According to the real rational root theorem, what are all the potential rational roots of f(x)=5x3-7x+11

Answer:

$150

Step-by-step explanation:

$100 + 100% = $200 in the first year

$200 - 25% = $150 in the second year

Eva should pour you a drink from jug B for a stronger cranberry taste, as it has a higher ratio of cranberry to apple cubes compared to jug A, demonstrating the use of ratios in mathematics.

To decide which jug of fruit punch has a stronger cranberry taste, we should look at the ratio of cranberry flavored cubes to apple flavored cubes in both jugs. For jug A, the ratio is 4 cranberry cubes to 3 apple cubes, which simplifies to approximately 1.33 cranberry cubes for every apple cube. For jug B, the ratio is 3 cranberry cubes to 2 apple cubes, which simplifies to 1.5 cranberry cubes for every apple cube.

Since jug B has a higher ratio of cranberry to apple, it has a stronger cranberry taste compared to jug A. So, Eva should pour you a drink from jug B if you want a drink with a stronger cranberry flavor. This involves a practical application of ratios and proportions, which are key concepts in mathematics used to compare quantities.

Answer:

48

Step-by-step explanation:

304 - 256 equals 48

Answer:65 inches

Step-by-step explanation:

15+14+36=65

Jasper used a total of 65 inches of ribbon.

To calculate the total length of ribbon used by Jasper, we need to convert the 3 feet of red ribbon to inches.

Since 1 foot is equal to 12 inches, 3 feet would be equal to 12 x 3 = 36 inches. Then, we can add up the lengths of all three ribbons: 15 inches of blue ribbon + 14 inches of yellow ribbon + 36 inches of red ribbon = 65 inches of ribbon.

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Answer:

6) 24+4x

7) -24x+32

8) -21+42x

9)-24x-12

10) 72- 18x

Step-by-step explanation:

for each problem, you need to distribute the single variable to the parenthesis  for the final answer. For example, 3 (4x-25) > 3 x 4x = 12x > 3x-25 = -75 now you put both answers together making it 12x-75

The correct answer should be B. $40

I'm guessing the question is asking for a precise amount..

Hope we thought this through correctly and you get it right!,

Davinia.

3(bc - ac - ab)/(a²-ab+bc-ac) is the simplified form of the given equation.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given an expression:

(a²-4ac+3bc)/(a²-ab+bc-ac) + (a+3b)/(b-a) + (a+2c)/(a-c)

Simplifying Using PEMDAS starts from the right:

(a²-4ac+3bc)/(a²-ab+bc-ac) + [tex]\frac{a^{2} + 3ab - ac - 3bc }{-a^{2} + ab -bc +ac }[/tex]

Taking negative common from the last term

(a²-4ac+3bc)/(a²-ab+bc-ac) - (a² + 3ab - ac -3bc)/(a²-ab+bc-ac)

Since the base is the same,

(-4ac + 3bc - 3ab +ac +3bc)/(a²-ab+bc-ac)

3(bc - ac - ab)/(a²-ab+bc-ac)

therefore, the simplified form of the given equation is 3(bc - ac - ab)/(a²-ab+bc-ac).

Learn more about Mathematical operations here:

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The solution involves evaluating a complex algebraic expression step by step after substituting given values for variables.

Given the expression, (a2-4ac+3bc)/(a2-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c), substitute a = 1, b = 0.0211, and c = -0.0211 to simplify.

After substitution, perform the necessary calculations to evaluate the expression step by step.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have m = -2 and the points (0, d) and (-8, 9). Substitute:

[tex]\dfrac{9-d}{-8-0}=-2\\\\\dfrac{9-d}{-8}=-2\qquad\text{multiply both sides by (-8)}\\\\9-d=16\qquad\text{subtract 9 from both sides}\\\\-d=7\qquad\text{change the signs}\\\\\boxed{d=-7}[/tex]

The function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.

Linear Graph Linear means straight and a graph is a diagram that shows a connection or relation between two or more quantities.

The given graph is;

[tex]\rm f(x)=x^2[/tex]

The graph of g(x) = f(2x) is given by;

[tex]\rm g(x) = f(2x)\\\\g(x) = f(2x)^2\\\\g(x)=4x^2[/tex]

Hence, the function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.

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The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (15, 130) amd (1, 160). Substitute:

[tex]m=\dfrac{160-130}{1-15}=\dfrac{30}{-14}=-\dfrac{15}{7}[/tex]

Hi there! :)

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{160-130}{1-15}=\frac{30}{-14}=\frac{30/2}{-14/2}=\frac{15}{-7}=-\frac{15}{7}[/tex]

Therefore, the slope is -15/7.

