A pair of parallel lines is cut by a transversal:

A pair of parallel lines cut by a transversal is shown. The inside bottom right angle is labeled 85 degrees. The alternate interior angle is cut by a ray and is labeled as x on one side and 25 degrees on the other.

What is the measure of angle x?

50 degrees
55 degrees
60 degrees
80 degrees

Answer:

The ratio of sides of triangle = 13:14:15

perimeter = 84 CM

perimeter of a triangle = Sum of all sides

let the sides of a triangle be 13x, 14x and 15x

84 = 13x + 14x + 15x

84 = 42x

x = 2

13x = 13* 2 = 26 CM

14x = 14*2 = 28 CM

15x = 15*2 = 30 CM

Answer:

-12x²-25x+13

Step-by-step explanation:

First open parenthesis.

(3 − 13x − 7x²) − (5x² + 12x − 10)

3 − 13x − 7x² − 5x² - 12x + 10

Now combine like terms.

3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²

Now put into standard form, exponents greatest to least.

-12x²-25x+13

Hope this helps!

If not, I am sorry.

Answer:-12x²-25x+13

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

First take the equation and subtract 19 on both sides. You get x^2+8x-20=0

using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)

simplify it and you get x= (-8 +or- 12) / 2  

Separate the equation into two and you get (-8 + 12) / 2    and (-8 - 12) / 2

first one gives: 4/2=2

second gives -20/2=-10

answer x=-10,2

Answer:

All answers are correct.

Step-by-step explanation:

A. 1.84 is between 1.74 and 1.84.

B. 1.84 < 1.85. Lower values go to the left.

C. 1.84 > 1.83. Higher values go to the right.

D. 1.84 is between 1.0 and 2.0.

The figure is given in the below diagram.

The steps of constructing a square inside a circle are as follows:

Start from the middle O of the provided circle.

Finding the center of a circle's approach can be used to create the center of the circle's center point is not known.

1. Draw a circle and label point A. This will turn into one of the square's vertices.

2. Create point C by drawing a diameter line from point A through the center and back out to the outside of the circle.

3. Set the width of the compass to a little bit more than the distance to O.

4. Sketch an arc above and under O.

5. Repeat by moving the compass to C.

6. To create the new points B and D, draw a line across the intersection of the arc pairs that is long enough to touch the circle at both the top and bottom.

This diameter is perpendicular to the first AC.

7. Draw a line connecting each pair of points A, B, C, and D.

Done. The circle is circled by the square ABCD.

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Answer: (2,9)

Step-by-step explanation:

It lies in the region that is shaded both red and blue (representing the fact that it satisfies both inequalities).

Answer:

D. 0 < x < 20

Explanation:

Domain is in the x axis, Range lies in the y axis.

Here it is seen that function's domain lies between 0 to 20.

Here, as the circle's are open. Domain: 0 < x < 20

Additionally,

Answer:

The dog is 16 years old.

Step-by-step explanation:

X/4 + 6 = X/8 + 8

X/4-X/8 = 8-6

0.125X = 2

X = 2/0.125

X = 16

Answer:

16 years old

Step-by-step explanation

Dividing the dog’s age by 4 and adding 6

D÷4  + 6

dividing the dog’s age by 8 and adding 8

D÷8  + 8

equating both

D÷4  + 6 = D÷8 + 8

=> D÷4 - D÷8  = 2

multiplying by 8 both sides

=> 2D - D = 16

=> D = 16

hence, the dog is 16 years old

Considering the given histogram, the mean of the data-set is closest to:

B. 5.

An histogram is a graph that shows the number of times each element of x was observed.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, considering the histogram, the mean is given by:

M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.

Which is closest to 5, hence option B is correct.

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The boat's travel from when it was first noticed until it stopped is 554.89 ft.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB =  753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

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Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Solve the equation for y=0

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

Y coordinate

Verted at (4,-4)

I assume you meant r(x) = |x-2| -1.

