In the figure given below L || m .find the value of x

Answer:

[tex] \mathsf{ {5x}^{2} + 28x + 21}[/tex]

Option A is the right option.

Step-by-step explanation:

Let's find the area of large rectangle:

[tex] \mathsf{(3x + 6)(2x + 4)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = 3x(2x + 4) + 6(2x + 4)}[/tex]

Calculate the product

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}[/tex]

Multiply the numbers

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}[/tex]

Collect like terms

[tex] \mathsf{ = {6x}^{2} + 24x + 24}[/tex]

Let's find the area of small rectangle

[tex] \mathsf{(x - 3)(x - 1)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = x( x - 1) - 3(x - 1)}[/tex]

Calculate the product

[tex] \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}[/tex]

Multiply the numbers

[tex] \mathsf{ = {x}^{2} - x - 3x + 3}[/tex]

Collect like terms

[tex] \mathsf{ = {x}^{2} - 4x + 3}[/tex]

Now, let's find the area of shaded region:

Area of large rectangle - Area of smaller rectangle

[tex] \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}[/tex]

Collect like terms

[tex] \mathsf{ = {5x}^{2} + 28x + 21}[/tex]

Hope I helped!

Best regards!

Answer:

$35

Step-by-step explanation:

Using the formula provided, d=(p−c)÷2 (where d is the discount, p is the original price, and c is the store's cost for the dress.) we can determine the discount.

The original price is 120,

d=(120−c)÷2

The store's cost is 50,

d=(120−50)÷2

So we subtract 120 and 50 to get

d=(70)÷2

70 divide by two is

d= 35

The discount is $35

Answer:

60

Step-by-step explanation:

We want to find the number of ways to wear a suit, shirt, and pair of shoes.

Therefore, we can use the fundamental counting principal, which is: If there is x ways to do one thing, y ways to do another and z ways for another, then there are x * y * z ways to do all things.

Therefore, we must multiply the suits, shirts and shoes.

suits * shirts * shoes

The man has 3 different suits, 4 different shirts and 5 different pairs of shoes.

3 * 4 * 5

12 * 5

60

There are 60 different ways to wear a suit, shirt and pair of shoes.

Answer:

4

Step-by-step explanation:

Given:

A, B, C, D have distinct positive values for mod 6

A (mod 6) = 1

B (mod 6) = 2

C (mod 6) = 4

D (mod 6) = 5

Each mod 6 value cannot be a zero since the product ABCD is not a multiple of 6.

Furthermore, in order that ABCD mod 6 > 0, we cannot  have a residue equal to 3, else the product with a residue 2 or 4 will make the product a multiple of 6.

Thus the only positive residues can only be 1,2,4,5

A*B*C*D  (mod 6) > 0  = 1*2*4*5 (mod 6) = 4

Answer:

Option D. 5 EE 6 ÷ 6.6 EE 4

Step-by-step explanation:

Data obtained from the question include the following:

Area of land purchased = 6.6×10^4 square miles

Cost = $ 5×10^6

To determine the key strokes on a calculator which will give the cost the

United States paid for each square mile of Florida, let us calculate cost of 1 square mile.

This can be obtained as follow:

6.6×10^4 sq mile = $ 5×10^6

Therefore,

1 sq mile = $ 5×10^6 ÷ 6.6×10^4

In calculator, the key strokes will be:

5 EE 6 ÷ 6.6 EE 4

Answer:

Like Eduard22sly said D). 5 EE 6 ÷ 6.6 EE 4 is correct.

plus i took the test 100% :)

Answer:

30.5 cm

Step-by-step explanation:

0 < h ≤ 10 ⇔ Midpoint = 5

10 < h ≤ 20 ⇔ Midpoint = 15

20 < h ≤ 30 ⇔ Midpoint = 25

30 < h ≤ 40 ⇔ Midpoint = 35

40 < h ≤ 50 ⇔ Midpoint = 45

50 < h ≤ 60 ⇔ Midpoint = 55

⇒ Multiply each corresponding midpoint with it's frequency

(5 × 1) + (15 × 4) + (25 × 7) + (35 × 2) + (45 × 3) + (55 × 3) = 610

⇒ Divide the total of 610 by the frequencies added together

610 ÷ (1 + 4 + 7 + 2 + 3 + 3) = 610 ÷ 20 = 30.5

Answer:

90°

I think.

