Item 17
Are the expressions 8x2+3(x2+y) and 7x2+7y+4x2−4y equivalent? Which best explains your reasoning?

Final answer:

The sum of the two numbers is 60 and their quotient is 4. Using the substitution method, we find that the two numbers are 48 and 12.

Explanation:

Let's call the two numbers x and y. We're given that the sum of the two numbers is 60, so we can write the equation:

x + y = 60

We're also given that their quotient is 4, so we can write the equation:

x / y = 4

To solve this system of equations, we can use the substitution method. Solving the second equation for x, we get:

x = 4y

Substituting this value of x into the first equation, we get:

4y + y = 60

Combining like terms, we have:

5y = 60

Dividing both sides by 5, we find:

y = 12

Substituting this value of y back into the equation x = 4y, we get:

x = 4(12)

Simplifying, we find:

x = 48

So the two numbers are 48 and 12.

Answer:

0

Step-by-step explanation:

These are two lines with equal slopes and different y intercepts so they will be parallel and will never intersect

Answer:

Step-by-step explanation:

8)Volume of cylinder = πr²h= π*3*3*10 =90π cubic inches

Volume of cone = 1/3πr²h = π*3*3*5/3= 15π cubic inches

Volume of rocket = 90π + 15π = 105π cubic inches

9) Matt made an error. radius = diameter/2 = 15/2= 7.5 cm.Instead using 7.5 in volume formula, he used diameter.

The x-intercepts appear on this polynomial are 3 x intercepts.

Step-by-step explanation:

To find the x intercepts of the polynomial [tex]f(x)=x^{4} -5x^{2}[/tex] is by equating [tex]f(x)=0[/tex]

Thus, the equation becomes

[tex]\begin{array}{r}{x^{4}-5 x^{2}=0} \\{x^{2}\left(x^{2}-5\right)=0}\end{array}[/tex]

Equating, we get,

[tex]x^{2}=0,\left(x^{2}-5\right)=0[/tex]

[tex]x=0[/tex], [tex]\begin{aligned}x^{2}-5 &=0 \\x^{2} &=5 \\x &=\pm \sqrt{5}\end{aligned}[/tex]

Thus, the x-intercepts are [tex]x=0, x=\sqrt{5} , x=-\sqrt{5}[/tex]

Hence, the x-intercepts appear on this polynomial are 3 x intercepts.

Answer:

1 x-intercepts

Step-by-step explanation:

has same question on a test

Answer: 4x + 76 = 688, $153 per ticket

Step-by-step explanation:

there are 4 tickets but you don't know the price of the tickets. Let x represent the price. Insurance costs $19. They got insurance ($19) on all 4 tickets (19 x 4) to get a insurance total of $76.

To get the price of one ticket we need to solve the equation.

4x + 76 = 688

subtract 76 from both sides.

4x = 612

divide by 4.

x = 153

each ticket costs $153

Final answer:

The price of one airline ticket, without insurance, is $153. This was found by setting up an equation for the total cost (4 tickets plus insurance for each at $19 per ticket) and solving for the price of one ticket.

Explanation:

To solve the problem, we first set up an equation to represent the total cost for the family's purchase of 4 airline tickets with travel insurance. We let x represent the price of one ticket, and since the travel insurance costs $19 per ticket, the cost of insurance for one ticket can be represented as 19 + x. There are 4 tickets, so the total cost of insurance for four tickets is $19 multiplied by 4 (which equals $76). Therefore, the equation for the total cost is:

Total Cost = 4x (price of tickets) + $76 (cost of insurance for all tickets)

According to the question, the total cost for the family is $688. So we can set up the equation:

4x + 76 = $688

To find the value of x, we subtract 76 from both sides of the equation:

4x = $688 - $76

4x = $612

Now divide both sides by 4 to solve for x:

x = $612 / 4

x = $153

Therefore, the price of one ticket is $153.

Answer:

Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]

Step-by-step explanation:

Given:

point G( x₁ , y₁) ≡ ( 2 ,-3)  

point D( x₂ , y₂) ≡ (2 , 4)  

To Find:

Distance between GD=?

Solution:

Distance Formula between two point is given by

[tex]l(GD) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(GD) = \sqrt{((2-2)^{2}+(4-(-3))^{2} )}[/tex]

[tex]l(GD) = \sqrt{((0)^{2}+(4+3))^{2} )}=\sqrt{49}=7\\l(GD)=7\ units[/tex]

Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]

Answer:

I believe the answer to this question is: X=square root(39), and square root(-39).

Answer:

x = -43/6

Step-by-step explanation:

To solve this equation, you solve for 'x' by isolating it. This means to move every other number to the other side of 'x'. You can move numbers when they 'cancel' out by doing the opposite (Adding and subtracting are opposites. Dividing and multiplying are opposites).

