Algebraic Woru
An algebraic word problem can be presented in either a real-life or
require you to set up and solve an equation or inequality to arrive at the
require you to translate words into an expression, equation, or inequate
1. Kyle has three times as much money in his savings account as
Hayden. Hayden has twice as much money in his savings account
as Jeremy. Combined Kyle, Hayden, and Jeremy have a total of
$612. How much money does Kyle have in his account?
(A) $68 Khles Hot money = 3
(B) $136
(C) $204
(D) $306
(E) $408​

To obtain y - x from x - y, add 2y - 2x to x - y which simplifies to y - x.

To transform x - y into y - x, we need to add something that effectively swaps x and y while also changing the sign of both variables. This is a classic example of using the property that A - B is the same as A + (-B). Applying this to our expression, if we add 2y to x - y, we'll get x + y. But, we need y - x, not x + y. So, we need to subtract x twice. Once to cancel out the original x, and a second time to create the negative x in the desired expression. Essentially, we add -2x to our new expression, x + y. So, the final answer is (x - y) + 2y - 2x, which simplifies to y - x.

Answer:

y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2

Step-by-step explanation:

Solve for y:

y^2 + y - 7 = 0

Add 7 to both sides:

y^2 + y = 7

Add 1/4 to both sides:

y^2 + y + 1/4 = 29/4

Write the left hand side as a square:

(y + 1/2)^2 = 29/4

Take the square root of both sides:

y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2

Subtract 1/2 from both sides:

y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2

Subtract 1/2 from both sides:

Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2

Answer:

y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2

Step-by-step explanation:

y^2+y-7=0

completing the square,

(b/2)^2=(1/2)^2=1/4

(y+1/2)^2=7+1/4

(y+1/2)^2=28/4+1/4

(y+1/2)^2=29/4

y+1/2=sqrt(29/4)

y=sqrt(29/4)-1/2

y=sqrt(29)/2-1/2

y=-sqrt(29)/2-1/2

Number of fruit baskets purchased by Mrs. William is 5

Given that  

Annual membership fee of store where Mrs. William shops = $30

Cost of one fruit basket which Mrs. William as gifts for her co-workers = $15

Total amount spent by Mrs. William = $150

Given that "b" represents number of basket purchased

Equation which models the above scenario is as follows

15b+ 30=105   ------ (1)

Where b represents number of fruit basket purchased by Mrs. William

Need to calculate number of fruit basket purchased by Mrs. William

For which we need to solve equation (1) for b  

On solving we get

15b+ 30 = 105    

On Subtracting 30 from both sides we get

15b + 30 – 30 = 105 – 30

=> 15b = 75

On dividing both sides by 15 we get  

[tex]\begin{array}{l}{\frac{15 b}{15}=\frac{75}{15}} \\\\ {=>b=5}\end{array}[/tex]

As variable "b" represents number of basket purchased, hence we can conclude that number of fruit baskets purchased by Mrs. William is 5

Answer:

A) 3x-5=25

I'll try my best on the others

B) x+y^2=18

C)x•6/5=x+4 ????

D).5+x=2-4???

That's all I know :/

Step-by-step explanation:

yeah I'm not sure lol

Answer:

48

Step-by-step explanation:

Answer:

The answer is 48 games out of 84.

Step-by-step explanation:

So first we go through a step by step process.

We have a problem set up that looks something like this.

8/14 = ?/84

Step 1:

So we will first divide 84 by 14, giving us 6.

Step 2:

So 14x6 is equal to 84. Now we have to multiply the top half of the equation by 6. This is 8x6 giving us 48.

Step 3:

Now we substitute the ? with the 48. In the end if playing 84 games the hockey team would win 48 at the rate it was going.

Hope this helped!

Answer:

y=-20

Step-by-step explanation:

-6(y+5)-24=66

-6y-30-24=66

-6y-54=66

-6y=66+54

-6y=120

y=120/-6=-20

Answer:

(3,2)

Step-by-step explanation:

The coordinates of the point P on the given graph is (-1,5).

So, when we translate point P on the graph by 4 units to the right its x-coordinate will change to (- 1 + 4) = 3.

Again, when we translate point P on the graph by 3 units down then its y-coordinate will change to (5 - 3) = 2.

