Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.
A x= -1.1
B x= -2.2
C x= 0
D x=-10
E x= 10

Answer:

[tex]\large\boxed{m<\dfrac{49}{12}}[/tex]

Step-by-step explanation:

x-intercepts are for y = 0.

Put y = 0 to the equation y = 3x² + 7x + m.

Calculate the discriminant of quadratic equation ax² + bx + c = 0:

Δ = b² - 4ac

if Δ < 0, then an equation has no solution

if Δ = 0, then an equation has one solution

if Δ > 0, then an equation has two solution.

a = 3, b = 7, c = m

Δ = 7² - 4(3)(m) = 49 - 12m

Two x-intercepts for Δ > 0.

Solve the inequality:

[tex]49-12m>0[/tex]           subtract 49 from both sides

[tex]-12m>-49[/tex]          change the signs

[tex]12m<49[/tex]          divide both sides by 12

[tex]m<\dfrac{49}{12}[/tex]

The values of m that make the graph of y=3x²+7x+m have two x-intercepts are m less than 49/12.

To find the values of m that make the graph of the equation y = 3x² + 7x + m have two x-intercepts, we need to determine when the discriminant is greater than zero. The discriminant can be calculated using the formula b² - 4ac, where a is the coefficient of x², b is the coefficient of x, and c is the constant term. In this case, a = 3, b = 7, and c = m. Setting the discriminant greater than zero and solving for m, we get:

7² - 4(3)(m) > 0

Simplifying the equation, we have:

49 - 12m > 0

Now, we can solve for m by isolating it on one side of the inequality:

-12m > -49

m < 49/12

Therefore, for any value of m that is less than 49/12, the graph of y = 3x² + 7x + m will have two x-intercepts.

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The solution to the equation 27x = 9x - 4 is x = -2/9, which is not listed in the provided options. None of the options (8, 4, -4, -8) are correct, and the correct solution can be verified by substituting back into the original equation.

The correct option is (d).

When solving the equation 27x = 9x − 4, we aim to find the value of x that satisfies the equation. To do this, we can follow a step-by-step approach:

We must then verify if any of the provided options (8, 4, -4, -8) match our solution. As none of these values is equal to -2/9, none of the options provided is correct.

To check our solution, we can substitute x back into the original equation and verify that it leads to an identity, confirming that we have found the correct solution. Here, our verification step would show that 27(-2/9) is indeed equal to 9(-2/9) - 4, verifying the solution is correct.

complete question given below:

27x = 9x − 4

a.x = 1/8

b.x = 4

c.x = −4/3

d.x = −2/9

Answer:

Step-by-step explanation:

[tex]x^2=121\to x=\pm\sqrt{121}\\\\x=\pm11\qquad\text{because}\ 11^2=(-11)^2=121\\\\==================\\\\\sqrt{a}=b\iff b^2=a[/tex]

Answer:

the answer is D

Step-by-step explanation:

i hope this helps

Answer: principle APEX

Step-by-step explanation:

As the loan amortizes and nears the end, the majority of the payment is used to pay the principal is the correct answer.

A loan is a commitment that you (the borrower) will receive money from a lender, and you will pay back the total borrowed, with added interest, over a defined time period. A loan may be secured by collateral such as a mortgage or it may be unsecured such as a credit card.

For the given situation,

At the beginning of the loan's term, the majority of the payments are given to interest and just a small part to the loan's principal.

Near the end of the loan's term, the majority of each payment given to principal, and only a small portion is allocated to interest.

Hence we can conclude that as the loan amortizes and nears the end, the majority of the payment is used to pay the principal is the correct answer.

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Answer:

There are 35 different sets of 3 books Joe could choose

Step-by-step explanation:

* Lets explain how to solve the problem

- Combination is a collection of the objects where the order doesn't

 matter

- The formula for the number of possible combinations of r objects from

 a set of n objects is nCr = n!/r!(n-r)!

- n! = n(n - 1)(n - 2)................. × 1

Lets solve the problem

- Joe has one book each for algebra, geometry, history, psychology,

 Spanish, English and Physics in his locker

∴ He has seven books in the locker

- He wants to chose three of them

∵ The order is not important when he chose the books

∴ We will use the combination nCr to find how many different sets

  of three books he can choose

- The total number of books is 7

∴ n = 7

∵ He chooses 3 of them

∴ r = 3

∵ 7C3 = 7!/3!(7 - 3)! = 7!/3!(4!)

∴ [tex]7C3=\frac{(7)(6)(5)(4)(3)(2)(1)}{[(3)(2)(1)][(4)(3)(2)(1)]}=35[/tex]

∴ 7C3 = 35

* There are 35 different sets of 3 books Joe could choose

8 out of 12 people were happy.

