Colin buys gas for her car at $4 a gallon. Write an equation using two variables to show the relationship between the number of gallons of gas, g, and the total amount of amount she spends, s.

The rate at which the distance between the car and the truck is changing when the car is 9 m from the intersection and the truck is 40 m from the intersection is about 19.187 m/s

The rate of change of a function is an indication of how fast the function's output changes per unit change in the input of the function.

Let y represent the distance of the car from the intersection, and let x represent the distance of the truck from the intersection, we get;

The distance between the car and the truck, d, can be obtained from Pythagorean Theorem as follows;

d² = y² + x²

2·d·d/dt = 2·y·dy/dt + 2·x·dx/dt

dy/dt = The speed of the car = 48 km/h = 40/3 m/s

dx/dt = The speed of the truck = 60 km/h = 50/3 m/s

y = The distance of the car from the intersection = 9 m

x = The distance of the truck from the intersection = 40 m

d² = 9² + 40² = 1681

d = √(1681) = 41

d = 41 m

Therefore;

2×41×d/dt = 2×9 × 40/3 + 2 × 40 × 50/3 = 4720/3

d/dt = 4720/3/(2 × 41) = 2360/123 ≈ 19.187

d/dt ≈ 19.187 m/s

The rate of change distance between the car and the truck d/dt is about 19.187 m/s

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Answer:

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Find the prime factors of 1352:

We need another factor of 2 as a minimum added in order to have even number of same factors:

Hence we need to multiply the given number by 2.

Answer:

Unfortunately, the provided statement does not contain sufficient information to determine the loan term of the truck.

Step-by-step explanation:

The loan term refers to the length of time over which the loan for the truck is scheduled to be repaid. It is typically determined at the time of purchase and specified in the loan agreement.

To determine the loan term of the truck, we would need to know additional information such as the date of purchase, the loan agreement terms, the payment schedule, and any other relevant details about the loan.

Answer:

a) 750 and 600,

b) 145 and 116.

Step-by-step explanation:

A) For 1350 divided to two as 5 : 4, we need to add 5 and 4 first = 9:

Then, with the following, calculate the amount for 5:

[tex]\frac{1350}{9}[/tex] x 5

150 x 5

= 750 for 5, then for 4:

150 x 4

= 600 for 4.

B) For 261 divided with into 5 : 4, we need to add 5 and 4 = 9:

Then, with the following, calculate the amount for 5:

[tex]\frac{261}{9}[/tex] x 5

29 x 5

= 145 for 5. Finally, for 4:

29 x 4

= 116 for 4.

The correct numerical expression for the given statement "multiply the sum of 7 and 6 by the sum of 4 and 5" is (7 + 6) x (4 + 5).

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The given statement, "multiply the sum of 7 and 6 by the sum of 4 and 5", can be represented as:

sum of 7 and 6 = (7 + 6)

sum of 4 and 5 = (4 + 5)

multiply: (7 + 6) x (4 + 5)

Hence, the correct numerical expression for the given statement is (7 + 6) x (4 + 5).

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Answer:

(7 + 6) x (4 + 5).

Step-by-step explanation:

hope this helps!

The width of the rectangle border is 3 in.

What is area of rectangle?

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here We know that ,

Area of the rectangle = length* width square unit.

Here area of the picture and border is 80 [tex]in^2[/tex] Then,

=> (7+w)*(5+w)=80

=> [tex]35+5w+7w+w^2=80[/tex]

=> [tex]12w+w^2=45[/tex]

=> [tex]w^2+12w-45=0[/tex]

=> [tex]w^2+15w-3w-45=0[/tex]

=> w(w+15)-3(w+15)=0

=> (w-3)(w+15)=0

=> w=3 , w=-15( negative is neglected)

Hence the width of the rectangle border is 3 in.

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taking 23(origin amount) as the 100%, what is 27 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 23 & 100\\ 27& x \end{array} \implies \cfrac{23}{27}~~=~~\cfrac{100}{x} \\\\\\ 23x=2700\implies x=\cfrac{2700}{23}\implies x\approx 117.39[/tex]

the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

The statements that are true about the reflectional  symmetryof a regular heptagon are:

It has only one line of reflectional symmetry.

The line of reflectional symmetry passes through the center of the heptagon.