Therefore, the new coordinates of the point P will be (3,2) (Answer)

minus the exponents ( when dividing)

r^9- r^3

answer:

r^6

Which expression is equivalent to [tex]r^9/r^3[/tex] ?  The correct answer is b) [tex]r^6[/tex].

To simplify the expression [tex]r^9/r^3[/tex], we need to apply the rule of exponents. When dividing two terms with the same base, you can subtract the exponents.

In this case, both [tex]r^9[/tex] and [tex]r^3[/tex] have the same base 'r', so we subtract the exponent of [tex]r^3[/tex] from the exponent of [tex]r^9[/tex].

[tex]r^9/r^3[/tex] = [tex]r^{9-3}[/tex] = [tex]r^6[/tex].

In this problem, we are given the expression [tex]r^9/r^3[/tex] and we need to find an equivalent expression for it. To do that, let's understand the rules of exponents.

In general, when you have a term raised to a certain power and you divide it by the same term raised to a different power, you can simplify it by subtracting the exponents. For example, [tex]a^m / a^n = a^{m-n}[/tex].

Now, looking at our expression, [tex]r^9/r^3[/tex], we notice that both terms have the same base 'r'. According to the rule mentioned above, we can simplify the expression by subtracting the exponent of r3 from the exponent of [tex]r^9[/tex].

[tex]r^9/r^3[/tex] = [tex]r^{9-3}[/tex] = [tex]r^6[/tex].

So, the expression [tex]r^9/r^3[/tex] is equivalent to [tex]r^6[/tex]. This means that when you have a term raised to the power of 9 and you divide it by the same term raised to the power of 3, the result is the term raised to the power of 6.

In conclusion, the correct answer is b) [tex]r^6[/tex], as it represents the equivalent expression to [tex]r^9/r^3[/tex] after applying the rules of exponents.

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Answer:

X= -0.4545

Step-by-step explanation:

YOU HAVE TO SUBTRACT .2Z FROM .4Z WHICH GETS YOU .2 ON THE RIGHT SIDE

THAT WOULD MEAN YOU HAVE TO CLEAR OUT THE SEVEN BY ADDING IT ON BOTH SIDES GETTING -1

THEN YOU WOULD HAVE -1=.2Z

THEN DIVIDE BY .2 GETTING YOU A TOTAL OF -0.4545 WHEN YOU FINISH DIVIDING

Final answer:

To find out how much was spent on fresh flowers, 10% of the monthly budget of $5,000 was calculated, resulting in $500 spent on fresh flowers.

Explanation:

If the monthly budget for the front of the house is $5,000, and you spent 10% of the budget on fresh flowers, you can calculate the amount spent on fresh flowers by finding 10% of $5,000. To do this, you simply multiply the total budget by the percentage (expressed as a decimal).

To express 10% as a decimal, you divide 10 by 100, which gives 0.10. Next, multiply the monthly budget by this decimal:

0.10 × $5,000 = $500

Therefore, you spent $500 on fresh flowers.

Final answer:

To factor −1/2 out of −1/2x+6, we identify the common factor, divide each term by −1/2, and write the expression as −1/2 times the simplified expression. The result is −1/2(x − 12).

Explanation:

To factor −1/2 out of −1/2x+6, we can think of pulling out the −1/2 as a common factor from both terms in the expression. Here's a step-by-step breakdown:

Applying these steps, we get:

So, −1/2x+6 factored with −1/2 taken out is −1/2(x − 12).

The solution of the equation is  [tex]x=\frac{11}{7}[/tex]

Step-by-step explanation:

To simplify an equation of x

∵ The equation is [tex]2x + \frac{1-x}{4}=3[/tex]

- Multiply all terms of the equation by 4 to cancel the denominator

 of the 2nd term in the left hand side

∵ The equation is [tex]4(2x) +4 (\frac{1-x}{4})=4(3)[/tex]

∴ 8x + (1 - x) = 12

∴ 8x + 1 - x = 12

- Add like terms

∴ (8x - x) + 1 = 12

∴ 7x + 1 = 12

- Subtract 1 from both sides

∴ 7x = 11

- Divide both sides by 7

∴ [tex]x=\frac{11}{7}[/tex]

The solution of the equation is  [tex]x=\frac{11}{7}[/tex]

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Answer:

[tex]k = - \frac{3}{2}[/tex]

Step-by-step explanation:

If y varies directly with x, then from the relation of direct variation we can write y ∝ x

Now, converting the variation relation to equation relation,

⇒ y = kx  ........... (1) {Where k is the constant of variation}

Now, given that at y = - 3, x = 2 and this solution will satisfy the equation (1).

