Solve the following quadratic equation by factoring.

x^2 - 5x = 14

(Answers are in photo)

10 points!!!
Please explain how you got your answer.

Answer:

(p+3)(p-7) = 0

Step-by-step explanation:

Given p=x^2+6p and (x^2+6)^2-21=4x^2+24

We are to substitute the the p = x²+6 into the expression as shown;

The expression (x^2+6)^2-21=4x^2+24 will become

(x²+6)²-21 = 4(x²+6)

On substituting p, the expression becomes;

p²-21 = 4p

Subtract 4p from both sides

p²-21-4p = 4p-4p

p²-4p-21 = 0

p²-7p+3p-21 = 0

p(p-7)+3(p-7) = 0

(p+3)(p-7) = 0

Hence the expression in terms of p is (p+3)(p-7) = 0

Answer:

Step-by-step explanation:

Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

[tex]18.75= 1.25x +3.75y[/tex]

Multiply the whole equation by 4 to remove the decimals:

[tex]75= 5x +15y[/tex]

Simplify by dividing the whole equation by 5:

[tex]15 = x + 3y[/tex]

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

[tex]\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}[/tex]

x +3y= 15 -----(2)

x= -3y +15

[tex]\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}[/tex]

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

Answer:

6 games=$7.5  3 rides=$11.25

1.25*6=7.5

3.75*3=11.25

7.5+11.25=18.75

Step-by-step explanation:

Let's make the number we're finding to be [tex]a[/tex]. So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be [tex]\frac{a}{4} +12\\[/tex]. It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be [tex]\frac{a}{3} -5\\[/tex]. Since they are the same, we have the equation below.

[tex]\frac{a}{4} +12 = \frac{a}{3} -5\\[/tex]

All we have to do now is to find [tex]a[/tex].

[tex]\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204[/tex]

Our number must be [tex]204[/tex]. I think

Answer:

a. 10 by 25,000

b. 25,000 interval because the x and y axis would both have 10 marks

c. 1-10 because it meets the exact number needed, and gives the graph a nice, square look

d. 1 because it will give the graph a nice size and perfect range.

Step-by-step explanation:

Answer:

b......................

Answer:

31.5 cups of salsa can be made

Step-by-step explanation:

4 x 4.5 =18

7 x4.5=31.5

Step-by-step explanation:

[tex]w = \frac{1}{2} {x}^{2} y \\ (2)w = \frac{1}{2} {x}^{2} y(2) \\ 2w = {x}^{2} y \\ \frac{2w}{ {x}^{2} } = \frac{{x}^{2} y}{ {x}^{2} } \\ \frac{2w}{ {x}^{2} } = y[/tex]

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

Answer

the answer is D

Step-by-step explanation:

the square root of 300 is 17.3

so there for it lies between 17 and 18

Answer:

c

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

5.5

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Answer:

14.58

Step-by-step explanation:

1.08 is tax multiplied by 15 is 16.20 after tax. 90% of that is 14.58

Answer:

you pay 15.3 dollars

Step-by-step explanation:

15 times 0.1 is 1.5

15 times 0.08 is 1.2

15-1.5+1.2=15.3

Answer: 0.66 or 66%? (34% decrease)

Step-by-step explanation: 21+13=34 and 100-34 is 66

Answer:

x=12

Step-by-step explanation:

divide by 4 on both sides

the solution to the equation is x = 12.

To solve the equation 4x = 48,

we need to isolate the variable x.

We can do this by dividing both sides of the equation by 4.

4x / 4 = 48 / 4

When we divide 48 by 4, we get 12.

So, 4x = 48 simplifies to x = 12.

Therefore, the solution to the equation is x = 12.

This means that if we substitute 12 for x in the equation 4x, we get

4 multiplied by 12, which equals 48, satisfying the original equation.

Learn more about Equation here

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Answer:

a = [tex]\frac{h-r}{b}[/tex]

Step-by-step explanation:

Given

h = ab + r ( subtract r from both sides )

h - r = ab ( isolate a by dividing both sides by b )

[tex]\frac{h-r}{b}[/tex] = a

Answer:

$10,825

Step-by-step explanation:

let C: represent the total cost which is what we are looking for

let a: represent the cost of renting a truck

let b: represent the cost of each tone of sugar

let s: represent the quantity of the tons of sugar

From the question the additional cost of the sugar depends on the tons

so we multiply the tons by $175

so our equation will be

C = a + bs

in this case our value of b is $175

so we have

C = a + $175s

C = $7500 + ($175 * 19)

C = $7500 + $3325

C = $10,825

Answer:

Please provide more details.

Step-by-step explanation:

Answer:

6.7082039325                         If you want to round it is 7

Step-by-step explanation:

a squared + b squared = c squared, where as 6 is a, 3 is b, and x is c.

6 squared + 3 squared is 36+9=45, so x is the square root of 45.

6.7082039325

Answer:

1 sig figs = 1st number is a non zero number and all following numbers are zero (if no decimal point present)

if decimal point is present then it can be 0.x where the x can be any number but nothing can come after it

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Unlikely

Step-by-step explanation:

There are more chances that tomorrow there will be no rain than the raining we can say that it is unlikely to rain tomorrow.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The weather forecast calls for a 20% chance of light rain tomorrow.

Probability of rain:

P(rain) = 20% = 0.2

Complement event: Not rain tomorrow

Probability of complement event P(not rain) = 1 – 0.2 = 0.8 or 80%

P(not rain) > P(rain)

Thus, there are more chances that tomorrow there will be no rain than the raining we can say that it is unlikely to rain tomorrow.

Learn more about the probability here:

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Answer:

m∠2 = 37°

m∠3 = 143°

m∠4 = 37°

Step-by-step explanation:

From the figure attached,

Two arms of the scissors represent he two lines intersecting each other at a point forming pairs of vertical angles ∠1, ∠3 and ∠2, ∠4.

By the definition of vertical angles,

∠1 ≅ ∠3 and ∠2 ≅ ∠4

Since, m∠1 = 143°

Therefore, m∠1 = m∠3 = 143°

m∠1 + m∠2 = 180° [Since linear pair of angles are supplementary]

143° + m∠2 = 180°

m∠2 = 180° - 143° = 37°

Therefore, m∠2 = m∠4 = 37°  

Answer: 6

Step-by-step explanation: 10/5=2 2*3=6 which means Mr. Kelly received 4 and Mr. Smith received 6 dollars.

Answer:

a) 3710

b) 3932.6

Step-by-step explanation:

well I'm assuming youre not cheating, but i hope you can understand this because it's pretty crucial beyond math class

anyway it's just

a) 3500 + .06(3500) = 3710

b) (3500 + .06(3500)) + (3500 + .06(3500))*.06 = 3932.6

Answer:

-3(x+3) + 4x

simplifies to

x-9

Step-by-step explanation:

have a good day

Answer: -9

Step-by-step explanation:

−3(x+3)+4x

Distribute:

=(−3)(x)+(−3)(3)+4x

=−3x+−9+4x

Combine Like Terms:

=−3x+−9+4x

=(−3x+4x)+(−9)

=x+−9

Answer:

=x−9

Have a good day can u give me brainliest pls.