8/12 reduces to 2/3 of the people were happy.

Multiply the total people surveyed by 2/3:

126 x 2/3 = (126 x 2) /3 = 252/3 = 84

84 people were happy.

Answer:

Step-by-step explanation:

If it's any help, these numbers, rearranged in ascending order, are

-5/2, 0, 3/4, 3.

Place a bold dot at -5/2 on your number line.  This is halfway between -2 and -3.  Next, place such a dot at 0.  Next, place a dot at 3/4, which is between 0 and 1 but closer to 1.  Last, place a dot at 3.

Answer:

The sum of the six terms is 9331

Step-by-step explanation:

* Lets explain what is the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric sequence:

# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

# [tex]U_{n}=ar^{n-1}[/tex], where a is the first term , r is the constant

  ratio between each two consecutive terms, n is the position

  of the term

- The sum of n terms of the geometric sequence is:

  [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex] , where n is the number of the terms

  a is the first term and r is the common ratio

* Lets solve the problem

∵ The geometric sequence is 1 , -6 , 36 , .........

∵ The common ratio r = U2/U1

∵ U1 = 1 and U2 = -6

∴ r = -6/1 = -6

∵ The first term is 1

∴ a = 1

∵ There are 6 terms in the sequence

∴ n = 6

∴ The sum = [tex]\frac{1[1 - (-6)^{6}]}{1-6}=\frac{1[1-46656]}{-5}=\frac{-46655}{-5}=9331[/tex]

* The sum of the six terms is 9331

Answer:

Step-by-step explanation:

The vetex form of an equation of a parabola y = ax² + bx + c:

y = a(x - h)² + k

(h, k) - coordinates of a vertex

We have the equation y = 3x² + 3.

y = 3(x - 0)² + 3 → h = 0, k = 3

Answer:

[tex]\large\boxed{(2p+q)(-3q-6p+1)=-3q^2-12p^2-12pq+2p+q}[/tex]

Step-by-step explanation:

Use the distributive property: a(b + c) = ab + ac

[tex](2p+q)(-3q-6p+1)=(2p+q)(-3q)+(2p+q)(-6p)+(2p+q)(1)\\\\=(2p)(-3q)+(q)(-3q)+(2p)(-6p)+(q)(-6p)+2p+q\\\\=-6pq-3q^2-12p^2-6pq+2p+q\qquad\text{combine like terms}\\\\=-3q^2-12p^2+(-6pq-6pq)+2p+q=-3q^2-12p^2-12pq+2p+q[/tex]

Answer:

[tex]\large\boxed{x\in\left(-\dfrac{13}{3},\ \infty\right)}[/tex]

Step-by-step explanation:

[tex]4(x+1)+4>x-5\qquad\text{use the distributive property}\\\\4x+4+4>x-5\\\\4x+8>x-5\qquad\text{subtract 8 from both sides}\\\\4x>x-13\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x>-13\qquad\text{divide both sides by 3}\\\\x>-\dfrac{13}{3}\to x\in\left(-\dfrac{13}{3},\ \infty\right)[/tex]

The equation y = -10 (x) (x - 5) models the height.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

66x = 8 is an equation.

We have,

From the table,

We can make ordered pairs in the form of (x, y).

(0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0).

So,

We will choose the equation that satisfies the ordered pairs.

y = -10 (x) (x – 5)

This can be used as the equation.

For (0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0)

i.e x = 0, 1, 2, 3, 4, 5

y = -10 x 0 = 0

y = -10 x 1 x -4 = 40

y = -10 x 2 x -3 = 60

y = -10 x 3 x -2 = 60

y = -10 x 4 x -1 = 40

y = - 10 x 5 x 0 = 0

y = 10 (x) (x - 5)

This can not be used since the y value is a negative value.

y = -10 (x – 5)

This is not possible.

y = 10 (x – 5)

This is not possible.

Thus,

The equation y = -10 (x) (x - 5) satisfy the given table values.