(i) The area of the cross section ABCDEFG is 1771.6cm³

(ii) The volume of the concrete lab is 212592 cm³

(iii) the total surface area of the concrete slab is 30284 cm²

(iv) The mass of the concrete slab is 40746.8 kg/m³.

Given, dimensions are 120 cm by 60 cm by

40 cm.

(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2

                                     = 1771.6 cm³

(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10   ₋10)/2)² . 120

= 212592 cm³

(iii) The total surface area is:

=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120

= 30284 cm²

(iv) Mass of the concrete slab given density is 2300 kg/m³

Mass = Volume × density

Mass = 17.716 m³ ×  2300

         = 40746.8 kg/m³

Hence we get the mass as 40746.8 kg/m³.

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Answer:

the cost price is Rs. 4500 and the sale price is Rs. 5040.

Step-by-step explanation:

Let the cost price of the compute be Rs. x.

The profit earned is, Rs. 540.

The profit percentage is, 12%.

The formula to compute profit is:

Profit = SP - CP

\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500

Compute the selling price as follows:

SP = CP + profit

     = 4500 + 540

     = 5040

Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.

Answer:

Slope =  - 1

Step-by-step explanation:

The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex]  is the intercept on [tex]y[/tex] axis.

Hence, in [tex]y=-x+3[/tex] , slope is -1  and intercept on [tex]y[/tex] axis is 3.

The simplified radical for the given equation is 2√3.

The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

[tex]\frac{3}{x} =\frac{x}{4}[/tex]

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Answer:

3) r = 1.5

7) y = 18

11) x = -10

Step-by-step explanation:

3) Isolate the variable by dividing each side by factors that don't contain the variable.

7) Solve for y by simplifying both sides of the equation, then isolating the variable.

11) Move all terms that don't contain x to the right side and solve.

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

A polynomial is a mathematical expression consisting of variables , constants and mathematical operators.

The standard form of a polynomial is

[tex]\rm a_1x^n +a_2x^{n-1}+............+a_0[/tex]

The only equation that is in its standard form or in other words

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

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Answer: [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

perpendicular = opposite recipricol

-3 = [tex]\frac{1}{3}[/tex]

switch the sign and flip it (3/1 => 1/3)

Step-by-step explanation:

[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]

Hope it helps

Z – 6 < 3

Z < 3 + 6

Z < 9

Answer:

x=3.5

Step-by-step explanation:

x × 2 = 7

   ÷2     ÷2

    x=3.5

Answer:

d=8t

Step-by-step explanation:

Answer: x

Step-by-step explanation:

    For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.

Answer: f(-2) = 8

Step-by-step explanation: On the graph there’s a point (-2,8), so f(-2), which just means -2’s y value on the graph, is 8.

The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.

Let the age of Kwaku is x

Let the age of Esi is y

From the given data

The age of Kojo is 2y

y = x +5

Sum of their age = 47

2y = 2x +10

therefore the equation formed is

x + y +2y = 47

x + x+5 + 2x +10 = 47

4x +15 = 47

4x = 32

x = 8

y = 13

2y = 26

Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

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Answer:

x > 9

Step-by-step explanation:

for this inequality, we want to isolate x, so that we know the inequality of x

5x + 3 > 48

     - 3      -3        {subtract 3 from both sides to get x alone}

5x > 45

/5      /5                {divide both sides by 5 to find 1x}

x > 9

So , x > 9 is the inequality in terms of x {is the solution}

hope this helps! :)

Answer:

[tex]\huge\boxed{\sf x > 9}[/tex]

Step-by-step explanation:

5x + 3 > 48

Subtract 3 to both sides

5x > 48 - 3

5x > 45

Divide 5 to both sides

x > 9

[tex]\rule[225]{225}{2}[/tex]

Answer:

Distance between A and C = 16km

Bearing of A from C = 257°

Step-by-step explanation:

please see photo for detailed analysis