Find the measure of

One of the many branches of mathematics is algebra, which is derived from the Arabic word al-jabr, which means "reunion of fractured pieces, bonesetting."Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.

Solve the problem?

      16x+12y=744

    =  16x+12y=744

      16x= 744-12y

   divide both sides by 16

     16x/16=744-12y/16

     x= 744-12y/16

    744-12y by 16

    x =-3y/4+93/2

   solving y

   16x+12y=744

     12y =744-16x

    divide by 12

   12y/12 =744-16x/12

   y= 744-16x/12

     y=-4x/3+62

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Answer:

$6633.04

Step-by-step explanation:

6000x1.034^3=6633.04

The value of his investment after 3 years will be $6633.04.

In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.

Compound interest is the interest added to the principal amount of a loan or deposit, also known as interest on interest plus interest.

Given that Harry invests £6000 in a savings account. The account pays 3.4% compound interest per year.

The compound interest will be calculated as,

[tex]A = P( 1 + \dfrac{r}{100})^{nt[/tex]

Substitute the values in the equation above and solve,

A = 6000 x 1.034³

A = $6633.04

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The expression that represents the situation is 5/2(x) and the family uses  350 gallons of water for each week.

Showerheads:

The showerhead is a bathroom fixture that directs the flow of water in a bathroom shower.

Given,

Low flow showerheads use 2 1/2 gallons of water per minute.

And the family uses 2 1/3 hours per week.

Here we need to find the expression for this situation and we also need to find the amount of water used by the family.

First, we have to convert the mixed fraction into improper fraction, then we get,

2 1/2 =5/2

So, for one minute the showerhead use 5/2 gallon of water.

So, the expression for this situation is,

=> 5/2(x).

Where x represents the amount of time in minutes.

Now, we know that the family uses the showerhead for 2 1/3 hours per week.

So, we have to convert this mixed fraction into improper fraction,

2 1/3 = 7/3

We know that, 1 hour = 60 minutes.

So, 7/3 hours is equal to,

=> 7/3 x 60 = 7 x 20 = 140

Then, the amount of water used by the family is,

=> 5/2 (140)

=> 5 x 70

=> 350

Therefore, the amount of water used by the family is 350 gallons per week.

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The expression that represents the perimeter and area of the rectangle are 10x + 4 and 6x²- 24.

The rectangle is a quadrilateral with opposite sides equal to each other.

Opposite sides of a rectangle is also parallel to each other.

Therefore,

perimeter of a rectangle = 2(l + w)

where

Therefore,

l = 3x + 6

w = 2x - 4

Hence,

perimeter of a rectangle = 2(3x + 6 + 2x - 4)

perimeter of a rectangle = 2(5x + 2)

perimeter of a rectangle = 10x + 4

Let's find the expression that represent the area of the rectangle.

Hence,

area of a rectangle = lw

area of a rectangle = (3x + 6)(2x - 4)

area of a rectangle = 6x² - 12x + 12x - 24

Therefore,

area of a rectangle = 6x²- 24

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The translation moves 5 units to the left and 2 units down, so we have:

c = -5

d = -2

To identify the translation, let's follow a single vertex of the triangle.

The top vertex of triangle A is at (2, -3)

After a reflection about the x-axis only the y-value changes, so after the reflection the coordinates of that vertex will be:

(2, 3).

In now we apply the given translation, the new coordinates will be:

(2 + c, 3+ d)

And the coordinates of this vertex on triangle B is (-3, 1), so we have:

(2 + c, 3+ d) = (-3, 1)

2 + c = -3

c = -3 - 2 = -5

3 + d = 1

d = 1 - 3

d = -2

So the translation is defined by the values:

c = -5

d = -2

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4)  the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes is n(0.34, 0.0424) - option A

5)  the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes is pnorm(0.4,0.34,0.0424) - pnorm(0.28,0.34,0.0424) - Option A

4) Given data:

P = 0.34 and n = 125

Since, np = 0.34 * 125 = 42.5 > 10

& n(1 - p) = 125 * 0.66 = 82.5 > 10

Therefore, the normal distribution can be used here:

Mean is μp = p = 0.34

The standard Deviation is σp = [tex]\sqrt \frac{P(1-p)}{n} = \sqrt\frac{(0.34)(0.66)}{125} = 0.0424[/tex]

The distribution of sample proportion will be;

N (0.34, 0.0424)

Therefore, option (a) is correct that is n(0.34, 0.0424)

5) The likelihood that between 28% and 40% of the 125 taxpayers in the sample used tax preparation software is calculated as follows:

pnorm (0.4, 0.34. 0.0424) - pnorm (0.28, 0.34, 0.0424)

Therefore, option A is correct that is pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424)

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Based on the case, we know that four friends want to share their cookies package. The number of the cookies is represent by 'm'. So, how many part for each friends will get?

