A certain hybrid car can travel 1 9/11 times as far as a similar no hybrid car will on one gallon of gasoline . If the non hybrid car can travel 33 miles per gallon of gasoline, how far can the hybrid travel on 4/5 gallon of gasoline ?
On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.
How to solve Algebra Word Problems?Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline
Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline
Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon
Then, hybrid car travel, 1 ⁹/₁₁ * x = 1 ⁹/₁₁ * x * 33 = 60 miles per gallon
On 1 gallon of gasoline hybrid car travel 60 miles
On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles
On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.
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Use the factor theorem to write a polynomial equation that has solutions of 2, -2, and 4. (Hint: Suppose the solutions of a quadratic equation are 3 and 5. This means that x = 3 or x = 5 which gives us x - 3 = 0 or x - 5 = 0. The expressions are the factors of the polynomial which means that the equation is (x - 3)(x - 5) = 0.)
The equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
What is the polynomial equation that has solutions of 2, -2, and 4?Roots are the points where the graph intercepts with the x-axis ( y = 0 ).
Given the roots in the question;
x = 2, -2, 3
Now, the root of x = 2 was found solving for x when x - (2) = y but y = 0.
Hence, (x - 2) is a factor.
Next, the root of x = -2 was found solving for x when x - (-2) = y but y = 0.
Hence, (x + 2) is a factor
And the root of x = 4 was found solving for x when x - (4) = y but y = 0.
Hence, (x + 2) is a factor
Now, combine all the factors into a single equation and simplify.
( x-2 )( x + 2 )( x - 4 ) = y
( x² + 2x - 2x - 4 )( x - 4) = 0
( x² - 4 )( x - 4) = 0
x( x² - 4 ) -4( x² - 4 ) = 0
x³ - 4x - 4x² + 16 = 0
x³ - 4x² - 4x + 16 = 0
x³ - 4x² - 4x + 16 = 0
Therefore, the equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
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The price of a computer is 899.00. The sales tax is 7%. What is the sales tax on this computer in dollars and cents?
Answer:
$62.93
Step-by-step explanation:
Convert 7% to a decimal and multiply by the price:
$899.00 x .07 = $62.93
What is the greatest common factor of 18 12 16
The greatest common factor of 18 12 16 is the number 2.
What numbers are a distance of 34 unit from 18 on a number line?
Select the locations on the number line to plot the points.
Answer:
[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]
Step-by-step explanation:
To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]
One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away
Compute [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4} :[/tex]pls help asap I’ll give brainliest immediately.. plsss..
Answer:
You have the right form (vertex form). All that you have left to do is learn what parts of the equation signify what.
Step-by-step explanation:
Explanation:
In a quadratic function of form y = a
(
x
−
p
)
2
+ q, the axis of symmetry is found at x = p. As a result, in y = -4
(
x
−
8
)
2
+ 3, the axis of symmetry is at x = 8, since the formula is x - p = x - (+8).
The vertex of a parabola is at (p, q). As for the axis of symmetry, the p value is 8, and in this function the q value is 3. So the vertex is at (8,3).
With this information, the x and y intercepts, and a few other points found by plugging in x values and solving for y, you will be able to graph this parabola. Your graph, if done properly, will look like the following:
graph{y = -4(x - 8)^2 + 3 [-20, 20, -10, 10]}
i need help asap. plsss give me the right answer
Answer:
x < 3
Step-by-step explain: I used quizlet
Apply it
What is the value of the expression 4(x - y)
when x = 7 and y = 1?
A 26
7
B 29
C 32
D 48
Apply your thinking
Students, write your response!
Pear Deck Interactive Slide
Curriculum Associal Do not remove this bar
Answer:
USE AIR MATH!!
Step-by-step explanation:
Have this question.. 5x-3y=14
Simplify the expression. (2+1)×42÷2
Answer:
63
Step-by-step explanation:
Simplifying the expression,
→ (2+1) × 42 ÷ 2
→ 3 × 42 ÷ 2
→ 126 ÷ 2 = 63
Hence, the answer is 63.
Find X if
• B is between A and C;
• AB = x+5;
BC= 2 (x-3); and
AB ~ BC
Linear Equations: Mastery Test
Select the correct answer.
