one positive integer is 2 less than another. The product of the two integers is 24. what are the two integers?

Answer:

1. ∠1 = 120°

2. ∠2 = 60°

3. ∠3 = 60°

4. ∠4 = 60°

5. ∠5 = 75°

6. ∠6 = 45°

Step-by-step explanation:

From the diagram, we have;

1. ∠1 and the 120° angle are corresponding angles

Corresponding angles are equal, therefore;

∠1 = 120°

2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;

∠2 + 120° = 180°

∠2 = 180° - 120° = 60°

∠2 = 60°

3. Angle ∠3 and ∠2 are vertically opposite angles

Vertically opposite angles are equal, therefore, we get;

∠3 = ∠2 = 60°

∠3 = 60°

4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;

∠1 + ∠4 = 180°

∠4 = 180° - ∠1

We have, ∠1 = 120°

∴ ∠4 = 180° - 120° = 60°

∠4 = 60°

5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6

Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;

x = y

The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles

∴ x + y + 90° = 180°

From x = y, we get;

y + y + 90° = 180°

2·y = 180° - 90° = 90°

y = 90°/2 = 45°

y = 45°

Therefore, we have;

∠4 + ∠5 + y = 180° (Angle sum property of a triangle)

∴ ∠5 = 180 - ∠4 - y

∠5 = 180° - 60° - 45° = 75°

∠5 = 75°

6. ∠6 and y are alternate angles, therefore;

∠6 = y = 45°

∠6 = 45°.

Answer:

Slope: 2/1 Y-Intercept: 1

Step-by-step explanation:

Mr. Pope decreased his weight by 4 percent.

A percentage is a portion of a whole thing written as a number between 0 and 100 instead of fraction.

Given that, Mr. pope lost 10 pounds in one month. At the end of the month, he weighed 240 pounds.

we need to find the percentage of decrease of his weight,

So, basically we will use here the concept of percentage change,

Formula = final amount - initial amount / initial amount x 100

Since, he lost 10 pounds and has 240 pounds so, initially he weighted = 240 + 10 = 250 pounds

So, percentage decreased = -10 / 250 x 100 = -4% [minus is the sign for decrease]

Hence, Mr. Pope decreased his weight by 4 percent.

Learn more about percentage, click;

https://brainly.com/question/29306119

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Answer:

C 61,705

Step-by-step explanation:

10.9% of 35,000 = 3,815

3,815 x 7 = 26,705  (interest is added per year and 3,815 is the interest amount)

35,000 + 26,705 = 61,705 ( the original loan plus the interest for 7 years)

Answer:

92

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

70+60 =130

180-130 = 50 degrees

Answer: 50

Step-by-step explanation: Every triangle is 180 degrees so add the 60 and the 70 to get 130. 180-130=50. So 50 is your answer.

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Pythagorus theorem,

here, the perpendicular height = 24 ft and the base = 10ft ,

hence then length of the ladder is the Hypotenuse.

so we get as,

[tex]l \: = \sqrt{ {24}^{2} + {10}^{2} } [/tex]

[tex]l \: = \sqrt{576 + 100} [/tex]

[tex]l \: = \sqrt{676} [/tex]

hence, l = 26 ft

so the length of the ladder is 26 feets.

Answer: 26

Step-by-step explanation:

The surface area of the right rectangular prism has a length of 7 m, a width of 8 m, and a height of 14 m, is 532 square meters.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

The figure below is a net for a right rectangular prism.

Then the surface area of the rectangular prism will be

Surface area = 2(LW + WH + HL)

Surface area = 2(7 × 8 + 8 × 14 + 14 × 7)

Surface area = 2(56 + 112 + 98)

Surface area = 2 × 266

Surface area = 532 square meters

More about the rectangular prism link is given below.

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Answer:

x = 10

Step-by-step explanation:

Answer:

C. 2x^2 + 3x - 1

is the answer

Answer:

I would choose A

Step-by-step explanation:

Answer:

The answer is "7.62 cm ".

Step-by-step explanation:

Given:

[tex]Width = 6\ cm \\\\Depth = 4 \ cm\\\\Vertical \ height = 7 \ cm\\\\[/tex]

Dividing the prism's face into two halves:

As just a result, the vertical height becomes 7cm, as well as the width, becomes [tex]\frac{6\ cm}{2} = 3 \ cm[/tex]. If the 's' on both sides of the edge is equal:

[tex]s^2 = width^2 + height^2\\\\[/tex]

   [tex]= \sqrt{(width^2 + height^2)}\\\\[/tex]  

   [tex]= \sqrt{(3^2 + 7^2)}\\\\= \sqrt{9 + 49}\\\\= \sqrt{58}\\\\= 7.62 \ cm[/tex]

Answer:

A) 5/7

Step-by-step explanation:

Equation:

-0.7n = -0.5

n = 5/7

Answer:

hope this helps you out good luck

Answer:

The left side

−

16

does not equal to the right side

−

7

, which means that the given statement is false.

