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Rom4ik [11]
3 years ago
10

(x+10)°+(2x+20)°=180°. For what value of X is the quadrilateral a parallelogram?​

Mathematics
1 answer:
egoroff_w [7]3 years ago
3 0

Answer: X = 50

Step-by-step explanation: We shall first solve for X in the algebraic expression as follows ;

(X + 10) + (2X + 20) = 180

By removing brackets and collecting like terms we now have

X + 2X + 10 + 20 = 180

3X + 30 = 180

Subtract 30 from both sides of the equation

3X = 150

X = 50

If X has been identified as equal to 50, then the two angles given shall be

Angle 1 = X + 10

Angle 1 = 50 + 10

Angle 1 = 60

Also

Angle 2= 2X + 20

Angle 2 = 2(50) + 20

Angle 2 = 100 + 20

Angle 2 = 120

One of the properties of a parallelogram is, “Opposite angles are congruent.”

The other two angles would also measure 60 and 120, and the sum of all the interior angles shall be;

60 + 120 + 60 + 120 = 360

360 = 360.

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Answer/Step-by-step explanation:

Let's solve your equation step-by-step.

4−(2y+5)=3(1−4y)

Step 1: Simplify both sides of the equation.

4−(2y+5)=3(1−4y)

4+−1(2y+5)=3(1−4y)(Distribute the Negative Sign)

4+−1(2y)+(−1)(5)=3(1−4y)

4+−2y+−5=3(1−4y)

4+−2y+−5=(3)(1)+(3)(−4y)(Distribute)

4+−2y+−5=3+−12y

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−2y+−1=−12y+3

−2y−1=−12y+3

Step 2: Add 12y to both sides.

−2y−1+12y=−12y+3+12y

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10y−1+1=3+1

10y=4

Step 4: Divide both sides by 10.

10y

10

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Item (D)

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In the stratified random sample we would divide our population into homogeneous groups / strata and then  we randomly select the individuals in each group / stratum.

In general, when comparing with the simple  random sample, we realize that stratified random sampling has the advantage of increasing accuracy and decreasing  variability.

In the question, we have two strata: female students and male students. On each one of the  strata, a random sample of 25 names was made in the list.

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The accompanying data on x= head circumference z score (a comparison score with peers of the same age - a positive score suggest
djverab [1.8K]

Answer:

r=0.77, \hat{y}=770.50+39.37x and volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.9 is  \hat {y}=920.10

Step-by-step explanation:

We attached a table below,

(a)  We attached a table below,

Therefore ,

correlation coefficient  r=\frac{\frac{1}{18}(21766.7)-(\frac{27.25}{18} )(\frac{13890}{18} ) }{\sqrt{\frac{1}{18} (59.8435)-(\frac{27.25}{18} )^2}\sqrt{\frac{1}{18}(10767400)-(\frac{13890}{18} )^2 }  }

                                         =\frac{41.04}{53.19}

                                         =0.77

(b)    We calculate the least squares equation.

      b_1=r(\frac{\sigma_y}{\sigma_x} )\\      =(0.77)(\frac{\sqrt{\frac{1}{18} (10767400)-(\frac{13890}{18} )^2} }{\sqrt{\frac{1}{18}(59.8435)-(\frac{27.25}{18} )^2 } } )\\      =0.77(\frac{52.15}{1.02} )\\      =0.77(51.13)\\      =39.37

Now , calculate intercept coefficient.

b_0=\bar{y}-r\bar{x}\\

    =(\frac{\sum{y}}{n} )-0.77(\frac{\sum{x}}{n} )\\=(\frac{13890}{18} )-0.77(\frac{27.25}{18} )\\=771.67-1.17\\=770.50

Therefore, the regression equation is, \hat{y}=770.50+39.37x

(c)    Find the volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.8

\hat{y}=770.50+39.37x

   =770.50+39.37(1.9)\\=770.50+74.80\\=920.10

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