What is 8 - 6 7-12 ?

Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.

The distance a car can go on a given quantity of gasoline is measured as gas mileage, also known as fuel efficiency. By dividing the distance driven by the amount of gasoline used, one may determine gas mileage. For instance, a car's gas mileage is 25 mpg (300/12 = 25) if it can go 300 miles on 12 gallons of petrol. Many variables, including traffic, speed, weather, road gradient, and vehicle maintenance, can have an impact on gas mileage.

Given that, Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon.

Thus, when his tank is 1/4 full, it contains:

1/4 * 14 2/5 = 14 2/5 / 4 = 3 1/2 gallons.

Hence, Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.

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Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,

In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.

Common denominator is going to be [tex]24[/tex]

[tex]8=2*2*2\\6=2*3\\24=2*2*2*3[/tex]

[tex]8[/tex] should be multiplied by [tex]3[/tex]

[tex]6[/tex] should be multiplied by [tex]4[/tex]

[tex]7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24[/tex]

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We're given the angle measure to be 46 for No. 8. The length of 1 leg is x and the hypotenuse is 28.

We can use cosine to solve this. Since cosine is adjacent over hypotenuse, we can do cos(46) = x/28. Cross multiply to get cos(46)*28 = x. That solves to be 19.5

Using this principle allows us to solve the other ones. I'll let you figure them out.

TLDR: We can use the definition of trig functions to plug in what we know and place variables where we don't have enough information to find the length of a side.

Answer:

4=20

3=?

so 20×3 divide by 4 = 15

Step-by-step explanation:

Answer:25

Step-by-step explanation: 25 25 25

Answer: m∠G = 41°

Step-by-step explanation:

      Opposite angles of parallelograms are congruent. This means that m∠G = m∠E, so we can write an equation using the given information.

Given:

      m∠G = m∠E

Substitue:

      5x - 9 = 3x + 11

Add 9 to both sides of the equation:

      5x = 3x + 20

Subtract 3x from both sides of the equation:

      2x = 20

Divide both sides of the equation by 2:

      x = 10

      Then, we will substitute this value of x back into the expression for m∠G.

5x - 9 = 5(10) - 9 = 50 - 9 = 41°

Answer:19?

Step-by-step explanation:

Answer:

In business and economics, cost, revenue, and profit are key concepts that relate to the financial aspects of a business.

Cost refers to the expenses incurred by a business in order to produce, sell or distribute its products or services. This includes direct costs, such as the cost of raw materials, labor and overhead expenses, as well as indirect costs, such as marketing and administrative expenses.

Revenue, on the other hand, refers to the income generated by a business through the sale of its products or services. Revenue can be calculated by multiplying the price of a product or service by the number of units sold.

Profit is the difference between revenue and cost, and is a measure of how much money a business earns after all of its expenses are paid. A business earns a profit when its revenue exceeds its total costs, including both fixed and variable costs.

Profit can be further broken down into gross profit and net profit. Gross profit is the difference between revenue and the direct cost of producing or delivering a product or service. Net profit, on the other hand, is the profit that remains after all expenses, including indirect costs, taxes and interest payments, have been deducted from revenue.

In summary, cost refers to the expenses incurred by a business, revenue refers to the income generated by the sale of products or services, and profit is the difference between revenue and cost, indicating how much money a business earns after all expenses are paid.

Step-by-step explanation:

The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.

Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.

The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.

Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.

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10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)

All statements and reasons are shown below.

A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.

According to the given figure:

4. In ΔFGH and ΔFJH,

        Statement                                   Reason

5. In ΔTVY and ΔXWY,

        Statement                                   Reason

6. In ΔKML and ΔPMN,

        Statement                                   Reason

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The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.

The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -

[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]

where -

A0 is the initial amοunt of the substance

A is the amοunt of the substance remaining after t years

T is the half-life οf the substance

In this case, the half-life is 8 years, sο T = 8.

We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.

We can plug these values intο the formula to get -

[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]

A ≈ 0.2 grams

Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.

The equation that best mοdels this situation is -

[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]

where A represents the amοunt of the substance remaining after t years, in grams.

Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].

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Answer:

Step-by-step explanation:

To solve the equation graphically, we need to first rearrange it into the form of y = f(x). So, let's simplify the given equation:

(x - 3)² - 2 = x + 1

Expanding the left side:

x² - 6x + 9 - 2 = x + 1

Simplifying:

x² - 7x + 6 = 0

Now we can graph the function y = f(x) = x² - 7x + 6 and the line y = x + 1 on the same coordinate axes and find their intersection points.

