Answer:
[tex]P(x)=2x^3-2x^2-49x+48[/tex]
Step-by-step explanation:
Let the original polynomial be [tex]P(x)[/tex].
We know that when it is divided by [tex](x-5)[/tex], the quotient is [tex]2x^2+8x-9[/tex] and we get a remainder of 3.
Therefore, this means that:
[tex]\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}[/tex]
Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 over 3. We put the remainder over the divisor. This is the same thing for polynomials.
So, to find our original polynomial, multiply both sides by [tex](x-5)[/tex]:
[tex](x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})[/tex]
The left side will cancel. Distribute the right:
[tex]P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)[/tex]
Distribute:
[tex]P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)[/tex]
Combine like terms:
[tex]P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)[/tex]
Evaluate:
[tex]P(x)=2x^3-2x^2-49x+48[/tex]
And we're done!
i need help in finding the sum for (16 − x2) + (−14x2 + 7x5 − 17x4 + 9) plz help :( im rlly bad at math
Answer:
-50
Step-by-step explanation:
Solve for the value of z.
(5z-4) 39
Answer:
[tex]{\huge{\pink{\underline{\underline{Solution:}}}}}[/tex]
As we know,sum of angles on a straight line is 180 degree..
(5z-4)+90+39=180
=>5z-4+90+39=180
=>5z-4+129=180
=>5z+125=180
=>5z=180-125
=>z=55÷5
Hence,the value of z=11 degree
Find the value of the variable.
The required value of variable m is 15.
Gvien that,
A line segment AC is given, On which B is the midpoint,
AB = 3m + 5
and BC = 4m - 10
AB = BC
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
AC is the line segment where B is the midpoint on the line AC. So,
AC = AB + BC
AB = BC
3m + 5 = 4m - 10
m = 15
Thus, the required value of variable m is 15.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
i need help with my 8th grade math
Answer:
x = -2.38
Step-by-step explanation:
divide 3 to up 3x then 4 and divide them by 2.
What is the square of 9 is less than 100. True or false?
Square of 9 is 81 and it is less than 100
Kristen has been waiting all summer for her family's annual road trip. This year, they're headed to Yellowstone National Park. Kristen just saw a sign that said the park is 10 miles away, so the drive is almost over. If Kristen's father drives 50 miles per hour, how many more minutes will it take to reach the park?
Answer: It will take 12 minutes to the reach the park.
Step-by-step explanation:
We know that, [tex]\text{Speed }=\dfrac{\text{distance}}{\text{time}}[/tex]
[tex]\Rightarrow\ \text{Time}=\dfrac{\text{Distance}}{ \text{Speed}}[/tex]
Given: Speed = 50 miles per hour
Distance needs to travel = 10 miles
Now, Time required to reach the park = [tex]\dfrac{10}{50}=\dfrac{1}{5}\text{ hour}[/tex]
Since 1 hour = 60 minutes
So, [tex]\dfrac15\text{ hour}=\dfrac15\times 60=12\text{ minutes}[/tex]
Hence, it will take 12 minutes to the reach the park.
In a fruit salad, the ratio of watermelon to strawberries is 2:3. if there are 27 strawberries in the fruit salad, How many pieces of watermelon are there?
Answer: 18
Step-by-step explanation:
27 strawberries divided by 3 strawberries = 9
2 watermelon times 9 = 18 watermelon
Factor each completely.
10a² - 9a + 2
Answer:
a= [tex]\frac{2}{5}[/tex] or [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Equate the equation to zero
[tex]10a^{2}[/tex]-9a+2=0
[tex]10a^{2}[/tex]-5a-4a+2=0
5a(2a-1)-2(2a-1)=0
Write out the factors
(5a-2)(2a-1)=0
Then equate each factor to zero
5a-2=0 OR 2a-1=0
5a=2 OR 2a=1
a= [tex]\frac{2}{5}[/tex] OR a= [tex]\frac{1}{2}[/tex]
a=[tex]\frac{2}{5}[/tex] or [tex]\frac{1}{2}[/tex]
Jason bought a TV that was $1099.99. He made a
down payment of 199.99 and wants to pay the rest in
9 equal monthly payments. How much would he pay
each month?
To show that the triangles are congruent, triangle ABC could be transformed by
which movement(s) to fit exactly on triangle XYZ?