Which property of equality was used to solve this equation?
X-5=-14
X-5+5=14+5
X=-9b
A addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
The property of equality was used to solve this equation is addition property of equality
Addition property of equalityThe property states that the additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
Given the expression
X-5=-14
Add 5 to both sides to have;
x-5 + 5 = -14 + 5
x = -14 + 4
x = -9
Hence the property of equality was used to solve this equation is addition property of equality
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[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
Find the critical points of [tex]f_1[/tex] and [tex]f_2[/tex].
By the fundamental theorem of calculus,
[tex]{f_1}'(x) = \displaystyle \prod_{j=1}^{21} (x-j)^j = (x-1) (x-2)^2 (x-3)^3 \cdots (x-21)^{21}[/tex]
and [tex]{f_1}'=0[/tex] for [tex]x\in\{1,2,3,\ldots,21\}[/tex]. The stationary points at odd values have odd multiplicity, while the even ones have even multiplicity. At the points of odd multiplicity, [tex]{f_1}'[/tex] passes through the [tex]x[/tex]-axis and the sign of [tex]{f_1}'[/tex] changes, while at the points of even multiplicity, [tex]{f_1}'[/tex] is tangent the to [tex]x[/tex]-axis. We also have
[tex]\displaystyle \lim_{x\to-\infty} {f_1}'(x) = (-1)^{1+3+5+\cdots+21} \infty = (-1)^{11^2} \infty = -\infty[/tex]
[tex]\displaystyle \lim_{x\to\infty} {f_1}'(x) = \infty[/tex]
so the plot of [tex]{f_1}'[/tex] looks more or less like the attached curve. (Not drawn to scale)
Wherever the sign of [tex]{f_1}'[/tex] changes from negative to positive, as it does in the case of [tex]x\in\{1,5,9,13,17,21\}[/tex], there is a local minimum, so [tex]m_1 = 6[/tex]. Similarly, wherever the sign changes from negative to positive, as it does when [tex]x\in\{3,7,11,15,19\}[/tex], there is a local maximum, so [tex]n_1 = 5[/tex].
Repeat for [tex]f_2[/tex].
[tex]{f_2}'(x) = 4900 (x-1)^{49} - 29400 (x-1)^{48} = 4900 (x-1)^{48} (x-7)[/tex]
has roots at [tex]x=1[/tex] and [tex]x=7[/tex], but only the latter is a critical point due to odd multiplicity. A rough sketch of the plot of [tex]{f_2}'[/tex] is also attached. The sign of [tex]{f_2}'[/tex] changes from negative to positive at [tex]x=7[/tex], so [tex]m_2 = 1[/tex] and [tex]n_2=0[/tex].
We conclude that
Q.9) [tex]2m_1+3n_1+m_1n_1 = \boxed{57}[/tex]
Q.10) [tex]6m_2+4n_2+8m_2n_2 = \boxed{6}[/tex]
A 12- by 16-foot rectangular floor will be
covered by square tiles that measure 2 feet
on each side. If the tiles are not cut, how many
of them will be needed to cover the floor?
I WILL GIVE BRAINLYIST Which number is prime? Choose each correct answer. 41 41 42 42 43 43 44 44 45 45 46 46 47. THIS IS MULTIPLE ANSWER.
Answer:
It is 41, 43, 47! :D
Step-by-step explanation:
What do I write for 23???
Can you please help me
Answer:
1) -√9
2) √18
3) |4.5|
Step-by-step explanation:
-√9 = -3
√18 = 4.2426406871 = 4.2
|4.5| = 4.5
↑
Absolute value - Those two lines mean that any number, positive or negative, will be positive.
Hope this helps :)
maths geometry question
Step-by-step explanation:
with ABCD and ABDE being parallelograms, this means a indicated by the marks
AB = ED = CD
and with BD = DF that means that the line segments BF and CE are intersecting each other at their midpoint.
so they represent a pair of diagonals of a parallelogram, which makes BCFE a parallelogram.
group of 280 elementary school students and 40 adults are going on a field trip. They are planning to use two different types of buses to get to the destination. The first type of bus holds 50 people and the second type of bus holds 56 people.
Andre says that 3 of the first type of bus and 3 of the second type of bus will hold all of the students and adults going on the field trip.
Is Andre correct?
Answer:
yes!!! because the first 3 types of bus can hold 50 people and the other 3 types of bus can hold 56 people so the total will be 320 people
What kind of passenger be considered a true negative ?
Answer: A someone with dangerous material passed by security
Step-by-step explanation:
28% of 80 is what number?
Answer:
22.4
Step-by-step explanation:
28% of 80 = [tex]\frac{28}{100}[/tex] of 80
=[tex]\frac{28}{100}[/tex] of 80 = [tex]\frac{28}{100}[/tex]*80
cut the zeros
=[tex]\frac{28}{10}[/tex]*8
=[tex]\frac{28}{5}[/tex]*4
=[tex]\frac{112}{5}[/tex]
=22.4
order of operations MC
Joshua purchased a game card for the arcade for a total of $15. He played two basketball hoop games for $2.75 each and three rounds of air hockey for $1.25 each. How much did he have left on the game card?
Answer: $5.75
Step-by-step explanation: 2.75 x 2 = 5.5 1.25 x 3 = 2.75 2.75 + 5.5 = 9.25 $15 - $9.25 = $5.75
i need help with 23-26 help please
2.5, 0.92, 0.75, 0.925
Each of the positive integers from 1 to 100 are written on a sheet of paper.
Some of these integers are erased. The product of those integers still on the paper leaves a remainder of 4 when divided by 5. Find the least number of integers that could have been erased.
Answer:
9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89 94 99
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 18 gallons of water. Ryan used 9.7 gallons to water his garden in June and 3 and one eighth gallons in July. How much water is left in the barrel?
24.575 gallons
5.175 gallons
3.168 gallons
3.125 gallons
The quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons
Calculating quantityFrom the question, we are to determine how much water is left in the barrel
From the given information,
"The barrel is filled with 18 gallons of water"
and
"Ryan used 9.7 gallons to water his garden in June"
After this time,
The quantity of water that would be left in the barrel will be 18 gallons - 9.7 gallons
= 8.3 gallons
Then,
3 and one eighth gallons in July
3 and one eighth = 3 1/8 = 3.125 gallons
The quantity of water that would be left is 8.3 gallons - 3.125 gallons
= 5.175 gallons
Hence, the quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons
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Answer:
b
Step-by-step explanation:
a parte inferior de una escalera debe colocarse a 3 pies de una pared. La escalera mide 10 pies de largo. ¿Qué tan por encima del suelo toca la escalera la pared?
[tex]\sqrt{10^2 - 3^2}=\boxed{\sqrt{91} \text{ ft}}[/tex]
How do I factor 7.2x2y - 0.9xy2
Answer:
[tex]xy\left(7.2x-0.9y\right)[/tex]
Step-by-step explanation:
[tex]Rule: a^{b+c}=a^ba^c\\(x^2y=xxy,\:xy^2=xyy)\\=7.2x(xy)-0.9xyy\\=xy\left(7.2x-0.9y\right)[/tex]
to construct a rectangle you must have one side and :
(1) it’s opposite sides
(2) it’s adjacent sides
(3) two angles
(4) four angles
If u answer this question i will give brainlyest and 40 marks
Answer:
Adjacent sides.
Step-by-step explanation:
Answer:
To construct a rectangle, you must have the measurement of one side and it's adjacent side.
Step-by-step explanation:
to construct a rectangle you must have one side and :
(1) it’s opposite sides
(2) it’s adjacent sides
(3) two angles
(4) four angles
Find the area of a rectangle that has a length of 4.5 units and a width of 7.2 units. Write the numerical answer only.
Find the sum of 3√2 and 2√8 in simplest form. Also, determine whether the result
is rational or irrational and explain your answer.
Answer:
7√2
7√2 is irrational since √2 is irrational
Step-by-step explanation:
3√2 + 2√8 = 3√2 + 2 × 2√2 = 3√2 + 4√2 = 7√2
7√2 is irrational since √2 is irrational