Here's a graph of the function and the line:

Graph of y=x^2-7x+6 and y=x+1

We can see that the two curves intersect at two points, which have x-coordinates of approximately 1.2 and 5.8. So, the solutions to the equation are x ≈ 1.2 and x ≈ 5.8.

The missing term of question is "distance".

Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.

Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.

The missing term in the question is "distance". The sentence can be completed as:

"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."

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The answer is 6.03 did this help?

The  orientation and ratio of the sides of the similar right triangles are  presented as follows;

(a)  ΔZXY ` ΔZYW ~ ΔYXW

(b) ZX/YX =  XY/WX

ZW/ZY =  ZY/ZX

Similar triangles are triangles that have the same shape but may have different  size.

(a) Similar triangles are triangles that have congruent internal angles.

Making use if the angles of the triangle, we get;

∠x ≅ ∠x  (reflexive property of congruency)

∠YZW ≅  ∠YZWX (All 90 degrees angle are congruent)

Therefore; ΔZXY ~ ΔZYW by AA similarity postulate

Similarly; ΔZXY is similar to ΔYXW by AA similarity postulate

The similar triangles are therefore;

(b) The proportion of the corresponding sides of similar triangles are equivalent, and the cosine of an angle in a right  triangle is the ratio of the adjacent side to the hypotenuse side, therefore;

ZX/YX =  XY/WX

The tangent  of an interior angle of a right triangle is the ratio of the opposite side to the adjacent side of the right triangle, therefore;

ZW/ZY =  ZY/ZX

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Answer:

[tex]\textsf{1.} \quad \left(f \cdot g \right)(x)=x^6+2x^5 -6x^4+3x^2+6x -18[/tex]

[tex]\textsf{2.} \quad\left(f -g \right)(x)=- x^4+x^2+2x-9[/tex]

Step-by-step explanation:

To calculate (f ⋅ g)(x), multiply function f(x) by function g(x) by distributing the parentheses:

[tex]\begin{aligned}\left(f \cdot g \right)(x)&=(x^2+2x-6)(x^4+3)\\&=x^2 \cdot x^4 +x^2 \cdot 3+2x \cdot x^4+2x \cdot 3 -6 \cdot x^4 -6 \cdot 3\\&=x^6+3x^2+2x^5+6x -6x^4 -18\\&=x^6+2x^5 -6x^4+3x^2+6x -18\\\end{aligned}[/tex]

To calculate (f - g)(x), subtract function g(x) from function f(x) by applying the distributive law -(a + b) = -a - b:

[tex]\begin{aligned}\left(f -g \right)(x)&=(x^2+2x-6) - (x^4+3)\\&=x^2+2x-6 - x^4-3\\&=- x^4+x^2+2x-6 -3\\&=- x^4+x^2+2x-9\end{aligned}[/tex]

Note:  The standard form of a polynomial is expressed by writing the term with the highest degree first, followed by the other terms in order of decreasing powers.

Answer:

Step-by-step explanation:

[tex]16^\frac{1}{n}=2[/tex]     (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])

[tex](2^4)^\frac{1}{n}=2[/tex]

[tex]2^\frac{4}{n}=2[/tex]

[tex]2^\frac{4}{n}=2^1[/tex]

∴[tex]\frac{4}{n} =1[/tex]    (indices must be equal when bases are equal)

∴[tex]n=4[/tex]

2 times the square root of 48 minus the square root of 3 simplified is 7√3.

what is square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the inverse operation of squaring a number. For example, the square root of 16 is 4 because 4 multiplied by itself (4 x 4) equals 16.

The symbol used to represent the square root is √. So, the square root of 16 is written as √16.

To simplify this expression, we can first simplify the square root of 48.

We know that 48 can be written as 16 x 3, and since 16 is a perfect square, we can simplify the square root of 48 as follows:

√48 = √(16 x 3) = √16 x √3 = 4√3

Now we can substitute this value into the expression:

2(4√3) - √3 = 8√3 - √3 = 7√3

Therefore, 2 times the square root of 48 minus the square root of 3 simplified is 7√3.

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The decay of Element X can be modeled by the equation:

N = N0 * (1/2)^(t/t1/2)

where N is the amount of Element X remaining after time t, N0 is the initial amount of Element X, t1/2 is the half-life of Element X, and ^(t/t1/2) denotes exponentiation with base 1/2.

