2x − y = 3
4x = 6 + 2y

a. infinitely many solutions

b. x = 2, y = 1

c. y = 2x - 3

d. x = 4, y = 5

r = the number of rides

0.75r + 6.50 ≤ 20.00

[They charge $0.75 per ride (r) plus an admission fee of $6.50, and he can spend at most (maximum) $20. This means that he can spend $20 or less]

Your answer is C

Answer:

Option C is the correct answer.

Step-by-step explanation:

The price of admission to the carnival is $6.50.

Cost per ride = 0.75

Money Cameron having = 20 $

Let the number of rides be r, he cannot spend more than 20 $

That is

                6.50 + 0.75 r ≤ 20.00    

Option C is the correct answer.

Answer:

d = 8t

Step-by-step explanation:

Neither of the "t + ..." answers work for t=0. The d=16t answer does not work for t ≠ 0. The only choice that works for all of the table values is ...

... d = 8t

Check the picture below.

The length of the missing side (the other leg) is approximately 6.47 units.

To find the measure of the missing side of a right triangle when you know the hypotenuse and one of the other sides, you can use the Pythagorean Theorem. The theorem states:

a² + b² = c²

Where:

- a and b are the lengths of the two shorter sides (legs) of the right triangle.

- c is the length of the hypotenuse.

In this case, you know the hypotenuse (c) is 7.4 and one of the legs (height, let's call it 'a') is 3.6. You want to find the length of the other leg (b).

Plug the values into the Pythagorean Theorem:

3.6² + b² = 7.4²

Solve for b:

b² = 7.4² - 3.6²

b² = 54.76 - 12.96

b² = 41.8

To find b, take the square root of both sides:

b = √41.8

b ≈ 6.47 (rounded to two decimal places)

So, the length of the missing side (the other leg) is approximately 6.47 units.

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Answer:

c ∈ {-7, -3, 2, 5}

Step-by-step explanation:

"Illegal" values are those values that make the expression undefined—that is, they make the denominator zero.

The denominator of the product factors as (c+7)(c-2)(c-5)(c+3), so the values of c that will make this product zero are ones that make the factors zero:

... c = -7, +2, +5, -3

_____

Comment on factoring

Each of the quadratics is factored by finding two factors of the constant whose sum is the coefficient of the linear term. You want ...

... factors of -14 = -1·14 = -2·7 . . . . that add to give +5. They are -2 and 7, so the quadratic factors as (c-2)(c+7)

... factors of -15 = 1·(-15) = 3·(-5) . . . . that add to give -2. They are 3 and -5, so the quadratic factors as (c+3)(c-5).

Answer:

8.3%

Step-by-step explanation:

Answer:

Axis of symmetry are lines x=-6 and y=-4, center  (-6,-4)

Step-by-step explanation:

Consideer the equation [tex]x^2+y^2+12x+8y=48.[/tex]

First, complete perfect squares:

[tex](x^2+12x)+(y^2+8y)=48,\\ \\(x^2+12x+36-36)+(y^2+8y+16-16)=48,\\ \\(x+6)^2+(y+4)^2-36-16=48,\\ \\(x+6)^2+(y+4)^2=100.[/tex]

This equation represents a circle with center at point (-6,-4) and radius r=10.

Axis of symmetry are lines x=-6 and y=-4 (vertical and horizontal lines passing through the center).

A. d = 5 − 15t; d = 18t

Derrick's distance from home is initially 5 miles and is decreasing at the rate of 15 miles per hour. His distance from home can be modeled by ...

... d = 5 - 15t . . . . . . d in miles; t in hours

Mark's distance from home is initially zero and is increasing at the rate of 18 miles per hour. His distance from home can be modeled by ...

... d = 18t . . . . . . . . . d in miles; t in hours

Together, these equations form the pair ...

_____

Comment on the equations

There is nothing in the problem statement or definition of the variables to suggest that one distance is measured in the same direction as the other, or that one value of d has any relationship to the other.

Usually, a "system of equations" expresses relationships among variables that all have the same definition with respect to some problem statement. Here, both values of d are "distance from home", but they don't necessarily have any relationship to each other. Their being the same value doesn't mean the boys have met, for example.

Answer:

none shown

Step-by-step explanation:

1/x^3 = x^(-3) has a negative exponent. It does not match the requirement that exponents be a non-negative integer. Therefore, any expression containing 1/x^3 will not be a polynomial.

Answer:

# of granola bars and it's cost.

Step-by-step explanation:

It is asking for the meaning of 2B. Note that inside the question, it states that:

"The price of a granola bar is B dollars".

It also states that:

"Donovan eats 2 granola bars".

This means that to solve for the total spent on granola bars, you multiply the price (B) with the amount gotten (2 in this case).

~

Answer:

2B

Step-by-step explanation:

Means the amount Donovan spends on granola bars each day. Since he has 2 granola bars and the price is B dollars.

Answer:

25.1 kg

Step-by-step explanation:

A suitable probability calculator can tell you the 5th percentile of this distribution.

The correct answer to the subtraction problem is 246 yards of Joshua's fishing line remaining in the water after reeling in 113 yards out of 359 yards. Joshua's initial answer of 489 yards is incorrect.

The student is asking for verification of Joshua’s solution to a subtraction problem that involves determining how much fishing line remains in the water after some has been reeled in. Joshua initially had 359 yards of line in the water and reeled in 113 yards. To find the remaining length of the line in the water, we subtract the length of the line reeled in from the initial length.

Step-by-Step Explanation

Start with the initial length of the fishing line in the water: 359 yards.

Subtract the length of the line that was reeled in: 113 yards.

Perform the subtraction: 359 yards - 113 yards = 246 yards.

So, the length of the fishing line that remained in the water was 246 yards.

Joshua’s answer of 489 yards is not reasonable because it does not reflect the correct subtraction (359 - 113 = 246). The correct answer is 246 yards still in the water.

$6.00

A fairly easy way to do the mental calculation of a 15% tip is to realize that ...

... 15% = 10% + (1/2)·10%

Of course, you can compute 10% by moving the decimal point 1 place left, so ...

... 10% of $40.00 = $4.00

Half that is $2.00, so the 15% tip is $4.00 +2.00 = $6.00.

To calculate the total bill including sales tax and tip, convert the percentages to decimals and multiply by the meal cost. Add the computed sales tax and tip to the original meal cost to get the total payable amount. In the example provided, the total comes to $58.90, including sales tax and tip.

The question involves calculating the total bill for a dinner, which includes the meal cost, sales tax, and tip. To solve this problem, one must perform a series of calculations:

Firstly, figure out the sales tax by converting the percentage to a decimal and multiplying it by the total cost of the meal.

Next, decide on the tip percentage, convert it to a decimal, and again multiply by the cost of the meal.

Add both the sales tax and the tip to the original cost of the meal to get the total amount to be paid at the register.

Using the provided example, if the meal cost is $47.50 and the sales tax is 6%, you would calculate the tax as follows:

0.06  x47.50 = $2.85 (sales tax)

And if they decide to leave an 18% tip:

0.18 x $47.50 = $8.55 (tip)

Finally, you add the meal cost, sales tax, and tip:

$47.50 + $2.85 + $8.55 = $58.90

The total amount to be paid at the register with a credit card is $58.90, which includes the meal cost, sales tax, and tip.

Answer:

£2,520

Step-by-step explanation:

The exchange rate of U.S. dollars to British pounds is .63. You have $4000 to convert to British pounds (?). 4,000 * .63 = 2,520. Therefore the amount of British pounds you will receive is: £2,520.

Answer:

Option B is correct.

2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

As per the given statement: Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium.

Let x be the fluid ounce of milk.

then, by using proportion method we have;

[tex]\frac{7}{236.25} = \frac{x}{67.5}[/tex]                       ......[1]

Cross multiply states that an equation of fractions when each side consists of a fraction with a single denominator by multiplying the numerator of each side by the denominator of the other side and then, equating the two products obtained.

Apply cross multiply in [1];

[tex]7 \times 67.5 = 236.25 \times x[/tex]

Simplify:

[tex]472.5 = 236.25x[/tex]

Divide 236.25 we get;

[tex]x = \frac{472.5}{236.25}[/tex]

Simplify:

x = 2.0

therefore, 2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium

Answer:

x = 12  

Step-by-step explanation:

√(x + 4) - 3 = 1     Add 3 to each side

   √(x + 4) = 4      Square each side

       x + 4 = 16     Subtract 4 from each side

             x = 12

=====

Check:

√(12 + 4) – 3 = 1

       √16 – 3 = 1

           4 – 3 = 1

                  1 = 1

Answer:

Step-by-step explanation:

We have equation

[tex]\sqrt{x+4} -3=1[/tex]

to solve for x we first add 3 to both side

[tex]\sqrt{x+4}-3+3=1+3\\\sqrt{x+4} =4[/tex]

now we need to remove square root from left side, so we square both sides

[tex]x+4=4^{2}[/tex]

[tex]x+4=16[/tex]

now we subtract 4 from both sides

[tex]x+4-4=16-4\\x=12[/tex]

The sale price was 30% off the original price, which means it was on sale for 70% of the original cost ( 100% - 30% = 70%)

To find the original cost, divide the sale price by the percent of the original cost:

21 / 0.70 = 30

The original price was $30

check:

30 x 0.3 = 9 ( amount of discount)

30 - 9 = 21 ( sale price)

Final answer:

To find the original price of the sweatshirt that Zoe found, which was sold at a 30% discount, we use the sale price of $21 to calculate that the original price was $30 by dividing by 0.70. An example with sales tax involves an $85 jacket with 7.5% tax, where sales tax is rounded to $6.38 and added to the original price for a total of $91.38.

Explanation:

To determine the original cost of the sweatshirt that Zoe found, which was discounted by 30%, we need to work backwards from the sale price. The sale price represents 70% of the original cost since the item is 30% off. If the sale price is $21, we can set up the equation 0.70 * original price = $21 to find the original price.

Dividing both sides of the equation by 0.70 gives us the original price. Therefore, original price = $21 / 0.70. After performing this calculation, we find that the original cost of the sweatshirt was $30

Emily bought a jacket for $85. If the sales tax is 7.5%, the amount of sales tax would be calculated as 0.075 * $85, which equals $6.375. To get the total cost, we would round $6.375 to the nearest penny to get $6.38, and then add it to the original price of the jacket. The total cost is $85 + $6.38 = $91.38.

Answer:

5 x-intercepts at most.

Step-by-step explanation:

Polynomial function with degree of 5

End behavior: falls to the left and rises to the  right OR falls to the right and rises to the left .

Can have 0,1,2,3 or 4 turning points; can have

0,1,2,3,4 or 5 x-intercepts

A quintic polynomial, which is of degree 5, can have at most 5 x-intercepts as per the Fundamental Theorem of Algebra.

A quintic polynomial is a polynomial of degree 5. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots, or solutions. However, not all roots necessarily represent x-intercepts, as some might be complex roots.

On a graph, x-intercepts are points where the polynomial touches or crosses the x-axis, corresponding to the real roots of the polynomial equation. So, in general, a quintic polynomial will have at most 5 x-intercepts. This is because a polynomial of degree n can intersect the x-axis at most n times.

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Answer:

-25x⁵y⁵

Step-by-step explanation:

Coefficients include (-5)(5) = -25

x-factors include (x^3)(x^2) = x^5

y-factors include (y^2)(y^3) = y^5

Then the product is ...

... -25x^5·y^5

Answer:

0.45

Step-by-step explanation:

9/20=0.45

Travis spent 9/20, which in decimal form is 0.45, of his 20-minute preparation time eating breakfast, which is equivalent to 9 minutes.

Travis spent a total of 20 minutes getting ready for school. Out of this time, he spent 9/20 of it eating breakfast. To express this fraction of time as a decimal, we simply perform division: 9 divided by 20.

9 / 20 = 0.45

Therefore, Travis spent 0.45 of the 20 minutes, or 45% of his preparation time, eating breakfast. When converting this to minutes, 0.45 * 20 minutes equals 9 minutes. Thus, Travis spent 9 minutes eating breakfast.

49°

∠DEF = ∠1 +∠2 = 50° +48° = 98°

∠ABC = ∠DEF because they are alternate exterior angles, hence congruent.

∠3 = ∠4 because they are vertical angles.

∠3 = (1/2)∠ABC = (1/2)·98° . . . . . ∠4 is half of ∠ABC

∠3 = 49°

Answer:

D  2n+2

Step-by-step explanation:

We can check the slope of the function

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

   = (10-8)/(4-3)

   = 2/1

The slope is 2

We can use the point slope form of a line to calculate the equation for a line

y-y1 = m(x-x1)

y-2 = 2(x-2)

Distribute

y-6=2x-4

Add 6 to each side

y-6+6  = 2x-4+6

y = 2x+2

Add all the hours together:

1 3/4 + 1 1/4 = 3 + 1 1/2  = 4 1/2 + 1 1/5

To add fractions with different denominators, find the common denominator and rewrite the fractions

Common denominator of 2 and 5 is 10

1/2 becomes 5/10

1/5 becomes 2/10

now you have 4 5/10 + 1 2/10 = 5 7/10 + 2 = 7 7/10

Now subtract that from 12:

12 - 7 7/10 = 4 3/10 hours

24. (A) 1.6

23. (A) 4

Amy's distance is proportional to the time spent riding, so in 12/30 of the time (12 minutes out of 30 minutes), she will ride 12/30 of the distance:

... (12/30)·(4 mi) = 48/30 mi = 1.6 mi

Sally's speed is (66 mi)/(3 h) = 22 mi/h. Molly's speed is (72 mi)/(4 h) = 18 mi/h.

