Can somebody help with number 5?

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

3 0

3 years ago

Find the product 9,361×7=

timofeeve [1]

Answer:

65,527

Thank you and please rate me as brainliest as it will help me to level up

5 0

3 years ago

Starbucks reports net income for 2015 of $2,634.4 million. Its stockholders' equity is $5,605 million and $6,151 million for 201

ExtremeBDS [4]

Answer:

A. 44.82%

B.

Option b. Return On Equity usually increases since the repurchase of shares reduces the denominator (avg. stockholders' equity)

C.

Option b. The Companies would tend to repurchase their own stock if they feel the stock is been undervalued by the market

Step-by-step explanation:

a. Computation for return on equity for 2015

Using this formula

Return on equity = The Net income amount /The Average stockholders' equity amount

Let plug in the formula

Return on equity=2,634.4/[(5,605+6,151)/2]

Return on equity=2,634.4/(11,756/2)

Return on equity=2,634.4/5,878

Return on equity=0.4482×100

Return on equity= 44.82%

b. In a situation where they repurchased over $1.4 billion of its common stock in the year 2015 this means that the RETURN ON EQUITY will usually tend to increases reason been that the repurchase of shares will often reduces the denominator (average stockholders' equity)

Therefore the repurchase increase Starbucks’ Return On Equity.

c. In a situation where Starbucks had not repurchased common stock in the year 2015, what their Return On Equity would have been is that they will repurchase their own stock if they feel the stock is been undervalued by the market

6 0

3 years ago

Is this right ? Im honestly confused

fgiga [73]

Answer:

In step by step

Step-by-step explanation:

For #1, everything is perfect.

For #2, you wrote your functions out incorrectly, but your x input and y output are correct

#3 is a little messed up.

Your function is f(x)=-3x+1. Your given x's are -3, -1, 0, 1, 2, and 3. Plug all of these in.

1. f(-3)=-3(-3)+1

f(-3)=9+1
f(-3)=1

2. f(-1)=-3(-1)+1

f(-1)=3+1
f(-1)=4

3. f(0)=-3(0)+1

f(0)=0+1
f(0)=1

4. f(1)=-3(1)+1

f(1)=-3+1
f(1)=-3

5. f(2)=-3(2)+1

f(2)=-6+1
f(2)=-5

3 0

2 years ago

Can you please explain to me what the end behavior of the function f(x)=-2x^4-x^3+3 looks like?

Artist 52 [7]

The dominant term is -2x⁴.

As X approaches infinite, y is naturally going to be really large as well.

Remember that a number with an even exponent, regardless of whether it's positive or negative, will be positive.
As x approaches infinite, y will approach -2 * ∞, or -∞. Therefore, the end behavior in the positive direction is y=-∞
As x approaches negative infinite, y will approach -2 *∞ again. This is because -∞⁴ = ∞. Therefore, the end behavior in the negative direction is also y=-∞

Basically, due to the dominance of the -2x^4 term, the function will look more or less like a downward facing parabola with a y-intercept of 3.

7 0

2 years ago