Find the area (in square units) of the region under the graph of the function f on the interval [-1,5].

F(X) = 2x+8

Square units: ?

Table second represents the proportional relationship between x and y the answer is the second table.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

As we know,

The proportional relation can be expressed mathematically:

y ∝ x

y = kx

Here k is the constant of proportionality.

k = y/x

From table second:

k = 3/2 = 6/4 = 9/6

Thus, the table second represents the proportional relationship between x and y the answer is the second table.

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Answer:

look at the picture.

Step-by-step explanation:

look at the picture.

Step-by-step explanation:

simply count them.

there are 7 little rectangles building the whole.

from these 7, 4 are gray and 3 are white.

so, 3 of 7 are white.

that means,

3/7 of all the parts are white.

Answer:

1/4 = 0.25

Step-by-step explanation:

I assume you mean

lim((ln(x) - ln(4)) / (x - 4))

ln(x) - ln(4) = ln(x/4)

rule of l'hopital

lim f(x)/g(x) = lim f'(x)/g'(x)

if g'(x) <> 0

f(x) = ln(x/4)

g(x) = x - 4

ln(x)' = 1/x

ln(x/4)' = 1/x/4 × 1/4 = 1/x

(x - 4)' = 1

so,

lim f'(x)/g'(x) = 1/x / 1 = 1/x

which is for x approaching 4 : 1/4 = 0.25

Answer:

B.) 2x¹⁰y¹²

Step-by-step explanation:

To begin, because all of the terms in the top and bottom are combined (right next to each other being multiplied), the coefficients can be divided like any normal number. When you divide variables with powers, you need to subtract the denominator powers from the numerator powers.

Therefore,

60 / 30 = 2

x²⁰ / x¹⁰ = x²⁰ ⁻ ¹⁰ = x¹⁰

y²⁴ / y¹² = y²⁴ ⁻ ¹² = y¹²

Combined, the simplified expression is 2x¹⁰y¹².

Answer:

2.48 seconds

Step-by-step explanation:

See attached

There are two ways to confirm the identity.

Method 1

[tex]\tan(x)\cot(x) = 1\\\\\tan(x)\frac{1}{\tan(x)} = 1\\\\\frac{\tan(x)}{\tan(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]

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

Method 2

[tex]\tan(x)\cot(x) = 1\\\\\left(\frac{\sin(x)}{\cos(x)}\right)\left(\frac{\cos(x)}{\sin(x)}\right) = 1\\\\\frac{\sin(x)\cos(x)}{\cos(x)\sin(x)} = 1\\\\\frac{\sin(x)}{\sin(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]

answer: A: 16

B: 16

C: 12.57

D: 12.57

E: 3.43 (do area of square-area of circle 16-12.57

Answer:

a) [tex]\frac{450}{100}[/tex] x 45 = 202.5g of sugar is in the can

b)[tex]\frac{4}{100}[/tex] x 80 = 3.2L is left

c)[tex]\frac{2400}{100}[/tex] x 70 = 1480 acres were planted with wheat

a. 202.5g

Since 45% of the energy drink is sugar

⇒ 45% of the total 450 grams will be made up of sugar

∴ sugar = [tex]\frac{45}{100}[/tex] * 450

             = 202.5g

Thus, the can contains 202.5g of sugar

b. 3.2L

Since Simon used up 20% of the paint, the paint left in the can will now be 80% of the original 4 liters

∴ paint left = [tex]\frac{80}{100}[/tex] * 4

                  = 3.2L

Thus, the can has 3.2 liters of paint left.

c. 1680 acres

Here, 30% of the farmer's crop is and the rest is wheat

⇒ 70% is wheat

Total acres of land planted= 2400

∴ Acres planted with wheat = [tex]\frac{70}{100}[/tex] *2400

                                              = 1680 acres

Thus 1680 acres is planted with wheat

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Solution of 9x+8y=26 and 3x+2y=9 are given by (C)  [tex]\mathbf{x=\frac{10}{3},y=-\frac{1}{2}}[/tex].

We have to plot the graphs of the given two lines or curves, then we have to find the intersection point(s) of the curves or lines. That point is the solution for the system of the equations.

Given equations are,

9x+8y=26 .................(1)

3x+2y=9 ...................(2)

Now multiplying 3 with (2) and then subtracting (1) from that we get,

3(3x+2y)-(9x+8y)=3(9)-26

9x+6y-9x-8y=27-26

-2y=1

y=-1/2, on dividing both sides by -2

Substituting the value of y in (1) we get,

9x+8(-1/2)=26

9x-4=26

9x=26+4

9x=30

x=30/9=10/3

Also if we draw the graphs of the given equations by using graphing calculator we get,

Here in the graph we can see that the lines represented by the given equations intersects each other at point [tex]\left(\frac{10}{3},-\frac{1}{2}\right)[/tex].

Hence the solution is [tex]x=\frac{10}{3},y=-\frac{1}{2}[/tex].

Thus the correct option is (C).

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The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The length of the tree is 23.66 meters.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Let the height of the tree be represented by x.

The length of the shadow when the angle of elevation is 45°.

Length of shadow = x/ Tan(45°)

The length of the shadow when the angle of elevation is 60°.

Length of shadow = x/ Tan(60°)

Now, since the difference between shadows is 10 meters. Therefore, we can write,

x/ Tan(45°) - x/ Tan(60°) = 10m

x[1/ Tan(45°) - 1/ Tan(60°) ] = 10 m

x (0.42265) = 10 m

x = 23.66 m

Hence, the length of the tree is 23.66 meters.

