Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.

The greatest common factor of the expression is 4m⁴.

GCF simply means the greatest common factor.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Hence,

56m⁵

68m⁴

The greatest common factor of the expression  is the largest positive expression that divides evenly into all numbers with zero .

Hence, the greatest common factor is 4m⁴

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Answer:

The small piece is 6 yards and the large piece is 8 yards.

Step-by-step explanation:

Let x  = small

Let y = large

x + y = 14       3y = 4x

3y = 4x  Divide both sides of the equation by 3 to solve for y

y = [tex]\frac{4}{3}[/tex] x  Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.

x + y = 14

x + [tex]\frac{4}{3}[/tex] x = 14  x and 1 x mean the same thing.  Another name for 1 is [tex]\frac{3}{3}[/tex]

[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14

[tex]\frac{7}{3}[/tex]x = 14  Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x

([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6

x = 6

If x = 6, then y must be 8 because 6 + 8 = 14

Convert [tex]-1+i[/tex] to polar form.

[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]

By de Moivre's theorem,

[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]

QED

Answer:

[tex]tan(30) = \frac{5}{b} [/tex]

Step-by-step explanation:

Trigonometric Ratios.

To solve for b, we check the parameters that are given in the triangle.

If we're considering 30°, we can see that the opposite is given as 5cm and the adjacent is b.

Applying:

[tex]tan \alpha = \frac{oppsite}{adjacent} \\ \\ tan \: (30) = \frac{5}{b} [/tex]

Answer:

a

Step-by-step explanation:

just did the quiz!!!!

It's very simple. Subract 554.26 from 866.32

then, we got the difference is

312.06

thank you

Brainlist please.

From the number line, the values which completes the sum in the table are:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

From the table of values (see attachment), the values on the number line are represented as follows:

a + b = a + b

R = -1 - 2

R = -3.

a + b = a + b

S = -4 + 1

S = -3.

a + b = a + b

T = -6 - 3

T = -9.

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The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

In this question we are before a type of ordinary differential equation known as equation with separable variables, that is to say, that variables t and y can be separated at each side of the expression in order to find a solution:

dy / dt = 3 · y · (1 - y /14)

dy / [(- 3 / 14 ) · y · (y - 14)] = dt

Then, we simplify the expression by partial fractions and integrate the resulting expression:

- (1 / 14) ∫ dy / y + (1 / 14)∫ dy / (y - 14) = - (14 / 3)∫ dt

- (1 / 14) · ㏑ |y| + (1 / 14) · ㏑ |y - 14| = - (14 / 3) · t + C, where C is the integration constant.

㏑ |(y - 14) / y| = - (14 / 3) · t + C

[tex]1 - \frac{14}{y} = C\cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]\frac{14}{y} = 1 - C \cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex]

The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

If y(0) = 10, then the particular solution of the differential equation is:

10 = 14 /(1 - C)

1 - C = 1.4

C = - 0.4

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

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Answer:

hexagon and pentagon structure. also known as a truncated icosahedron

Step-by-step explanation:

hope that gives you a good enough description.

The answer is x=21 the explanation is on the picture above I hope I helped

If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:

Speed=Distance/ Time.

We have been given that the speed of stream is 7miles per hour.

Let v be the speed of the boat, and t the time to travel

98=t*(7+v) (1)

49=t(v-7) (2)

(1)+(2) => 2tv=147

7t+(49+7t)=98

14t+49=98

14t=49

t=49/14

t=7/2

Put the value of t in equation 1 to get the value of v:

98=t(7+v)

98=7/2(7+v)

196/7=7+v

28=7+v

v=28-7

v=21

Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

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The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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30 + 110 + 30 + 110 = 280

360-280 = 80

2y = 80

y = 40 degrees

If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.

30 + 40 = 70

The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.

In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180

Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.

Angles in triangle add to 180.

180 - 110 - 30 = 40.

Thus, x = 40 degrees

There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)

Hope this helps!

Step-by-step explanation:

b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.

The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.

b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.

The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.

Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        [tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     [tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 [tex]\sf \boxed{\bf y = 55}[/tex]

Plugin y = 55 in equation (I)

       x = 55 -10

        [tex]\sf \boxed{\bf x = 45}[/tex]

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

Answer:

A

Step-by-step explanation:

$30.00 ÷ 5 = $6.00

$6.00 × 3 = $18.00

Answer:

#3 5(2a+4)

#4 5(a+2+4)

#5 5a+5(2+4)

Step-by-step explanation:

I think so, I am probably wrong

Answer:

$21200

Step-by-step explanation:

6% × 20000 = 1200.

