the first container of milk has twice as many gallons as the second if john uses 2 gallons from the second and 3 gallons from the first if the first one has 4.5 times more than the second how much did they each have originally

Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

We know the area of the kite = pq/2

Where p and q are the length of the diagonals

p = 10+10 = 20 ft

q = 7+11 = 18 ft

Area = (20×18)/2

Area = 180 square feet

Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.

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Answer:

$42.80

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9.75%/100 = 0.0975 per year.

Solving our equation:

A = 39(1 + (0.0975 × 1)) = 42.8025

A = $42.80

The total amount accrued, principal plus interest, from simple interest on a principal of $39.00 at a rate of 9.75% per year for 1 years is $42.80.

Answer:

Sales tax is $3.8.  So total would be 39.00+3.8= $42.8

Step-by-step explanation:

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

Answer:

[tex]g(x) = \sqrt[4]{x-7},~ x\geq 7[/tex]

Step by step explanation:

[tex]y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}[/tex]

Answer:

i just need points

Step-by-step explanation:

sorrry ehburbvuygvuywhefe2b yvfb we

Answer:

I think the answer is 1,714 tubes

Step-by-step explanation:

Answer:

The distribution of the ages of vice president shows that the youngest age is about 36 while the oldest age is around 72. The median age of vice president is 53. On the lower end, the common age is 48 while the age of 60 is upper median age.

[tex]\large\boxed{Formula: I= \frac{PRT}{100}}[/tex]

First, we'll have to multiply, principal amount (12500), rate (10) and time period (3).

[tex]12500×10×3[/tex]

[tex]=375000[/tex]

Now, we'll have to divide the amount (375000) by 100.

[tex]\frac{375000}{100}[/tex]

I=$3750

Now, we can find the total amount paid.

[tex]\large\boxed{A=SI+P}[/tex]

Let's substitute according to the formula.

[tex]A=3750+12500[/tex]

A=$16250

Therefore, simple interest is $3750 and $16250 was paid in total.

50 students preferred science...

Explanation:

we can consider the numbers 5 and 4 in the ratio as units

now we need to know how much each unit represent

units = 5 + 4 = 9

my sample = 90 students

each unit = 90/9 = 10 students

so each unit represents 10 students

back to the ratio

who preferred science = 5

who preferred English = 4

Number of students choose Science = 5 * 10 = 50

If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.

Final price - initial price

Calculate the percentage $2300 is equivalent to by using the information you already have.

33.3% is the profit percentage.

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The number of second it takes the apple to hit the ground is 4 seconds

To answer the question, we need to know what functions are

Functions are mathematical equations that show the relationship between two variables

Given that when an apple is dropped from a tower 256 feet high, the function h(t) = -16t² + 256 modelshe height of the apple, in feet, after t seconds.

The time it takes the apple hits the ground is when h(t) = 0

So, h(t) = 0

-16t² + 256 = 0

-16t² = -256

t² = -256/-16

t² = 16

t = ±√16

t = ±4

Since t ≥ 0, t = 4 seconds

So, the number of second it takes the apple to hit the ground is 4 seconds

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The class which has a greater percent of students who ride the bus is Walter's class

Walter's class:

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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Recall that (a + b)² = a² + 2ab + b².

Let a = x² and b = y². Then

(x² + y²)² = (x²)² + 2x²y² + (y²)²

⇒   x⁴ + y⁴ = (x² + y²)² - 2 (xy)²

Given that x² + y² = 13 and xy = 6, we have

x⁴ + y⁴ = 13² - 2×6² = 97

Answer:

360 g

Step-by-step explanation:

Amount of Salt = 2.5% x Amount of Mango

Taking 9 g as the amount of salt :

Answer:

The slope of the line y = x + 1 is equal to 1.

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = x + 1[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 1. Let's rewrite our given expression:

Here, we can identify our slope m to be 1.

∴ the slope of the given line is equal to 1.

___

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___

Topic: Algebra I

Answer: -7 < x < 3

Step-by-step explanation:

-21 < 3x < 9

-7 < x < 3

Answer:

28

Step-by-step explanation:

[tex]sin=\frac{opp}{hyp}[/tex]

[tex]cos = \frac{adj}{hyp}[/tex]

[tex]cos^{-1}\left(\frac{45}{51}\right)[/tex]

which is 28.07 degree

[tex]sin\left(28.07\right)=\frac{x}{51}[/tex]

x= 23.99

23.99+4=h=28

Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

Answer:

360 people out of 1200 are likely to have red hair.

Step-by-step explanation:

So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?

Answer:

see the attachment photo!

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]

Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.

[tex]\frac{SinC}{c} =\frac{SinR}{r}[/tex]

Substitute

Note: the capital letters are for the angles and the small letter are for the sides.

But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.

[tex]\frac{Sin(7)}{1.9} =\frac{Sin100}{x}[/tex]

now you do the butterfly method or cross multiplication method.

[tex]xsin(7)=1.9sin(100)[/tex]

You have to isolate the x

[tex]\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}[/tex]

now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.

[tex]x= 15.35[/tex] or if u want to round it [tex]15.4[/tex]

<R = 100 and side CK= 15.35 or 15.4

Hope I helped! ^w^

TheOneAndOnlyLara~

If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Translation is a way of changing the position of an object on the xy plane

Given the coordinates of the vertices (1, 4), (1, 1), (3,1)

If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Note that 4 was subtracted from the x-axis and 2 added to the y-coordinates.

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Answer:

9 is 15% of 60.

Step-by-step explanation:

[tex]\text{Formula}=\frac{\text{Number x 100}}{\text{Percent}} =\frac{9 \times100}{15} =60[/tex]

Following shows the steps on how to derive this formula and find out 15% of what number is 9.

Step 1: If 15% of a number is 9, then what is 100% of that number? Setup the equation.

[tex]\frac{9}{15} = \frac{Y}{100}[/tex]%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

[tex]15Y=6\times100\\15Y=600[/tex]

Y = [tex]\frac{600}{100} =60[/tex]

The requried 15% of 60 is equal to 9, as of the given percentage situation.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To find the number that 15% of is equal to 9, we can set up a proportion:

15% of x = 9

Converting 15% to a decimal:

0.15x = 9

Dividing both sides by 0.15 gives:

x = 60

Therefore, 15% of 60 is equal to 9.

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Answer:

3

Step-by-step explanation:

got it on edge

Answer:

10 degrees

Step-by-step explanation:

A straight line equals 180 degrees. We already know we have 110 degrees, so we subtract 180-110 and get 70. Now, we can set up an equation:

We have to isolate x, so divide both sides by 7

70=7x

_____  =  10=x

   7

x=10 degrees

Hope this helps!