The length of one parallel side of a trapezium measures 24 m and the distance between parallel sides measures 28 m. The area of the trapezium is 756 m2. What is the measure of the other parallel side?​

Answer:

ASA

Step-by-step explanation:

As you can see in the picture it is giving us 2 angles, in between those 2 angles are aside. Therefore it is ASA.

We can also eliminate SSS because 2 angles and shown and SAS can also be eliminated because there are 2 angles, not sides.

The equation that generate the table in slope intercept form is y = 2 / 5 x + 4

The equation of a linear table can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's represent the equation of the table of money spent and pounds of food.

using slope intercept form,

y = mx + b

where

Therefore, let's find the slope using (0, 4) and (20, 12)

m = slope = 12 - 4 / 20 - 0

slope = 8 / 20

slope = 2 / 5

Therefore, let's find the y-intercept using (0, 4)

4 = 2 / 5(0) + b

b = 4

Therefore, the equation is y = 2  /5 x + 4

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The value of tan(m - p), where the value of sin(m) = -(4/5), and the value of cos(p) = -(15/17) using trigonometric identities is; [tex]tan(m - p) = \dfrac{36}{77}[/tex]

Trigonometric identities are equations that involve trigonometric functions which are true for all values of the input variables.

The information in the question are;

Therefore;

[tex]cos(m) = \sqrt{1- \left(-\dfrac{4}{5}\right)^2} =\pm\dfrac{3}{5}[/tex]

The location of m is in Quadrant III, therefore;

[tex]cos(m) =-\dfrac{3}{5}[/tex]

[tex]sin(p) = \sqrt{1- \left(-\dfrac{15}{17}\right)^2} =\pm\dfrac{8}{17}[/tex]

The angle p is located in Quadrant III, therefore;

[tex]sin(p) = -\dfrac{8}{17}[/tex]

180° ≤ Angle ∠m ≤ 270°; definition of angles in Quadrant III

180° ≤ Angle ∠p ≤ 270°; definition of angles in Quadrant III

Therefore;

270° - 270° ≤ |∠m - ∠p| ≤ 270° - 180°
0° ≤ |∠m - ∠p| ≤ 90°

The trigonometric identity for tan(m - p) is presented as follows;

[tex]tan(m - p) = \dfrac{tan(m) -tan(p)}{1+tan(m)\cdot tan(p)}[/tex]

[tex]tan(m - p) = \dfrac{\dfrac{sin(m) }{cos(m) } -\dfrac{sin(p) }{cos(p) } }{1+\dfrac{sin(m) }{cos(m) } \cdot \dfrac{sin(p) }{cos(p) } }[/tex]

Therefore;

[tex]tan(m - p) = \dfrac{\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) -\left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) }{1+\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) \times \left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) } }= \dfrac{36}{77}[/tex]

[tex]tan(m - p) = \dfrac{36}{77}[/tex]

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Answer:

It is positive and increasing

Step-by-step explanation:

After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"

The derivative function f' for the function f is f'(x) = -10 / (5x+3)^2 and Equation of the line tangent to the graph of f  is 5x+2y+7=0.

Given function:

f(x) = 2/5x+3

a.

f'(x) = d/dx(2/5x+3)

According to power rules:

1/u = -1/u^2

= 2(1/(5x+3)^2) d/dx(5x+3)

= 2*5 / (5x+3)^2

= -10/(5x+3)^2

Hence derivative function f' for the function f is f'(x) = -10 / (5x+3)^2.

b.

(a,f(a)) and a = -1

f(-1) = 2/5(-1)+3

= 2/-5+3

= 2/-2

= -1

point (-1,-1)

slope f'(x) = -10/(5x+3)^2

f'(-1) = -10/(5(-1)+3)^2

= -10/(-2)^2

= -10/4

m = -5/2

Equation of the line is  y - y1 = m(x-x1)

y - (-1) = -5/2(x-(-1)

2(y + 1) = -5x - 5

5x + 2y + 2 + 5 = 0

5x+2y+7=0.

Equation of the line tangent to the graph of f  is 5x+2y+7=0.

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Answer:

Step-by-step explanation:

Ok:

Area's formula is width* length

1. 120 square meters and width of 8 meters. Reversing the formula, divide area by width to get length!

120/8=15 meters

2. Answer: 15 meters

The number of ladies in the club = 18

and the number of gentlemen in the club = 2

Let x be the number of gentlemen.

So, the number of ladies would be 3x + 12

Total number of people in garden = x + (3x + 12)

                                                         = 4x + 12

In a garden club, 90% is ladies.