We can solve the case by 'fraction'. Fractions represent the parts of a whole objects. A fraction is arranged by two parts. First, numerator is the number on the top of the line. Basically, numerator is how many equal parts of the whole objects are taken.  Second, denominator is the number below the line. In the other word, denominator is the total number.

If four friends want to share the whole package of cookies, is means that the package will be divided to 4 parts. The whole part is represented by 'm'. So, the fraction form that can describe this case is each friends will get [tex]\frac{1}{4}[/tex] m.

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△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

So, to prove that △PQR ≅ △STU:

So, with these three conditions, △PQR ≅ △STU is under ASA condition.

Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

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Answer:

option a as x=8 hope you understand my writing , if got some problem comment down

The best measure of how big Jerry can build his house as required in the task content is; 60' by 90'.

It follows from the task content that the dimension of the family lot purchased by Jerry in a bid to build his house has dimensions; 90' × 120'.

Since the city requires 20' setback on the front and 10' setback at the back, it follows that the vertical length remaining and available to build his house is; 120' - 20' - 10' = 90'.

Also, the horizontal width available for him to build his house after the 15' setback along the sides is; 90' - 15' - 15' = 60'.

Therefore, the space available for Jerry to.build his house is; 60' × 90'.

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The most appropriate choice for area of rectangle will be given by-

a) Area of the wall =  [tex]26508[/tex] [tex]in^2[/tex]

b) Area of wall left uncovered = [tex]25347[/tex] [tex]in^2[/tex]

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle. If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Width of the wall = [tex]15\frac {2}{3}[/tex] feet = [tex]\frac{47}{3}[/tex] feet

Height of the wall = [tex]\frac{3}{4} \times \frac{47}{3}[/tex] feet

                               = [tex]\frac{47}{4}[/tex] feet

a) Area of the wall = [tex]\frac{47}{3} \times \frac{47}{4}[/tex] [tex]ft^2[/tex]

                               =[tex]\frac{2209}{12} \times 12 \times 12[/tex] [tex]in^2[/tex]

                               = [tex]26508[/tex] [tex]in^2[/tex]

b) Length of painting = [tex]40 \frac{1}{2}[/tex]  in = [tex]\frac{81}{2}[/tex] in

Breadth of painting = [tex]28\frac{2}{3}[/tex] in = [tex]\frac{86}{3}[/tex] in

Area of painting = [tex]\frac{81}{2} \times \frac{86}{3}[/tex] [tex]in^2[/tex]

                           = [tex]1161[/tex] [tex]in^2[/tex]

Area of wall left uncovered = (26508 - 1161) [tex]in^2[/tex]

                                             = 25347 [tex]in^2[/tex]

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Answer:

1 knife cost £6.6

Step-by-step explanation:

Simultaneous equation is;

4x = y ----------(equation 1)

12y + 16x = 105.64 ----------- (equation 2)

Rewrite equations:

4x=y;16x+12y=105.64

Step: Solve4x=yfor y:

4x=y

4x+−y=y+−y(Add -y to both sides)

4x−y=0

4x−y+−4x=0+−4x(Add -4x to both sides)

−y=−4x

−y/−1 = −4x/−1

(Divide both sides by -1)

y=4x

Step: Substitute 4x for y in 16x+12y=105.64:

16x+12y=105.64

16x+124x=105.64

64x=105.64(Simplify both sides of the equation)

64x/64 = 105.64/64

(Divide both sides by 64)

x=1.650625

Step: Substitute 1.650625 for x in y=4x:

y=4x

y=(4)(1.650625)

y=6.6025(Simplify both sides of the equation)

1 knife cost = 4x = 4(1.65) = 6.6

∴ 1 knife cost £6.6

The total distance Steve jogged is 5 miles.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Given:

Steve completed 60% of the Jog.

Also, he travelled 3 miles.

Let the total distance he travelled be x miles.

Then,

60% of x =3

60/100 x= 3

x= 3 x 100 / 60

x= 300/60

x= 5 miles.

Hence, total he had to jog 5 miles.

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Answer:

The slope is 0.

Step-by-step explanation:

Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.

When plugging it in we get -18 - (-18)/ -15 - 12.  You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.

