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Answer:

x = 13, y = 26, z = 5

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

2x + 110 + 44 = 180

2x + 154 = 180 ( subtract 154 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13

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

2x and y are alternate angles and congruent , so

y = 2x = 2(13) = 26

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

The opposite sides of a parallelogram are equal

3z - 1 = 14 ( add 1 to both sides )

3z = 15 ( divide both sides by 3 )

z = 5

Question:

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.

Answer:

101.5cm²

Step-by-step explanation:

The figure for the trapezium ABCD is attached to this response.

To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;

A  = [tex]\frac{1}{2}[/tex] x (a + b) x h            ------------------(i)

Where;

A = area of the trapezium

a and b are the parallel sides of the trapezium

h = height of the trapezium.

As shown in the figure,

AB and CD are parallel

Therefore, we can say that;

a = AB

b = CD

Also, from the figure,

The height of the trapezium is BP

Therefore, we can say that;

h = BP

We know that;

a = AB = 4cm

b = CD = 25cm

h = BP = 7cm

Substitute these values of a, b and h into equation (i) as follows;

A  = [tex]\frac{1}{2}[/tex] x (4 + 25) x 7    

A  = [tex]\frac{1}{2}[/tex] x (29) x 7    

A = 101.5

Therefore, the area of the trapezium is 101.5cm²

Answer:

m∠E = 60°

Step-by-step explanation:

The given information in the diagram are;

The shape of the drawing, ΔEDF = A right triangle

The length of the hypotenuse side opposite the right angle = 16·√46

The length of the leg adjacent to the reference angle ∠E = 8·√46

By trigonometric ratio, we have;

[tex]\dfrac{Adjacent\ leg \ length}{Hypotenuse \ length} = cos\angle E[/tex]

Plugging in the values gives;

[tex]cos\angle E = \dfrac{8 \cdot \sqrt{46} }{16\cdot \sqrt{46} } = \dfrac{1}{2}[/tex]

∴ m∠E = arccos(1/2)

Using a calculator or from tables or an online trigonometric ratio tool, we have

arccos(1/2) = 60°

∴ m∠E = arccos(1/2) = 60°.

Answer:

17

Step-by-step explanation:

2(3x+3) = 6x-16+4x-10

6x+6=10x-26

-4x=-32

x=8

6x-16 = 48-16=32

3x+3 = 24+3=27

4x-10= 32-10=22

as arithmetic sequence WZ should be 17

Answer:

y < 4 or y > 9

Step-by-step explanation:

The symbol < means less than, while the symbol > means greater than. So, the inequality y < 4 means that y is less than 4, and the inequality y > 9 means that y is greater than 9. When put together you have all real numbers y that are less than 4 or greater than 9.

Answer:

37.2

Step-by-step explanation:

when you turn the small triangle LMN to its right angle to cover the right angle of KLM, you find that they are similar triangles.

therefore the corresponding side lengths are at the same ratio.

LM/KM = MN/LN

LM = 24

MN = 13

we can get LN via Pythagoras of the small triangle

LN² + MN² = LM²

LN² + 13² = 24²

LN² = 24² - 13² = 576 - 169 = 407

LN = sqrt(407) = 20.174241

now back to our main problem

24/KM = 13/sqrt(407)

24×sqrt(407)/13 = KM = 37.2

Answer:

Solution given:

x²+4x+4

x²+(2+2)x+4

x²+2x+2x+4

x(x+2)+x(x+2)

(x+2)(x+2)

(x+2)²

your

answer is

((+) +2)²

Answer:

-9w^3

Step-by-step explanation:

Combine like terms. -20+11 = -9

Answer:

-9 w^3

Step-by-step explanation:

-20w^3+11w^3

Combine like terms

(-20+11) w^3

-9 w^3

Answer:

D

[tex]8x - 2y = 12 \\ 2y = 8x - 12 \\ y = 4x - 6[/tex]

Answer:

P: parenthesis

E: Exponents

M: multiplication

D: division

A: Addition

S: substraction

Step-by-step explanation:

Answer:

x = 49

Step-by-step explanation:

The central angle AOB is equal to the measure of the arc that subtends it, so

∠ AOB = 82°

OA = OB ( both radii of the circle ), then Δ AOB is isosceles and the 2 base angles are congruent, then

x = [tex]\frac{180-82}{2}[/tex] = [tex]\frac{98}{2}[/tex] = 49

Answer:

30%

Step-by-step explanation:

3+4+6+7= 20

6 (green) / 20

= 30%

Answer:

V≈134.0

Step-by-step explanation:

divide 8 by 2 to get the radius .

V=πr2h /3

V=πr2 h /3=π·42·8 /3≈ 134.0

Answer:

-6

Step-by-step explanation:

substitute

(2 + 3) -11

5 - 11

-6

Answer:

The answer is -6

Step-by-step explanation:

First, plug in the numbers into the original equation - (2+(3))-11

Then, simplify.  (5)-11

Simplify one more time.  -6

(I dont see anywhere to use the (t) in your equation)

Answer:

6√x

Step-by-step explanation:

Given :-

For combining , take √x as common ,

=> √x ( 9 - 3 )

=> √x * 6

=> 6√x

Answer:

180

60

40

Step-by-step explanation:

Angles in a triangle add up to equal 90 degrees

Equilateral - has all congruent angles and congruent sides

If a triangle has 3 angles and the angles add up to equal 180 then the measure of one angle in an equilateral = 180 / 3 = 60

Bisect means to split into to equal parts

So if you bisect an 80 degree angles you will have two 40 degree angles. ( Because 80/2 = 40 )

Answer:

40°

Step-by-step explanation:

bisecting an angle gives equal angles equivalent to half the size of the bisected angle for each of them

Awnser: 16022 in3

Step-by-step explanation:

find the volume of the 2 cones find the volume if the semicircle then add the 2 volumes together.