This means, (3x + 12) is 90 percent of (4x + 12)

We get an equation,

(3x + 12) = 90/100 * (4x + 12)

We solve above equation to find the value of x.

30x + 120 = 36x + 108

6x = 12

x = 2 (number of gentlemen)

So, the number of lades would be:

3x + 12 = 3(2) + 12

            = 18

Therefore, the number of ladies in the club = 18 and the number of gentlemen in the club = 2

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Answer:

19

Step-by-step explanation:

add it all up its easy

Step-by-step explanation:

Shelby buys 3 barrettes...

2*3=6

and 1 comb

1*1=1

she spent $7 in total

6+1=7

Kendra buys 2 barrettes...

2*2=4

and 4 combs

1*4=4

so Kendra spent $8 in total

4+4=8

the amount spent from the to girls was...

8+7=15

Answer:

84

Step-by-step explanation:

80 x 0.05 = 4

80 + 4 =84

An equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.

First, let us understand the standard form of a quadratic equation:

In Mathematics, the standard form of a quadratic equation is given by;

y = g(x) = ax² + bx + c = 0

To write a quadratic function equation in standard form, we would construct the following system of equations from the data in the given table:

5 = a(-5)² + b(-5) + c  ⇒ 5 = 25a - 5b + c     .......equation 1.

2 = a(-4)² + b(-4) + c  ⇒ 2 = 16a - 4b + c      .......equation 2.

5 = a(-3)² + b(-3) + c  ⇒ 5 = 9a - 3b + c       .......equation 3.

14 = a(-2)² + b(-2) + c  ⇒ 14 = 4a - 2b + c    .......equation 4.

From equation 1 and equation 3, we derive:

25a - 5b + c = 9a - 3b + c

⇒ 25a - 9a = -3b + 5b

⇒ 16a = 2b

⇒ b = 8a

Substituting the value of b into equation 2 and 4, we derive the following equations:

2 = 16a - 4 * 8a + c     ⇒ 2 = - 16a + c

14 = 4a - 2 * 8a + c     ⇒ 14 = -12a  + c

By using the elimination method, the value of a is given by:

2 - 14 = (-16a + 12a) + (b - c)

-12 = - 4a

a = 3

Next, we would determine the value of b as follows:

b = 8a

b = 8 * 3

b = 24

For the value of c, we have:

2 = - 16a + c

c = 16 * (3)+ 2

c = 48 + 2

c = 50.

Substituting the respective values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

3x² + 24x + 50 = 0

Thus, an equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.

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Answer:

The two graphs have the same shape, but the second graph shifted 3 units left.

The angle B is 66°

Given,

In the question:

If angle A is (2x) and angle B is (3x+11)°

and, the sum of angle A and angle B is 66°

To find the angle of B.

Now, According to the question:

Based on the given condition:

Angle A = 2x

Angle B = (3x + 11)°

The sum of angle A and B is 66°

2x +  (3x + 11)° =  66°

5x + 11 =  66°

Calculate the sum or difference

5x = 66 - 11

3x = 55

x = 55/3

The angle B is = 3x + 11

Plug the value of x in angle B

3 × 55/3 + 11

= 66

Hence, The angle B is 66°

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Step-by-step explanation:

9 < 2(x - 7)

hope this helpful

Answer:

Step-by-step explanation:

after 9 months, the man will have received $836. It would take 4 years to get $992 with a 6% simple interest annually

Answer:

y = - 3x - 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (- 4, - 2 ) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = - 3x - 14 ← equation of line

The number of tiles need to cover the closet floor is 180 tiles

The length of the side of the tile = 1/3 feet

The area of the square = Side × Side

The area of the tile = (1/3) × (1/3)

= 1/9 square feet

The width of the closet = [tex]3\frac{1}{3}[/tex] feet

Convert the mixed fraction to simple fraction

[tex]3\frac{1}{3}[/tex] feet = 10/3 feet

The length of the closet = 6 feet

Total area of the closet = 10/3 × 6

= 20 square feet

Number of tiles needed = The area of the closet /  The area of the tile

Substitute the values in the equation

= 20 / (1/9)

= 180 tiles

Hence, the number of tiles need to cover the closet floor is 180 tiles

The complete question is

Vanessa wants to cover her closet floor with SRB tiles that are 1/3 foot on each side. The closet is   [tex]3\frac{1}{3}[/tex] feet wide and 6feet deep, How many tiles will Vanessa need to cover the closet floor?