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Answer:

-2

Step-by-step explanation:

-9/3=-3

-3+b=-1

b=-1+3

b=-2

Answer:

first one L second one D

Step-by-step explanation:

Answer:

x2-4 = 0

x2= 4

x = 2 or x = (-2)

The equations that are true for x = -2 and x = 2 are:

x² - 4 = 0

2(x - 2)² = 0

Options A and D are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

The values given for x are -2 and 2.

Therefore, we can substitute each value of x into the given equations to determine which are true for those values.

x² - 4 = 0

When x = -2, we have (-2)² - 4 = 0, which is true.

When x = 2, we have (2)² - 4 = 0, which is also true.

x² = -4

When x = -2, we have (-2)² = 4 which is not equal to -4, so this equation is false for x = -2.

When x = 2, we have (2)² = 4 which is not equal to -4, so this equation is false for x = 2.

3x² + 12 = 0

When x = -2, we have 3(-2)² + 12 = 0, which is false.

When x = 2, we have 3(2)² + 12 = 24, which is not equal to 0.

Therefore, this equation is false for x = 2.

14x² = 16

When x = -2, we have 14(-2)² = 56, which is not equal to 16.

Therefore, this equation is false for x = -2.

When x = 2, we have 14(2)² = 56, which is also not equal to 16.

Therefore, this equation is false for x = 2.

2(x-2)² = 0

When x = -2, we have 2(-2-2)² = 0, which is not equal to 0.

Therefore, this equation is false for x = -2.

When x = 2, we have 2(2-2)² = 0, which is equal to 0.

Therefore, this equation is true for x = 2.

Therefore,

The equations that are true for x = -2 and x = 2 are:

x² - 4 = 0

2(x-2)² = 0

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Answer:

Mean: 19.366666666667

Step-by-step explanation:

Mean: Average of the Data set

If you add the numbers below and divide them by the amount of numbers there are, you will get the average of the data set.

14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25

Average= sum/count

Mean= 1162 / 60

Mean= 19.366666666667

Rounded to the nearest tenth: 19.4

Rounded to the nearest hundredth: 19.37

We conclude that after 50 days, there will be 67 lily pads.

We know that the number increases by 25% every 10 days.

In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.

We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:

N = 22*(1 + 25%/100)*...*(1 + 25%/100%)

( the factor (1 + 25%/100%) appears five times)

So we can rewrite:

N = 22*(1 + 25%/100%)⁵

N = 22*(1 + 0.25)⁵ = 67.1

Which can be rounded to the nearest whole number, which is 67.

So we conclude that after 50 days, there will be 67 lily pads.

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Answer:

60 on the first day and 80 on the second

Step-by-step explanation:

the first day was lesser than the second day by 20 minutes.

so the second day was more than the first day by 20 minutes.

Answer:

D.

Step-by-step explanation:

It contains all the y-values of the points.

Answer:

Coordinates of all points

first = (-1 , 3)

second = (-2, 1 )

third = (-3 , -3)

fourth = (-4 , -5)

option 3

The value of x and y from the given figure are 3 and 36

From the given similar triangles, the following expression is true

4/6 = x/54

Cross multiply

6x = 4 *54

x = 4 * 9

x = 36

Similarly

y/6 = 27/54
y/6 = 1/2

x =3

Hence the value of x and y from the given figure are 3 and 36

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Answer: B

Step-by-step explanation:

In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.

Answer:

y = -2x

Step-by-step explanation:

It passes through -5, 10 and 5, -10

gradient = Δy/Δx

gradient = -10 - 10 / 5 -- 5

gradient = -20 / 10

gradient = -2

let's use -5, 10 for y = mx + b

10 = -2(-5) + b

10 = 10 + b

b = 10 - 10

b = 0.

the equation of the line is just y = -2x

Answer:

something like below

Step-by-step explanation:

(12n) - (n * 10/100 )

Answer:

$38.50

Step-by-step explanation:

(100-30)% of $55

= 70% of $55

= $38.50

Hope this helps :)

Step-by-step explanation:

10 that's what my teacher told me

Answer:

Step-by-step explanation:

money given to children=1300x5

                                        =6500

total money =6500+450

                    =6950

Answer:

My answer: 15.87%

Step-by-step explanation:

The Final grades follows normal distribution.

It means =70

The Given standard deviation =10

The normal random variable of a standard normal distribution is called a standard score or a z-score. In Every normal condition, random variable X will be transformed into a z score via the following equation:

z=(X)

But when X is a normal random variable, μ is the mean of X.

For That, it is X=60

Z=(60−70)/10=−1

P(X<60)=P(Z<−1)

=0.1587

Hence percent of students failed in test is 15.87%

Answer:

thats not even understandable

The solution set is {3, -3} and is represented by the number line shown below.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

To solve the equation -2|x| = -6,

We can begin by dividing both sides by -2:

|x| = 3

This means that the absolute value of x is equal to 3.

The solutions to this equation are x = 3 and x = -3.

The number line that represents these solutions is:

<--(+)===================(+)--->

   -3                                       3

The open circles indicate that the solutions are not included in the solution set since the absolute value of x cannot be negative.

Therefore,

The solution set is {3, -3} and is represented by the number line shown above.

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Answer:

[tex](5+3\sqrt{2} )^{2} =43+30\sqrt{2}[/tex]  

≈85.43

Step-by-step explanation:

apply the binomial theorem to the square

[tex]=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}[/tex]

[tex]=25+30\sqrt{2} +18\\[/tex]

[tex]=43+30\sqrt{2}[/tex]

≈85.43

Hope this helps

Hello!

Here, we apply the algebraic identity :

[tex]\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}[/tex]

Let's solve!

⇒ (5 + 3√2)²

⇒ (5)² + 2(5)(3√2) + (3√2)²

⇒ 25 + 30√2 + 18

⇒ [tex]\boxed {43 + 30\sqrt{2}}[/tex]

∴ The final answer will be 43 + 30√2.