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To find which equation models the height of a projectile \( y \) seconds after being fired based on the given data, we can substitute the given x-values (time in seconds) into each equation and check whether the result matches the corresponding y-values (height in meters).
Let's go through each of the given equations and the provided points one by one:
1. Equation \( y = -10(x)(x – 5) \)
When \( x = 0 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(0)(0 – 5) = 0 \), which matches the given point (0, 0).
When \( x = 1 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(1)(1 – 5) = -10(-4) = 40 \), which matches the given point (1, 40).
When \( x = 2 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(2)(2 – 5) = -10(-1) = 60 \), which matches the given point (2, 60).
When \( x = 3 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(3)(3 – 5) = -10(-2) = 60 \), which matches the given point (3, 60).
When \( x = 4 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(4)(4 – 5) = -10(-1) = 40 \), which matches the given point (4, 40).
When \( x = 5 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(5)(5 – 5) = -10(0) = 0 \), which matches the given point (5, 0).
Since all the points match perfectly with the results from Equation 1, we confirm that Equation 1 models the height of the projectile accurately. Therefore, the correct equation is:
\( y = -10(x)(x – 5) \)
This quadratic equation represents a parabolic trajectory, which is typical for the motion of a projectile under gravity, with no air resistance, and assuming that the projectile lands at the same level from which it was fired.

Answer:

B.

-4, 1, 5, 8

Step-by-step explanation:

Your domain is your set of x values.

Your points are as follows:

(-4, 8)

(8, 10)

(5, 4)

(1, 6)

(5, -9)

Your x-values here are -4, 8, 5, 1, and 5. Your domain only consists of unique x-values, so your domain consists of -4, 8, 5, and 1.

Answer:

Step-by-step explanation:

No, the graph fails the vertical line test.

If a vertical line intersects a curve more than once then the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.

Answer:

a. 35≤x≤45 where x represents speed

b. 16≤y≤100 where y represents age

Step-by-step explanation:

a. Explain how compound inequalities can be use to describe the speed restrictions on roads.  

x represents the speed, then

the maximum speed is 45 miles

x≤45

the minimum speed is 35 miles

x≥35

Both inequalities represent the speed restrictions

The compound inequality will be:

35≤x≤45

b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)

Let y be the age

then

Minimum driving age is 16 years

y≥16

most drivers stop renewing their licenses by age 100.)

y≤100

The compound inequality will be:

16≤y≤100 ..

Answer:

a. 35 ≤ x ≤ 45

b. 16 ≤ x ≤ 100.

Step-by-step explanation:

On a road in the city of Madison, the maximum speed is 45 miles per hour and minimum speed is 35 miles per hour.

If x represents the speed then

x ≥ 35

and x ≤ 45 are the inequalities to represent the speed restrictions.

(a) combined inequality will be 35 ≤ x ≤ 45

    which shows the combined speed limits on the road.

(b) Let the driving age of a driver is x years.

     So by the statement x ≥ 16 and x ≤ 100

When we combine these inequalities 16 ≤ x ≤ 100.

Answer:

x > -52.5.

Step-by-step explanation:

5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)

15.3 + 11.22x > -14.25 - 10.2x - 24

1.02x > -14.25 - 24 - 15.3

1.02x > -53.55

x > -53.55 / 1.02

x > -52.5.

Answer:

(–2.5, ∞)

Step-by-step explanation:

for a rational, we find the vertical asymptotes where its denominator is 0, thus

(x-2)(x+1) = 0, gives us two vertical asymptotes when that happens, x = 2 and x = -1.

if we expand the denominator, we'll end  up with a quadratic equation, namely a 2nd degree equation, whilst the numerator is of 3rd degree.  Whenever the numerator has a higher degree than the denominator, the rational has no horizontal asymptotes, however when the numerator is exactly 1 degree higher like in this case, it has an oblique asymptote instead.

Answer:

A

x=2,x=-1

Step-by-step explanation:

Answer:

≈ 7854 m²

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4π r² ← r is the radius

here diameter = 50, hence r = 25, so

A= 4π × 25²

  = 4π × 625 = 2500π ≈ 7854 m²

Answer:

The surface area of the structure ≅ 7854 meter²

Step-by-step explanation:

* Lets revise the surface area of the sphere

- The surface area of a sphere is the same as the lateral surface area

  of a cylinder having the same radius as the sphere and a height

  equal the length of the diameter of the sphere.

- The lateral surface area of the cylinder is 2πrh

- The height of the cylinder = 2r , then the surface area of the sphere is

  2πr(2r) = 4πr²

* Now lets solve the problem

∵ The sphere has diameter = 50 meters

∵ The diameter is twice the radius

∴ 2r = 50 meters ⇒ divide both sides by 2

∴ r = 25 meters

∵ The surface area of the sphere = 4πr²

∴ The surface area of the sphere = 4π(25)² = 7853.98

∴ The surface area of the sphere ≅ 7854 meters²

Answer:

[tex]\large\boxed{y=\dfrac{4}{3}x}[/tex]

Step-by-step explanation:

The line passes through the origin has an equation y = mx

m - slope

The formula of a slope of a line passes through the origin

and a point (x, y):

[tex]m=\dfrac{y}{x}[/tex]

We have the point (6, 8). Substitute:

