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Crank
2 years ago
5

Simplify and find the perimeter of the triangle

Mathematics
2 answers:
lbvjy [14]2 years ago
7 0

Answer:

2x - 19

Step-by-step explanation:

Perimeter = sum of sides

First let's simplify each side

We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.

2(x + 5)

Distribute by multiplying x and 5 by 2

2 * x = 2x and 2 * 5 = 10

2x + 10

1/2(4x + 8)

Distribute by multiplying 4x and 8 by 1/2

1/2 * 4x = 2x and 1/2 * 8 = 4

2x + 4

-3(2x + 11)

Distribute by multiplying 2x and 11 by -3

-3 * 2x = -6x

-3 * -33

-6x - 33

Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )

2x + 10 + 2x + 4 - 6x - 33

Combine like terms

2x + 2x - 6x = -2x

10 + 4 - 33 = -19

Perimeter: -2x - 19

Novay_Z [31]2 years ago
3 0

Answer:

Perimeter = - 2x - 19

Step-by-step explanation:

Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\  = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x)  + ( \frac{1}{2}  \times 8)] \\  = (2x + 10) + ( - 6x - 33) + (2x + 4) \\  = 2x + 10  - 6x - 33 + 2x + 4 \\  = 2x - 6x + 2x + 10 - 33 + 4 \\  =  - 2x - 19

So, the perimeter is - 2x - 19.

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Previously 5% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of
mr Goodwill [35]

Answer:

p value = 0.03514

Step-by-step explanation:

Hypotheses would be

H_0: p = 0.05\\H_a: p

(left tailed test at 10% level of significance)

Here p stands for the sample proportion of mothers smoked more than 21 cigarettes during their pregnancy.

Sample size =130

persons who smoked = 2

Sample proportion = \frac{2}{130} \\=0.0154

Assuming H0 to be true

Std error= \sqrt{0.05*0.95/130} \\=0.01911

p difference = -0.0346

Test statistic z=-1.81

p value = 0.03514

Since p is less than 0.10, significance level, we reject H0

4 0
3 years ago
A. Lin is using the diagram to prove the statement, "If a parallelogram has one
BigorU [14]

The congruence of the angles and triangles are proven as follows;

a. The composition angles of FGH are alternate interior angles to the composition angles of angle AHEF

b. The three sides of triangle ∆EHG are congruent to the three sides of triangle ∆GFE, therefore, triangles ∆EHG and ∆GFE are congruent by SSS congruency rule

<h3>What are congruent triangles?</h3>

The lengths of the three sides of triangles that are congruent.

a. The shape of quadrilateral EFGH = A parallelogram

The measure of angle HEF = 90°

Angle HEF = 90°

Angle HEF = Angle HED + Angle DEF

Angle HED is congruent to angle FGD (Alternate interior angles theorem)

Angle HED = angle FGD

Angle DEF is congruent to angle DGH (Alternate interior angles theorem)

Angle DEF = angle DGH

Angle FGH = Angle FGD + Angle DGH

Angle FGH = Angle HED + Angle DEF (Substitution property)

Angle FGH = Angle HEF (Transitive property)

Angle FGH = Angle HEF = 90°

Therefore, the statement that will help prove angle FGH is also a right is that angle FGH is the sum of angles FGD and angle DGH which are alternate interior angles to angles HED and DEF which makes up angle HEF, which is a right angle.

b. The two-column method can be used to prove that triangle EHG and triangle GFE are congruent as follows;

Statement. Reason

EF is congruent to HG. Opposite sides of a parallelogram are congruent

EH is congruent FG Opposite sides of a parallelogram are congruent

EG is congruent to EG Reflexive property of congruency

∆EHG is cong. to ∆GFE SSS, Side-Side-Side, congruency rule

Learn more about the triangle congruency rules here:

brainly.com/question/15338506

#SPJ1

4 0
1 year ago
HELP ASAP!!! IM BEING TIMED. Use synthetic division to test one potential root. Enter the numbers that complete the division pro
Diano4ka-milaya [45]

Step-by-step explanation:

1 * (-5) = -5     a = -5

6 + (-5) = 1      b = 1

1 * (-5 ) = -5     c = -5

-7 + -5 = -12     d = -12

3 0
3 years ago
Read 2 more answers
Ha: μ ≠ 30 we know that the sample standard deviation is 10 and the sample size is 70. for what sample mean would the p-value be
Andrew [12]

From the given problem the same size is n = 70. Df = n – 1 = 70 – 1 = 69.

The population mean is u = 30, sample standard deviation is s = 10 and the sample size is n = 70. Then,

t = x – u / s sqrt of n

1.995 = x – 30 / (10 sqrt of 70)

1.995 = x – 30 / 1.1952

X – 30 = 1.995 (1.1952)

X – 30 = 2.3844

X = 30 + 2.3844

X = 32.3844

 

The sample mean is 32.3844

<span> </span>

3 0
3 years ago
What is 8×9=?<br> ?-2=70.
Nonamiya [84]

Answer:

? = 72

Step-by-step explanation:

8x9= 72

And...

72-2 = 70

Brainiest?

6 0
3 years ago
Read 2 more answers
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