kevin is planting a triangular garden where 2 sides of the garden come together at an angle of 35°. If 1 unknown angle in the triangle is 4 times as large as the second unknown angle in the triangle, what are the measures of the unknown angles in Kevin's triangular garden?

a. The second angle is 105, and the third angle is 29°

b. The second angle is 140°, and the third angle is 35º

c. The second angle is 120°, and the third angle is 30°.

d. The second angle is 116, and the third angle is 29°

Answer:

Explanation:

1. Ratio of campers to counselors in june:

2. Ratio of campers to counselors in july:

3. Equivalent ratios:

Solve for x:

The camp needs approximately 22 counselors in July to maintain the original camper-to-counselor ratio of 12.5:1 that was present in June, when there were 325 campers and 26 counselors.

The question asks how many counselors the camp needs in July to keep an equivalent ratio of campers to counselors from June. In June, the camp had 325 campers and 26 counselors. The ratio of campers to counselors is 325:26, which simplifies to approximately 12.5:1. If 265 campers leave in July and 215 new ones arrive, the total number of campers for July is 325 - 265 + 215 which equals 275. To maintain the same ratio, we divide the number of July campers by the original ratio:

The camp needs approximately 22 counselors in July to maintain the same camper-to-counselor ratio as in June.

Answer: 46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son     = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x     = 3y - 9 + 3

x     = 3y - 6 .......................................... equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x       = 2y + 10 - 5

x       = 2y + 5 ........................ equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4      = 15

sum of their ages in four years time will be

31 + 15 = 46 years

Answer:

46 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

In solving this, we'll make some keen assumptions to solve the question.

We'll represent the father's age with "a"

And represent the sons age as "b"

Lets interpret the question.

3 years ago, (means in the past), we'll subtract.

Therefore:

Father's age = a - 3

Sons age = b - 3

The sentence said, " 3 years ago, father was 3 times the sons age*. Interpreting that becomes:

a - 3 = 3 times (b - 3)

Simplifying that gives :

a - 3 = 3(b - 3)

a - 3 = 3b - 9

a = 3b - 9 + 3

a = 3b - 6 ( FIRST EXPRESSION )

The next line says: In five years time (that's in the future, hence we add) he'll be twice his sons age.

Therefore I become:

Father : a + 5

Son : b + 5

a + 5 = 2(b + 5)

a + 5 = 2b + 10

a = 2b + 5 ( SECOND EXPRESSION)

Equating the first and second equation to solve for "a" - the father's age

3b - 6 = 2b + 5

b = 5 + 6

b = 11 years (Sons age)

Substitute b = 1 in the first expression.

a = 3b - 6

a = 3(11) - 6

a = 33 - 6

a = 27 years (Father's age)

Let resolve, the last sentence:

What will be the sum of their ages in 4 years time. (SINCE IT'S IJ THE FUTURE, WE ADD)

Father's age in four years time: 27 + 4 = 31

Son's age in four years time: 11 + 4 = 15.

The sum of their ages in same four years time becomes:

31 + 15 (years)

46 years

Answer:

Step-by-step explanation:

5x - 45 = 5(x - 9) <==

The actual amount that should be credited is $757.58.

Solution:

Given that,

2% Discount if paid in 10 days.

1% Discount if paid in 15 days, (but greater that 10 days)

Net due in 60 days.

That is,

[tex]\bold{1400\times0.98 = 1372}[/tex] will close the acount on days 1-10

[tex]\bold{1400\times0.99 = 1386}[/tex] will close the acount on days 11-15

And August 8 is Day 15 and falls under the 1% discount rule.

Therefore, we have to divide the partial payment by the complement of the discount rate.

[tex]\bold{\Rightarrow\frac{750}{0.99} = 757.58}[/tex] from the balance, and [tex]\bold{1400.00 - 757.58 = 642.42}[/tex] is due by day 60.

Answer:

.4

Step-by-step explanation:

Use a caluculator

Answer:

.4

Step-by-step explanation:

Answer:

B, C, and D

Step-by-step explanation:

By doing 5÷8 = .625 you know that Hang can read .625 of a page per minute.

You can do this for the rest of the people finding that Kira reads .5 page per minute which is a slower/ smaller ratio, Joe rate is .66, Quon's ratio is .71 and Lulus rate is .76, the only rate that is smaller than Hangs is Kira,s, leaving you with Joe, Quon, and Lulu to be your answer

Joe, Quon, and Lulu have a greater ratio of pages read to minutes than Hang. Their respective ratios are 0.6667, 0.714, and 0.769, each higher than Hang's ratio of 0.625.

