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3 years ago

Only Question #5! If JKLM is a rectangle, find Measure NML

Mathematics

1 answer:

Allushta [10]3 years ago

8 0

Answer;

5. 22°

6. 74°

Step-by-step explanation:

5. Since rectangle JKLM has two equal diagonals that intersect each other, therefore JN = MN.

If JN = MN therefore:

m<NMJ = m<NJM

Thus:

3x + 38 = 7x - 2

Solve for x. Collect like terms

3x - 7x = -38 - 2

-4x = - 40

Divide both sides by -4

x = 10

✔️Find m<NMJ

m<NMJ = 7x - 2

Plug in the value of x

m<NMJ = 7(10) - 2 = 70 - 2

m<NMJ = 68°

✔️Find m<NML;

m<NML = 90 - 68° (Complimentary angles)

m<NML = 22°

6. Diagonal of a rhombus bisects teach vertex angle, this means that <U is divided into two equal parts. Therefore:

10x - 23 = 3x + 19

Solve for x. Collect like terms

10x - 3x = 23 + 19

7x = 42

Divide both sides by 7

x = 6

✔️Find m<RST:

m<SUT = m<RST (opposite angles of a rhombus are congruent)

Thus,

m<SUT = (10x - 23) + (3x + 19)

Plug in the value of x

m<SUT = (10(6) - 23) + (3(6) + 19)

= (60 - 23) + (18 + 19)

= 37 + 37

m<SUT = 74°

Also, m<RST = 74°

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20 cm × 40 cm

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The area formula of a circle is:
$\pi$ r²
The diameter of the plate is 20cm
so the radius is half the diameter which is 10cm
Apply the given to the formula:
$\pi$ (10)²
100 $\pi$
314.16 cm²

2 plates in the bottom drawer
Area of two plates:
2 × 314.16
628.32 cm²

Area of the non-covered space in the bottom drawer:
Area of drawer - area of two plates
800 - 628.32
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3 years ago

The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 co

Lapatulllka [165]

Answer:

<h2>The demand at a price of $1.50 per cone is 44 cones</h2>

Step-by-step explanation:

let us apply the interpolation formula to solve this problem

we have

$\frac{y-y1}{x-x1} =\frac{y2-y1}{x2-x1}$

Now let us set the values to the notation above

x= $1.20

x1= $2.20

x2= $1.50

y = 50 cones

y1= 30 cones

y2= ?

$y2= \frac{(y-y1)}{(x-x1)} (x2-x1)+y1$

Substituting our given data we have

$y2= \frac{(50-30)}{(1.2-2.2)} (1.5-2.2)+30\\\\y2= \frac{20}{-1} (-0.7)+30\\\\y2= (20*0.7)+30\\y2= 14+30\\y2= 44$

the demand at a price of $1.50 per cone is 44 cones

4 0

3 years ago

4 Consider the triangle below.

Maurinko [17]

<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

$= \tt x + 1.4 = 2x + 0.1$

$= \tt x + 1.4 - 0.1 = 2x$

$= \tt \: x + 1.3 = 2x$

$= \tt 1.3 = 2x - x$

$\color{plum} \hookrightarrow \tt x = 1.3$

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

$= \tt x + 1.4$

$= \tt 1.3 + 1.4$

$\color{plum} \tt leg \: AM= 2.7 \: inches$

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

$= \tt 2x + 0.1$

$= \tt2 \times 1.3 + 0.1$

$= \tt 2.6 + 0.1$

$\color{plum} \tt\: leg \:MG = 2.7 \: inches$

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

$= \tt 3x - 0.4$

$= \tt 3 \times 1.3 - 0.4$

$= \tt 3.9 - 0.4$

$\color{plum}\tt \: Base \: AG = 3.5 \: inches$

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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3 years ago

Which statements are true about these lines? Select three options.

shepuryov [24]

RS is perpendicular to MN and PQ.

We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=.

Using the coordinates for M and N, we have:
m=.

Since PQ is parallel to MN, its slope will be as well, since parallel lines have the same slope.

Using the coordinates for points T and V in the slope formula, we have
m=.

This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.

Using the coordinates for R and S in the slope formula, we have
m=. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.

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3 years ago

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Which statement best describes parallel lines?

Margaret [11]

Answer:

Step-by-step explanation:

Parallel lines have identical slopes and different y intercepts.

y = 3x + 2

y = 3x + 9

These lines are parallel with the same slopes (3) and different y intercepts (2 and 9)

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