Final answer is -15/7.

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

:D

Answer:

Step-by-step explanation:

The installation cost is $300 and the cost per square foot is $4 . So the total price is y= 4x + 300 (where x is square foot).

slope is 4 and y intercept is 300

for 375 sqft. the cost is y= 4(375) +300 = 1800

the cost is $1800

The equation of the line passing through (-6,-5) and perpendicular to y=-2/3x is y=(3/2)x+4.

To find an equation of a line passing through the point (-6,-5) that is perpendicular to the line described by y=-2/3x, we first need to determine the slope of the perpendicular line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of our line will be the negative reciprocal of -2/3, which is 3/2.

Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute our point (-6, -5) and slope 3/2 into the formula:

y - (-5) = (3/2)(x - (-6))

Simplifying this, we get:

y + 5 = (3/2)(x + 6)

y + 5 = (3/2)x + 9

Subtracting 5 from both sides, we get the final equation of the line:

y = (3/2)x + 4

Answer: No

Step-by-step explanation:

23,453 is not a perfect square, this is because no rational number times itself equals 23,453, which can be proven if you go into a calculator and find the square root of 23,453, which is about 153.1437 (but it continues going, making it an irrational number.)

Hope this helps!

Answer: 2

You can use a calculator to compute the square root of 4 to get 2.

Or you can think of a geometric square with side lengths of some number that multiply to an area of 4. The only possible square is a 2 by 2 square since 2*2 = 4. This is where the term "square root" comes from for the most part.

Answer: Marcus can make 6 sandwiches.

Step-by-step explanation:

If you have 12 slices of bread and use 2 for each sandwich you would do 12/2, which equals 6.

Final answer:

To find the length of FG in triangle FGH, we can use the Pythagorean Theorem. By substituting the given values into the formula and solving for FG, we find that FG is approximately 27.9 units.

Explanation:

To find the length of FG, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, FH and GH are the two sides of the right triangle FGH, and FG is the hypotenuse. So we have FH² + GH²= FG².

Substituting the given values, we have 10² + 26² = FG². Simplifying this equation, we get 100 + 676 = FG². Adding the numbers gives us 776 = FG². And taking the square root on both sides, we find that FG ≈ 27.9 units.

Any irrational number never ends. So, you can take square roots. 4 is the square root of 16, and 6 is the square root of 36. So, take the square root of any number between 16 and 36 except for 25. For example, 17 is between 16 and 36. So, sqrt(17) is therefore irrational. You can't take the square root of 25 because that would result in a rational number, 5.

Answer:

v2 - v02 = 2ad

v = final speed = 0 (came to a full stop)

v0 = initial speed (what you want to solve for)

d = stopping distance = 175 feet

Then

v0 = √(-2ad)  [Remember a is negative, so the argument of the square root is positive.]

But as you can see, we need the acceleration.

If we knew the time it took to come to a full stop, we could still answer the question.  Either way, we need more information than just the stopping distance.

Step-by-step explanation:

The speed of the vehicle before the brake were applied was about 83.7 feet/s

Acceleration is rate of change of velocity.

[tex]\large {\boxed {v^2 = u^2 + 2ad}[/tex]

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

This problem is about accelerated motion.

Given:

final speed of the vehicle = v = 0 feet/s

length of skid marks = d = 175 feet

maximum deceleration = a = 20 feet/s² ( assumption )

Unknown:

initial speed = u = ?

Solution:

[tex]v^2 = u^2 - 2ad[/tex]

[tex]0^2 = u^2 - 2(20)(175)[/tex]

[tex]u^2 = 7000[/tex]

[tex]u = \sqrt{7000}[/tex]

[tex]u = 10\sqrt{70} \texttt{ feet/s}[/tex]

[tex]u \approx 83.7 \texttt{ feet/s} [/tex] (rounded to the nearest tenth)

[tex]\texttt{ }[/tex]

The speed of the vehicle before the brake were applied was about 83.7 feet/s if we assume that maximum deceleration of the vehicle is about 20 feet/s²

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

Answer: Your answer would be "B" Hope this helps you!

