Quadratic equations and factoring

8x^2 +10x+3=0

Answer:

Part 1) The equation for the monthly charges for Runfast is [tex]y=8x+8[/tex] and for BA&D is [tex]y=4x+15[/tex]

Part 2) The solution of the system of equations is the point  (1.75.22)

Step-by-step explanation:

Let

x -----> the number of gig of data

y -----> the total monthly charges

we know that

Runfast Company

[tex]y=8x+8[/tex] -----> equation A

BA&D Company

[tex]y=4x+15[/tex] -----> equation B

Part 2) Use your mathematical skill to solve this system of equations using the substitution method

we have

[tex]y=8x+8[/tex] -----> equation A

[tex]y=4x+15[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]4x+15=8x+8[/tex]

[tex]8x-4x=15-8[/tex]

[tex]4x=7[/tex]

[tex]x=1.75\ Gb[/tex]

Find the value of y

[tex]y=8(1.75)+8=\$22[/tex]

so

The solution is the point (1.75.22)

That means

For the number of gig equal to 1.75 the monthly charge is equal to $22 in both company's

therefore

For a number of gigs less than 1.75 the company Runfast has the better pricing, while for a number of gigs greater than 1.75 the company BA&D has the better pricing

Answer: 4 + (-1)^10 = 4+ 1 = 5

The tenth term of the sequence is 5.

Given to us,

Sequence, [tex]\bold{a_n=4+(-1)^n}[/tex]

For tenth term,

n = 10,

Subsituting the value of n we get,

[tex]{a_n=4+(-1)^n}\\a_{10}=4+(-1)^{10}\\a_{10} = 4 + 1\\a_{10} = 5[/tex]

Hence, the tenth term of the sequence is 5.

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Answer:

84 m²

Step-by-step explanation:

If you mention "hypotenuse," I automatically assume that this is a right triangle.  We can find the length of the third side using the Pythagorean Theorem:  7² + x² = 25², or x² = 625 - 49 = 576.

Then the 3rd side (which is also the height of the triangle) is x = √576 = 24.

The base of this triangle is 7 m and the height is 24 m.

The area is thus:

A = (1/2)(base)(height) = (1/2)(7 m)(24 m) =   84 m²

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 5 and (a, b) = (2, - 1), so

y - (- 1) = - 5(x - 2), that is

y + 1 = - 5(x - 2) → A

The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y + 1 = - 5 (x - 2)

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Here, Given that;

Slope = - 5

Point on line = (2, - 1)

Hence, The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y - y₁ = m (x - x₁)

⇒ y - (- 1) = - 5 (x - 2)

⇒ y + 1 = - 5x + 10

⇒ y =- 5x + 10 - 1

⇒ y = - 5x + 9

Thus, The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y + 1 = - 5 (x - 2)

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Answer:

d = C /t

Step-by-step explanation:

C = td

We want to isolate d, so divide each side by t

C/t = td/t

C/t = d

d = C /t

Answer: c/d = t

Since d is being multiplied by t, to get d by itself we simply divide both sides of the equation by t and we have c/d = t which is our final answer.

Answer:

6

Step-by-step explanation:

Given in the question that,

length of the diagonal of a square = 6√2

As we know that a square have all lengths equal in size and lengths are perpendicular to each other so to solve this question we will use pythagorus theorem

hypotenuse² = base² + height²

here,

hypotenuse is the diagonal of the square

base and height side length of the square

Plug value in the formula

6√2² = l² + l²

36(2) = 2l²

72 = 2l²

l² = 72/2

l² = 36

take square root on both sides of the equation

l = √36

Answer:

6

Step-by-step explanation:

The diagonal of the square represents the hypotenuse of a right triangle formed by the diagonal and 2 sides of the square.

Using Pythagoras' theorem

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the side of the square then

x² + x² = ( 6[tex]\sqrt{2}[/tex])²

2x² = 72 ( divide both sides by 2 )

x² = 36 ( take the square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6

See the attached picture:

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] +X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right]\\\\\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]+X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]\\\\X=\left[\begin{array}{ccc}6-8&4-(-7)\\0-1&5-(-5)\end{array}\right]\\\\X=\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right][/tex]

Answer:

the answer is D

Step-by-step explanation:

To solve the inequalities 3x + 1 ≥ 8 and 10x ≤ 15, we find that no x can satisfy both inequalities simultaneously. Thus, the solution set is empty and the correct answer is B. No solution.

