:

The other 3 don't make sense and are not true for the question

Answer: 8 gumballs

Step-by-step explanation:

We can solve this problem with the Rule of three, since we are given as data three factors and one is unknown.

If 2 gumballs cost 8 cents, how many gumballs can we buy with 32 cents?:

[tex]2 gumballs[/tex]-----[tex]8 cents[/tex]

[tex]x[/tex]-----[tex]32 cents[/tex]

Then:

[tex]x=\frac{(2 gumballs)(32 cents)}{8 cents}[/tex]

[tex]x=8 gumballs[/tex] We can buy 8 gumballs with 32 cents

Answer:

It’s A. I go To Uva too

Step-by-step explanation:

To find the slope of g(x), use the slope formula(m):

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]        And plug in two points, I will use:

(0, 2) = (x₁, y₁)

(5, 4) = (x₂, y₂)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-2}{5-0}[/tex]

[tex]m=\frac{2}{5}[/tex]

You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:

[tex]m=\frac{rise}{run}[/tex]

Rise is the number of units you go up(+) or down(-) from each distinguished point

Run is the number of units you go to the right from each distinguished point

If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is  [tex]\frac{2}{3}[/tex]

Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A

Answer:

Neither positive nor negative—the sum is zero.

Step-by-step explanation:

Final answer:

The mathematics problem involves cancelled positive and negative numbers. Adding a number to its negative results in zero. Therefore, the expression simplifies to zero.

Explanation:

The question provided appears to be a mathematics problem that involves adding a number and its negative equivalent. Specifically, it looks like the sum of 123 and 1/23 plus the negative of 123 and 1/23 is being asked.

When you sum a number and its negative, they cancel each other out, resulting in zero. This is because the definition of a negative number is that it's the additive inverse of its positive counterpart, meaning when the two are added together, their sum is zero. The calculation is straightforward:

123 and 1/23 + (-123 and 1/23) = 0.

Answer:

Step-by-step explanation:

y = 5/3x + 5...in y = mx + b form, the slope is in the m position and the y int is in the b position.

so we have a slope of 5/3 and a y int of 5.....(0,5)

the x int can be found by subbing in 0 for y and solving for x

0 = 5/3x + 5

-5/3x = 5

x = 5 * -3/5

x = -15/5

x = -3......so ur x int is (-3,0)

go ahead and plot ur intercepts....(0,5) and (-3,0).....now start at (-3,0)....and since ur slope is 5/3....go up 5 spaces and to the right 3 spaces...plot that point.....then go up 5 and to the right 3...plot that point....keep doing this pattern....u should cross the y axis at (0,5). Then just connect ur dots and u have ur line.

Answer:

15 29/64

Step-by-step explanation:

You will turn them both improper and then multiply

a) 5/7

b) 4459 cm cube

c) 2275 cm cube

Step-by-step explanation:

Step 1 :

a)

The Side AB (28 cm) has been scaled to side DE (20 cm)

Let x b the scale factor.

Then we have 28 *x = 20

=> x = 20/28 = 5/7

Hence the scale factor is 5/7

Step 2 :

b)

Given the height of the triangular prism is 15 cm

Volume = ( 1/2 ) * base* height of the triangle * height of the prism

= (1/2)* 21*28*15 = 4410 cm cube.

Step 3 :

c)

Given volume of the triangular prism with base ABC is 4459 cm cube

The scale factor is 5/7

Hence the volume of the prism with DEF as base is

4459 * (5/7)*(5/7) = 2275 cm cube.

Final answer:

The approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth is about 14.7 meters.

Explanation:

To find the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth, we can use the formula for the period of a pendulum:

T = 2π √(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Given that the period is 2.4 pi seconds, we can substitute this value into the formula:

2.4 pi = 2π √(L/g)

Simplifying the equation, we can divide both sides by 2π:

1.2 = √(L/g)

Squaring both sides of the equation, we get:

1.44 = L/g

Since we don't have the value of g, we cannot solve for L exactly. However, if we assume that g is approximately 9.8 m/s², which is the average acceleration due to gravity on Earth, we can estimate the value of L:

1.44 = L/9.8

Multiplying both sides by 9.8, we find:

L ≈ 14.7 m

Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.

To find out how many of each bill Dalton has, we can set up a system of equations.

Let's assume Dalton has x number of ten-dollar bills and y number of twenty-dollar bills. The total number of bills he has is given as 7, so we have the equation: x + y = 7.

Additionally, the total value of the bills is given as $100. Since each ten-dollar bill is worth 10 dollars and each twenty-dollar bill is worth 20 dollars, we have the equation: 10x+20y = 100.

Now we can solve the system of equations to find the values of x and y.

Multiplying the first equation by 10 to eliminate x, we have: 10x + 10y = 70.

Subtracting this equation from the second equation, we get: 10x + 20y - (10x + 10y) = 100 - 70.

Simplifying, we have: 10y = 30.

Dividing both sides of the equation by 10, we find that y = 3.

Substituting this value back into the first equation, we can solve for x: x + 3 = 7.

Subtracting 3 from both sides, we find that x = 4.

Therefore, Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.

Step-by-step explanation:

(9-4)/(5+7)= 5/12

y - 4 = 5/12(x + 7)

y - 48/12 = (5/12)x + 35/12

y = (5/12)x + 83/12

Answer: x = 4y/3+2

   y = 0

Step-by-step explanation:

Yo sup??

area of a square =a*a

=a^2

where a is the lenght of its side

area=3.2*3.2

=10.2 unit2

pls do the conversion into inches

Hope this helps

The answer is: 10.24 in^2

Answer:

B is the right answer.