Answer:

- 5, 2, 9, 16 and d = + 7

Step-by-step explanation:

to obtain the first four terms substitute n = 2, 3, 4 into the recursive formula

f(1) = - 5 ← given

f(2) = f(1) + 7 = - 5 + 7 = 2

f(3) = f(2) + 7 = 2 + 7 = 9

f(4) = f(3) + 7 = 9 + 7 = 16

common difference d = 16 - 9 = 9 - 2 = 2 - (- 5) = 7

[tex]\displaystyle\bf\\\sqrt{-100}=\sqrt{100\times(-1)}=\sqrt{10^2\times(-1)}=10\sqrt{-1}=10i=\boxed{\bf0+10i}[/tex]

Answer:

x(2x-17)

Step-by-step explanation:

2x^2 -11x-6x

2x^2-17x

x is common

x(2x-17)

Answer:

x(2x-17)

Step-by-step explanation:

[tex]2x^2-11x-6x\\2x^2-17x\\x(2x-17)[/tex]

Steps:

Combine Like Terms (-11x and -6x)

Factor out the common term (x)

Answer:

1/32

Step-by-step explanation:

1/8 divided by 4 = .03125

.03125= 1/32

Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.

To calculate the total interest Larry will pay when using his credit card to purchase a video game system for $445.07, with a monthly payment limit of $200 and an annual rate of 13.6% compounded monthly, we can follow these steps:

1. Calculate the total amount to be paid off by subtracting the monthly payment from the total purchase amount:

Total amount to be paid off = $445.07 - $200 = $245.07

2. Determine the number of months it will take to pay off the balance by dividing the total amount to be paid off by the monthly payment:

Number of months = $245.07 / $200 = approximately 1.22535 months (round up to the nearest whole month, which is 2 months)

3. Calculate the monthly interest rate by dividing the annual rate by 12 (since it's compounded monthly):

Monthly interest rate = 13.6% / 12 = 1.1333%

4. Use the formula for compound interest to find the total interest paid:

Total interest = Total amount paid - Total principal amount

Total principal amount = $445.07

Total amount paid = $200 * 2 = $400

Total interest = $400 - $445.07 = $45.07

Therefore, Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.

Answer:

A and C represent a function and B doesn't represent.

Step-by-step explanation:

A function is a relation that maps one output value of y for each input value of x.

A. Ordered pairs can be written as relation

Here each input value of x determines one output value of y and this set of ordered pairs represents function.

B. Ordered pairs can be written as relation

Here for input value x=9 there are 2 output values of y (y=3 or y=-3). This set of ordered pairs doesn't represent function.

C. Ordered pairs can be written as relation

There is exactly one y for each x, then this set of ordered pairs represents function.

Answer:

The cost of the one word is $30 .

Option (b) i.e [tex] \frac{8.4- 6}{0.08}[/tex] is used to determine the total number of words in the ad mr.grant placed.

Step-by-step explanation:

Let us assume that the number of words in the ad be x.

As given

Mr.grant spent $8.40 to place an ad in the newspaper.

This price included one time fee of $6.00 plus $0.08 per word.

Than the equation becomes

8.40 = 6 .00 + 0.08x

Simplify the above

8.4 = 6 + 0.08x

8.4 - 6 = 0.08x

[tex]x = \frac{8.4- 6}{0.08}[/tex]

[tex]x = \frac{2.4}{0.08}[/tex]

[tex]x = \frac{24\times 100}{8\times 10}[/tex]

[tex]x = \frac{2400}{80}[/tex]

x = $30

Therefore the cost of the one word is $30 .

Option (b) i.e [tex] \frac{8.4- 6}{0.08}[/tex] is used to determine the total number of words in the ad mr.grant placed.

Answer:

See below.

Step-by-step explanation:

a. 973 * 80

= 973 * 8 * 10

= 7784 * 10

= 77,840.

b. 56 * 2000

= 2*56 *  1000

= 112,000.

c. 5.7 * 300

= 5.7 * 3 * 100

= 17.1 * 100

= 1710.

d. 0.46 * 50

= (0.46 * 100) / 2

= 46  / 2

= 23.

Answer with Step-by-step explanation:

a. 973 × 80

= 973 × 8 × 10

= 7784 × 10

=77840

b. 56 × 2,000

=56 × 2 × 1000

=112 × 1000

=112000

c. 5.7 × 300

=5.7 × 3 × 100

=17.1 × 100

=1710

d. 0.46 × 50

=0.46 × 5 × 10

=2.3 × 10

=23

Answer:

The answer would me 15m

Step-by-step explanation:

1. you multiply both of them together in order to get the area

L x W = A