Winston ate 77 out of g gumdrops. Write an expression that shows how many gumdrops Winston has left.

Answer:

The remaining side and angles are [tex]a = 20\sqrt{3}[/tex], [tex]\angle A = 60^{\circ}[/tex] and [tex]\angle B = 30^{\circ}[/tex].

Step-by-step explanation:

According to the information given on statement, we are in front of a right triangle because [tex]\angle C[/tex], opossite to side [tex]c[/tex], is a right angle. Hence, [tex]c[/tex] is the hypotenuse of the right triangle and [tex]b[/tex], a leg. The missing length can be calculated by the Pythagorean Theorem:

[tex]a = \sqrt{c^{2}-b^{2}}[/tex] (1)

If we know that [tex]c = 40[/tex] and [tex]b = 20[/tex], then the length of the missing leg is:

[tex]a = \sqrt{c^{2}-b^{2}}[/tex]

[tex]a = 20\sqrt{3}[/tex]

Lastly, we find the value of the missing angles by means of direct and inverse trigonometric relations:

Angle A

[tex]\angle A = \tan^{-1}\left(\frac{a}{b} \right)[/tex] (2)

Angle B

[tex]\angle B = \tan^{-1} \left(\frac{b}{a} \right)[/tex] (3)

If we know that [tex]a = 20\sqrt{3}[/tex] and [tex]b = 20[/tex], then the values of the missing angles are, respectively:

Angle A

[tex]\angle A = \tan^{-1}\left(\frac{a}{b} \right)[/tex]

[tex]\angle A = 60^{\circ}[/tex]

Angle B

[tex]\angle B = \tan^{-1} \left(\frac{b}{a} \right)[/tex]

[tex]\angle B = 30^{\circ}[/tex]

The remaining side and angles are [tex]a = 20\sqrt{3}[/tex], [tex]\angle A = 60^{\circ}[/tex] and [tex]\angle B = 30^{\circ}[/tex].

Answer and Step-by-step explanation:

1.

First, move all the points of the triangle to the right by 4 units. After, move all the points of the triangle down by 4 units.

2. For all of the x-values, make them negative since we are going across the y-axis. The Y-values will be the same.

#teamtrees #PAW (Plant And Water)

Answer:

All real numbers (the last option)

Step-by-step explanation:

The line on the graph has arrows, which means that it's going to keep going both ways forever. So the answer is all real numbers.

Answer:

[tex]j^{13}[/tex]  is correct. This expression is showing j to the 13 power.

The equivalent expression is [tex]j^{13}[/tex]

Option C is the correct answer.

We have,

The expression:

j (j) (j) (j) (j) (j) (j) (j) (j) (j) (j) (j) (j)

There are 13 j's so,

This can be written as,

[tex]j^{13}[/tex]

Thus,

The equivalent expression is [tex]j^{13}[/tex]

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ7

Answer: 24 years

Step-by-step explanation:

Let Laurel's age be represented by x.

Since Maye is 28 years and he is 12 years older than 2/3 of Laurel's age, this can be represented in an equation as:

(2/3 × x) + 12 = 28.

2x/3 = 28 - 12

2x/3 = 16

Cross multiply

2x = 16 × 3

2x = 48

Divide by 2

x = 48/2

x = 24

Therefore, Laura is 24 years

Answer:

696 hours

Step-by-step explanation:

Answer:

x=-2

y=5

Step-by-step explanation:

x+2y=8   equation-1  

-x+3y=17 equation-2

5y=25

Both side divided 5,

y=5

Equation-1, y=5

x+2(5)=8

x+10=8

Both side -10

x+10-10=8-10

x=-2

Equation-2, y=5

-x+3(5)=17

-x+15=17

Both side -15

-x+15-15=17-15

-x=2

x=-2

Answer:

5,280,000

Step-by-step explanation:

He uses 200 ft to cover up 1 pound. To find how much he uses for 26,400. You'll multiply 200 times 26400

Answer:

6

Step-by-step explanation:

if you divide the square into 2 pieces, then use pythagoream theroem you will get 6

Answer:

65/16 exact form, 4.0625 in decimal form, and 4 1/16 in mixed number form.

Answer:

44 inches

Step-by-step explanation:

Given that :

Scale of drawing = 1 inch : 8 inches

Height of building in drawing = 5 1/2 inches

Using the scale provide for the drawing, the actual height of the building is :

Height of building in drawing * 8 inches

5 1/2 * 8

5.5 * 8 inches

= 44 inches

Answer:

the number of cups of strawberries needed in the recipe is ⁵/₄

Step-by-step explanation:

Given;

cups of strawberries needed for the smoothies =  1 and 1/4 cups

To obtain the number of cups of strawberries needed in the recipe as a single fraction, the given mixed fractions will be converted into an improper fraction.