Hope this helps :)

function:

number of tiles: 12b+38

Where;

b=number of bundles

150+30 = 12b+38

Solve for b:

150+30 = 12b+38

180 = 12b+38

180-38 =12b

142 =12b

142/12 =b

11.8 =b

12 bundles

Answer:

x = -3/4, x = 0, x = 5

Explanation:

The equation can be rewritten as

The roots are found by equating the above to zero:

One root we immediately notice is x = 0. The other roots are found using the fact that

To solve for x we use the quadratic formula which says for

the x is given by

2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.

4.>>>>>>

[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]

ATTACHED IS THE SOLUTION

Answer:

203.5

Step-by-step explanation:

just divide 814 by 4

Answer:

203.5 miles per day

Step-by-step explanation:

divide 814 by 4= 203.5

A set of parallel lines and a set of perpendicular lines are: BF║CG, AD⊥BF.

Parallel lines are straight lines that are of equal distance at every point away from each other, and therefore, do not intersect each other at any point. The sign "║" is used to indicate that two lines are parallel lines.

Lines that are said to be perpendicular lines are lines that intersect each other at right angle or 90 degrees. That is, at the point of their intersection, a right angle is formed which is 90 degrees. The sign "⊥" is used to indicate that two lines are perpendicular lines.

In the image given, lines BF and CG do not intersect at any point and they are of equal distance away from each other at every point, therefore, CG and BF are perpendicular lines.

Also, we can see that a right angle is formed at the point of intersection of lines AD and BF, therefore AD and BF are perpendicular lines.

Thus, we can state that: BF║CG, AD⊥BF.

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Given: A right triangle with dimensions as shown in the figure

To Determine: The ratio for sin A and cos A

Solution

Given a right triangle ABC with a reference angle A, the trigonometry ratio is

From the given right triangle with reference angle A, the hypothenuse is the side facing the right angle. The side facing angle A is the opposite, and the other side is adjacent. This is as shown below

Hence

OPTION A is the correct option

Answer:

c.   ∠MPN

Step-by-step explanation:

Supplementary angles sum to 180°.  

(Note that supplementary angles don't have to be next to each other).

Given ∠NPI = 55.6°.

Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:

⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.

The angle that measures 124.4° is ∠MPN.  

Therefore, ∠MPN is supplementary to ∠NPI.

Answer:

Step-by-step explanation:

x

=

−

2

x

=

−

5

Explanation:

x

2

+

7

x

+

10

=

0

We could right the equation in another form using brackets.

(

x

+

2

)

(

x

+

5

)

=

0

In order to get two numbers to multiply and give 0, at least one number has to be 0.

a stands for the first bracket and b for the second.

a x b = 0

a=0 or b=0 to make this equation valid.

Therefore x= -2 or x= -5 because -2+2=0 and -5+5=0 according to both brackets.

Answer: it would be -13

Step-by-step explanation: -13-8=-21

The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.

The value of the basket in 2018 can be calculated by using multiplication and addition.

First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.

Lollipop: $0.80 × 15 = $12

Chocolate: $3.75 × 10 = $37.5

Peanut butter: $4.25 × 4 = $17

Ice-cream cake: $12.99 × 2 = $25.98

Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;

Value of basket = $12 + $37.5 + $17 + $25.98

Value of basket = $92.48

Hence the value of the basket in 2018 is $92.48

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Given the equation,

Complete squares as shown below,

Thus,

Similarly,

Therefore,

Finally, the standard form is.

As for the vertices, foci, and asymptotes,

Foci: (-1,-1/2), (9,-1/2)

Vertices

Vertices: (8,-1/2), (0,-1/2)

Asymptotes:

Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2

The four consecutive integers are 20, 21, 22, and 23 whose sum is 86.

using sequential means.

Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

86 is obtained by adding together the four consecutive integers x, (x+1), (x+2), and (x+3)

x + (x+1), (x+2), and (x+3) = 86

the smallest one, x, is now solved for: 4x + 6 = 86

The numbers are 20, 21, 22, and 23, because 4x = 80 x = 20.  

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Answer:

20, 21, 22 & 23

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) + (x + 2) + (x + 3) = 86

→ 4x + 6 = 86

Now the the value of x will be,

→ 4x + 6 = 86

→ 4x = 86 - 6

→ x = 80/4

→ [ x = 20 ]

Then the required numbers will be,

→ x = 20

→ x + 1 = 20 + 1 = 21

→ x + 2 = 20 + 2 = 22

→ x + 3 = 20 + 3 = 23

Hence, numbers are 20, 21, 22, 23.