The difference between their speeds is (22 -18) mi/h. = 4 mi/h.

Final answer:

A) 1.6 and A)4

Amy can ride her bike 1.6 miles in 12 minutes, and the difference in average speed between Sally and Molly is 4 mph.

Explanation:

To find the distance Amy can travel in 12 minutes, first determine her speed in miles per minute. Since Amy can ride her bike 4 miles in 30 minutes, her speed is 4 miles / 30 minutes = 0.1333 miles/minute. To find out how far she can go in 12 minutes, multiply her speed by the time: 0.1333 miles/minute x 12 minutes = 1.6 miles. Therefore, Amy can ride 1.6 miles in 12 minutes, which corresponds to answer choice (A).

Calculating the Difference in Average Speed

Sally's average speed is 66 miles / 3 hours = 22 mph, and Molly's average speed is 72 miles / 4 hours = 18 mph. The difference in their average speeds is 22 mph - 18 mph = 4 mph, which corresponds to answer choice (A).

Answer:

[tex]3GR=27[/tex]

Step-by-step explanation:

Since area of rectangle BCND is given as 90 and one of its side is 10, the other side MUST be 9.

[tex]CN*BC=90\\CN*10=90\\CN=9[/tex]

In Rhombus CGNR, CN and GR are congruent (property of Rhombus). Hence GR = 9 as well.

Thus 3GR = 3(9) = 27

First answer choice is right.

∠A ≅ ∠C

Angles complementary to the same angle are congruent to each other. Angles A and C are both complementary to angle B, hence they are congruent.

If angle A is complementary to angle B, and angle C is also complementary to angle B, then angles A and C must be equal. This is because complementary angles add up to 90 degrees.

If ∠A is complementary to ∠B, and ∠C is also complementary to ∠B, then ∠A and ∠C are equal.

Complementary angles add up to 90 degrees. This means that ∠A + ∠B = 90° and ∠C + ∠B = 90°. Therefore, if ∠B is the same in both instances, it can be deducted that ∠A = ∠C because they are both equal to the remaining measure after subtracting ∠B from 90°.

In simpler terms, if you know that two different angles are both complementary to a same angle (∠B in this case), then those two angles must be equal to each other.

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Answer:

55,900 cm²

Step-by-step explanation:

The area of a triangle is half the product of its base and height.

... A = (1/2)·b·h

... = (1/2)(430 cm)(260 cm)

... = 55,900 cm²

Answer:

see below

Step-by-step explanation:

a)  w <= 40 lbs

b)  Do you have any bag that weigh 0 lbs or negative lbs?

We need to rewrite the inequality so that these are not there

0<= w <= 40 lbs

Domain

The argument of the square root function must be non-negative, so ...

... x+2 ≥ 0

... x ≥ -2

The denominator cannot be zero, so there is a disallowed value of x at ...

... x/2 -3 = 0

... x/2 = 3

... x = 6 . . . . . . . . . excluded from the domain

Range

The value of the expression is 8 for x=-2. As x approaches 6, the value of y approaches -∞.

Because the denominator is squared (has an even exponent), the sign does not change as x crosses 6, so function values increase from -∞ toward the horizontal asymptote at y=8.

Thus the range is (-∞, 8].

[tex]a-digit\ of\ tens\\b-digit\ of\ ones\\10a+b-the\ number\\10b+a-the\ number\ with\ reversed\ digits\\\\\left\{\begin{array}{ccc}a+b=12&\to b=12-a\\10b+a=15(10a+b)\end{array}\right\\\\\text{Substitute}\\\\10(12-a)+a=15(10a+12-a)\\10(12-a)+a=15(9a+12)\qquad\text{use distributive property}\\(10)(12)+(10)(-a)+a=(15)(9a)+(15)(12)\\120-10a+a=135a+180\\120-9a=135a+180\qquad\text{subtract 120 from both sides}\\-9a=135a+60\qquad\text{subtract 135a from both sides}\\-144a=60\qquad\text{divide both sides by (-144)}\\\\a=-\dfrac{60}{144}[/tex]

a is negative and it's not a digit.

Answer:

a) brenda is right

Step-by-step explanation:

five prime numbers: 2, 3, 5, 7 and 11. A prime number is an integer, or whole number, that has only two factors — 1 and itself