A regular heptagon is a polygon with seven equal sides and angles. Each vertex of the heptagon is equidistant from the center of the heptagon, and the lines connecting the center to the vertices divide the heptagon into seven congruent triangles.

To understand the reflectional symmetry of the regular heptagon, we need to define what it means. Reflectional symmetry is a type of symmetry where a figure is symmetric with respect to a line. In other words, if we fold the figure along this line, one half will coincide with the other half.

In the case of the regular heptagon, we can observe that if we draw a line passing through the center of the heptagon and perpendicular to any of its sides, we obtain a line of reflectional symmetry. This line divides the heptagon into two congruent halves. However, if we draw any other line of reflectional symmetry, it will not coincide with the sides of the heptagon, and therefore, it will not divide the heptagon into congruent halves.

Therefore, we conclude that the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

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This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

The energy levels in a three-dimensional box are provided by the formula E = (h2/8m) [(n x2/a2) + (n y2/b2) + (n z2/c2)].

where n x, n y, and n z are the quantum numbers for the x, y, and z dimensions, respectively, and h is Planck's constant, m is the particle'smass, a, b, and c are the dimensions of the box.

The amount of various quantum number combinations that result in the same energy is the degeneracy of an energy level.

The degeneracies of the first four energy levels for a three-dimensional box with a=b=1.5c are as follows:

1 degeneracy at first energy level (n=1)

Third degeneracy at second energy level (n=2)

6 degeneracies at third energy level (n=3)

10 degeneracies at energy level four (n = 4)

Hence, This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

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Answer:

C) 60º, 60º, 120º, 120º

Step-by-step explanation:

We know the sum of all the angles in a rectangle is 360 degrees, whether it's irregular or not.

Given: x + 2x + 2x + x = 360

Calculate the linear equation, to find x.

x + 2x + 2x + x = 360

3x + 3x = 360

6x = 360  (Divide both sides by 6)

x = 60 degrees.

Then you can calculate the polygons.

x + 2x + 2x + x

For the first x, = 60.

Then for 2x, 60 * 2 = 120.

Then for 2x again, = 120.

Finally for the last x, = 60.

Therefore, the answer is C) 60º, 60º, 120º, 120º.

The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

When we round 61.604 to the nearest whole number, we get 62, and when we round 48.44 to the nearest whole number, we get 48.

Therefore, we can estimate 61.604 - 48.44 by subtracting 48 from 62:

62 - 48 = 14

So, the estimated answer is 14.

Using synthetic division for the given dividend and divisor the required quotient is given by option a. x^3 + 2x - 5.

Dividend is equal to,

x^4-2x^3+2x^2-9x +10

Divisor is equal to,

( x - 2 )

Using synthetic division we have,

Use double equals to method to simplify the dividend we have,

x^4-2x^3+2x^2-9x +10

= x^4 - 2x^3 + 2x^2 - 4x -5x + 10

= x^3 (x -2) +  2x ( x -2 ) - 5 ( x - 2 )

= ( x - 2 ) ( x^3 + 2x - 5 )

Now ,

Simplify by dividing it,

( x^4-2x^3+2x^2-9x +10 ) ÷ ( x - 2 )

= ( x - 2 ) ( x^3 + 2x - 5 ) ÷ ( x -2 )

= ( x^3 + 2x - 5 )

Therefore, the quotient of the synthetic division for the given dividend is equal to option a . ( x^3 + 2x - 5 ).

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Answer:

Step-by-step explanation:

The distance BC from Tower 2 to the plane is equal to 18,674 feet.

The height of the plane from the ground is equal to 7,595 feet.

In order to determine the distance from Tower 2 to the plane (BC), we would apply the law of sine (sine law) because we have two angles and one side length.

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

[tex]\frac{sin8}{7600} =\frac{sin20}{BC}[/tex]

BCsin8 = 7600sin20

BC = 2599.35/0.1392

Distance, BC = 18,673.50 ≈ 18,674 feet.

Next, we would determine the height of the plane from the ground (CD);

sin24 = CD/18,674

CD = 18,674sin24

Height, CD = 7,595.40 ≈ 7,595 feet.

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Answer:

a)  The length of BC is 15,052 ft to the nearest foot.

b)  The length of CD is 6,122 ft to the nearest foot.

Step-by-step explanation:

Angles on a straight line sum to 180°. Therefore:

[tex]\implies m \angle ABC +24^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle ABC =156^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCA+16^{\circ}+156^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCA=8^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Use the Sine Rule to find the length of BC.

[tex]\implies \dfrac{AB}{\sin BCA}=\dfrac{BC}{\sin CAB}=\dfrac{AC}{\sin ABC}[/tex]

[tex]\implies \dfrac{7600}{\sin 8^{\circ}}=\dfrac{BC}{\sin 16^{\circ}}[/tex]

[tex]\implies BC=\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}[/tex]

[tex]\implies BC=15052.0746...[/tex]

[tex]\implies BC=15052\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of BC is 15,052 ft to the nearest foot.

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCD+24^{\circ}+90^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCD=66^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

To find the length of CD, use the sine trigonometric ratio.

[tex]\implies \sin 24^{\circ}=\dfrac{CD}{BC}[/tex]

[tex]\implies CD=BC\sin 24^{\circ}[/tex]

Substitute the found value of BC into the equation:

[tex]\implies CD=\left(\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}\right)\sin 24^{\circ}[/tex]

[tex]\implies CD=6122.23031...[/tex]

[tex]\implies CD=6122\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of CD is 6,122 ft to the nearest foot.

To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:

Slope = (y2 - y1) / (x2 - x1)

Using the points given in your question, the slope formula to find the slope of the line is:

Slope = (2 - 8) / (4 - (-4))

Using the order of operations, the calculation of the slope formula is as follows:

Slope = -6 / 8

Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.

The height of the tree is closest to 8.66 meters (option B).

Angle of elevation is the angle between a horizontal line of sight and an object above the line of sight, as measured from the observer's eye.

In other words, it is the angle formed between the observer's line of sight and the line drawn from the observer's eye to the object being observed, when the object is above the observer's eye level.

To solve this problem, we can use the property of similar triangles, which states that the ratios of corresponding sides of similar triangles are equal.

For the boy and his shadow, we have:

height of boy / length of boy's shadow = height of tree / length of tree's shadow

Substituting the values given, we get:

56 / 48 = height of tree / x, where x is the length of the tree's shadow

Solving for the height of the tree, we get:

height of tree = (56 / 48) * x

We are not given the length of the tree's shadow, but we can use the information given in the second part of the problem to find it.

For the tree and its shadow, we have:

height of tree / length of tree's shadow = tan(30)

Substituting the value of the length of the tree's shadow as 15 meters and solving for the height of the tree, we get:

height of tree = 15 * tan(30)

height of tree ≈ 8.66 meters

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Answer:

Step-by-step explanation:

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

Answer:

[tex]xy^8[/tex]

Step-by-step explanation:

Notice if you have the same base you can ADD the exponent, for example:

[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]

[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]

so the answer is

[tex]xy^8[/tex]

Answer: 325

Step-by-step explanation:

65% is more than half of the 500 people. Half of the number of people is 250. 325 is the only answer over 250

Answer: I really don't know I'm just trying to get a quest done sorry

This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.

 [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.

The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:

[tex]P \times(1-r/100)^² = P[/tex]

By simplifying and dividing both sides by P, we obtain:

[tex](1-r/100)^² = 1[/tex]

Taking the square root of both sides, we get:

1-r/100 = ±1

Each time we solve for r, we obtain:

[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]

and

 [tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]

We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.

Therefore,  [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

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True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.

Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.

If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.

Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.

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The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²

Area = 1/2(base)(height).

Given the parameters:

If a = 4 and c = 2, then:

Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)

Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)

Area = 1/2(32)(38)

Area = 608 cm²

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Answer: A

y < 2x + 1

y > 1/2x + 2

Answer:

9 x 3/9

27/9

27 ÷ 9

Step-by-step explanation:

You're welcome.

The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.

Martin features a spinner with four compartments marked A, B, C, and D.

To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.

Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

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By conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

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

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

The number that the other number is deducted from is known as a minuend.

Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend.

Difference: A difference is an outcome obtained by deducting a subtractor from a minimum.

So, more miles Michael ran on day 3 than on day 2:

= 7 - 2

= 5 miles

Therefore, by conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

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