Answer:

slope is 0 because its rise over run and there is no run so 0 or undefined

Step-by-step explanation:

Answer:

It has an undefined slope because this vertical line does not run horizontally, meaning the "run" in rise/run is 0 and you cant divide anything by 0

Step-by-step explanation:

Answer:

Maria should budget $105 for the trip.

Step-by-step explanation:

First divide every 30 miles she is going doing for the trip.

900 divided by 30 = 30

So she will need 30 gallons to drive 900 miles.

30 x 3.50 = 105.

105 is how much she will pay for the gas.

Answer:

14 kids

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

To find percents I usually just divide the 100% number by 100 in order to get the number that would be 1% of the whole. Thjen, I just multiply the 1% number by however many degrees you need to find.

700÷100=7

7×2=14

14 kids with red hair

Answer:

B.

Step-by-step explanation:

The opportunity cost means what Henry will be missing out on by not working at the library. He loses the chance to earn by working in a library.

Answer:

B.  The chance to earn by working in a library

Step-by-step explanation:

This is a guess

Answer: 50

Step-by-step explanation:

Given

There are maximum of 103 people in room and principal and 2 counselor need to discuss eligibility requirements.

If each student must bring a parent with them

No of seats left after principal and 2 counselor occupied the seats are 103-3=100

A student and parent occupies at least 2 seats. For maximum students, only one parent is feasible.

So, maximum no of students are

[tex]\Rightarrow \dfrac{100}{2}=50[/tex]

Answer:

7) Option D.

8) Option C.

9) Option C.

10) Option A.

Step-by-step explanation:

7) The "x" value can be found using the following trigonometrical identity:

[tex] sin(30) = \frac{12}{x} [/tex]

[tex] x = \frac{12}{sin(30)} = 24 [/tex]

Since "x" (the hypotenuse) is related to the opposite side by sin(θ).

So, the correct option is D.

8) The "y" value can be calculated with tan(θ):

[tex] tan(30) = \frac{12}{y} [/tex]

[tex] y = \frac{12}{tan(30)} = \frac{12}{\frac{\sqrt{3}}{3}} = 12\sqrt{3} [/tex]

Hence, the correct option is C.

9) The hypotenuse can be calculated with cos(θ):

[tex] cos(45) = \frac{5\sqrt{2}}{x} [/tex]

[tex] x = \frac{5\sqrt{2}}{cos(45)} = \frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}} = 10 [/tex]

Thus, the correct option is C.

10) The value of the sides can be found by Pitagoras:

[tex] h^{2} = x^{2} + x^{2} [/tex]

[tex] x = \sqrt{\frac{h^{2}}{2}} = \sqrt{\frac{(12\sqrt{5})^{2}}{2}} = \sqrt{360} = 6\sqrt{10} [/tex]

Therefore, the correct option is A.

I hope it helps you!

First, we have to understand the slope-intercept form.

[tex] \large \boxed{y = mx + b}[/tex]

A linear function/equation has three forms and the slope-intercept is one of the form. It is also commonly used in Function topic while the other two forms are commonly used in Analytic Geometry.

In the slope-intercept form, the m-term represents the slope while b-term represents the y-intercept of a graph.

Which equation represents a linear function that has a slope of 5 and a y-intercept of -6.

As you notice the bold, italic and underlined words in the question that I quoted or rewrote. I've just explained that the slope is m-term and y-intercept is b-term.

Therefore, substitute m = 5 and b = -6 in the equation.

[tex] \large{y = mx + b \longrightarrow \bold{y = 5x + ( - 6)}} \\ \large \boxed{ \tt{ \purple{y = 5x - 6}}}[/tex]

I hope this helps! Let me know if you have any questions regarding the linear function, don't hestitate to ask. Good luck with your assignment and have a nice day!

Answer:

C

Step-by-step explanation:

Using the rules of logarithms

loga + logb = log(ab)

loga - logb = log([tex]\frac{a}{b}[/tex] )

log[tex]x^{n}[/tex] ⇔ nlogx

Given

4lnx + ln3 - lnx

= 3lnx + ln3

= lnx³ + ln3

= ln(x³ × 3)

= ln(3x³) → C

Answer:

y = x + 3/5

Step-by-step explanation:

1.  Label this function 'y':  y = x - 3/5

2.  Interchange x and y:  x = y - 3/5

3.  Solve this for y:  y = x + 3/5

This last result is the inverse of the given function.

Answer:

y = x + 3/5

Step-by-step explanation:

change f(x) to 'y'

y = x - 3/5

interchange 'x' with 'y'

x = y - 3/5

solve for y

y = x + 3/5

Answer:

15L

Step-by-step explanation:

divide the number of km's you will travel(165) by the number you are given originally(66)- 165/66 is 2.5

then multiply 2.5 by the amount  of litres it takes for the original 66 km (6L)- 2.5*6 is 15L

Answer: [tex]-6,13[/tex]

Step-by-step explanation:

Given

The sum of the two numbers is 20

and the difference of the two is -6

Suppose, the numbers are x and y

[tex]\therefore x+y=20\quad \ldots(i)\\\Rightarrow x-y=-6\quad \ldots(ii)\\\text{Solving} (i)\ \text{and}\ (ii)\ \text{we get}[/tex]

[tex]\Rightarrow 2x=14\\\Rightarrow x=7[/tex]

[tex]\therefore y=13[/tex]

Therefore, the numbers are [tex]-6,\ \text{and}\ 13[/tex]