Final answer:
[tex]\[ h(2) = 55, \quad h(-1) = 3 \][/tex]
Explanation:
To evaluate [tex]\(h(x)\)[/tex] at the given values using synthetic division, we start with the coefficients of the polynomial [tex]\(x^6 - 4x^4 + 5x^2 + 1\).[/tex]
1. For [tex]\(h(2)\):[/tex]
- Write down the coefficients: 1, 0, -4, 0, 5, 0, 1.
- Using synthetic division with 2 as the divisor, perform the operations to obtain the result 55.
2. For [tex]\(h(-1)\):[/tex]
- Repeat the process with -1 as the divisor, using the coefficients: 1, 0, -4, 0, 5, 0, 1.
- After the calculations, the result is 3.
In both cases, the final values represent the result of evaluating the function [tex]\(h(x)\)[/tex] at x = 2 and [tex]\(x = -1\)[/tex] respectively.
1. Factor the expression 3x^3 + 4x^2 - 15x - 20 Please show work!
The expression 3x^3 + 4x^2 - 15x - 20 can be factored into the form (3x + 4)(x^2 - 5) by grouping terms, factoring out common components, and simplifying.
Explanation:The provided expression to be factored is [tex]3x^3 + 4x^2 - 15x - 20.[/tex]Factoring this involves finding common factors and breaking the terms down until we cannot do so any further.
Group terms that look like they might have common factors: [tex](3x^3 + 4x^2) - (15x + 20).[/tex]Factor out the common factors: [tex]x^2(3x + 4) - 5(3x + 4).[/tex]Notice that we have the binomial of (3x + 4) common between both terms. We can now factor that out: [tex](3x + 4)(x^2 - 5).[/tex]
So, the factored form of the expression is [tex](3x + 4)(x^2 - 5).[/tex]
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The scale on a map indicates that 1 inch corresponds to an actual distance of 95 miles. two cities are 4.5 inches apart on the map. what is the actual distance between the two cities?
Miguel is going for a walk. he takes 3 hours to walk 7.5 miles. what is his speed?
divide total distance by time
7.5 miles / 3 hours = 2.5 miles per hour is his speed
3.Cornelia spends 2 2/3 hours studying for her big science test. She spent 2/3 of an hour finishing her writing assignment and 1/4 of an hour playing outside. How much time did she spend overall on the three activities?
A prism is named for the shape of its bases.
True
False
true
Step-by-step explanation:
Hope is helps and good luck
A bag contains 8 blue marbles, 5 green marbles and 7 red marbles. If Alicia removes two marbles without replacing them, what is the probability that he will choose red, then green?
To find the probability of choosing a red marble, then a green marble without replacement, multiply the probabilities of the individual events which is 7/76.
Explanation:To find the probability that Alicia will choose red, then green marbles, we need to calculate the probability of drawing a red marble and then a green marble without replacement.
Given that there are 8 blue marbles, 5 green marbles, and 7 red marbles in the bag, the probability of drawing a red marble first is 7/20.
After removing the red marble, there are 19 marbles left in the bag, including 5 green marbles. Therefore, the probability of drawing a green marble second is 5/19.
To find the combined probability, we multiply the probabilities of the individual events:
P(Red, then Green) = P(Red) * P(Green | Red) = (7/20) * (5/19) = 35/380 = 7/76.
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Which function represents the graph of f(s)=-4[x] after it is translated 3 units down?
In Indianapolis, the Market Tower has 2/3 as many stories as the Chase Tower. If the Market Tower has 32 stories, how many stories does the Chase Tower have?
Oranges are on sale for $1.59 per pound. Write a funtion as a standard equation and in a funtion notation.
What is the distance between points A and B?
___ units
we know that
the distance's formula between two points is equal to
[tex]d=\left|xB-xA\right|[/tex]
substitute
[tex]d=\left|1-(-5)\right|[/tex]
[tex]d=6\ units[/tex]
therefore
the answer is
[tex]6\ units[/tex]
The distance between two point [tex]A{\text{ and }}B[/tex] is [tex]\boxed{{\mathbf{6 units}}}[/tex].
Further explanation:
The distance between two points is the modulus of difference of the given two points.
The distance between two points can be found by the distance formula as,
[tex]\left| {B - A} \right|[/tex]
Here, [tex]A{\text{ and }}B[/tex] are the points on the number line.
The distance cannot be negative therefore modulus is applied in the formula.
Step by step explanation:
Step 1:
First we determine the points from the given number line.
It can be observed from the given number line that there are two points one is on the left side of the origin and the second is right side of the origin.
The point [tex]A[/tex] is [tex]- 5[/tex] and the point [tex]B[/tex] is 1.
Step 2:
Now use the distance formula to obtain the distance between the two points [tex]A{\text{ and }}B[/tex].
Here, the value of A is [tex]-5[/tex] and B is 1.
Substitute the value of [tex]A{\text{ and }}B[/tex] to obtain the distance as,
[tex]\begin{aligned}d&= \left| {B - A} \right| \\&= \left| {1 - \left( { - 5} \right)} \right|\\&= 6{\text{ units}}\\\end{aligned}[/tex]
Therefore, the distance between two point [tex]A{\text{ and }}B[/tex] is [tex]6{\text{ units}}[/tex].
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Number line
Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference.