Let's determine who has a greater ratio of pages read to minutes than Hang.

Hang's ratio is 5:8 or 5/8 = 0.625.

ratio = 2/4 = 0.5 (less than 0.625)

    2. Joe: 6 pages in 9 minutes,

ratio = 6/9 = 0.6667 (greater than 0.625)

    3. Quon: 5 pages in 7 minutes,

ratio = 5/7 ≈ 0.714 (greater than 0.625)

    4. Lulu: 10 pages in 13 minutes,

ratio = 10/13 ≈ 0.769 (greater than 0.625)

So, Joe, Quon, and Lulu have a greater ratio of pages read to minutes than Hang.

Answer:

5 times

Step-by-step explanation:

First, we need to read the change in price in 2000 and 2007, from the graph.

So, the change in price in 2000 was $0.14 and in 2007 it was $0.71.

Now, we do the same thing we always do when comparing two values - we divide them. So:

0.71 / 0.14 = 5.07

Of course, we could multiply these values with 100, in order to avoid decimal numbers. Then we would get:

71 / 14 = 5.07

We could also divide this in the form of fractions:

71/100 / 14/100 = 5.07

There are several ways we could divide rational numbers, but the result will always be the same.

Change in price in 2007 was around 5 times greater than the change in 2000.

Answer:1,2,3,4,5,6

Step-by-step explanation:

Count

Answer:

2.2

Step-by-step explanation:

It is a 2.2 slope because you just have to divide the depth of water by the time by 2.2 or multiply the time by 2.2 to get the depth of water :)

Answer:

(0,0)&(2,4.4)

(4.4-0)/(2-0)= 4.4/2= 2.2 is the overall slope

Answer:

y = -1/3x + 2

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

The line y = 3x - 2 has slope 3.

The perpendicular line has slope -1/3.

Now we find the equation of the line that has slope -1/3 and passes through (-9, 5).

y = mx + b

y = -1/3x + b

5 = (-1/3)(-9) + b

5 = 3 + b

b = 2

The equation of the perpendicular is

y = -1/3x + 2

To solve the equation 5(2c + 7) - 3c = 7(c + 5), distribute the values inside the parentheses, combine like terms, and solve for c.

To solve the equation 5(2c + 7) - 3c = 7(c + 5), we will distribute the values inside the parentheses. This gives us 10c + 35 - 3c = 7c + 35. Next, we will combine like terms by subtracting 7c from both sides of the equation and adding 3c to both sides. This simplifies the equation to 10c - 7c = 35. By combining the terms on the left side, we get 3c = 35. Finally, we can solve for c by dividing both sides of the equation by 3, which gives us c = 35/3 or 11.67.

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Answer:

D. [tex]y=-0.927x+13.634[/tex]

Step-by-step explanation:

We graph the points on the graph. The graph is attached.

Let us take two points (1, 14) and (15, 1), and calculate the slope [tex]m[/tex]between them (we choose these points because the line passing through them will be the best fit for all points)

[tex]m=\frac{14-1}{1-15} =\frac{13}{-14} =-0.9286[/tex]

Thus we have the equation

[tex]y=-0.9286x+b[/tex]

Let us now calculate [tex]b[/tex] from the point [tex](1,14)[/tex]

[tex]14=-0.9286(1)+b[/tex]

[tex]b=14.9286[/tex]

So the equation we get is

[tex]y=-0.9286x+14.9286[/tex]

Let us now turn to the choices given and see which choice is closest to our equation: we see that choice D. [tex]y=-0.927x+13.634[/tex] is the closest one, so we pick it.

Answer:

X= 7

Step-by-step explanation:

Hello ^w^

I believe the answer you are looking for is A

I found this answer by adding up the lengths of all the sides.

S -> T = 8

S -> R = 7

Q -> R = 6

P -> Q = 6

P -> T = 10

10 + 6 + 6 + 7 + 8 ->  37

A -> 37

If I am incorrect, please inform me.

Have a good day!

Answer:

84, 82, 246

Step-by-step explanation:

first multiply by 3 for first term

next term, use previous term minus 2

Answer:

Step-by-step explanation:

14(x + 8)....distribute thru the parentheses by multiplying the number directly to the left of the parenthesis, by everything in the parenthesis.

14(x + 8) = 14(x) + 14(8) = 14x + 112 <== equivalent

this is called the distributive property

Answer:

Step-by-step explanation:

Multiply each term in the parentheses by 14 and then add the products.

Answer:

  1/2

Step-by-step explanation:

Put the numbers where the corresponding variables are and do the arithmetic.