[tex]m=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}[/tex]

Finally:

[tex]y=\dfrac{4}{3}x[/tex]

Answer: 27

Step-by-step explanation:

F(6)=42-15=27

Answer:

A 27

Step-by-step explanation:

f(x) = 7x - 15

Let x=6

f(6) = 7*6 -15

     = 42  -15

     = 27

Answer:

0.65m

Step-by-step explanation:

Given the function as

[tex]P(h)=P_0*e^{-0.00012h}[/tex]

Lets take the air pressure at the surface of the Earth to be x

[tex]P_0=x[/tex]

Then 65% of this will be the air pressure P(h)

[tex]P(h)=\frac{65}{100} *x=0.65x[/tex]

The function will be

[tex]0.65x(h)=x*e^{-0.00012h}[/tex]

Divide both sides by x

[tex]0.65=e^{-0.00012h}\\ \\\\e=2.71828182846\\\\\\0.65=2.7182818284^{-0.00012h} \\\\\\0.65=0.99989h\\\\\\\frac{0.65}{0.99989} =\frac{0.99989h}{0.99989} \\\\\\h=0.65m[/tex]

Option: A is the correct answer.

                     A.   3589.9 m

The function which determines the pressure h height above the surface of earth is:

[tex]P(h)=P_0\cdot e^{-0.00012h}[/tex]

where [tex]P_0[/tex] is the pressure at the surface of the earth.

We are asked to find the height when the pressure above the surface of earth is equal to 65% of the pressure at the surface of earth.

i.e.

[tex]P_0\cdot e^{-0.00012h}=0.65\cdot P_0\\\\i.e.\\\\e^{-0.00012h}=0.65\\\\i.e.\\\\e^{0.00012h}=\dfrac{1}{0.65}\\\\i.e.\\\\\ln(e^{0.00012h}}=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\0.00012h=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\h=3589.8576\ m[/tex]

which is approximately equal to:

[tex]h=3589.9\ m[/tex]

Answer:

1

Step-by-step explanation:

Assuming g(n)=pn, and plugging in

g=600 and n=600:

600=p(600)

600/600=p

1=p

profit per candy bar is $1

Answer:

[-3 ±√(89)]/10

Step-by-step explanation:

Points to remember

Quadratic formula for finding the solution of a quadratic equation ax² + bx + c = 0 is given by,

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation,

5x² + 3x - 4

To find the solution using formula

Here a = 5, b = 3 and c = -4

x = [-b ± √(b² - 4ac)]/2a

= [-3 ± √((-3)² - 4*5*(-4))]/2*5

= [-3 ±√(9 +80)]/10

= [-3 ±√(89)]/10

Subtract the rental fee, then divide the left over amount by the cost per hour.

38-10 = 28

28 / 7 = 4

The answer is 4 hours.

Answer: BA and AE are adjacent angles

Answer:

Arc AB and AE are adjacent arc.

Step-by-step explanation:

Given; A circle P with diameter AD and BE.

To find : which pair of arcs are adjacent arcs.

Solution : We have given A circle P with diameter AD and BE.

Arc length is the distance between two points along a section of a curve.

Here curve AB and AE  are two arc which are adjacent to each other.

Therefore, Arc AB and AE are adjacent arc.

Answer:

a) 6.67% b) 500% c) 40% d) 7.5%

Step-by-step explanation:

a. ? % of 75 = 5

Let ? be y.

Of means multiply so we will replace it with a multiplication sign.

y% x 75 = 5

y% = 5/75

y% = 1/15 x 100

y = 6.67 %

b) ?% of 28 = 140

Let ? be y.

Of means multiply so we will replace it with a multiplication sign.

y% x 28 = 140

y% = 140/28

y% = 5

y = 5 x 100

y = 500%

c) ?% of 100 = 40

Let ? be y.

Of means multiply so we will replace it with a multiplication sign.

y% x 100 = 40

y% = 40/100

y% = 2/5

y = 2/5 x 100

y = 40%

d) ?% of 200 = 15

Let ? be y.

Of means multiply so we will replace it with a multiplication sign.

y% x 200 = 15

y% = 15/200

y% = 3/40

y = 3/40 x 100

y = 7.5 %

!!

To find what percent one number is of another, divide the 'part' by the 'whole' and multiply by 100. Answers provided were calculated according to this method and rounded to the nearest hundredth when necessary.

To find what percent of a number another number is, you use the formula part over whole times 100. Let's apply this to the questions at hand.

Always remember to round your answer to the nearest hundredth, as per the instruction.

Answer: -1/2

Step-by-step explanation:

Answer:

-1/2 (2nd option)

Step-by-step explanation:

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