Step-by-step explanation:

Cause... As you see it's a right angle triangle... And also when you ad 6+15 u get 90...

I

If Amir is not courageous, then he will not join the indian army.

Answer:

Hey there!

Let the cost of one uniform be c, so the expression becomes

c+13+11+18

Thus, we have c+42

Hope this helps :)

Answer:

32

Step-by-step explanation:

13+11+8=32

Answer:

1 and 3/7 hour

Step-by-step explanation:

Every hour they get 140 miles closer (100 + 40). So you divide 200 by 140 which gets you 1.42... or 1 and 3/7 of an hour.

Answer:

Slope = m = -5/2

Y-intercept = b = -3

Step-by-step explanation:

[tex]-5x-2y = -6[/tex]

Getting it in a slope - intercept form:

[tex]-2y = 5x+6\\Dividing \ both \ sides \ by \ -2\\y = \frac{-5x}{2} + (-3)\\y = \frac{-5x}{2} -3\\[/tex]

Comparing it wit the slope intercept equation [tex]y = mx+b[/tex] we get

Slope = m = -5/2

Y-intercept = b = -3

Answer:

4

Step-by-step explanation

+8  + (-7)  + (+11) + (-2)= 4

The value of the series plays is 10.

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

In this question, we have to find the total amount of points, considering the number of points on each series.

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

The total is:

[tex]T = 8 - 7 + 11 - 2 = 1 + 9 = 10[/tex]

10 points.

A similar question is given at https://brainly.com/question/14350453

Answer:

see explanation

Step-by-step explanation:

If x = 3 is a zero then p(3) = 0 , that is

p(3) = 3(3)² - 27 = 3(9) - 27 = 27 - 27 = 0

Thus x = 3 is a zero of p(x)

Answer:

Step-by-step explanation:

p(x) = 3x² - 27

p(3) = 3*3² - 27

      = 3 * 9 - 27

     = 27 - 27

    = 0

p(3) =0 . Therefore, 3 is z zero of p(x)

Answer:

hi:) If chen needed 3 1/5 and 3 2/3, the answer should be 7. 7 cups. i hope this is right but feel free to correct me if im wrong.

B. 7 cups

The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.

Number of cups used to make muffins = 3 1/5

Estimation = 3 cups

Number of cups used to make banana bread = 3 2/3

Estimation = 4 cups

Number of cups of flour needs to bake both recipes = Estimated number of cups used to make muffins + Estimated number of cups used to make banana bread

= 3 + 4 cups

= 7 cups.

The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.

Learn more about fraction here:

https://brainly.com/question/78672

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x = 64°

Step-by-step Explanation

x = 1/2[(360° - 2*58°)-2*58°]

x = 1/2[(360° - 2*58°) - 2*58°]

x = 1/2[(360° - 116°) - 116°]

x = 1/2[244° - 116°]

x = 1/2[128°]

x = 64°

Answer:

Step-by-step explanation:

Use BODMAS rule:

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Now, let's Solve,

[tex]52 + 2 \times (9) + 6[/tex]

First, we have to multiply the numbers:

[tex] = 52 + 18 + 6[/tex]

Add the numbers:

[tex] = 76[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

m² - 100 = -99

Step-by-step explanation:

Two numbers are 10 units away from the midpoint m in different directions.

So, one number is (m + 10 ) away form 'm' and another is ( m + 10) away from 'm' in opposite direction.

