Noah ran 54 miles in 9 days.The graph relating Greta’s total distance to the number of days passes through the points (0,0) and (5,45).Who ran more miles per day?

The inequality that represents the dollar amount, a, that Alex can spend on apples is a < $9.25.

To determine the inequality, we need to consider that Alex has $23.25 in his pocket and wants to buy apples, limes, and kale. The kale and limes together cost over $14, which means their combined cost is greater than $14. To find the maximum amount Alex can spend on apples, we subtract the amount spent on kale and limes from the total amount he has.

Let's represent the amount spent on kale and limes as k + l, where k represents the cost of kale and l represents the cost of limes. The inequality representing the dollar amount, a, that Alex can spend on apples is given by:

a < $23.25 - (k + l)

Since the cost of kale and limes is greater than $14, we have k + l > $14. Substituting this into the inequality, we get:

a < $23.25 - $14

Simplifying, we have:

a < $9.25

Therefore, the inequality that represents the dollar amount, a, that Alex can spend on apples is a < $9.25.

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The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Answer:

80

Step-by-step explanation:

took the test

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that n ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

YZ = 2n ≥ 2 × 5 = 10

ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Explanation

if you know 2 points of a line you can easily find the slope using

Let

P1(-1,5)

P2(7,1)

replace,

I hope this helps you

Answer:

x - 6 < 2x + 2

-8 < x, so x > -8

x = -1 and x = -5 are solutions to this inequality.

Given :

Calculators cost $12.99 each, rulers cost $0.49 each, pencils cost $0.10 each, and erasers  cost $0.05 each.

To Find :

How much would Mrs. Algebra's single order be.

Solution :

Total price paid by Mrs. Algebra = Price of pencil + price of ruler + price of calculator + price of eraser.

T = $(0.10 + 0.49 + 12.99 + 0.05)

T = $13.63

Therefore, Mrs. Algebra's single order cost is $13.63 .

Hence, this is the required solution.

Answer:

D

Step-by-step explanation:

It has 2 equal sides

Answer:

D) Isosceles

Step-by-step explanation:

An isosceles triangle is the triangle that has 2 sides that are the same.

Answer:

5:8

5 to 8

Step-by-step explanation:

There are 8 students total and 3 boys wear glasses so there is 5 girls left that wear glasses.

Hope this helps :)

Answer:

0.42

Step-by-step explanation:

when your multiplying decimals that small, it usually doesnt go into the whole number range

x²/21 + y²/25 = 1 is the equation of the ellipse

Given: the length of the major axis = 10 and foci = (0, ± 2)

Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:

x²/b² + y²/a² = 1

Since the length of the major axis = 2a. Thus:

2a = 10

a = 10/2 = 5

a² = 5² = 25

c = 2

c² = a² - b²

2² = 5² - b²

4 = 25 - b²

b² = 25 - 4 = 21

Substitute a² = 25 and b² = 21 into the equation:

x²/b² + y²/a² = 1

x²/21 + y²/25 = 1

Therefore,  the equation of the ellipse is x²/21 + y²/25 = 1

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Answer:

Step-by-step explanation:

For every time you have a probability of getting 1 is:

For all 6, the probability of outcome of 1 is:

Probability of 1

Probability of 6

P(1×6)

The conclusion that can be drawn from Jimmy's income with the change in insurance is that Jimmy's net income would decrease.

When expenses rise, net income will decrease. Net income is calculated by subtracting expenses from gross income, so if expenses increase, the amount of net income will decrease.

This means that with the increase in insurance by $ 50, Jimmy can expect that his net income would decrease by a total amount of $ 50 which is the amount the insurance increased by.

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Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be \(900-880=20\) meters from the starting point.

Answer:

x = 36

y = 34

Step-by-step explanation:

✔️Sum of the interior angles of an n-sided polygon = (n - 2) × 180

Thus, the figure given is a hexagon with 6 sides.

Therefore, the sum of its interior angles = (6 - 2) × 180

= 4 × 180 = 720.

This means:

(5x) + (4x + 2) + (5x + 5) + (2x - 2) + (3x + 5) + (x - 10) = 720

Solve for x

5x + 4x + 2 + 5x + 5 + 2x - 2 + 3x + 5 + x - 10 = 720

Add like terms

20x = 720

Divide both sides by 20

x = 36

✔️(2y - 1) + (3x + 5) = 180 (angles on a straight line)

Plug in the value of x

2y - 1 + 3(36) + 5 = 180

2y - 1 + 108 + 5 = 180

Add like terms

2y + 112 = 180

Subtract 118 from each side

2y = 180 - 112

2y = 68

Divide both sides by 2

y = 68/2

y = 34

The limit of y(t) as t approaches infinity is y = 1.

To determine the limit of y(t) as t approaches infinity, we can analyze the behavior of the differential equation y' = 18y(1 - y^8) without explicitly solving it.

We start by examining the equation y' = 18y(1 - y^8). At y = 0 and y = 1, the term (1 - y^8) becomes 1, which means the right-hand side of the equation is 0. This implies that y(t) will remain constant at y = 0 and y = 1.

Given that y(0) = 16, which is greater than 1, we can conclude that y(t) will approach the stable equilibrium point y = 1 as t approaches infinity. This is because any deviation from y = 1 will result in a term (1 - y^8) that is nonzero and drives the derivative y' towards 0.

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Answer:7/9

Step-by-step explanation:

The value of m∠J in the triangle is 65°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.