False

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

9+6-31=-7 -16=-7

Answer:

a square can be a rectangle so I would think that the first and second option would be rectangles.

Step-by-step explanation:

I hope this helped sorry if not

Answer:

thus therefore thy answer musnt be 6 thus forth -3

Answer:

720 ft³

Step-by-step explanation:

volume is  length × width× height

2×20×18 = 720

Answer:

-4.515

Step-by-step explanation:

Answer:

u = 4

Step-by-step explanation:

Divide by 16 on both sides. [Division Property of Equality]

64/16 = 16u/16

u = 4

==================================================================Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

     -Aadi x

Answer:

8 in

Step-by-step explanation:

First of all we have to find the area of the base triangle.

For do this we can use this formula:

A = (base edge x base height)/2

A = (9 x 4)/2 = 18 in^2

The formula for find the volume of a pyramid is:

V= Base area x height)/3

So the height can be find in this way

3 x  V = base area x height

height = (3 x V)/base area

height = (3 x 48)/18 = 8 in

Answer:

pretty sure it is 8in I think

Answer:

He will have $5175.

Step-by-step explanation:

3% of 4500 is 135. 135x5=675. Add 675 to 4500 which equals 5175.

Answer:

56

Step-by-step explanation:

Answer:

7.03 ft/s

Step-by-step explanation:

To obtain speed using the model :

Speed = sqrt(gL)

L = Length of leg, g = acceleration due to gravity

Length of leg of a giraffe = 6.03

g = 9.8 m/s or 32 ft/s²

Speed of giraffe in ft/s = sqrt(32 * 6.03) = 13.89 ft/ s

Speed of coyote ; L = 0.46 m

L in feets = 0.46 * 3.23 = 1.4858 feets

s = sqrt(1.4858 * 32) = 6.895 ft/s = 6.86 ft/s

Difference in speed :

13.89 - 6.86 = 7.03 ft/s

Giraffe has 7.03ft/s more speed Than a coyote

Answer:

15m times 2m

Step-by-step explanation:

Answer:

There are two possible options: [tex]P(x,y) = (1, -6)[/tex] or [tex]P(x,y) = (3, -4)[/tex].

Step-by-step explanation:

There are two possible options depending on what the point of origin is. Vectorially speaking, we can determine the coordinates of the point that partitions the segment is described below:

[tex]P(x,y) = A(x,y) + r\cdot [B(x,y) - A(x,y)][/tex] (1)

Where:

[tex]A(x,y)[/tex] -  Point of origin.

[tex]B(x,y)[/tex] - Point of destination.

[tex]r[/tex] - Partition factor.

Option 1: [tex]A(x,y) = (-1, -8)[/tex], [tex]B(x,y) = (5, -2)[/tex], [tex]r = \frac{1}{3}[/tex]

[tex]P(x,y) = (-1, - 8) + \frac{1}{3}\cdot [(5,-2)-(-1,-8)][/tex]

[tex]P(x,y) = (-1, -8) + \frac{1}{3}\cdot (6,6)[/tex]

[tex]P(x,y) = (-1,-8) + (2,2)[/tex]

[tex]P(x,y) = (1, -6)[/tex]

Option 2: [tex]A(x,y) = (5,-2)[/tex], [tex]B(x,y) = (-1,-8)[/tex], [tex]r = \frac{1}{3}[/tex]

[tex]P(x,y) = (5,-2) + \frac{1}{3}\cdot [(-1,-8)-(5,-2)][/tex]

[tex]P(x,y) = (5,-2) +\frac{1}{3}\cdot (-6,-6)[/tex]

[tex]P(x,y) = (5,-2) +(-2,-2)[/tex]

[tex]P(x,y) = (3, -4)[/tex]

There are two possible options: [tex]P(x,y) = (1, -6)[/tex] or [tex]P(x,y) = (3, -4)[/tex].

Answer:

[tex] \bf \huge ± 5 [/tex]

Step-by-step explanation:

⟼ - x^ 2 - 8 = - 33

step 1 : add 8 to both sides

⟼ − x² − 8 + 8 = − 33 + 8

⟼ - x² = - 25

step 2 : Divide both sides by -1

⟼ - x² / - 1 = - 25 / - 1

⟼ x² = 25

step 3 : take square root

⟼ x² = 25

⟼ x = ± √25

⟼ x = ± 5

∴ x = ± 5.

Answer:

88 degrees.

Step-by-step explanation:

Since AB is equal to BC, ABC is an isosceles triangle. Therefore, the angle of B will be 180-39-39=102 degrees. As the angle of a straight line is 180 degrees, take 180-102-32=46 degrees. This 46 degrees is angle B. Since DEB is an isosceles triangle, 180-46-46=88 degrees. 88 degrees is angle E which is your answer. Edit: (Just added on the explanation.)