(m + 10) ( m-10) = -99

m² - 10² = -99

m² - 100 = -99

Answer:

4[tex]x^{2}[/tex]+6x-5

Step-by-step explanation:

Factor out 8x from the numerator.

Answer:38.4

Step-by-step explanation:

(32x3)+(48x2)-40x/8x

96+96-40x/8x

192-5x=0

192=5x

192/5=38.4

Answer:

[tex]y = .5x^2 -2x -5[/tex]

Step-by-step explanation:

Well we can start by seeing if the parabola is the same width by comparing it to its parent function ( y = x^2 )

In y = x^2 the 2nd lowest point is just up 1 and right 1 away from the vertex.

This is not true for our parabola.

So we can widen it by to the desidered width by making the x^2 into a .5x^2.

So far we’ve got y = .5x^2

Now the parabola y intercept is at -5.

So we can add a -5 into the equation making it.

y = .5x^2 - 5

Now for the x value.

So we can find the x value by seeing how far away the parabola is from from the y axis.

So the x value is -2x.

So the full equation is [tex]y = .5x^2 -2x -5[/tex]

Look at the image below to compare.

Answer:  [tex]Vertex: y=\dfrac{1}{2}(x-2)^2-7[/tex]

               [tex]Standard: y=\dfrac{1}{2}x^2-2x-5[/tex]

               Transformations: vertical shrink by a factor of 1/2,

                                            horizontal shift 2 units to the right,

                                            vertical shift 7 units down.

Step-by-step explanation:

Vertex form: y = a(x - h)² + k

Standard form: y = ax² + bx + c

Given: Vertex (h, k) = (2, -7), the y-intercept (0, c) = (0, -5)

Input those values into the Vertex form to solve for the a-value

-5=a(0 - 2)² - 7

2 = a(- 2)²

2 = 4a

[tex]\dfrac{1}{2}=a[/tex]

a) Input a = 1/2 and (h, k) = (2, -7) into the Vertex form

[tex]\large\boxed{y=\dfrac{1}{2}(x-2)^2-7}[/tex]

b) You can plug in a = 1/2, c = -5, (x, y) = (2, -7) to solve for "b"

    or

   You can expand the Vertex form (which is what I am going to do):

[tex]y=\dfrac{1}{2}(x-2)^2-7\\\\\\y=\dfrac{1}{2}(x^2-4x+4)-7\\\\\\y=\dfrac{1}{2}x^2-2x+2-7\\\\\\\large\boxed{y=\dfrac{1}{2}x^2-2x-5}[/tex]

c) Use the Vertex form to describe the transformations as follows:

[tex]y=\dfrac{1}{2}(x-2)^2-7[/tex]

a = 1/2  --> vertical shrink by a factor of 1/2

h = 2    --> horizontal shift 2 units to the right

k = -7   --> vertical shift 7 units down

=========================================

Explanation:

We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.

We need to find factors of 30 that add to 11

1+30 = 31

2+15 = 17

3+10 = 13

5+6 = 11

we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method

10x^2 + 11x + 3

10x^2 + 5x + 6x + 3

(10x^2 + 5x) + (6x + 3)

5x(2x + 1) + 3(2x + 1)

(5x+3)(2x+1)

We see the two factors are 5x+3 and 2x+1.

To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.

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

As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2

Using x = -3/5 and x = -1/2, we can do the following

Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.

Answer:

The probability of event A happening which is P(A) = 1/2

Step-by-step explanation:

To answer this question, we will have to make use of the mathematical formula for independent events.

Firstly, what do we mean by independent events?

Independent events are events that occur freely of each other. What this means is that the occurrence or non-occurrence of one of the events does not disturb the occurrence or non-occurrence of the other event.

Given that A and B are independent events, then mathematically;

P(A ∩ B) = P(A) P(B)

Now from the question, we know that We are to find P(A), inputing the values we have;

1/6 = P(A) * 1/3

P(A) = 1/6/1/3

P(A) = 1/2

Answer:

Option D.