Solving the System of Inequalities

We need to find the solution set for the system: 3x + 1 ≥ 8 and 10x ≤ 15.

3x + 1 ≥ 8

Subtract 1 from both sides: 3x ≥ 7

Divide by 3: x ≥ 7/3 x ≥ 2.33

10x ≤ 15

Divide by 10: x ≤ 1.5

For the two conditions x ≥ 2.33 and x ≤ 1.5 to both be true, there is no number x that satisfies both.

Therefore, the solution set is empty.

The correct answer is B. No solution.

The equivalent expression would be,

⇒ (x - 5) (x + 5)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² - 25

Now, We can simplify as;

⇒ x² - 25

⇒ x² - 5²

⇒ (x - 5) (x + 5)

Thus, The equivalent expression would be,

⇒ (x - 5) (x + 5)

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Final answer:

The expression x²- 25 is a difference of squares and can be factored into (x - 5)(x + 5), which is the product of two binomials.

Explanation:

The expression x²² – 25 can be factored into a product of two binomials because it represents a difference of squares. A difference of squares is a specific type of polynomial that takes the form a²– b², which can be factored into (a – b)(a + b). In the case of x² – 25, we can identify a as x and b as 5 since 52 equals 25.

Therefore, we can factor the expression x² – 25 into:

(x – 5)(x + 5)

This utilizes the factoring technique, which is a crucial algebraic skill for simplifying expressions and solving equations.

ANSWER

Option D

EXPLANATION

The parent radical function is

[tex]f(x) = \sqrt{x} [/tex]

The transformed function is

[tex]g(x) = 2 \sqrt{x - 3} [/tex]

This is a transformation of the form.

[tex]y = a \sqrt{x - k} [/tex]

which shifts the parent function horizontally by k units to the right and stretches the parent function vertically by a factor of 'a'.

In this case a=2 and k=3,

there is a horizontal shift of 3 units to the right and a vertical stretch by a factor of 2.

The last choice is correct.

Answer:

about 785.4

Step-by-step explanation:

The circumference of a circle is pi times the diameter:

C = πd

C = π·(250 ft) ≈ 785.4 ft

_____

Most scientific or graphing calculators have the value of π built in. If yours doesn't, a value good for at least 6 significant figures is the ratio 355/113.

The ferris wheel rotates approximately 785 feet in one complete turn. This was calculated using the circumference formula, 2πr, with the radius derived from the given diameter of 250 feet.

To solve this problem, we need to determine the circumference of the Ferris wheel as that would be equivalent to the distance the ferris wheel rotated in one complete turn. The formula to calculate the circumference of a circle (or ferris wheel in this case) is 2πr (2 times pi times the radius), where 'r' is the radius of the circle. However, since we're given the diameter of the Ferris wheel as 250 feet, we know that the radius 'r' would be half of the diameter. That would imply that the radius in this case is 250/2 = 125 feet. So, using the aforementioned formula, the circumference would therefore be 2 × π × 125, or approximately 785 feet. Therefore, with each complete turn, the Ferris wheel would rotate by about 785 feet.

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Answer:

Area= 615 ft²

Step-by-step explanation:

Apply the formula for area of a circle to find the area watered when a sprinkler covers a full circle

Area of a circle= [tex]\pi r^{2}[/tex]

r= 14ft

Area= 3.14 × 14²

Area=615.44 ft²

Area= 615 ft²

Answer:

$21.34

Step-by-step explanation:

You and 3 friends went out for dinner, total 4 people

The bill is $85.36

So

Each person owes = $85.36 / 4 = $21.34

Answer:28.45

Step-by-step explanation:divide 3 by 85.36

Answer:

the answer is 9

Answer:

27 - t · 3

27 - 6 · 3

27 - 18

9

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

It is linear because it have two variables (x and y) and the highest powers that they are raised to are 1

For this case we have that by definition, a linear equation is of the form:

[tex]ax + b = 0[/tex]

That is, the largest exponent of the variable is 1.

Then, according to the options given, we have that the correct option is option D, that is:

[tex]4x + 6 = 30[/tex]

Answer:

Option D

To fond the price before the increase divide the new price by 1 plus the percent of increase:

720 / 1.03 = 699.029

Rounded to the nearest penny = 699.03

Answer:

c. 10

Step-by-step explanation:

First of all, the sum can be simplified.

