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Luba_88 [7]
2 years ago
14

Find the values of the variables and the measures of the angles

Mathematics
2 answers:
yuradex [85]2 years ago
8 0

Answer:

x = 13

39° and 51°

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

This is a right angle triangle, so one side has a size of 90 degrees.

3x + 4x - 1 + 90 = 180

7x + 89 = 180

7x = 91

x = 91/7

x = 13

Put x as 13 to work out the size of the angles.

3(13) = 39

4(13) - 1

52 - 1 = 51

Tems11 [23]2 years ago
6 0

Answer:

x = 13 \\

Measure of the angles

39 \:  \: degrees \\ 51 \:  \: degrees

Step-by-step explanation:

<em>sum</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>interior</em><em> </em><em>angles</em><em> </em><em>in</em><em> </em><em>a</em><em> </em><em>triangle</em><em>=</em><em> </em><em>1</em><em>8</em><em>0</em><em>°</em>

<em>3x + 4x - 1 + 90 =1 80 \\ 7x + 89 =1 80 \\ 7x = 180 - 89 \\ 7x =9 1 \\  \frac{7x}{7}  =  \frac{91}{7}  \\ x = 13</em>

<em>x</em><em> </em><em>=</em><em> </em><em>1</em><em>3</em><em>,</em>

<em> </em><em>now</em><em> </em><em>lets</em><em> </em><em>work</em><em> </em><em>out</em><em> </em><em>for</em><em> </em><em>the</em><em> </em><em>angles</em>

<em>3x \\ 3 \times 13 \\  = 39</em>

<em>4x - 1 \\ 4 \times 13 - 1 \\ 52 - 1 \\  = 51</em>

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Step-by-step explanation:

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Answer:

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3 years ago
The difference between the areas of the figures is less than 4.
coldgirl [10]

Answer:

1. |40 – 4x| < 4

2. 9 < x < 11

Step-by-step explanation:

We'll begin by calculating the area of each figure. This can be obtained as follow:

For triangle:

Area = ½ × base × height

Base = 8

Height = 6

Area =?

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For Rectangle:

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Summary:

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

1. Writing an absolute value for the inequality.

From the question given above, we were told that the difference between the areas of the figures is less than 4. This can be written as:

Aₜ – Aᵣ < 4

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

24 – (4x – 16) < 4

Simplify

24 – (4x – 16) < 4

Clear bracket

24 – 4x + 16 < 4

24 + 16 – 4x < 4

40 – 4x < 4

Thus, we can write the absolute value for the above inequality as:

|40 – 4x| < 4

2. Determination of the solution of the inequality.

This is illustrated below:

|40 – 4x| < 4

Thus the above equation can be written as

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Subtract 40 from both side

– 4 – 40 < 40 – 4x – 40 < 4 –40

– 44 < – 4x < – 36

Divide through by –4

– 44/–4 < x < – 36/–4

11 > x > 9

Note: the inequality sign changed because we divided by a negative number

Thus, 11 > x > 9 becomes 9 < x < 11

Therefore, the solution to the inequality is 9 < x < 11

3 0
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Answer:

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Step-by-step explanation

when multiplying fractions, you just multiply straight across.

so youd do the numerator (7*4=28) then the denominator (8*9=72)

so then youd have 28/72 which can be reduced to 7/18

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Because 3 is less than or equal to 4, you would round down, it would be 33. I am talking about the three(s) after the decimal.
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