Find three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.

Answer:

A = 55

Step-by-step explanation:

take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom

The area of triangle is 55 square centimeters.

Area is the amount of space occupied by a two-dimensional figure.

The formula for the area of triangle is

[tex]Area = \frac{1}{2} \times base\times height[/tex]

According to the given question.

We have a figure of a quadrilateral which is made up of four right angled tringles.

Now,

The area of a triangle with base 5cm and height 7 cm

= [tex]\frac{1}{2} \times 5\times 7[/tex]

[tex]=\frac{35}{2}[/tex]

[tex]= 17.5[/tex] square centimeters

And, the area of triangle with base 4cm and height 5cm

= [tex]\frac{1}{2} \times 4\times 5[/tex]

[tex]= 10[/tex] square centimeters

Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.

Therefore, the area of quadrilateral or the given fiure

= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )

= 2(17.5 + 10) square centimeter

= 2 × 27.5

= 55 square centimeters

Hence, the area of triangle is 55 square centimeters.

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Answer: [tex]\frac{3x+1}{x^{2}-6}[/tex]

Step-by-step explanation:

(f/g) represents the division of function f by function g.

Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.

The function is:

[tex]A(t) = A(0)e^{-kt}[/tex].

In which:

The information given is as follows:

A(0) = 440, A(8) = 40.

Hence:

[tex]A(t) = A(0)e^{-kt}[/tex].

[tex]40 = 440e^{-8k}[/tex].

[tex]e^{-8k} = 0.09090909[/tex]

[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]

[tex]-8k = \ln{0.09090909}[/tex]

[tex]k = -\frac{\ln{0.09090909}{8}[/tex]

k = 0.29973691

Then the function is:

[tex]A(t) = 440e^{-0.29973691t}[/tex]

2001 is 11 years after 1990, hence the amount is:

[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]

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Answer:

121°

Step-by-step explanation:

Angles around a point add to 360°.

[tex]a=360-74-165=\boxed{121^{\circ}}[/tex]

The  number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is:  32 pints of 95% juice, and 48 pints of 45% juice.

Let x be the amount of 95% juice.

Let the  amount of 65% juice be 80-x

Hence:

.95x+.45(80-x)=.65(80)

.5x+36=52

Collect like term

5x=16

Divide both side by 5x

x=16/5

x=32

Therefore the number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is:  32 pints of 95% juice, and 48 pints of 45% juice.

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The percentage of students that have scored more than you is 1.39%

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²

It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.

Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;

where radius, r = D/2 = 30/2.

Area = πr² = 3.14 × (30/2)² = 706.5cm²

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Answer:36

Step-by-step explanation:

Let name the missing angle in the triangle w.

We know that x+z+w=180

We also know that z+w=3z=y.

That means that w=2z.

x=2z, so, 2z+2z+z=180

z=36

Answer:

Z=36 degrees

Step-by-step explanation:

Since angles x and y are supplementary, you know that they add up to 180 degrees.

Since we know that:

=x+y

=2z+3z

=5z

=180 degrees

180/5=36 degrees, so Z=36 degrees

Numbers whose decimals form goes on forever are best represented as fractions because they are non-terminating decimals

The decimal numbers are represented as:

A and B

Where

A > B

Numbers whose decimals form goes on forever are non-terminating numbers, and the complete form cannot be represented using decimals except with the sign .......

Because non-terminating decimals have no end, it is best to represent them as fractions

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Step-by-step explanation:

try this option, answer is marked with red colour.

The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

The graph represents a parabola.

The graph can be a function if it passes the vertical line test.

The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

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Answer: x = 6

NS = 8.5

Step-by-step explanation:

JK = KL= KP + LP

26 = 13 + 2x + 1

2x = 12

x = 6

NS = PS

PS = 8.5

NS = 8.5

The area enclosed by the given 2 curves is; 8/3 or 2.67

We want to find the area enclosed by the curves;

y = x² - 2x

y = -x² + 2x

The point of intersection of the parabola and the line is given by;

x² - 2x = -x² + 2x

2x² - 4x = 0

Solving this gives;

x = 0, 2

Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;

A = ∫₀² (-x² + 2x - x² + 2x)

A = ∫₀² (-2x² + 4x)

Using online integration calculator here gives;

A = 2.67

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The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8

It is important that a 2D shape arrow is a shape with 8 sides

Sum of angles of a polygon = (n - 2) × 180

⇒ ( 8 - 2) × 180

⇒ 6 × 180

⇒ 1080

The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow

Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8

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Using the normal distribution, it is found that:

A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.