We know that the initial amount of Element X is 470 grams, the half-life is 8 minutes, and we want to find the time it takes for Element X to decay to 10 grams. Let t be the time in minutes.

Then, we can set up the following equation:

10 = 470 * (1/2)^(t/8)

Dividing both sides by 470, we get:

(1/47) = (1/2)^(t/8)

Taking the natural logarithm of both sides, we get:

ln(1/47) = (t/8) * ln(1/2)

Solving for t, we get:

t = -8 * ln(47)/ln(2)

t ≈ 59.3

Therefore, it would take about 59.3 minutes, to the nearest tenth of a minute, for Element X to decay to 10 grams.

Step-by-step explanation:

1) length of YZ:

[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]

2) angle X:

[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]

3) angle Z:

[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]

Answer:

difference: -4 cubic inches

% change: -10%

Step-by-step explanation:

The difference between the new volume and the original volume is ...

 (new volume) - (original volume) = (36 in³) - (40 in³) = -4 in²

__

The percentage change is figured with respect to the original volume:

 % change = (difference)/(original volume) × 100% = (-4 in³)/(40 in³) × 100%

 = -1/10 × 100% = -10%

Answer:

Yes he was correct in returning the 100

Step-by-step explanation:

Pen 68.75

Pencil 73.50

Paint box 112.35

Add all together, you get 254.60

If he paid 500 to the shopkeeper, he will collect (500.00-254.60) =245.40

If the shopkeeper gave him 345.40, then he had an excess and should give back the 100

The area of the part that is painted blue is 679 ft.

What are the basic arithmetic operations?

The four basic arithmetic operations are addition, subtraction, multiplication, and division.

Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.

Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.

The area

= 20×30+(1/2)×20×(40-30) -3x5 - 2×3

= boot 10x10- 15-6

= 700-21

= 679

Hence, The area of the part that is painted blue is 679 ft.

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The value of x will be 12. For the given image.

The arc length formula for a circle is times the radius of a circle. Arc length ( Angle x radius ) is a way to express the arc length formula in radians.

By dividing the arc length by the circle's circumference and multiplying the result by 360 degrees, one can calculate the angle of an arc. 0

To calculate the value of x make the equation below,

x / 4 = 18 / 6

x = ( 18 x 4 ) / 6

x = 12

Therefore, the value of x will be 12.

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use the process of elimination, once you solve, it will give you one variable that will work for both equations, once you plug that in, it will give you the other variable.

7x + 3y = 13

2x -3y   = -4

add the "y"; 3y + (-3y) = 0

9x = 9

x = 1

plug in the "x" value into either question to solve for "y"

7(1) + 3y = 13

7 + 3y = 13

3y = 6

y = 2

Answer:

Step-by-step explanation:

7x + 3y = 13

2x -3y   = -4

add the "y"; 3y + (-3y) = 0

9x = 9

x = 1

plug in the "x" value into either question to solve for "y"

7(1) + 3y = 13

7 + 3y = 13

3y = 6

y = 2

Answer:

9 ft

Step-by-step explanation:

63 divided by 7 is 9.

Hope this helped!

The price after the reduction is 0.72x

From the question, we have the following parameters that can be used in our computation:

Original price = x

Reduction = 28%

Using the above as a guide, we have the following:

Reduced price = Original price * (1 - Reduction)

Substitute the known values in the above equation, so, we have the following representation

Reduced price = x * (1 - 28%)

Evaluate

Reduced price = 0.72x

Hence, the reduced price is 0.72x

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Answer:

26

Step-by-step explanation:

(6x + 4) + (4x + 6) = 90

180 - (4x + 6) = (6x + 4) + 90

Rearrange the equation.

180 - (-90) = (6x + 4) + (4x + 6)

270 = 6x + 4 + 4x + 6

270 = 10x + 10

260 = 10x

26 = x

I don't know if this is correct, so I apologize if its wrong.

Answer:

x = 8

Step-by-step explanation:

According to the picture,

These given two angles are complementary. That is, those two angles are added up to 90°.

Therefore,

( 6x + 4 ) + ( 4x + 6 ) = 90

Combine like terms.

6x + 4 + 4x + 6 = 90

10x + 10 = 90

Subtract 10 from both sides.

10x = 90 - 10

10x = 80

Divide both sides by 10.

x = 8