20000 + 1200 = 21200

basically yout find 6% of 20000 then add it the original 20000

The amount of paint that would be contained in each of the can would be 8.

Using the information in the question we have the following

We have to solve the equation as

(2  1/2)   + 2(4)  + 1(5  1/2)  =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

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Answer:

4 pints

Step-by-step explanation:

the expert is wrong

1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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Answer:

67 years old. (you only gave 4 people and missed out one person)

Step-by-step explanation:

take all the ages first and put the unknown (age of the person who entered the room) as x.

14, 16, 16, 13, x

all of these numbers added to together would be:

59 + x

Because the question is talking about the mean age, to find mean:

add all the values in the data (ages) and divide by the total number of values on the list. (in your case would be 6 people (following your question) but you gave only 5 people including the x).

then (59 + x) / 6 = 21

21 x 6 = 126

126 = 59 + x

x = 67

[tex]B'=\{f,g,h,p,x\}\\B'\cup A=\{f,g,h,p,q,r,x\}\\(B'\cup A)\cap C=\{g,h,p,q\}[/tex]

The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

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The point of intersection of both graphs will have the coordinate (5, 9).

We are given the functions;

f(x) = x + 4

g(x) = -2x + 19

Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;

x + 4 = -2x + 19

x + 2x = 19 - 4

3x = 15

x = 15/3

x = 5

Thus;

f(x) = 5 + 4 = 9

g(x) = -2(5) + 19 = 9

Thus, the point of intersection of both graphs will have the coordinate (5, 9)

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Answer:

Step-by-step explanation:

hello : y = -2x - 5

          y = 2/3x + 3

means :  -2x-5 = 2/3 x+3

-6x-15 = 2x +9

-8x=24   so : x = -3

put the value for : x in the first equation :y = -2(-3)-5  =1

the  ordered pair (-3;1) is solution

Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962

Step-by-step explanation:

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:

x² - 8 · x + 13 = 0

x² - 8 · x + 16 = 3

(x - 4)² = 3

x - 4 = ± √2

x = 4 ± √2

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

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Option 4,option 6, and option 2 is the respective contrapositive to the statements given. This can be obtained by understanding what contrapositive is and converting the statements.

Statement = If a figure is a square, then it is a quadrilateral.

Contrapositive = If a figure is not a quadrilateral, then it is not a square.

Here,

Contrapositive: If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. (Option 4)

Contrapositive: If the product of two numbers isn't even, then the two numbers aren't even. (Option 6)

Contrapositive: If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon. (Option 2)    

Hence Option 4,option 6, and option 2 is the respective contrapositive to the statements given.

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The exponential growth function is P(t) = 6.38 million x (1.0238^t).

The population of the city in 2018 is 7.35 million.

The year the population would be 9 million is 14.46 years.

The doubling time is 29.12 years.

FV = P (1 + r)^n

6.38 million x (1.0238^t)

Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million

Number of years when population would be 9 million : (In FV / PV) / r

(In 9 / 6.38) / 0.0238 = 14.46 years

Doubling time = In 2 / 0.0238 = 29.12 years

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The complete  table will be:

Fraction      Decimal       Percent

39/100            0.39           39%

82/100            0.82           82%

22/100           0.22          22%

3/4                   0.75          75%

80/100           0.8             80%

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{25}{100} =0.25*100=25%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks  etc.

Fraction      Decimal       Percent

39/100            0.39           0.39*100=39%

Fraction      Decimal       Percent

82/100            0.82         0.82*100=82%

Fraction      Decimal       Percent

22/100           0.22        22%

Fraction      Decimal       Percent

3/4                 0.75        0.75*100=75%

Fraction      Decimal       Percent

80/100           0.8         0.80*100=80%

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The solution values in order from smallest to largest are;

let

(x - 5)-2 = 14

-2x + 10 = 14

-2x = 14 - 10

-2x = 4

x = 4/-2

x = -2

4x - 5 = -8

4x = -8 + 5

4x = -3

x = -3/4

x = -0.75

(x + 3) / 5 = -2

x + 3 = -2(5)

x + 3 = -10

x = -10 - 3

x = -13

1/2x + 4 = -1

1/2x = -1 - 4

1/2x = -5

x = -5 ÷ 1/2

= -5×2/1

x = -10

x + 2 = 6/-4

-4(x + 2) = 6

-4x - 8 = 6

-4x = 6 + 8

-4x = 14

x = 14/-4

x = -3.5

Therefore, the smallest value is -13 and the largest value is -0.75.

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