Given m || n
find the value of x and y.
(6x+19)° (2y+1)⁰
(3x+8)°
m
n

By solving a linear equation, it can be calculated that

There are 4 guppies in  each family

What is a linear equation?

At first it is important to know about equation.

An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh

A one degree equation is known as linear equation.

Here a linear equation needs to be solved

Let the number of guppies in each family be x

Allison has 2 aquariums.

In each aquarium she has 2 families of guppies and 3 tetras.

Total number of fishes Allison have = 2(2x + 3) = 4x + 6

Leigh has 1 aquarium with 10 tetras and 3 families of guppies.

Total number of fishes Leigh have  = 3x + 10

By the problem,

4x + 6 = 3x + 10

4x - 3x = 10 - 6

x = 4

There are 4 guppies in each family

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The value of a from the equation is a = 0.32

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be 2 1/7 : 15a = 5/14 : 0.8

Now , on simplifying the equation , we get

15/7  : 15a = 5/14 : 0.8

Multiply by 14 on both sides of the equation , we get

( 15 x 2 ) : 15a = 5 : 0.8

30 : 15a = 5 : 0.8

So , on simplifying the equation , we get

30 / 15a = 5 / 0.8

Divide by 5 on both sides , we get

6 / 15a = 1 / 0.8

Multiply by 0.8 on both sides of the equation , we get

15a = 6 x 0.8

15a = 4.8

Divide by 15 on both sides , we get

a = 4.8 / 15

a = 0.32

Therefore , the value of a = 0.32 or a = 8 / 25

Hence , the value of a in the equation is a = 0.32

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Answer:

25 percent.

Step-by-step explanation:

25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.

Hope it helps.

By using property of triangle and trapezium, it is obtained that

a) value of x is 35°

b) Third option is correct

What is a triangle and trapezium?

Triangle is a three sided two dimensional figure.

Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel

Here property of triangle is used

[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]

[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]

In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)

Third option is correct

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Answer: 49

Step-by-step explanation:

by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.

Answer:

Step-by-step explanation:

1.) -112*-7=784

784=v+4

2.)784-4=780

v=780

Answer:

v = 12

Step-by-step explanation:

-112 = -7v -28

7v = 112 - 28

7v = 84

7/7 v = 84/7

v = 12

Answer:

0

Step-by-step explanation:

to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.

Answer: 78

Step-by-step explanation:

3z2-6z for z=5

Answer:

[tex]\frac{3}{40}=0.075[/tex]

Step-by-step explanation:

The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:

[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]

Answer:

A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).

Step-by-step explanation:

shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.

8×2 = 17

15×2 = 30

17×2 = 34

The volume of the crate if there is no extra space in the crate is 36m³.

From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.

In this case, the volume will be:

= Length × Width × Height

= 2 × 1 × 1

= 2m³

Since there are 18 crates, the total volume will be:

= 2m³ × 18

= 36m³

The volume is 36m³.

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Complete question

A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?

The measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

According to the question,

We have the following information:

Angle CAB = 2x

Angle CBA = 3x-20

And the given triangle is a right-angled triangle which means that one of its angle is 90°.

Now, we know that the sum of three angles of a triangle is 180°.

So, we have the following expression:

2x+3x-20+90 = 180°

5x+70 = 180

5x = 180-70

5x = 110

x = 110/5

x = 22°

Now, putting the value of x in given angles:

Angle CAB = 2x

Angle CAB = 2*22

Angle CAB = 44°

Angle CBA = 3x-20

Angle CBA = 3*22-20

Angle CBA = 66-20

Angle CBA = 46°

Hence, the measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

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1. Dianely's salary can be represented with the following table of values for 5 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

5          $50,000

2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement equating two or more mathematical expressions.

Equations use variables, numbers, mathematical operands, and the equation symbol (=).

Dianely's initial salary = $40,000

Salary raise per year = $2,500

Dianely's salary after n years in equation form, S = 40,000 + 2,500n.

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

5          $50,000 ($47,500 + 2,500)

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The values of x in the equations are as follows:

1. x = 8 or 4

2. x = 2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

log₄ x² - 12x + 48 = 2

using law of logarithm

4² = x² - 12x + 48

16 = x² - 12x + 48

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

x² - 4x - 8x + 32 = 0

x(x - 4) - 8(x - 4) = 0

(x - 8)(x - 4) = 0

Therefore,

x = 8 or x = 4

[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]

[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]

[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]

[tex]3^{12x-18} =3^{-4x+14}[/tex]

Cancel the base

Therefore,

12x - 18 = - 4x + 14

12x + 4x = 14 + 18

16x = 32

x = 32 / 16

x = 2

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As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .

As given in the question,

Time period to calculate the compound interest  = 3years

Interest rate compounded monthly = 5.50%

Each month interest output is 5.64079

Rate of interest compounded semi- annually = 5.70%

Each month interest output is 5.78123

Compounded monthly gives interest every month and semi-annually gives twice a year.

Monthly is more frequent  compare to semi-annually.

Investor should choose monthly.

Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .

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The required number is 1 which represents "6 times as large as 9 minus 3".

The analysis of mathematical representations is algebra, and the handling of those symbols is reasoning.

We have to determine the number that is "6 times as large as 9 minus 3".

Let the required number would be x

Translate the phrase "6 times as large as 9 minus 3" into the algebraic form :

⇒ 6 × x = 9 - 3

⇒ 6x = 6

⇒ x = 6 / 6

⇒ x = 1

Thus, the required number is 1 which represents "6 times as large as 9 minus 3".

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The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.

The identity is presented as follows:

[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]

Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:

[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]

The following identity relates the square of the secant and of the tangent:

[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]

Hence:

[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]

Thus the remaining expression is:

[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]

The equations of the cotangent, secant and tangent are given as follows:

Hence:

[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]

One divided by the sine is the cosecant, as follows:

[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]

Hence the simplified expression is:

[tex]\csc{\beta} + 1[/tex]

Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.

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The number of trips after the cost of the plan A and plan B is 16.

According to the question,

We have the following information:

Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.

So, this will make an arithmetic progression.

The formula to find nth term of an A.P:

an = a+(n-1)d where a is the first term

Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.

145+(n-1)5 = 40+(n-1)12

145+5n-5 = 40+12n-12

5n+140 = 12n+28

140-28 = 12n-5n

7n = 112

n = 112/7

n = 16

Hence, the number of trips after the cost of the plan A and plan B is 16.

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Answer:

so basically u do that and then u do that and then

Step-by-step explanation:

8

The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

The possible diagram that completes the question is added as an attachment

From the attached diagram, we have the following representation

<1 + <2 = 180 degrees --- by the theorem of supplementary angles

Also, we have the following angle measure

Given that

<1 = 86 degrees

Substitute the known values in the above equation

So, we have the following equation

86 + <2 = 180

Evaluate the like terms

<2 = 94

Also, we have

<3 = <1  --- by the theorem of vertical angles

Substitute the known values in the above equation

<3 = 86

This is so because <1 = 86 degrees

Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

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Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of even numbers in a deck of cards.

= 5 x 4

= 20

The number of diamonds in a deck of cards.

= 4

Now,

The probability of drawing an even number from a deck of cards.

= 20 / 52

= 10/26

= 5/13

Now,

The remaining cards.

= 52 - 20

= 32

The probability of drawing diamonds after drawing the even numbers.

= Number of diamonds / remaining cards

= 4 / 32

= 1/8

Thus,

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

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Answer:

Step-by-step explanation:

area=10×5+[(15-5)+7]/2×(10-6)

=50+(17)/2×4

=50+34

=?

The mean age is equal to: 44.09.

The standard deviation is equal to: 10.07.

First of all, we would determine the median of each class interval as follows:

Median 1 = (25 + 34)/2 = 29.5

Median 2 = (35 + 44)/2 = 39.5

Median 1 = (45 + 54)/2 = 49.5

Median 1 = (55 + 64)/2 = 59.5

Next, we would calculate the mean age by using this mathematical expression:

Mean age = ∑fx/∑f

Substituting the given parameters into the formula, we have;

Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)

Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118

Mean age = [5,203]/118

Mean age = 44.09.

Now, we can calculate the standard deviation as follows:

Standard deviation, S = √((∑f(xi - μ)²/∑f)

Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))

Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)

Standard deviation, S = √(11,970.48/118)

Standard deviation, S = √101.5

Standard deviation, S = 10.07.

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Answer:

Step-by-step explanation:

A is a point

AB is a line

ABC is a plane

Therefore,  ABC is a plane.

__________________

Hope this helps!

Have a great day!

The money available for private investment is $250 billion dollar

What is demand curve ?

The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.

Refer to the attachment for graph:

Once investments and government borrowing are added together, the total is = $400

if borrowing from the government is= $150

private investment

=( investment and and government borrowing) - (government borrowing )

= $400 - $150 = $250

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Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.

Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.

Answer:

The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.

Step-by-step explanation:

The image would be of a triangle.
Hope this helps! :))

4.8 × 10^4

Answer:

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

The average hourly pay of person making 4500 per year is 21.63 per hour.

Given that,

we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.

To calculate this

The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.

We have to multiply 52-week year and a 40-hour work week.

40×52

2080

Now, divide 45000 by 2080

45000/2080

21.63

Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.

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The value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3

The given function is

f(x) = [tex]x^3-2x^2+3[/tex]  

The function is the mathematical statement which represents the relationship between one variable and another variable. If one variable is dependent variable the other variable will be independent variable.

The given function is

f(x) = [tex]x^3-2x^2+3[/tex]

The value of x = 2

Then substitute the value of x in the function

f(x) = [tex]x^3-2x^2+3[/tex]  

f(2) = [tex]2^3-2(2)^2+3[/tex]

Solve the power of each terms

f(2) = 8 - 8 + 3

Do the arithmetic operations

f(2) = 3

Hence, the value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3

The complete question is:

Find the value of f(x) = [tex]x^3-2x^2+3[/tex] , when x = 2

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