Two angles that are complementary __________ form a right angle. 2. angles with a common side and a common vertex ______ form a linear pair. 3. two angles that are supplementary are _______ complementary.
The width of a poster is 4/5 of its length, It takes 36 ft. of metal framing to frame the poster. Find the dimensions of the poster.
the ordered pair (2 36) is a solution to which equation(s)
A. y=2x^2
B. y=(3x)^2
C. y=7x^2+2
D. y=(x+4)^2
(2, 36) → x = 2, y = 36
Substitute the value of x and y to the equations of the functions:
A. y = 2x^2
36 = 2(2)^2 → 36 = 8 FALSE
B. y = (3x)^2
36 = (3 · 2)^2 → 36 = 6^2 → 36 = 36 CORRECT
C. y = 7x^2 + 2
36 = 7(2)^2 + 2 → 36 = 7 · 4 + 2 → 36 = 30 FALSE
D. y = (x + 4)^2
36 = (2 + 4)^2 → 36 = 6^2 → 36 = 36 CORRECT
Answer: B. y = (3x)^2 and D. (x + 4)^2
One car rental company charges $30 per day plus $0.25 per mile driven. a car company charges $40 per day plus $0.10 per mile driven. how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company? write an inequality to solve.
Answer:
66.667 miles
Step-by-step explanation:
Given: One car rental company charges $30 per day plus $0.25 per mile driven.
Second car company charges $40 per day plus $0.10 per mile driven.
To find: how many miles must you drive for a one-day rental at the second company to be less expensive than the same rental at the first company?
Solution: Let the distance driven on a day be x miles.
As per question,
The first rental company will charge [tex]=30+0.25x[/tex]
The second rental company will charge [tex]=40+0.10x[/tex]
Now, we want the rental charges of second company to be less expensive then the first.
So we get the inequality,
[tex]30+0.25x>40+0.10x[/tex]
[tex]0.25x-0.10x>40-30[/tex]
[tex]0.15x>10[/tex]
[tex]x>\frac{1000}{15}[/tex]
[tex]x>66.667[/tex] miles
Hence, at least 66.667 miles should be driven on a day.
Evaluate ab for a = 2 3/4 and b = 4/5
A. 1 1/15
B. 8/15
C. 2 1/5
D. 2/3
Given the midpoint and one of the endpoints,find the other endpoint of the segment
What is the difference between 3/7 and 1/14
Twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch. Each student must pay an entrance fee to the museum and $7.25 for lunch. The total cost for the trip is $443.75. What is the entrance fee for one student?
Answer: $17.75
Step-by-step explanation: $443.75 / 25 = $17.75
if an angle is acute then its measure is 30 degrees true or false
An acute angle is any angle less than 90 degrees, and while 30 degrees is an example of an acute angle, it is not accurate to say that all acute angles must be 30 degrees.
Explanation:The statement 'If an angle is acute then its measure is 30 degrees' is false. An acute angle is defined as any angle that is less than 90 degrees. While 30 degrees is indeed an example of an acute angle, an acute angle can be any value less than 90 degrees. For example, 45 degrees, 20 degrees, or 1 degree are also acute angles. Therefore, it is not accurate to say that an acute angle must be 30 degrees.
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Simplify the expression 111,000 × 0.072 using scientific notation and express your answer in scientific notation.
Final answer:
The simplified expression is 7.992 × 10³.
Explanation:
To simplify the expression 111,000 × 0.072 using scientific notation, follow these steps:
Express 111,000 in scientific notation: 1.11 × 10⁵Express 0.072 in scientific notation: 7.2 × 10⁻²Multiply the two numbers: (1.11 × 10⁵) × (7.2 × 10⁻²)First, multiply the decimal parts: 1.11 × 7.2 = 7.992Next, add the exponents for the powers of 10: 5 + (-2) = 3Combine the results: 7.992 × 10³Finally, if necessary, adjust the number to have only one non-zero digit to the left of the decimal point: 7.992 × 10³ is already in correct form.The expression simplified in scientific notation is 7.992 × 10³.
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
14.6 units
15.5 units
21.0 units
21.6 units
Help please pre calculus
put 7.6*10^-1 into the equation to get:
10log(1/7.6*10^-4) = 31.19
what is 2 1/2x−3/4(2x+5)=3/8
Braic equation. two airplanes leave chicago at the same time and fly in opposite directions. if one travels at 490 miles per hour and the other at 470 miles per hour, how long will it take for them to be 4,800 miles apart
Roger can run one mile in 10 minutes. jeff can run one mile in 8 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up to roger? how far will each have run?
BRAINLIESTTTTTTTT!!!!!!!!!!!!!!!!!!
Sonia has three bracelets. she wears them all at the same time but if a different order each day. how many different combinations does sonia have to choose from
Harry and his friends share some watermelon equally. Each person gets of a watermelon. Which of the following shows a possible way that the watermelon is served?
2 watermelons divided among 7 people.
7 watermelons divided among 2 people.
of a watermelon divided among 2 people.
of a watermelon divided among 7 people.
Solve 5c + 4 = −26.
6
−6
−4.4
3
Answer:
-6 :))))))))))))))))))
Step-by-step explanation:
The first three numbers in sequence are 1, 4, and 9. Marie determined that the fourth number in the sequence is 16. Marie’s rule involved multiplication. What rule did she use to determine the fourth number in the sequence? Specific please