  1/2(-2)^(-4)·(4)^2 = 1/2(4^2/(-2)^4) = 1/2(16/16) = 1/2

__

We used the rule of exponents ...

  a^-b = 1/(a^b)

Answer:

(8m+24n) is our final answer.

Step-by-step explanation:

Given:

(m+3n)8 ...

We have to simplify this.

Applying distributive property of multiplication:

Distributive property:

When a number is multiplied by a sum of two numbers then we will multiply 'the number' first with the number inside the parentheses then add it and again multiply 'the number' with the next number.

[tex]a(b+c)=ab+ac[/tex]

So,

⇒[tex](m+3n)8[/tex]

⇒[tex]m\times 8 + 3n\times 8[/tex]

⇒[tex]8m+24n[/tex]

Our final answer is (8m+24n).

Answer:

First option:  [tex]6*10^{-4}[/tex]

Step-by-step explanation:

The expression is:

 [tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

Scientific Notation (which is also known as "Standard form"), is a way to write numbers. It is very useful to handle very small numbers and very large numbers.

By definition, Scientific Notation has the following form:

[tex]a*10^n[/tex]

Where the coefficient "a" is a number from 1 to 10 without including 10, and the exponent "n" is an Integer.

Given:

[tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

If you want to estimate the result, you can round the coefficients to the nearest whole number. Since the decimal point must be just after the first digit, you know that:

[tex](6*10^{-2})(10*10^{-3})=(6*10^{-2})(1*10^{-2})[/tex]

Now you need to remember the Product of powers properties:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then, solving the multiplication, you get:

[tex]6*10^{-4}[/tex]

Answer:

the answer is a

Step-by-step explanation:

i took the test... 100% i swear

Answer:

Its 4

Step-by-step explanation:

24÷3=8÷2=4

Answer:

the amount of pennies that Bryan lost is 16

Answer:

3 teaspoons of salt is needed to cook the recipe for 8 people.

So, the correct option is d. 3 teaspoons.

Step-by-step explanation:

Given:

Mike has a recipe that feeds one person that calls for 3/8 teaspoon of salt.

Now, to find the quantity of salt is needed to cook the recipe for 8 people.

As, given the recipe feeds:

[tex]\frac{3}{8}[/tex] teaspoon salt per person.

Now, to get the salt needed to cook the recipe for 8 people we multiply  [tex]\frac{3}{8}[/tex] by 8:

[tex]\frac{3}{8}\times 8[/tex]

[tex]=\frac{24}{8}[/tex]

[tex]=3.[/tex]

Thus, 3 teaspoons of salt is needed to cook the recipe for 8 people.

So, the correct option is d. 3 teaspoons.

Answer: 4

Step-by-step explanation:

To solve this problem we can use the Pythagorean Theorem to find the length of the other LEG of a right triangle

Pythagorean Theorem can be written as A^2+B^2=C^2

Now we plug in the values. C represents the hypotenuse while A and B represent the legs. We only are given one leg and the hypotenuse so we will be solving for B. (Or A if you swap the legs around)

3^2+b^2=5^2

9+b^2=25

Subtract 9 from both sides:

16=b^2

Now we take the square root of both sides

b=4

The length of the other leg of the triangle is 4 feet.


This is a basic 3-4-5 Triangle. Anytime the hypotenuse of a triangle is 5 and the leg is 3 the other leg will always be 4.

Answer:

iT WAS 3 Bum

Step-by-step explanation:

Answer:

i think it is 357  hope this helps

Step-by-step explanation:

Answer:

1428mm

Step-by-step explanation:

Area = 0.5 (a + b) h

Area= 0.5 (36 + 15) 14

Area = 0.5 ( 51) 14

Area = 1428 mm or 1.428m

To find the measure of each angle, we can set up an equation and solve it for x, which represents one of the angles. The other angle can be calculated by subtracting x from 90. The answers are x = 63.6° and 90 - 63.6 = 26.4°.

To solve this problem, we need to set up an equation based on the given information. Let x be the measure of one angle, and since the angles are complementary, the other angle will be 90 - x. According to the problem, x is 37.2° more than 90 - x. This can be written as the equation x = 90 - x + 37.2. Solving this equation, we find that x = 63.6°. Therefore, one angle measures 63.6° and the other angle measures 90 - 63.6 = 26.4°.

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Answer:

5/8

Step-by-step explanation:

1/4 = 2/8

2/8 + 3/8 = 5/8

Answer:

5/8

Step-by-step explanation

1/4 has a common denominator as 3/8 and when u find the common denominator add and ur good to go