Answer:
D a reflection over the x axis by a reflection over the y axis
Step-by-step explanation: if u put the triangle on the button left up then move it to the upper right it’s congruent.
Answer: A rotation of 270° clockwise about the origin followed by translation left 1 and up 10
Step-by-step explanation:
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full
barrel of ink in the pen is used up on writing 3300 words on an average. How many words can
be written in a bottle of ink containing one fifth of a litre?
Answer:
480,000 words
Step-by-step explanation:
For barrel of pen:
h = 7 cm, d = 5 mm
r = 5/2 = 2.5 mm = 0.25 cm
[tex]Volume \: of \: barrel = \pi {r}^{2} h \\ \\ = \frac{22}{7} \times {(0.25)}^{2} \times 7 \\ \\ = 22 \times 0.0625 \\ \\ = 1.375 \: {cm}^{3} \\ \\ one \: fifth \: of \: a \: litre \\ = \frac{1}{5} \times 1000 \: ml \\ \\ = 200 \: ml \\ \\ = 200 \: {cm}^{3} \\ \\ no \: of \: words = \frac{3300 \times 200}{1.375} \\ \\ = \frac{660000}{1.375} \\ \\ = 480,000 \\ [/tex]
Plz help!
Solve... 4x + 30 = -6(x - 2)
I got -4.2 but it's wrong!
Answer: x= -9/5 or x = -1.8
Step-by-step explanation:
4x + 30 = -6(x - 2) First apply the distributive property on the left side
4x + 30 = -6x + 12 Add 6x to both sides
+6x +6x
10x + 30 = 12 Subtract 30 from both sides
-30 -30
10x = -18 Divide both sides by 10
x = -9/5 or x = -1.8
Answer:
the answer is -1.8 if you want to use the decimal and -9/5 if you want to use the fraction
Step-by-step explanation:
4x + 30 = -6(x - 2)
4x+30 = -6x + 12
4x + 6x = 12 - 30
10x = -18
divide both side by 10
x = -9/5 or -1 4/5 or -1.8
( also not trying to gatekeep so i wanna say that i got this answer from an app named photomath. i scanned the question in the camera and it pulled the answer. hoped it helped love!)
Is the line through points p (3,-5) and Q(1,4)parallel to the line through points R( -1,1) and S (3,-3)
Answer:
No
Step-by-step explanation:
To find out if the lines that go through the pairs of points are parallel, we must find the slope of each line. If the slopes are equivalent, then they are parallel. If not, then they are not parallel.
We can use the slope formula to find the slope between two points. The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope between the points (x₁, y₁) and (x₂, y₂).
Lets first find the slope between points P and Q.
[tex]m=\frac{-5-4}{3-1}=\frac{-9}{2}=-4.5[/tex]
So the slope between P and Q is -4.5.
Now lets find the slope between the points R and S.
[tex]m=\frac{-3-1}{3-(-1)}=\frac{-4}{4}=-1[/tex]
So the slope between R and S is -1.
Since -4.5 does not equal -1, the lines are not parallel.
I hope you find my answer and explanation to be helpful. Happy studying.
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What is the y-intercept of the quadratic function
f(x) = (x - 6)(x - 2)?
Answer:
y = 12 → (0|12)
Step-by-step explanation:
f(x) = (x - 6)(x - 2)
y = (x - 6)(x - 2)
y = x² - 6x - 2x + 12
y = x² - 8x + 12
y = 0² - 8*0 +12
y = 12
help me pls u get 10 points
What is the slope of the line shown in the graph?
1. 4/5
2. 5/7
3. 6/7
4. 5/6
The slope of the line is B. 5/7
Which of the equations below will answer the following question? Select all that apply. Explain your answers.
I think of a number, add 7 and then multiply by 4. My answer is 80. What was my number?
x + 28 = 80
4(x+7) = 80
4x + 7 = 80
4x + 28 = 80
Please help me and explain the answer is the answer
Answer: C
Step-by-step explanation:
Can someone help me with this question I haven’t seen this answer yet
Determine the slope of the line from the given two points. (-2, 3) and (1, 8).
Answer:
5/3
Step-by-step explanation:
to find slope use the question:
y2-y1
x2-x1
8-3
1--2
5
3
Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.
Answer:
[tex]x=-7[/tex]
Step-by-step explanation:
Remember that:
Two lines are parallel if their slopes are the same.Two lines are perpendicular if their slopes are negative reciprocals.And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.We want to find the value of x such that [tex]\overline{BC}\parallel\overline{DE}[/tex].