[tex]\sum\limits^6_{n=1} {(x-3n)}=\sum\limits^6_{n=1} {x}-3\sum\limits^6_{n=1} {n}\\\\=6x-3\cdot\dfrac{6\cdot 7}{2} =6x-63[/tex]

This result can be used in the equation ...

6x -63 = -3

6x = 60 . . . . . add 63

x = 10 . . . . . . . divide by 6

_____

Comment on the ∑n

The sum of numbers 1 to n is n(n+1)/2. We have used that fact here. For this problem, the sum is short enough you can simply add it up: 1+2+3+4+5+6 = 21.

[tex]\bf \displaystyle\sum\limits_{n=1}^{6}~(x-3n)=-3\implies \sum\limits_{n=1}^{6}~x-\sum\limits_{n=1}^{6}~3n=-3\implies \sum\limits_{n=1}^{6}~x-3\sum\limits_{n=1}^{6}~n=-3 \\\\\\ 6(x)~~-~~3\left[ \cfrac{6(6+1)}{2} \right]=-3\implies 6x~~-~~3[3(7)]=-3\implies 6x - 63 = -3 \\\\\\ 6x=60\implies x=\cfrac{60}{6}\implies x=10[/tex]

Answer:

[tex]3x+5 + \frac{28}{2x-4}[/tex]

Step-by-step explanation:

If the volume of the rectangular prism is represented by [tex]6x^2 - 2x + 8[/tex] and the base area is [tex]2x - 4[/tex]

Volume of a prism = base area times height

we replace the volume and the base area

[tex]6x^2-2x+8 = (2x-4) \cdot height[/tex]

Divide both sides by 2x-4

[tex]height= \frac{6x^2-2x+8}{2x-4}[/tex]

we use long division.

                                      3x+5                          

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

  [tex]2x-4[/tex]                 [tex]6x^2 - 2x + 8[/tex]

                                   [tex]6x^2 - 12x[/tex]

                               -----------------------------------------------(subtract)

                                              [tex]10x+8[/tex]  

                                              [tex]10x-20[/tex]  

                               ------------------------------------------------(subtract)

                                                            28

[tex]3x+5 + \frac{28}{2x-4}[/tex]

Hello there! n < -2.

Solve for n. To do this, you want to get all other terms on the other side of the equation. The only other term is 7 in this case, so subtract 7 from both sides of the equation.

n +7-7< 5​-7

n < -2

This is your final answer! I hope this helps and have a great day!

Answer:

The solution is n<-2

Step-by-step explanation:

The given inequality is:

n+7 <5​

We solve this inequality by adding -7 to both sides of the inequality:

n+7 +-7<5​+-7

We simplify to get:

n+0<5​-7

this finally gives us:

n<-2

The solution is n<-2

Answer:

Step-by-step explanation:

Red = 6

Blue = 3

Green = 5

Total = 14

First marble = 6/14  = 3/7  You now have 5 reds and 13 total

Second Marble = 5 * 13  which brings you down to 4 red and 12 total.

Third Marble = 4/12 = 1/3

Result

P(3 Red) = 3/7 * 5/13 * 1/3     cancel the 3s

P(3 Red) = 1/7 * 5/13

P(3 Red) = 5/91

P(3 Red) = 0.0549 . Rounding to the nearest 1/100 depends on what you have been told about rounding. I would say the answer is 0.05 but your teacher may say something different.

I=PRT/100

1. Make R (rate) subject

R/100= I/PT

2. Substitute and calculate

r/100= i/pt

r/100= 40/400 × 1

(40 is from 440-400.The interest)

r/100= 0.1

r/100×100= 0.1×100

r=10% (interest rate per year)

To confirm

I=PRT

I= 400×10/100×1

I= $40 (Interest)

Answer:

$40

Step-by-step explanation:

find Y

$400=x

$440=x+y

x+$40=x+y

$40=y

THE ANSWER ABOVE/ BELOW IS WRONG!!!

The correct answer is actually:

140

Answer:

140

Step-by-step explanation:

Answer:

-6x + 15 = - 69 which x = 14

Step-by-step explanation:

You cannot solve this equation. There is no equal sign anywhere. Either you mean

-6x = 15 in which case the answer is

-6x/-6 = 15/-6

x = - 2 1/2 or x= - 2.5

or you mean that you use the distributive property

- 3(2x + 5)

You may have left something out of this.

-6x + 15 = -  69

You can do it now that you have the complete equation. But you need the entire equation before you can answer the question.