Note: Improper fractions are always greater than 1

Number of cups of strawberries [tex]=1 + \frac{1}{4} = \frac{4 + 1}{4} = \frac{5}{4}[/tex]

Therefore, the number of cups of strawberries needed in the recipe is ⁵/₄

Answer:

length:5

width:2

Hight:2

value:20

Step-by-step explanation:

The volume is 29 because length×width×hight=value so 5×2×2=20

Answer:

x = .2

Step-by-step explanation:

3x2 + x - 2 = 0

3x2 + x - 2 + 2 = 0 + 2

3x2 + x = 2

9x + x = 2

10x = 2

10x/10 = 2/10

x = .2

Answer:

0.055x = 1.54

x = 1.54 / 0.055

x = $28

Step-by-step explanation:

Let x = the original price of the board game before tax.

We know that the tax cost $1.54 and was 5.5% of the original price.

5.5% in decimal form = 0.055

5.5% of the original price = 0.055x

5.5% of the original price = tax = $1.54

Answer:

Step-by-step explanation:

This expression is a binomial; it has two terms.

Answer:

x less 21.5

Step-by-step explanation:

Given : the algebraic expression x - 21.5

a. 21.5 decreased by x

the expression becomes 21.5 - x

b. x more than 21.5

more than means we add , so expression becomes 21.5 +x

c. 21.5 minus x

For minus we use subtraction symbol,

so the expression becomes 21.5 -x

d. x less 21.5

x less 21.5 , we subtract 21.5

so the expression becomes x - 21.5 . that is the given expression

Answer:

165 Calories

Step-by-step explanation:

A gram of carbohydrate contains 4 calories. A gram of protein also contains 4 calories. A gram of fat, though, contains 9 calories

5x9=45 10x4=40 20x4=80 45+40+80= 165

Answer:

150 cm^3

Step-by-step explanation:

Volume of a prism = area of base × height

=( 5×6) × 5 cm^3

= 150cm^3

( lemme know if it's right . If the base is a paralellogram, then it'll be different )

Answer:

Exact form

5/8

Decimal form

0.625

Step-by-step explanation:

Answer:

-5/8 or -0.625

Step-by-step explanation:

divide both sides by 8

[tex]\frac{8(x+6)}{8} =\frac{43}{8}[/tex]

Simplify

[tex]x+6 = \frac{43}{8}[/tex]

Subtract 6 from both sides

[tex]x+6 - 6 = \frac{43}{8} -6[/tex]

Convert the fraction to decimal and simplify

[tex]5.375 - 6 = -0.625[/tex]

Simplified:

[tex]-\frac{5}{8}[/tex]

Hope this helps

~R3V0

Answer:

Step-by-step explanation:

B, i

Answer:

Arc length is equal to [tex]\theta r[/tex] where [tex]\theta[/tex] is the angle in radians and [tex]r[/tex] is the radius.

Question 1:

[tex]\frac{\pi}{2}=\frac{\pi}{6}\times3[/tex]

So the angle is CFD.

Question 2:

[tex]\pi=\frac{\pi}{3}\times3[/tex]

So the angle is AFE.

Question 3:

[tex]2\pi=\frac{2\pi}{3}\times3[/tex]

So the angle is AFB.

Question 4:

[tex]\frac{3\pi}{4}=\frac{\pi}{4}\times3[/tex]

So the angle is BFC.

Answer:

the 3rd choice is correct

Step-by-step explanation:

Answer:

9/25

Step-by-step explanation:

Our box contains 10 socks. (6, which are black and 4 which are red)

Probability of picking 1 black sock will be 6/10

Number of ways it can occur / Total number of outcomes.

In this question we pick two socks, one black firstly and another black, in the second turn. When we say AND, it means intersection

P (B₁ ∩ B₂) = 6/10 . 6/10

When the events are independent, the probability of the intersection will be the product of the probabilities,

P (B₁ ∩ B₂) = 36/100 = 9/25

Answer:

The volume is 4, 000 feet

Step-by-step explanation:

Volume equals length x width x height

40 x 20 x 5

4,000

Answer: The correct answer is 4,000 feet cubed

Step-by-step explanation:

Answer:

2x+2

Step-by-step explanation:

hello :

1/2 (4x + 4) =(1/2) (4x + (1/2) (4) = 2x+2