Since the sum of angle in a triangle is 180°. We can say:

m∠H +  m∠I +  m∠J = 180°

(4x + 1)° + (2x-6)° + (6x-7)° = 180°

4x + 1 + 2x-6 + 6x-7 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

To find m∠J = (6x-7)°, put x = 12 into  m∠J = (6x-7)°. That:

m∠J = 6(12) - 7

m∠J = 72 - 7

m∠J = 65°

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Answer: We will use long division to find the quotient of (x³ - 3x² + 5x + 3) ÷ (x + 1).

    x² - 4x + 9  

___________________

x + 1 | x³ - 3x² + 5x + 3

- (x³ + x²)

--------------

-4x² + 5x

-(-4x² - 4x)

------------

9x + 3

-(9x + 9)

-------

6

Therefore, the quotient of (x³ - 3x² + 5x + 3) ÷ (x + 1) is x² - 4x + 9 with a remainder of 6.

Step-by-step explanation:

Answer:

3 3/4 tins of food

Step-by-step explanation:

Number of cats = 3

Quantity of food for each cat per day = 1/4 of a tin

Total tins of cat food sue bought = 4 tins

Has Sue bought enough cat food to feed her cats for 5 days?

Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats

= 1/4 × 3

= 3/4 of a tin

Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days

= 3/4 × 5

= (3 * 5) / 4

= 15/4

= 3 3/4 tins of food

Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food

Recall,

Total tins of cat food sue bought = 4 tins

Therefore, Sue bought enough cat food to feed her cats for 5 days

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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The two positive numbers that satisfy the given requirements are 12 and 4.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Let's call the two positive numbers we're trying to find "x" and "y". We know that the product of x and y is 48, so:

x * y = 48

We also know that we want to minimize the sum of x and 3y, so we can set up an equation for that:

f(x,y) = x + 3y

Now we want to find the values of x and y that minimize this function, subject to the constraint that x * y = 48. We can use the method of Lagrange multipliers to solve this problem.

First, we set up the Lagrangian function:

L(x,y,λ) = x + 3y + λ(xy - 48)

Then we find the partial derivatives of L with respect to x, y, and λ:

∂L/∂x = 1 + λy

∂L/∂y = 3 + λx

∂L/∂λ = xy - 48

Setting the partial derivatives equal to zero, we get:

1 + λy = 0

3 + λx = 0

xy = 48

Solving for λ in the first equation, we get λ = -1/y. Substituting into the second equation and solving for x, we get x = -3/λ = 3y. Substituting x = 3y into the third equation, we get:

3y * y = 48

Simplifying, we get:

y² = 16

So y = 4 or y = -4. Since we're looking for positive numbers, we take y = 4. Then x = 3y = 12.

So the two positive numbers that satisfy the given requirements are 12 and 4.

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To determine the number of sections for each course, we need to find the number of sections required to generate $40,000 in revenue for each course. Let's denote the number of sections for Finite Math as "x," the number of sections for Applied Calculus as "y," and the number of sections for Computer Methods as "z."

Given that each section of Applied Calculus has 40 students and earns $1,000, the revenue generated by Applied Calculus sections is 40y($1,000) = $40,000y. Similarly, each section of Computer Methods has 10 students, so the revenue generated by Computer Methods sections is 10z($1,000) = $10,000z.

Since the total revenue required is $40,000, we have the equation:

$40,000y + $10,000z = $40,000

Now, let's consider the number of students in each course. Each section of Applied Calculus has 40 students, so the total number of students in Applied Calculus is 40y. Each section of Computer Methods has 10 students, so the total number of students in Computer Methods is 10z.

To determine the number of sections, we need to divide the total number of students by the number of students in each section. Therefore, the equations are:

x(40) = Total number of students in Finite Math

y(40) = Total number of students in Applied Calculus

z(10) = Total number of students in Computer Methods

Since the total number of students should not exceed the total enrollment, we have:

x(40) + y(40) + z(10) ≤ Total enrollment

Based on the given information, we can determine the appropriate number of sections for each course by solving these equations and inequalities. The specific values will depend on the total enrollment and the constraints imposed by the available resources and class sizes.

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Answer: \(x^2+\frac{11}{4}x+\frac{3}{2}\)

Step-by-step explanation:

Use FOIL:

\(x^2+\frac{3}{4} x+\frac{4}{2} x+\frac{12}{8}\)

\(x^2+\frac{3}{4} x+\frac{8}{4}x+\frac{12}{8} \\\)     Make 3/4x and 4/2x have the same denominator

\(x^2+\frac{11}{4}x+\frac{12}{8}\)            Add like terms

\(x^2+\frac{11}{4}x+\frac{3}{2}\)              Simplify

It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.

A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.

Now, consider an example;

When you wish to build a perpendicular line on a line segment, like line AB, you do the following;

A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.

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The answer to the question is: 10 books left in stock.The equation that used to solve this problem is 7 + 10 = x - 17.

This question can be solved by using an equation. The equation that used to solve this problem is 7 + 10 = x - 17. This equation can be solved by first multiplying both sides by 2. This will give us 2x17 = x. Then, subtract 17 from both sides, which gives us x = 119 - 17. Finally, subtract 7 from both sides to get 10 = x - 17. Therefore, the answer to the question is 10 books left in stock.

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The largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

Explanation:

To find where the function is increasing, we need to find where the first derivative of the function is positive. Taking the derivative of f(x), we get:

f'(x) = (-2x) / (x^2 + 1)^2

The denominator of this expression is always positive, so the sign of f'(x) is determined by the numerator. The numerator is negative for x < 0 and positive for x > 0. Therefore, f(x) is decreasing on (-∞, 0) and increasing on (0, ∞).

We also need to check the endpoints of these intervals to make sure that the function is increasing on the entire interval. As x approaches negative infinity, the function approaches 0, and as x approaches positive infinity, the function approaches 0. Therefore, the function is increasing on (-∞, 0) ∪ (0, ∞).

In summary, the largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

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