Rob loves to run. He set a goal to run more than 390 miles this year.
To date, he has run 127 miles. If he begins to run 18 miles per week,
how long will it take Rob to reach his goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.

Answer:

9.5

Step-by-step explanation:

Law of sine:

[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]

Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°

 ∠Z° = 76°

∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]

Cross- multiplication is applied:

(x)(sin76°) = (14)(sin41°)

x has to be isolated and made the subject of the equation:

x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]

x = 9.466

x = 9.5 (Rounded to the nearest tenth)

If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.

An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.

Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

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The balance will be at least $1200 after 8.18 months, if you deposit $1000 in an account that pays 3.5% annual interest compounded monthly.

The result of earning interest on a principal amount as well as the accumulated interest from earlier periods is known as compound interest. It occurs when money is reinvested rather being paid out, allowing interest to be generated on the principle and accrued interest over the next month.

The balance of an account with an initial deposit of $1000 earning 3.5% annual interest compounded monthly will reach $1200 after 8.18 months.

To find the time it takes for the balance to reach $1200, we can use the formula for compound interest, A = P[tex](1 + r/n)^{nt}[/tex],

where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = 1000, r = 0.035, n = 12 (because the interest is compounded monthly), and t is the unknown variable. We can rearrange the formula to solve for t:

t = (A/P) / (1 + r/n)

Plugging in the values, we get

t = (1200/1000) / (12(1 + 0.035/12))

which simplifies to

t = 8.18 months

Therefore, it will take 8.18 months for the balance of the account to reach $1200.

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Answer: = 1 (look at the image for the solution)

Step-by-step explanation:

Answer:

To find the final price for the jacket, we need to first calculate the amount of the discount and then add the sales tax.

The amount of the discount is $65.00 * 40% = $26.00. So the price after the discount is $65.00 - $26.00 = $39.00.

The sales tax is $39.00 * 5% = $1.95. So the final price for the jacket is $39.00 + $1.95 = $40.95.

Step-by-step explanation:

Answer:

he final price for the jacket is $40.95.

Step-by-step explanation:

First, let's calculate the discount for the jacket:

Discount = $65.00 * 40% = $26.00

The price of the jacket after the discount is:

$65.00 - $26.00 = $39.00

Next, let's calculate the sales tax:

Sales tax = $39.00 * 5% = $1.95

Finally, let's add the sales tax to the discounted price to find the final price:

Final price = $39.00 + $1.95 = $40.95

So, the final price for the jacket is $40.95.

Answer:

284 + 28d

Step-by-step explanation:

Because she has 284 it is known

She plans to obtain 28/day

Therefor, it should be 248+28d

Answer:

The company must make $450.

If the company must pay $300, then you will take 300, and since they want to make a profit, which means 1500 dollars more once they pay the 300, the you will add that to 300.

300 + 150 = 450

Now to find how many weeks it will take, you will divide 450 by 60:

450/60 = 7.5

It will take 7 1/2 (or round it to 8)weeks to gain $450, which is enough money to pay the bank $300, and make a profit of $150.

Step-by-step explanation:

Hope it helps! =D

Answer:

EF this is the correct answer

Answer:

3/400 per min

Explanation:

Divide the rate at which he can walk by the number how mins he can walk at that rate

The measure of the angle m∠AEB, found using the angle of intersecting secant theorem, where the measure of the arcs intercepted by the secants are m[tex]\widehat{AB}[/tex] = 54°, and m[tex]\widehat{CD}[/tex] = 66° is; m∠AEB = 6°

The angle of intersecting secant theorem states that the measure of the angle formed by the intersection of two secant is half the positive difference of the arcs intercepted by the secants.

Please find attached the possible drawing in the question, obtained based on the specified parameters and on similar questions on the internet, created with MS Word.

The parameters indicates that we get;

m[tex]\widehat{AB}[/tex] = 54°

m[tex]\widehat{CD}[/tex] = 66°

The angle of intersecting secants theorem indicates that we get;

m∠AEB = (1/2) × (m[tex]\widehat{CD}[/tex] - m[tex]\widehat{AB}[/tex])

Therefore;

m∠AEB = (1/2) × (66° - 54°) = 6°

m∠AEB = 6°

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Answer:

Step-by-step explanation:

Cardinality of a set refers to the number of elements in the set. There are two types of cardinality: finite and infinite. A set is considered to have finite cardinality if it has a finite number of elements, meaning that the elements can be counted. A set is considered to have infinite cardinality if it has an infinite number of elements and cannot be counted.

In the case of the set B = {x | x ∈ N and x > 5}, the set is comprised of all natural numbers greater than 5. The set of natural numbers is infinite, meaning that there are an infinite number of elements in the set B. As a result, the cardinality of the set B is also considered to be infinite.

The symbol "ℵ0" is used to represent the cardinality of the set of natural numbers, and it is often used to indicate the cardinality of infinite sets with the same size as the set of natural numbers. In this case, we can say that the cardinality of the set B is ℵ0, meaning that the set B has the same size as the set of natural numbers and therefore has infinite cardinality.

