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3 years ago

Given: m∠p =47BD∥AC What is the m∠m? Put only the number. Do not label your answer.

Mathematics

1 answer:

Anettt [7]3 years ago

3 0

Answer: $43\°$

Step-by-step explanation:

Observe the given figure.

You can identify that the measure of the angle "B" is:

$m\angle B=90\°$

Knowing this, you can conclude that the angle "p" and the angle "m" are Complementary angles, which means that the sum of their measures is 90 degrees. Then, you can write the following equation:

$m\angle p+m\angle m=90\°$ [Equation 1]

You know that:

$m\angle p=47\°$

Then you can substitute it into the [Equation 1] and then solve for $m\angle m$ . Therefore, you get:

$47\°+m\angle m=90\°\\\\m\angle m=90\°-47\°\\\\m\angle m=43\°$

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2 years ago

The ratio of cats to dogs in the shelter is 2:3. If there are 8 cats, how many dogs are there?

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1 year ago

Read 2 more answers

when asked to write a point slope equation for a line passing through the points (-3,-5) and (2,4) a student wrote y-4=-9/5(x-2)

Eduardwww [97]

(-3,-5)(2,4)
slope(m) = (4 - (-5) / (2 - (-3) = (4 + 5) / (2 + 3) = 9/5

y - y1 = m(x - x1)
slope(m) = 9/5
(2,4)...x1 = 2 and y1 = 4
sub
y - 4 = 9/5(x - 1)....this is the correct answer

the student figured the slope wrong....it is 9/5...not -9/5

5 0

3 years ago

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

Give the solution set for the inequality<br> 7x < 7(x - 2) in interval notation.

eduard

<u>ANSWER:</u>

The solution set for the inequality 7x < 7(x - 2) is null set $\varnothing$

<u>SOLUTION:</u>

Given, inequality expression is 7x < 7 × (x – 2)

We have to give the solution set for above inequality expression in the interval notation form.

Now, let us solve the inequality expression for x.

Then, 7x < 7 × (x – 2)

7x < 7 × x – 2 × 7

7x < 7x – 14

7x – (7x – 14) < 0

7x – 7x + 14 < 0

0 + 14 < 0

14 < 0

Which is false, so there exists no solution for x which can satisfy the given equation.

So, the interval solution for given inequality will be null set

Hence, the solution set is $\varnothing$

3 0

4 years ago