[tex]\frac{3x-2}{6}-\frac{4x+1}{4} = 3[/tex]

[tex]\frac{3x-2}{6}*\frac{2}{2}-\frac{4x+1}{4}*\frac{3}{3} = 3[/tex]     Multiply each fraction by a fraction that equals '1'. (2/2 = 1 and 3/3 = 1). This will give them a common denominator.

[tex]\frac{(3x-2)*2}{6*2}-\frac{(4x+1)*3}{4*3} = 3[/tex]     Multiply

[tex]\frac{(6x-4)}{12}-\frac{(12x+3)}{12} = 3[/tex]

[tex]\frac{(6x-4)-(12x+3)}{12}= 3[/tex]     Combine the fractions with the same denominator

[tex]\frac{(6x-4)-12x-3}{12}= 3[/tex]     Subtract binomials. -(12x+3) is -12x-3

[tex]\frac{6x-4-12x-3}{12}= 3[/tex]     Remove unnecessary brackets

[tex]\frac{-6x-7}{12}= 3[/tex]     Combined like terms.

[tex]\frac{-(6x+7)}{12}= 3[/tex]     Factor out the negative in the top.

[tex]-(6x+7)= 3*12[/tex]     Multiplied both sides by 12

[tex]-(6x+7)= 36[/tex]     Simplified right side

[tex]6x+7= -36[/tex]     Divided both sides by -1

[tex]6x= -36-7[/tex]     Subtract 7 from both sides

[tex]6x= -43[/tex]     Simplified right side

[tex]x= \frac{-43}{6}[/tex]     Divided both sides by 6. Answer in fraction form.

x = 7.166..67     Answer in decimal form

Therefore x is -43/6 or about 7.17.

Answer:

answer is y=10x

Step-by-step explanation:

multiply time by 10 to equal models sara's direct variaton.

The equation models Sara's direct variation if, Sara's earnings vary directly with the number of hours she works, which is y = 10x, so option B is correct.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

Sara's earnings vary directly with the number of hours she works,

x = number of hours worked, and y = earnings,

The equation for the above statement can be written as shown below,

earnings = number of hours worked  × salary

Assume the salary is a then,

y = ax

If she gets a salary of $10 then,

y = 10x

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Answer:

The system of equations will have an infinite number of solutions.

Step-by-step explanation:

i) when we arrive at a solution of a linear system with two equations and two

 variables and the solution of the equation does not give the value of any

 variable but rather is in the form of an identity like the one given, that is

 -6 = -6, then we can say that the two equations are exactly the same and

  that the system of equations will have an infinite number of solutions.

Answer:

Rayshawn originally had $30.

Step-by-step explanation:

i) Rayshawn has a certain amount of money. Let us say this amount is $x.

ii) Rayshawn spends $20 which means that he is left with $(x - 20)

iii) it is also given that amount of money left after spending $20 is [tex]\dfrac{1}{3}[/tex] of the original amount, $x, the amount remaining is [tex]\dfrac{\$x}{3}[/tex].

iv) from the information given in ii) and iii) we get

     $(x - 20) = [tex]\dfrac{\$x}{3}[/tex],  Therefore we get 3x - 60 = x , therefore 2x = 60,

  Therefore x = $30. Rayshawn originally had $30.

Therefore, Rayshawn had $60 initially.

If Rayshawn spends $20 and ends up with 1/3 of the original amount, we can deduce that $20 represents 2/3 of the original amount.

since 1 - 1/3 = 2/3. Thus, each part (1/3) of the original amount corresponds to $20. Consequently, to find the original amount, we multiply $20 by 3, yielding $60. Therefore, Rayshawn originally had $60. This conclusion emerges from understanding that after spending $20, Rayshawn retains 1/3 of his original funds, implying that the $20 spent was equal to 2/3 of his initial sum. Thus, the inverse operation, multiplying by 3, unveils the original amount. Therefore, Rayshawn had $60 initially.

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C(n, r) = (n!)/(r!*(n-r)!) is the combination formula

C(7, 5) = (7!)/(5!*(7-5)!)

C(7, 5) = (7!)/(5!*2!)

C(7, 5) = (7*6*5!)/(5!*2!)

C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled

C(7, 5) = (7*6)/(2*1)

C(7, 5) = 42/2

C(7, 5) = 21

Answer:

Mr Jackson should get $8.88 back.

Step-by-step explanation:

$50 - $41.12 = $8.88

An exterior angle is equal to the sum of the two opposite inside angles.