The solution to each of the exponent problems are;

a) 10¹¹

b) 10²

c) 10⁴

d) 10¹²

The seven laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

The given expressions are;

a) 10⁵ × 10⁶

= 10⁵⁺⁶

= 10¹¹

b) 10⁴ × 10⁻²

= 10⁴⁻²

= 10²

c) 10⁸/10⁴

= 10⁸⁻⁴

= 10⁴

d) 10⁹/10⁻³

= 10⁹⁻⁽⁻³⁾

= 10⁹⁺³

= 10¹²

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Answer:

11300

Step-by-step explanation:

The closest 100 to 11311 is 11300

If the number was 11351 you would round up to 11400

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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The radius of the circle is 7.8 cm.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given that the area of a circle is 192 cm².

The area of a circle is πr², where r is the radius of the circle.

Assume that the radius of the circle is r.

Therefore,

πr² = 192

Divide both sides by π:

r² = 192/π

r² = 61.115

r = 7.817

r  ≈ 7.8 cm

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The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0   .

We have to solve the algebraic  expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.

So , we subtract "2" from both sides of expression  ,

we get ;

⇒ 3x + 2 - 2 = 8 - 2  ;

Simplifying the left hand side, we get:

⇒ 3x = 6 ;

To solve for the variable x, we on divide both sides by 3 ;

⇒ 3x/3 = 6/3  ;

Simplifying, we get:

⇒ x = 6/3 = 2 .

Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.

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The given question is incomplete , the complete question is

What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.

The measure of the angles are 60 degrees each

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

AOB = 138 degrees

Also, we have:

The line OX bisects the angle AOB

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

AOX = AOB/2 = 138/2 = 69

Also, we have

XOB = AOB/2 = 138/2 = 69

Hence, the angles are 69 degrees each

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When a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

If Victoria signed up for a gym membership 21 weeks after Monica and we let a represent the number of weeks Victoria has been a member and b represent the number of weeks Monica has been a member, then we have a = b + 21.

Substituting a = 9, we get:

9 = b + 21

Solving for b, we subtract 21 from both sides:

b = 9 - 21

b = -12

Therefore, when a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

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The surface area of the pyramid is 116.4 sq. ft.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.

The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.

The area of the triangle is given as:

A = 1/2 (b)(h)

For the face of the pyramid:

b = 12 and h = 9

Substituting the values we have:

A = 1/2 (12)(9)

A = 54 sq. ft

The pyramid consists of three faces thus,

A = 3(54) = 162 sq ft

For the base of the pyramid:

b = 12 and h = 10.4 ft

A = 1/2(12)(10.4)

A = (6)(10.4)

A = 62.4 sq ft

The surface area of the pyramid is:

SA = 54 + 62.4

SA = 116.4 sq. ft

Hence, the surface area of the pyramid is 116.4 sq. ft.

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Answer:

Step-by-step explanation:

To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:

Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.

To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:

-x + 4 = x + 8

Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:

y = -6 + 4 = -2

So, the point of intersection between the two lines is (6, -2).

To find the distance between the point F and the line ℓ, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).

So, substituting the values into the formula:

distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3

Therefore, the distance between the line ℓ and point F is approximately 11.3 units.

Answer:

y = 3x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{3}[/tex] x + 4 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (- 1, - 3 ) into the partial equation

- 3 = 3(- 1) + c = - 3 + c ( add 3 to both sides )

y = 3x + 0 , that is

y = 3x

Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Dimensions of triangle he has to use for fencing are

15 feet, 8 feet, and 20 feet.

For making it a right triangle it must satisfy the "Pythagoras theorem" which states that

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

H²=B²+P²

20²=15²+18²

400=225+64

400≠289

No, it will not be able to make a right triangle.

Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.

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The complete question is given below:

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.

1. Will he be able to make a right triangle out of his fence? Why or why not?

Answer:

∠1 and ∠3

Step-by-step explanation:

The other pair of vertical angles are ∠2 and ∠4

The length of the side using cosine rule and approximating to a whole number gives 23

The law of cosines is used to find the missing parts of an oblique triangle when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.

This is expressed as;

b² = a² + c² - 2ac cos b

Plugging in the relevant values gives;

b² = 28² + 41² - 2(28 * 41) cos 32

b² = 2465 - 1947.118

b² = 517.882

b = √517.882

b = 22.757 ≈ 23

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Answer:

will earn in interest $ 180

To give Tara a lower price, coupon 2 should be applied first.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Tara has two store coupons.

Coupon 1 gives her $10 off on one item.

Coupon 2 gives her 10% off on one item.

Tara can use both coupons together on one item in the store and choose which coupon to apply first.

For an item that has an original price of x dollars,

let f be the function that models the discount price of the item using only coupon 1,

and let g be the function that models the discount price of the item using only coupon 2.

The price of each item in this store is more than $20.

Let the price is $50.

So applying coupon 1 and then coupan2,

we get,

(50 - 10) - ($50 - $10) x 0.10 = $36

Now, apply coupon 2 and then coupon 1,

we get,

$50 x 0.10 - $10 = $35

Therefore, she should apply coupon 2 and then coupon 1.

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