Area of the carpet needed = 38 ft²

Solution:

The given image is splitted into two shapes.

One is trapezoid and the other is triangle.

Top base of the trapezoid = 8 ft

Bottom base of the trapezoid = 12 ft

Height of the trapezoid = 3 ft

Area of the trapezoid = [tex]\frac{1}{2} (a+b)\times h[/tex]

                                    [tex]$=\frac{1}{2}(8+12)\times3[/tex]

                                    [tex]$=10\times3[/tex]

                                    = 30

Area of the trapezoid = 30 ft²

Base of the triangle = 12 ft – 8 ft = 4 ft

Height of the triangle = 4 ft

Area of the triangle = [tex]\frac{1}{2} b h[/tex]

                                 [tex]$=\frac{1}{2} \times4\times4[/tex]

                                 = 8

Area of the triangle = 8 ft²

Area of the carpet = Area of the trapezoid + Area of the triangle

                               = 30 ft² + 8 ft²

                               = 38 ft²

Area of the carpet = 38 ft²

Hence 38 square feet of outdoor carpet will need for this hole.

Answer:

65 degrees

25 degrees

Step-by-step explanation:

x=first angle

y=second angle

x+y=90            x-y=40

                       x=40+y

(40+y)+y=90

40+2y=90

2y=50

y=25

                      x=40+25

                         x=65

Final answer:

The sum and difference of two angles can be found by setting up a system of equations and solving it. In this case, the two angles are 65 degrees and 25 degrees.

Explanation:

The question is asking for the sum and difference of two angles. Let's represent the two angles as x and y. We know that the sum of the two angles is 90 degrees, so we can write the equation x + y = 90. We also know that the difference of the two angles is 40 degrees, so we can write the equation x - y = 40.

We can solve this system of equations using substitution or elimination. Let's use the substitution method. From the second equation, we can rewrite it as x = y + 40. Substitute this value of x into the first equation:

(y + 40) + y = 90. Combine like terms: 2y + 40 = 90. Subtract 40 from both sides: 2y = 50. Divide by 2: y = 25.

Now substitute this value of y back into the equation x = y + 40: x = 25 + 40 = 65.

So, the two angles are x = 65 degrees and y = 25 degrees.

Answer:

A

Step-by-step explanation:

I also took a quiz with this question and I got the right answer.

Answer:

49

Step-by-step explanation:

7:6:8 so 7+6+8=21

147 divided by 21 is 7

so 1 ratio equals 7

red = 7 so its gonna be 7x7=49

Answer:

yes

Step-by-step explanation:

Answer:

 Area of shades region [tex]=45[/tex] square inches

Step-by-step explanation:

In the given figure accordingly, we have to find the Area of the shaded region

Area of shaded region= Area of big triangle - Area of the small triangle.

          Area of a  triangle=  [tex]\frac{1}{2} *base*altitude[/tex]

Altitude is the perpendicular height of the triangle from its top to base.

Base of big triangle=12 inches,    Altitude of big triangle=6+3= 9 inches

Area of Big triangle  

                                     [tex]=\frac{1}{2}* 12*9\\\\=6*9\\\\=54[/tex]

Base of small triangle= 6 inches,    Altitude of small triangle= 3 inches

Area of the small triangle=

                                            [tex]=\frac{1}{2} *6*3\\\\=3*3\\\\=9[/tex]

        Area of shades region [tex]=54-9\\[/tex]

                                              [tex]=45[/tex] square inches

In a system of two linear equations if the slopes are same then no solutions and different slope means exactly one solution.

Step-by-step explanation:

Let us consider two linear equations, each linear equation has slope and y-intercept.

Among those slope plays a major role, if there are no slope means than the line equation will be parallel to the x-axis. The slope will indicate the line's direction.

If two linear equations, having an identical slope then they will become like parallel lines. Thus the parallel lines won't intersect with each other. So there will be no solutions to the system.  (refer 1st image of both equations having slope 5)

If two linear equations have different slope they will intersect at any point. That is, it will result in exactly one solution. (refer 2nd image of both equations having different equations 1 and -1).

Step-by-step explanation:

Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation

Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)

LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²

       = (sin²x - cos²x)(sin²x + cos²x)

       = sin²x - (1 - sin²x)  since sin²x + cos²x = 1

       = 2 sin²x - 1

       = RHS

Hence proved.

Answer:

The cost for painting will be $212.

Step-by-step explanation:

I am painting the walls and ceiling of a rectangular 20 x 30 ft room. The walls are 10 feet tall.

So, the total area to be painted = {2 × (20 + 30) × 10} + (20 × 30) = 1600 sq. ft.

Now, a gallon of paint covers 400 square feet and cost $53 per gallon.

So, the number of gallons of paint required will be [tex]\frac{1600}{400} = 4[/tex] gallons.

And the cost for painting will be $(4 × 53) = $212. (Answer)

Answer:

Emily solved for a part when she should have solved for the whole. 875,000 should be the numerator of the equivalent ratio. 70 x 12,500 is 875,000. So the answer is 100 x 12,500 which is 1,250,000.

Step-by-step explanation:

Shira Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold. The number of shoes that the company sold in June is 612500.

If we looked carefully at the question, we will understand that it was from the total pairs of sandals sold that they deduce the percentage of the shoes sold.

From the information given:

To determine the number of pairs of shoes sold, we have:

[tex]\mathbf{= 875000 \times \dfrac{70}{100}}[/tex]

[tex]\mathbf{= 8750 \times70}[/tex]

= 612500

Therefore, we can conclude that the number of shoes sold by the company in June is 612500

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