T + 31 = t + t-29

Simplify:

T + 31 = 2t -29

Add 29 to both sides:

T + 60 = 2t

Subtract 1t from both sides:

T = 60

Answer: (x−3)(x+7)

=(x+−3)(x+7)

=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)

=x^2+7x−3x−21

=x^2+4x−21

The product of (x-3) and (x+7) is x² + 4x - 21

The product of (x - 3) and (x + 7) can be found as follows:

(x - 3)(x + 7)

open the bracket by multiplying

Therefore,

x(x) +x(7) - 3(x) - 3(7)

x² + 7x - 3x - 21

combine like terms

x² + 4x - 21

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Answer:

[tex]AE=20\ units[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles AEB and DEC are similar by AA Similarity Theorem

so

[tex]\frac{AB}{DC}=\frac{AE}{DE}[/tex]

substitute the given values and solve for x

[tex]\frac{10}{4}=\frac{2x+10}{x+3}[/tex]

Multiply in cross

[tex]10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5[/tex]

Find the length side AE

[tex]AE=2x+10[/tex]

substitute the value of x

[tex]AE=2(5)+10=20\ units[/tex]

Answer:

She will need 191.55 pounds of flour.

Step-by-step explanation:

Given:

Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes.

If she plans on baking 72 birthday cakes and 5 wedding cakes.

Now, to find pounds of flour will she need.

So, the pounds of flour for 72 birthday cakes:

[tex]2.4\times 72[/tex]

[tex]=172.8\ pounds.[/tex]

And, the pounds of flour for 5 wedding cakes:

[tex]5\times 3.75[/tex]

[tex]=18.75\ pounds.[/tex]

Now, to get the pounds of flour she need we add the pounds of flour to make 72 birthday cakes and 5 wedding cakes:

[tex]172.8+18.75[/tex]

[tex]=191.55\ pounds.[/tex]

Therefore, she will need 191.55 pounds of flour.

Answer:

The vertex is the point (1,-8)

Step-by-step explanation:

we have

[tex]y=-4x^{2} +8x-12[/tex]

Convert to vertex form

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+12=-4x^{2} +8x[/tex]

step 2

Factor the leading coefficient

factor -4

[tex]y+12=-4(x^{2} -2x)[/tex]

step 2

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]y+12-4=-4(x^{2} -2x+1)[/tex]

[tex]y+8=-4(x^{2} -2x+1)[/tex]

step 3

Rewrite as perfect squares

[tex]y+8=-4(x-1)^{2}[/tex]

therefore

The vertex is the point (1,-8)

Answer: x≈3

Step-by-step explanation:

0.48 = log x , this could also be written as :

[tex]log_{10}[/tex] x = 0.48 , that is

x = [tex]10^{0.48}[/tex]

x = 3.01995172

x≈ 3

The solution to the equation 0.48 = log x is approximately 3.02 after converting it from logarithmic form into exponential form and calculating 10 to the power of 0.48.

To solve the logarithmic equation 0.48 = log x we have to rewrite this equation in exponential form. A logarithm log_b(x) = y in exponential form is represented as b^y = x. Considering that in your question it's not specified, this likely means a base of 10 is being used. Hence, the equation 0.48 = log x can be converted into exponential form: 10^0.48 = x.

Performing the calculation with a calculator (or by hand if you know how), we find x ≈ 3.02. Therefore, the solution for x in the given equation is approximately 3.02.

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Answer:

x = 130°

Step-by-step explanation:

Segment AC tangent to circle O then ∠A = 90°

Segment BC tangent to circle O then ∠B = 90°

finally ,

x = 360 -(90+90+50) = 360-230 = 130

Answer:

x = 130°

Step-by-step explanation:

Answer:

what do you need?

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

what is the question

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

going negative stops at 4

$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest

Solution:

Given that, total of $6000 was invested

Let "x" be the amount invested at 3 % interest

Then, (6000 - x) is the amount invested at 8 % interest

Given that,

The total yearly interest amounted to $380

Then, we can frame a equation as:

[tex]x \times 3 \% + (6000 - x) \times 8 \% = 380[/tex]

Solve the above expression for "x"

[tex]x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000[/tex]

Thus, $ 2000 is invested at 3 % interest

(6000 - x) = 6000 - 2000 = 4000

$ 4000 is invested at 8 % interest

Answer:

y = - 5x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Here m = - 5 and b = 7, thus

y = - 5x + 7 ← equation of line

Good morning ☕️

Answer:

Step-by-step explanation:

y=mx+b

m = slope = -5

b = y-intercept = 7

then the equation is : y = -5x + 7

:)

Final answer:

An algebraic expression that represents 'x squared is less than 15' can be written directly as 'x² < 15', without additional mathematical operations.

Explanation:

The question asks for an algebraic expression that represents the inequality 'x squared is less than 15'. This is straightforward to write and does not require completing the square or solving a quadratic equation. The algebraic expression that correctly represents this inequality is simply x² < 15.

To explain further, the inequality suggests that the square of x (x²) must be less than the value 15. We do not need to perform any additional steps or manipulations like factoring or applying the quadratic formula, as the expression represents a basic inequality in its simplest form.

Answer:

See below for the graph:

Step-by-step explanation: