What is the common difference d of the sequence? −15, −4, 7, 18, 29, ...

I think the answer is 6.381 gallons or 3.2?

The number of gallons of gasoline Jordan need each day is:

                            3.190476 gallons.

It is given that:

Jordan’s job is located 67 miles from his home.

His car’s gas mileage is 21 miles to the gallon.

i.e. for 21 miles he need 1 gallon of gas.

This means in order to cover 1 mile he needs 1/21 gallon of gas.

Hence,

In order to cover 67 miles he needs 67/21 gallon of gas

i.e.

for 67 miles he needs 3.190476 gallons of gas.

Area of shaded region is 463 square units.

Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height

The apothem of any polygon is equal to the line that connects the center of the polygon with one of its sides perpendicularly. Using the apothem, we can calculate the area of the polygons in an easier way.

Given

Apothem of the octagon = 13.28 units

Base of octagon = 11 units

Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height

= [tex]\frac{1}{2}[/tex] × [tex]11[/tex] × [tex]13.28[/tex] × [tex]8[/tex]

= 584.32

Area of square = side × side

= 11 × 11

= 121

Area of shaded region = Area of octagon - Area of square

= 84.32 - 121

= 463.32

≅ 463 square units.

Hence, area of shaded region is 463 square units.

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Answer: im sorry if im wrong but i think the answer is 0.3

Step-by-step explanation:

The circumference of the circle is found by first determining the side length of the square, then using that to calculate the diameter and radius of the circle. Using 3.14 as an approximation for pi, the circumference is calculated to be 37.7 meters when rounded to the nearest tenth.

To find the circumference of the circle when the square has an area of 144 m², we first determine the side length of the square using the formula for the area of a square, A = a², where A is the area and a is the side length.

A = 144m²

a = 12m

Since the area is 144 m², the side length of the square is "12 m (since 12 x 12 = 144).

Since the circle fits perfectly within the square, the diameter D of the circle is equal to the side length of the square. Therefore, D = 12 m. The radius r is half the diameter, so in this case, r = 6 m.

The formula for the circumference C of a circle is C = 2πr.

C = 2 x 3.14 x 6 m = 37.68 m

The circumference is 37.7 m.

Answer: A: one or more points of interest.

Step-by-step explanation:

The rule says that an image should be divided into 9 equal squares by two horizontal and two vertical lines and that the important objects of the image should be placed between the lines (in the centers of the squares) or in the intersections of the lines.

In this way, the eye is dragged to the different points that the artist wants the viewer to focus on the image, then the correct option is option A:  one or more points of interest.

Answer:

a.  Essential (flexible) expense

Step-by-step explanation:

Most people consider a cell phone an essential expense, since they are used in power outages or emergencies while traveling.

This is a flexible expense, since there are extra fees for extra usage.  

The phone bill expense is an Essential (flexible) expense so option (A) will be correct.

The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.

In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.

The mobile cost is an essential cost because it is can be used in an emergency situation or it is very useful for calling massaging or video calling.

Since the plan for mobile recharge varies higher or lower according to benefits so it will be a flexible expense.

Hence "The phone bill expense is an Essential (flexible) expense".

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Answer:

Slope-Intercept Form states that in the equation of a straight line y=mx+b the slope is the number represented by m that is multiplied on the x, and b is the y intercept i.,e the point where line cut the vertical  y-axis.

Given equation: 5x+2y=3              ......[1]

To convert this equation into slope intercept form;

Subtraction Property of equality states that you subtract the same number from both sides of an equation.

Subtract 5x from both sides in equation [1];

[tex]5x+2y-5x=3-5x[/tex]

Simplify:

[tex]2y=3-5x[/tex] or we can write this as;

[tex]2y=-5x+3[/tex]                 ......[2]

Division property of equality states that you divide the same number from both sides of an equation:

Divide by 2 from both sides of an equation in [2]

[tex]\frac{2y}{2} =\frac{-5x+3}{2}[/tex]

On simplify:

[tex]y=-\frac{5}{2}x+\frac{3}{2}[/tex]

Therefore, the given equation in slope intercept form is: [tex]y=-\frac{5}{2}x +\frac{3}{2}[/tex]

Final answer:

To find all cube roots of -125i in polar form, convert them to a+bi form by expressing -125i in polar form, finding the cube roots, and converting them to a+bi form.

Explanation:

To find all the cube roots of -125i in polar form and convert them to a+bi form, follow these steps:

Express -125i in polar form: -125i = 125∠-90°.

Find the cube roots by taking the cube roots of the magnitude and adding multiples of 360°/3 to the argument.

The cube roots of -125i in a+bi form are 5∠-30°, 5∠90°, and 5∠210°, which correspond to -2.5-4.33i, 0+5i, and 2.5-4.33i respectively.

Answer:

Margin of error: 6%; Confidence Interval Percentage: 90%; Confidence Interval: 74% and 86%

Step-by-step explanation:

Margin of error: 6%  --  It's already given in the question.

Confidence interval is at 90%. 9/10=.90

The exam creator is saying that they are 90% confident that the seniors test scores will be between 74% and 86%.

0.8 - 0.06 = 0.74

0.8 + 0.06 = 0.86

The confidence interval is (0.74, 0.86)

To find out how much 250 envelopes would cost, set up a proportion using the given information that 100 envelopes cost 70 cents. Cross-multiply and solve for the unknown cost, which is $1.75.

To find out how much 250 envelopes would cost, you can use the concept of proportions. Since 100 envelopes cost 70 cents, you can set up a proportion to find the cost of 250 envelopes: 100/70 = 250/x, where 'x' represents the unknown cost. Cross-multiplying, you get 100x = 70 * 250. Dividing both sides by 100, you find that x = 175.

Therefore, 250 envelopes would cost 175 cents.

In decimal form, 175 cents is equal to $1.75.

Final answer:

To find the value of 15 units when 7 units represent 98 liters, set up a proportion, cross multiply, and divide to find the value of 15 units, which is 210 liters.

Explanation:

To find the value of 15 units when 7 units represent 98 liters:

Answer:

D is your answer :)

Step-by-step explanation:

Answer:

The correct answer is c.

Step-by-step explanation:

Given the equation

[tex]ax^{2}+bx+c=0[/tex]

The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):

[tex]\frac{-b|\sqrt{b^{2}-4ac}}{2a}[/tex]

The solutions of [tex]4x^{2}+x=-3[/tex] are the same that the solutions of [tex]4x^{2}+x+3=0[/tex]

With [tex]a=4\\b=1\\c=3[/tex] we replace this in the quadratic equation ⇒

[tex]\frac{-1|\sqrt{(1)^{2}-4(4)(3)}}{(2)(4)}[/tex]  ⇒

[tex]\frac{-1|\sqrt{1-48}}{8}[/tex] ⇒

[tex]\frac{-1|\sqrt{-47}}{8}[/tex]

Given that [tex]i^{2}=-1[/tex] (imaginary numbers property)

[tex]\frac{-1|\sqrt{47i^{2}}}{8}=\frac{-1|i\sqrt{47}}{8}[/tex]

The solutions are [tex]\frac{-1+i\sqrt{47}}{8}[/tex]

and [tex]\frac{-1-i\sqrt{47}}{8}[/tex]

The correct answer is c.

Answer: C

Step-by-step explanation: I just took the test and got it right <3

With the given conditions of angle A being 30 degrees, side a being 1.5 cm, and side b being 2 cm in a triangle, only one possible triangle satisfies these properties according to the Law of Sines.

The question relates to determining the number of possible triangles given certain conditions. Specifically, it refers to a triangle with an angle A of 30 degrees, a side a of 1.5 cm opposite to A, and another side b of 2 cm. To decide the number of possible triangles that fit these criteria, we make use of the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

In the given scenario, since side a (1.5 cm), opposite to angle A (30 degrees), is shorter than side b (2 cm), it is possible that two different triangles could exist, often referred to as the ambiguous case in the Law of Sines. However, the fact that side a is shorter than side b coupled with angle A being acute (30 degrees) leaves us with only one possible triangle. This is because the side opposite the smallest angle (A) cannot form a valid triangle if it's longer than the other given side. Therefore, there is just one solution to this problem.

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To find the number of toppings at which the pizzas cost the same, we can set the total cost expressions for both pizzas equal to each other and solve for 'x'. After 4 additional toppings, the pizzas will cost the same. With 5 additional toppings, Johnson's Pizza costs more.

To find the point at which the pizzas cost the same, we need to determine the number of toppings that will make the total cost equal for both pizzas. Let's denote the number of additional toppings as 'x', and the cost of each additional topping at Fine Dough Pizza as $1.50, and at Johnson's Pizza as $2.00. The total cost for Fine Dough Pizza will be $10.00 + $1.50x, and the total cost for Johnson's Pizza will be $8.00 + $2.00x. To find the number of toppings at which the pizzas cost the same, we can set the two total cost expressions equal to each other and solve for 'x':

$10.00 + $1.50x = $8.00 + $2.00x

To solve the equation, we can subtract $1.50x from both sides:

$10.00 = $8.00 + $0.50x

Next, we subtract $8.00 from both sides:

$2.00 = $0.50x

To isolate 'x', we divide both sides by $0.50:

x = 4

Therefore, after 4 additional toppings, the pizzas will cost the same.

To determine which pizza costs more with additional toppings, we can compare the total cost expressions for both pizzas for a specific number of toppings. For example, let's consider 5 additional toppings:

Total cost at Fine Dough Pizza = $10.00 + $1.50(5) = $10.00 + $7.50 = $17.50

Total cost at Johnson's Pizza = $8.00 + $2.00(5) = $8.00 + $10.00 = $18.00

Therefore, with 5 additional toppings, Johnson's Pizza costs more.

Answer:

8y

Step-by-step explanation:I took the test

8y contain the variable term where the variable is 'y'.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

expression: 8y + 9

As, we know a symbol without a set value is referred to as a variable.

So, 8y contain the variable term where the variable is 'y'.

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