If f(x) = 2x2 + 1, what is f(x) when x = 3?.

In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.

In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:

80 + 2x = 180

Subtract 80 from both sides of the equation.

2x = 100

Divide both sides by 2.

x = 50

This means that angle F and angle H in ∆FDH both measure 50°.

Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.

First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.

**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**

In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:

Angle DHF + Angle DHG = 180°

50° + Angle DHG = 180°.

Angle DHG = 130°.

Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:

130 + 2x = 180

2x = 50

x = 25

The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.

Solution: 25°

8 0

3 years ago

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Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq

TiliK225 [7]

Answer:

The perimeter of rectangle is $18\ cm$

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

$x=y+5$ ----> equation A

$120=xy+2x^{2}+2y^{2}$ ---> equation B (area of the constructed figure)

substitute the equation A in equation B

$120=(y+5)y+2(y+5)^{2}+2y^{2}$

$120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0$

using a graphing calculator -----> solve the quadratic equation

The solution is

$y=2\ cm$

Find the value of x

$x=y+5 ----> x=2+5=7\ cm$

Find the perimeter of rectangle

$P=2(x+y)=2(7+2)=18\ cm$

4 0

3 years ago

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8,902 to the nearest thousand

7nadin3 [17]

Answer:

9,000

Step-by-step explanation:

5 0

3 years ago

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In how many ways can a

swat32

Answer:

720

Step-by-step explanation:

Using the equation given

$\frac{6!}{(6-6)!}=\frac{6!}{0!}=\frac{6!}{1}=720$

3 0

2 years ago

Statistics endeavors to: Choose one • 10 points a. Calculate means b. Make correlations c. To be used by experts d. All of the a

Daniel [21]

Answer:

d. All of the above

Step-by-step explanation:

a. Statistics provides the tool to measure the central tendency of a given data. One of such measure is the statistical mean popularly referred to as the mean.

b. The correlation between variables can be determined by the use of statistical tools. correlation is the degree to linearity between variables,

c. Experts in different fields from Accounting to Zoology make use of statistics in their analysis.

From the above analysis, it can be safely concluded that all of the above (i.e. option d.) is correct.

3 0

3 years ago