Step-by-step explanation:

From the given it is clear that the horizontal line intersect the y-axis at -1. So, the equation of horizontal line is y=-1.

The curves represent the graph of [tex]y=\tan x[/tex].

We need to find the equation which is represented by the intersection of the graphs.

We have two equations one is for curve and another for horizontal line.

[tex]y=\tan x[/tex]

[tex]y=-1[/tex]

Equate both equations to get the equation which is represented by the intersection of the graphs.

[tex]\tan x =-1[/tex]

Therefore, the correct option is D.

Answer:

The highest or the lowest point on the graph is the vertex of an absolute-value function!

Step-by-step explanation:

Answer:

The answer is

[tex]y = \frac{4}{5} x - 6[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

m / slope = 4/5

c / y intercept = - 6

Substituting the values into the above formula

We have the final answer as

[tex]y = \frac{4}{5} x - 6[/tex]

Hope this helps you

Answer:

the  correct answer is C.

Step-by-step explanation:

i got it right on edge 2020

Answer/Step-by-step explanation:

The scale factor is missing in the question. However, here's how to find the length of the new radius if given a known scale factor.

Length of new radius = length of the radius of the dilated circle × scale factor of dilation

Length of the radius of the dilated circle is given as 18m

Therefore,

Length of new radius = 18m × scale factor.

If the scale factor is a fraction, it means the new length would be smaller than 18m. But if the scale factor is a whole number, the new length of the radius would be greater than 18m.

Let's assume any of the following scale factors was what was given in the question:

*If scale factor given is ½, new radius length = 18m × ½ = 9m

*If scale factor given is 2, new radius length = 18m × 2 = 36m

Answer:

a = 1500

b = 0.97

Step-by-step explanation:

The equation we are modeling is ;

F(x) = ab^x

Now we have two parameters to fix.

These are the density and the annual percentage increase

We can substitute the value of 1500 for a and also make a corresponding substitution for b.

Now for b, the value to substitute is quite dicey.

3% = 3/100 = 0.03

To make any substitution, we need to subtract this value from 1 and that would be 0.97

So it is this 0.97 that we now raise x to for each of the number of years

Answer:

Step-by-step explanation:

y=x²+3

vetex=(h,k) in the equation : ax²+bx+c

y=x²+3 ( a=1,b=0,c=0)

h=-b/2a=0

k=c=3

Answer:

D

Step-by-step explanation:

This is an illustration of Pythagoras' identity.

The square on the hypotenuse x of a right triangle is equal to the sum of the squares on the other 2 sides, that is

x² = 8² + 6² = 64 + 36 = 100 ( take the square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10 cm → D

Answer:

D. 10 cm

The answer is 10 cm. This can be found through the use of Pythagorean. Theorem because it is a right triangle and you are finding the hypotenuse.

HOPE THSI HELPS

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THANK YOU..

This question is incomplete. Please find attached to this solved question, the diagram required to solve this question.

Answer:

11 units

Step-by-step explanation:

The shaded portion of the rectangle forms the shape of a trapezium

The area of a trapezium = 1/2(a + b)h

From the diagram, we can see than x = b

a = 7 units

b = 7 units

Area of the trapezium = Area of the shaded portion = 63 square units

A = 1/2(a + b)h

63 = 1/2(7 + b)7

63 = 1/2(49 + 7b)

63 × 2 = 49 + 7b

126 - 49 = 7b

7b = 77

b = 77/7

b = 11 units

Since x = b, x = 11 units

The value of x is 11

Start by calculating the area (A) of the trapezoid using

[tex]A= 0.5 * (a + b)h[/tex]

Using the parameters from the complete question, we have:

[tex]63 = 0.5 * (7 + x) * 7[/tex]

Multiply both sides by 2

[tex]126 = (7 + x) * 7[/tex]

Divide both sides by 7

[tex]18 = 7 + x[/tex]

Subtract 7 from both sides

[tex]x = 11[/tex]

Hence, the value of x is 11

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