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Answer:

(7,-4)

Step-by-step explanation:

y +  4 = -5(x-7)  Substitute in 7 for x and -4 for y

-4 + 4 = -5 (7-7)

0 = 5(0)

0 = 0  This is a true statement.

Answer:

y = -2/5 x + 1

Step-by-step explanation:

slope = -2/5

y-3 = -2/5 (x -(-5)

y-3 = -2/5 (x+5)

y - 3 = -2/5 x - 2

y = -2/5 x - 2 + 3

y = -2/5 x + 1

The value of the investment at the end of 5 years be $ 15,281.012.

Given, 10400 dollars are invested at an interest rate of 8%.

We have to find the value of the investment at the end of 5 years.

Now, on using the compound interest formula, we get

Amount = P(1 + r/100)^t

Amount = 10400(1 + 8/100)^5

Amount = 10400(1.08)^5

Amount = 10400(1.469)

Amount = 15,281.012

Hence, the value of the investment at the end of 5 years be $ 15,281.012.

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The values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.

Given that; the equation F=9/5C+32 and ordered pairs are (25, F1), (−30, F2)

To convert the values to degrees Fahrenheit, we have to substitute the given values into the equation to get F1 and F2 respectively:

For (25, F1);

F = 9/5 C+32      

Now put C= 25 in the equation;

F1 = 9/5(25) + 32

F1 = 45 +22

F1 = 77 degrees Fahrenheit

For (−30, F2);

F = 9/5 C+32      

Now put C= -30 in the equation;

F2 = 9/5(-30) + 32

F2 = -54 + 32

F2 = -22 degrees Fahrenheit

Hence, the values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.

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For the given equation -2(5x + 8) = 14 + 6x, the statements for the process used to achieve steps 1 - 4 should be completed as follows:

In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In this exercise, you're required to describe the steps that should be taken to rearrange and solve for x. Therefore, the appropriate and required steps that were used to achieve steps 1 - 4 include the following:

Multiplying 5x and 8 by -2, we have the following:

-2(5x + 8) = 14 + 6x

-10x - 16 = 14 + 6x

Subtracting 6x from both sides of the equation, we have the following:

-10x - 16 - 6x = 14 + 6x - 6x

-16x - 16 = 14

Next, we would add sixteen (16) to both sides of the equation as follows:

-16x - 16 + 16 = 14 + 16

-16x = 30

Dividing both sides of the equation by -16, we have the following:

x = -30/16

x = -15/8.

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Answer:2,300

Step-by-step explanation:

Taking into consideration the upstream and downstream speed, and the equal time taken to travel upstream and downstream distance, the speed of the boat in the still water is found out to be 10mph.

It is given to us that -

The speed of the river current = 2mph

Time taken for the boat to travel 30 miles downstream = Time taken for the boat to travel 20 miles upstream --- (1)

We have to find out the speed of the boat in still water.

Let us say that the speed of the boat in still water is x mph.

We know that -

Speed = Distance/Time

=> Time = Distance/Speed ----- (2)

When travelling upstream, the boat is slower and thus, we subtract speed of the current from the speed of the boat.

When travelling downstream, the boat is faster as it goes with the current and thus, we add the speed of the current with the speed of the boat.

From equation (1), we have

Time to travel 30 miles downstream = Time to travel 20 miles upstream

[tex]= > \frac{30}{x-2} =\frac{20}{x+2} \\= > 30(x+2)=20(x-2)\\= > 30x+60=20x-40\\= > 10x=100\\= > x=10[/tex]

Thus, taking into consideration the upstream and downstream speed, the speed of the boat in the still water is 10mph.

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Answer:

Step-by-step explanation:

360

Answer:

96

Step-by-step explanation:

Area of a triangle

A = (1/2) × base × height

A = (1/2) × 12 × 16

A = (1/2) × 192

A = 96 units²

I hope this helps!

Answer:

Step-by-step explanation:

M is slope

B is y intercept

X and y are given

using the equation for the y intercept

b=y1-mx1

B=1−(1/2)⋅(−6)=4

Write in y=Mx+b

=12+4

The general equation of the line is −2+8=0

The coordinates along the directed line segment is (-4, -6)

The points are given as:

A  = (-7, -4)

B = (2, -10)

The ratio on the segment can be represented as;

m : n = 1 : 2

So, we have the coordinates of the point that lies along the directed line segment to be

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

Point = 1/(1 + 2) * (1 * 2 + 2 * -7, 1 * -10 + 2 * -4)

Evaluate

Point = (-4, -6)

Hence, the coordinates of the point is (-4, -6)

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