B. 0.96 = 96% of packages that will be accepted.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]

Item A:

The proportion is the p-value of Z when X = 158, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{158 - 170}{4.9}[/tex]

Z = -2.45

Z = -2.45 has a p-value of 0.0071.

0.0071 = 0.71% of packages will be rejected because the average weight is too low.

Item B:

The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:

X = 179:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{179 - 170}{4.9}[/tex]

Z = 1.84

Z = 1.84 has a p-value of 0.9671.

X = 158:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{158 - 170}{4.9}[/tex]

Z = -2.45

Z = -2.45 has a p-value of 0.0071.

0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.

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Answer:

46+96=140°_÷__^_^^^^=^

The composite function G(F(x)) = x² + 4 is formed with these following original functions:

D. F(x) = x² and G(x) = x + 4.

The composite function of f(x) and g(x) is given as follows:

[tex](f \circ g)(x) = f(g(x))[/tex]

For g of f(x), we have that:

[tex](g \circ f)(x) = g(f(x))[/tex]

For this problem, we have that:

G(F(x)) = x² + 4.

Which is possible with option D, as:

[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]

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The equivalence of the equation is 5x + 48 = 5x + 3.

Since 48 cannot be equal to 3, hence there are no solution.

Given the equation; x-4[ x - 2( x + 6) ] = 5x + 3

We remove the parentheses

x-4[ x - 2( x + 6) ] = 5x + 3

x-4[ x - 2x - 12 ] = 5x + 3

x - 4x + 8x + 48 = 5x + 3

5x + 48 = 5x + 3

We can go further and collect like terms

5x - 5x + 48 = 3

48 ≠ 3

Since 48 cannot be equal to 3, hence there are no solution.

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Answer: A

Step-by-step explanation:

Answer: [tex]g(x)=\left(\frac{x}{5} \right)^2[/tex]

Step-by-step explanation:

See attached image.

By definition of real field and algebra properties we conclude that the product of three positive integers is always equal to a positive integer.

First, we state the conjecture: The product of three positive integers equals a positive integer. Second, we prove if the conjecture is true:

Integers are part of the real field, which mean that the product of two integers is also an element of that field. By algebra we know that the product of two positive integers is equal to another positive integer. Thus, the product of three positive integers is always equal to a positive integer.

Here is an example:

2 × 5 × 7

10 × 7

70

In a nutshell, the conjecture has been proved true.

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Answer:

(2, -11)

Step-by-step explanation:

(x + 3, y + 2) = (5, -9)

x + 3 = 5

y + 2 = -9

x = 2

y = -11

681×239 = 162,759

..... ......

162,759 is answer

happy to help

The retailer would remit $4,900 to the vendor on July 13.

What is invoice date?

The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date  is July 1.

Invoice receipt date?

This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.

2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.

From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available

discount=2%*$5000

discount=$100

The retailer would remit the invoice price of $5,000 minus the discount.

amount remitted=$5000-$100

amount remitted=$4,900

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Answer:

E

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Consider the triangle on the left

3rd angle = 180° - 60° - 90° = 180° - 150° = 30°

the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so

∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°

Hi! ◈

Answer:

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

1/4 of the cake was left

Step-by-step explanation:

  Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4

  [tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]

   _____________________

   [tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]

Hope this made sense to you !!

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

Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).

The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.

In step 5 where the multiplication property of equality is applied, we would have:

sin(A) = CD/b

Multiply both sides by b

sin(A) × b = CD/b × b

b(sin A) = CD

CD = b(sin A)

This same property is applied to sin B = CD/a to get CD = a(sin B).

Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).

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The total amount he will pay for 20 years of coverage is $61,980. Option D

To find the total amount, we use the expression

First, we multiply the value per $1,000.00 by the number of thousands of face value coverage. This gives an estimate of the annual premium for  life insurance policy.

Nikos's premium per year = [tex]\frac{300000}{1000} * 10. 33[/tex]

Niko's premium per year = [tex]300 * 10. 33[/tex]

Niko's premium per year = $3, 099

To find the total amount, we need to multiply by the number of years

=  $3,099 x 20

= $61,980

Thus, the total amount he will pay for 20 years of coverage is $61,980. Option D

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Answer:

278,861,394

Step-by-step explanation:

put in the calculator e but then just square the numbers add it and there is your answer

The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

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