Hence, - 3 = 2k

⇒ [tex]k = - \frac{3}{2}[/tex] (Answer)

This was a year ago and no one answered I hope you did find the answer

Answer:

(3x + 5)(x - 4)

Step-by-step explanation:

Given

x(3x + 5) - 4(3x + 5) ← factor out (3x + 5) from each term

= (3x + 5)(x - 4) ← in factored form

The unit rate is $2 per can.

Step-by-step explanation:

You divide 6 by 3 which then equals 2.

Answer:

$2.00 per can

Step-by-step explanation:

Answer:

1.

a. 2.75 seconds

b. 169 feet

2. x - 3 is a factor

Other factors: x + 2, 2x + 1, 3x - 4

3. Real zeros: [tex]x = -2[/tex]

Complex zeros: [tex]x_{2,3}=-3\pm 2i[/tex]

Step-by-step explanation:

1. Given equation of parabola

[tex]s(t)=-16t^2+88t+48[/tex]

a) The rocket reaches its maximum height at the vertex of parabola. Find t-coordinate of the vertex:

[tex]t_v=\dfrac{-b}{2a}\\ \\=\dfrac{-88}{2\cdot (-16)}\\ \\=\dfrac{11}{4}\\ \\=2.75\ seconds[/tex]

b) The maximum height is s-coordinate of the vertex. Find it:

[tex]s\left(\dfrac{11}{4}\right)\\ \\=-16\cdot \left(\dfrac{11}{4}\right)^2+88\cdot\left(\dfrac{11}{4}\right)+48\\ \\=-121+22\cdot 11+48\\ \\=169\ feet[/tex]

2. For x – 3 to be a factor of  [tex]f(x)=6x^4-11x^3-35x^2+34x+24,[/tex] the Factor Theorem says that x = 3 must be a zero of  f(x). Check it (whether f(3)=0):

[tex]f(3)\\ \\=6\cdot 3^4-11\cdot 3^3-35\cdot 3^2+34\cdot 3+24\\ \\=6\cdot 81-11\cdot 27-35\cdot 9+102+24\\ \\=486-297-315+126\\ \\=0[/tex]

So, x = 3 is zero of the function f(x) and x - 3 is the factor of the function f(x). Rewrite the function as follows:

[tex]f(x)\\ \\=6x^4-11x^3-35x^2+34x+24\\ \\=6x^4-18x^3+7x^3-21x^2-14x^2+42x-8x+24\\ \\=6x^3(x-3)+7x^2(x-3)-14x(x-3)-8(x-3)\\ \\=(x-3)(6x^3+7x^2-14x-8)\\ \\=(x-3)(6x^3+12x^2-5x^2-10x-4x-8)\\ \\=(x-3)(6x^2(x+2)-5x(x+2)-4(x+2))=\\ \\=(x-3)(x+2)(6x^2-5x-4)\\ \\=(x-3)(x+2)(6x^2+3x-8x-4)\\ \\=(x-3)(x+2)(3x(2x+1)-4(2x+1))\\ \\=(x-3)(x+2)(2x+1)(3x-4)[/tex]

3. [tex]x=-2[/tex] is a zero of the function [tex]f(x)=x^3+8x^2+25x+26,[/tex] then

[tex]f(x)\\ \\=x^3+8x^2+25x+26\\ \\=x^3+2x^2+6x^2+12x+13x+26\\ \\=x^2(x+2)+6x(x+2)+13(x+2)\\ \\=(x+2)(x^2+6x+13)[/tex]

Find the discriminant of the quadratic polynomial [tex]x^2+6x+13;[/tex]

[tex]D=6^2-4\cdot 1\cdot 13=36-52=-16[/tex]

This expression has no more real zeros (the discriminant is less than 0), it has two complex zeros:

[tex]x_{1,2}=\dfrac{-6\pm \sqrt{-16}}{2\cdot 1}=\dfrac{-6\pm 4i}{2}=-3\pm 2i[/tex]

Answer:

Andre is taller.