Therefore, the slopes of BC and DE must be equivalent.
So, let's find the slope of BC first.
BC)
We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{-3-5}{11-17}[/tex]
Subtract:
[tex]m=-8/-6=4/3[/tex]
So, the slope of BC is 4/3.
DE)
Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:
[tex]\displaystyle m=\frac{-6-2}{x-(-1)}[/tex]
We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:
[tex]\displaystyle \frac{4}{3}=\frac{-6-2}{x-(-1)}[/tex]
Solve for x. Simplify the right:
[tex]\displaystyle \frac{4}{3}=\frac{-8}{x+1}[/tex]
Cross multiply:
[tex]4(x+1)=-8(3)[/tex]
Multiply on the right:
[tex]4(x+1)=-24[/tex]
Divide both sides by 4:
[tex]x+1=-6[/tex]
Subtract 1 from both sides:
[tex]x=-7[/tex]
So, the value of x is -7.
And we're done!
The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?
Answer:
$12 per hour
Step-by-step explanation:
51 -39 =12 minutes 31 -27=12minutes
also took the test
$12 per hour
just took the test hope this helps:)
2x + 5 = 8x-7-6x What is the answer to this question?
Answer:
No solution
Step-by-step explanation:
Pls help
Write a recursive AND explicit formula AND find the 7th term for each sequence:
1. 5,0,-5,-10
2. 3,4.5,6,7.5,9
Answer:
1)5-5x
2)3+1.5x
Step-by-step explanation:
5-5(7)=-30
3+1.5(7)=13.5
A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes.
What does t represent?
What does a(t) represent?
What information will a(5.5) give?
Answer:
t represents the time in minutes since the balloon started descending.
a(t) represents the altitude of the balloon at t minutes.
a(5.5) gives the altitude at 5.5 minutes.
Answer:
What does t represent?
✔ time after the balloon begins to descend
What does a(t) represent?
✔ altitude of the balloon
What information will a(5.5) give?
✔ altitude of the balloon after 5.5 minutes
Step-by-step explanation:
edge 2021
plz make me brainliest
x^2 - 7x = -4
solve by factoring
Step-by-step explanation:
x= -[tex]\sqrt{[/tex]7x - 4
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
The equation with (x) in dogs and (y) in dollars is [tex]y=195x[/tex]
First, you must set up your equation.
[tex]y=80x+65x+50x[/tex]
Then, you must add like terms to simplify the equation
[tex]y=195x[/tex]
Answer:y=195x
Step-by-step explanation:
Ricky, Nathan, and Henry collect comic books. Ricky owns twice as many comic books as Nathan.
Henry owns
1
3
as many comic books as Ricky. If Nathan owns 129 comic books, how many does
Henry own?
Answer:
9/12
Step-by-step explanation:
Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures the angle from 35 feet away from the base of the tree and gets an angle of 62°. Tamara's eye level is 5.5 feet above the ground. How tall is the tree?
Answer:
71.32 feet
Step-by-step explanation:
We set up a trigonometric function to get height of tree
Distance ,x = 35 feet away from tree base
Angle = 62⁰ at eye level
Y = tan(angle) * x
= Y = tan(62⁰) x 35
Y = 1.881 x 35
Y = 65.82 feet
We add Tamara's height to the total height of the tree
= 65.82feet + 5.5 feet
= 71.32 feet is the height of the tree
y =(x - 2)3 + 2
.
Plz help I do not understand
Answer:
get photo math it will help alot
The graph represents the gallons of water in a water tank with respect to the number of hours since it was completely filled. The total capacity of the water tank is gallons, and the rate of change is gallons per hour.
Answer:
Total capacity of the water tank is 400 gallons
Rate of change in water level is 20 gallons per hour
Step-by-step explanation:
The graph attached represents the gallons of water in a water tank with respect to the number of hours since it was completely filled.
The total capacity of the water tank is represented by the y-intercept of the graph that is 400 gallons.
Now to calculate the rate of change in water level we will take two points on the given line and find the slope.
There are two points (0, 400) and (5, 300) on the line.
So the slope of the line is (400-300)/(0-5)= -100/5= -20
This minus notation of slope shows that level of water is reducing and rate of change in water level is 20 gallons per hour.