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Black_prince [1.1K]
3 years ago
5

If m∠5 =53° and m∠7 =125° , find the measures of each numbered angle.Then explain how u found each angle,citing definitions and

conjectures that support your steps.

Mathematics
1 answer:
bija089 [108]3 years ago
4 0
#5 = 53° #7 = 125° #6 = 55° #2 = 72° #3 = 55° #1 = 53° #4 = 127°

triangle = 180°
alternating interior angles are the same (#6 & #3 and #5 and #1)
#3 and #7 should equal 180°
#1 and #4 should also equal 180°
#6 and #7 should equal 180°
#4 and #5 should equal 180°
You might be interested in
the length of a rectangle is 5 units longer than its width. If the perimeter must be at least 34 units, what are the possible le
ololo11 [35]

Answer:

w ≥ 6

l ≥ 11

Step-by-step explanation:

The perimeter of a rectangle is equal to P = 2l+2w where l=length and w=width. Here the length is 5 feet longer than the width or 5+w. This means the width is w. Substitute P = 34, l=5+w and w into the perimeter equation. Then solve for w.

34 ≤ 2*(5+w) + 2w

34 ≤ 10+2w+2w

34 ≤ 10+4w

24 ≤ 4w

6 ≤ w

This means the width must be at least 6 so the solution is w ≥ 6.

To find the length substitute 6 into l ≤ 5+w.

l ≤ 5 + 6

l ≤ 11

The length is l ≥ 11.

6 0
3 years ago
The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².
SCORPION-xisa [38]
A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
A = 42 m^2
4 0
3 years ago
Lost as usual yep I am
denpristay [2]

Answer:

  y = -3x -4

Step-by-step explanation:

A perpendicular line has a slope that is the negative reciprocal of that of the given line. When the equation starts out in standard form, a line with negative reciprocal slope can be written by swapping the x- and y-coefficients and negating one of them.

The given x- and y-coefficients have the ratio 1:-3, so we can use the coefficients 3 and 1 for our purpose.

The usual process of making the line go through a given point can be used. That is, we can translate the line from the origin to the desired point by subtracting the point coordinates from x and y. Then we have ...

  3(x+3) +(y-5) = 0

__

This is "an" equation. It is in no particularly recognizable form. It can be rearranged to the form y = mx + b:

  3x +9 +y -5 = 0 . . . . . eliminate parentheses

  y = -3x -4 . . . . . subtract terms that are not "y"

8 0
3 years ago
Read 2 more answers
Solve the System of Equations
soldi70 [24.7K]

Answer:

Equations: x+y=80\,,\,2x+4y=216\,\,

number of chickens = 52

number of goats = 28

Step-by-step explanation:

Given: A small ranch has chickens and goats

Total number of heads = 80

Total number of legs = 216

To find: number of chickens and goats

To draw: the graph

Solution:

Let x denotes number of chickens and y denotes number of goats.

According to the question,

x+y=80\,\,(i)\\2x+4y=216\,\,(ii)

From (i), put x=80-y in (ii)

2(80-y)+4y=216\\160-2y+4y=216\\2y=216-180\\2y=56\\y=\frac{56}{2}=28

Put y=28 in equation (i)

x+28=80\\x=80-28=52

So,

number of chickens = 52

number of goats = 28

Download pptx
6 0
3 years ago
Joseph wants to buy a new tennis racquet which cost $200 from the factory. The sports shop marks up the price by 60%. Joseph bou
andriy [413]
Use multipliers:
The normal price the shop would sell the racquet for is:
1.6 * 200 = 320
'1.6' is the multiplier that I got using the percentage. Multiplying a value by 1.6 is the same as increasing the value by 60%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the question, now we can use the multiplier 0.75 because we are are reducing the price by 25% (0.25 as a decimal), so:
320 * 0.75 = 240
And now we want just the profit so we take off how much it cost the shop to buy ($200): 240 - 200 = 40
5 0
3 years ago
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