Step-by-step explanation:

I assume Andre's height is 1.7 m.

Let's convert Andre's height to cm.

1 m = 100 cm

1.7 m = 1.7 * 1 m = 1.7 * 100 cm = 170 cm

Andre is 170 cm tall. Diego is 165 cm tall.

Since 170 cm > 165 cm, Andre is taller.

1.7 m = 170 cm

170 cm > 165 cm

Andre > Diego

Answer:

The value of g'(10)=[tex]\frac{(-1)}{16}[/tex]

Step-by-step explanation:

Given function is f(x)=[tex]\frac{4}{x} + 2[/tex]

Take f(x)=y

y=[tex]\frac{4}{x} + 2[/tex]

Subtract 2 from both side.

y-2=[tex]\frac{4}{x}[/tex]

x=[tex]\frac{4}{y-2}[/tex]

The inverse of f(x) is written as [tex] \frac{4}{y-2}[/tex]

It is said as g is inverse of f

g(y)=\frac{4}{y-2}[/tex]

g(y)=[tex]\frac{4}{y-2}[/tex]

g(10)=[tex]\frac{4}{10-2}[/tex]

g(10)=[tex]\frac{1}{2}[/tex]

Differentiating both sides we get,

g'(y)=[tex]\frac{4(-1)}{(y-2)^{2}}+0[/tex]

g'(y)=[tex]\frac{(-4)}{(y-2)^{2}}[/tex]

To find g'(10)=[tex]\frac{(-4)}{(10-2)^{2}}[/tex]

g'(10)=[tex]\frac{(-1)}{16}[/tex]

Uncle Drew averaged 5.6 points per minute during that 5-minute game.

To find the average number of points Uncle Drew scored per minute during the 5-minute game, we divide the total number of points scored by the number of minutes played.

Given that Uncle Drew scored 28 points in 5 minutes, we divide 28 by 5:

[tex]\[ \text{Average points per minute} = \frac{28}{5} \]\[ \text{Average points per minute} = 5.6 \][/tex]

Answer:

Neil had a better free throw rate.

Step-by-step explanation:

This is because Neil Shot less, but made more.

I hope this helps you!

Final answer:

Neil had a better free throw percentage at approximately 62.87% compared to Avid's 60.07% by calculating the number of successful throws divided by the total attempts and multiplying by 100.

Explanation:

The question involves comparing the free throw rates of two basketball players to determine who had a better free throw percentage. To find the free throw percentage, we divide the number of successful free throws by the total number of attempts and then multiply by 100.

For Neil:

(215 free throws ÷ 342 attempts) × 100 = ~62.87%

For Avid:

(358 free throws ÷ 596 attempts) × 100 = ~60.07%

Neil had a better free throw percentage than Avid as 62.87% is higher than 60.07%.

The area of the circle is approximately [tex]\(69.46 \, \text{mm}^2\)[/tex] and the circumference is approximately [tex]\(53.49 \, \text{mm}\).[/tex]

To find the area A and circumference C of a circle given its diameter d, we can use the following formulas:

1. Area A of a circle:

[tex]\[ A = \pi \times \left(\frac{d}{2}\right)^2 \][/tex]

2. Circumference C of a circle:

[tex]\[ C = \pi \times d \][/tex]

Given that the diameter d is 17 mm, we can plug this value into the formulas to find the area and circumference.

1. Area A of the circle:

[tex]\[ A = \pi \times \left(\frac{17}{2}\right)^2 \]\[ A = \pi \times \left(\frac{17}{2}\right) \times \left(\frac{17}{2}\right) \]\[ A = \pi \times \frac{17 \times 17}{4} \]\[ A = \pi \times \frac{289}{4} \]\[ A = \frac{289}{4} \pi \][/tex]

[tex]\[ A \approx 69.46 \, \text{mm}^2 \][/tex]

2. Circumference (\(C\)) of the circle:

[tex]\[ C = \pi \times 17 \]\[ C = 17\pi \][/tex]

[tex]\[ C \approx 53.49 \, \text{mm} \][/tex]

The length of KD in triangle △AKM, with AK = 6 and KM = 10, and m∠AKM = 93° is 10, since KD is the height of a right triangle and KM is the hypotenuse.