Subtract - 15 from both sides.

-6x + 15 - 15 = -69 - 15

-6x = - 84

Divide by - 6

-6x/-6 = - 84/-6

x = 14

But what you want is

-6x + 15

-6*14 + 15

-84 + 15

-69

-6x + 15 = - 69

when x = 14 which is usually what you are asked.

Answer:

x= -7y

Step-by-step explanation:

Your answer would be x= -7y. Hope this helps!!

This equation represents the given horizontal line is y = - 7. the correct option is d.

To find the equation of the line passing through the points (-10, -7) and (3, -7), we can use the point-slope form of a linear equation:

The point-slope form is given by: y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points on the line, and m is the slope of the line.

First, let's calculate the slope (m) using the two points:

m = (change in y) / (change in x)

m = (-7 - (-7)) / (3 - (-10))

m = 0 / 13

m = 0

Now, we have the slope (m = 0), and we can choose either of the given points to plug into the equation. Let's use the point (-10, -7):

y - (-7) = 0(x - (-10))

y + 7 = 0

Now, we can simplify the equation:

y = -7

So, the equation of the line passing through the points (-10, -7) and (3, -7) is y = -7. This equation represents a horizontal line at y = -7, as the slope is 0.

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Calculate the mean, standard deviation, and a value one standard deviation below the mean for a data set.

Mean: To find the mean, add all the numbers together and divide by the total count. (62 + 37 + 48 + 67 + 44 + 58 + 47) / 7 = 49.6

Standard Deviation: Calculate the standard deviation using a formula or a calculator. For the given data, the standard deviation is approximately 9.7 rounded to the nearest tenth.

One Standard Deviation Below Mean: To find this value, subtract the mean from one standard deviation: 49.6 - 9.7 = 39.9

Final answer:

By setting up and solving a system of linear equations, we find that walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.

Explanation:

The question involves using a system of two linear equations to find the cost per pound of walnuts and chocolate chips. We can define w to be the cost of one pound of walnuts and c to be the cost of one pound of chocolate chips. From the information given, we can set up the following two equations:

3w + 2c = 13

8w + 4c = 33

To solve these equations, we can use either substitution or elimination. Let's use elimination:

Multiply the first equation by 2 to align the coefficients of c. This gives us: 6w + 4c = 26.

Now, subtract the newly obtained equation from the second one: (8w + 4c) - (6w + 4c) = 33 - 26, which simplifies to 2w = 7.

Divide both sides by 2 to find w: w = 7/2, so w = $3.50 per pound for walnuts.

Substitute the value of w back into the first equation: 3(3.50) + 2c = 13. Therefore, 10.50 + 2c = 13.

Subtract 10.50 from both sides to find c: 2c = 2.50.

Divide both sides by 2 to get: c = 2.50 / 2, so c = $1.25 per pound for chocolate chips.

Therefore, walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.

Step-by-step explanation:

That means it is rotated 90° clockwise about the origin.

Answer:

90° clockwise rotation .

Step-by-step explanation:

Given  : Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x).

To find : Which is another way to state the transformation.

Solution : We have given that Quadrilateral ABCD

(x, y) → (y, –x).

It can be stated as it is as 90° clockwise rotation .

Therefore,  90° clockwise rotation .

Answer:

hey can pay for 9 months

Step-by-step explanation:

585/65

Just simply divide 585 with 65 and you get number of months.

[tex]585\div65=\boxed{9}[/tex]

Tom can pay for 9 months for his gym membership.

Hope this helps.

r3t40

Answer:

Final answer is [tex]P(B|A)=0.40[/tex].

Step-by-step explanation:

Given that P(A)= .50, P(B)=.80 , and P(A and B)=.20.

Now we need to find about what is the value of P(B/A).

So apply the formula of compound probability :

P(A and B) = P(A)*P(B/A)

Plug the given values into above formula

0.20 = 0.50*P(B/A)

0.50*P(B/A) = 0.20

[tex]P(B|A)=\frac{0.20}{0.50}[/tex]

[tex]P(B|A)=0.40[/tex]

Hence final answer is [tex]P(B|A)=0.40[/tex].

Answer:

The answer I beleive is actually A because if you divide the x value by the y-value it gives you 0.11 and no other graph gives you that exact amount dividing either y or x values

Step-by-step explanation:

Sorry for being so late lol

The answer is, electticity cost.

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