The question asks to find the length of KD in triangle △AKM where KD is perpendicular to AM. Given AK = 6, KM = 10, and m∠AKM = 93º, we can solve for KD using trigonometric ratios.

Since KD ⊥ AM, we have a right triangle △KDM.

We know the hypotenuse KM and angle AKM, so we can use the sine function, where sin(AKM) = opposite/hypotenuse, to find the length of KD. The sine of angle AKM (which is slightly adjusted from 93º to 90º since we are looking for the height in a right triangle) gives us:

sin(90º) = KD/ KM

We know sin(90º) = 1 and KM = 10, so:

1 = KD / 10

Therefore, KD = 10.

Answer:

7x - 8y = 37

Explanation:

y+2 = ⅞(x-3) (distribute ⅞ -- x times 7/8, -3 times 7/8)

y+2 = ⅞x - 21/8 (subtract ⅞x from both sides)

y+2-⅞x = -21/8 (subtract 2 from both sides)

y-⅞x = -37/8 <--- result of -21/8 - 2

Multiply both sides by 8 to get ride of fractions

8y - 7x = -37 (rearrange)

-7x + 8y = -37

It's better to have a positive coefficient for x if you can.  So multiply both sides by -1.  That just means changing the sign of every term on both sides, you get

7x - 8y = 37

Answer:

x=-5, y=6. (-5, 6).

Step-by-step explanation:

x=y-11

2x+3y=8

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

2(y-11)+3y=8

2y-22+3y=8

5y-22=8

5y=8+22

5y=30

y=30/5=6

x=6-11=-5

To reciprocal the term for dividing, then multiply both fractions and get the solution to model  2/3 ÷ 3/4 = 8/9.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

The numeral model is given in the question following:

⇒ 2/3 ÷ 3/4 = 8/9

According to the given question, the required solution would be as:

Find the reciprocal in this situation to divide by a fraction:

3/4 divided by 2/3

This would be: 2/3 x 4/3

When you multiply the components, you get 8/9.

Thus, to reciprocal the term for dividing, then multiply both fractions and get the solution.

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Final answer:

To show that 2/3 divided by 3/4 equals 8/9, we multiply 2/3 by the reciprocal of 3/4, which is 4/3, yielding the answer 8/9. This illustrates that division by a fraction involves multiplying by its reciprocal.

Explanation:

To explain how the model shows that 2/3 ÷ 3/4 = 8/9, we need to understand division of fractions and the concept of reciprocals. Division of fractions is the same as multiplying by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. Therefore, to divide 2/3 by 3/4, we multiply 2/3 by 4/3:

(2/3) × (4/3) = 8/9

This demonstrates that dividing by a fraction is equivalent to multiplying by its reciprocal. We can also use familiar scenarios to rationalize the answer. For instance, we know that half of one half (1/2 × 1/2) equals one quarter (1/4) and this helps us understand the process - we are scaling a number by another when we multiply fractions.

When discussing multiplication and division of fractions, it is useful to remember that these operations are fundamentally linked; division is essentially multiplication by a reciprocal. Hence, dividing 2/3 by 3/4 is the same as multiplying 2/3 by the reciprocal of 3/4, which is 4/3, resulting in 8/9.

Answer:

No solution.

Step-by-step explanation:

2x+1/3=2x

1/3=2x-2x

1/3=0

no solution

Answer:

[tex]\large \boxed{\text{5.00 lb}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}[/tex]

Check:

[tex]\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}[/tex]

OK.

The number of pounds of peaches that Rammy can buy is 5 pounds.

Based on the information given in the question, the equation to solve the question will be:

1.20x + 3.60 ≤ 9.60

Collect like terms

1.20x ≤ 9.60 - 3.60

1.20x ≤ 6.00

Divide both side by 1.20

1.20x/1.20 ≤ 6.00/1.20

x ≤ 5.00

Therefore, the number of pounds of peaches that Rammy can buy is 5 pounds

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Answer:D

Step-by-step explanation:

Your first solution is to look at the 10x^2y in order to get 8 from ten you would need to subtract 2x^something y and there is only one answer with that

Answer:

yes its D.

Step-by-step explanation: