Answer:
a) f(x-1) = 2x^2-11x-1
b) x = -1.5 or 5
Step-by-step explanation:
a) To get f(x-1)
We proceed to substitute x-1 for x as follows
f(x-1) = 2(x-1)^2 -7(x-1) -10
f(x-1) = 2(x^2 - 2x + 1) -7(x-1)-10
f(x-1) = 2x^2 -4x + 2 -7x + 7-10
f(x-1) = 2x^2-11x-1
b) What we have to do here is substitute 5 for f(x) and solve for x
5 = 2x^2 -7x-10
2x^2 -7x -10-5 = 0
2x^2 - 7x - 15 = 0
2x^2 -10x + 3x -15 = 0
2x(x-5) + 3(x-5) = 0
(2x + 3)(x-5) = 0
2x + 3 = 0 or x -5 = 0
2x = -3 or x = 5
x = -3/2 or x = 5
x = -1.5 or 5
Solve 7x + 1 < 4(x - 2).
A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}
Given:- 7x + 1 < 4(x - 2)
Solving It:-7x + 1 < 4(x - 2)
7x + 1 < 4x - 8
7x - 4x < -8 -1
3x < -9
x < -9/3
x < -3
So Correct Solution Set Will BeC. {x | x < -3}Hope This Helps YouIf the woman in the picture below measured the angle of elevation from herself to the top of castle and found it to be 64 degrees, and she also measured the distance from herself to the base of the castle as being 124 meters, what would the height of the castle be? (round to the nearest whole meter.)
Answer:
254m
Step-by-step explanation:
The setup will be in form of a right triangle. Hence;
The angle of elevation = 64degrees
distance from herself to the base of the castle = 124 meters (Adjacent)
Required
Height of the castle (Opposite)
Using the SOH CAH TOA identity
Tan theta = opp/adj
Tan 64 = H/124
H = 124tan64
H = 124(2.05030)
H = 254.23
H ≈ 254m
Hence the height of the castle to the nearest whole meters is 254metres
Find the volume
Help me please
Answer:
54piecm^3
Step-by-step explanation:
pie x radius ^2 x h
= v
pie x 9
= 9pie x 6
= 54pie
Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?
Answer:
$6778.36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compounded ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 6000
r = 5% = 0.05
n = 1
t = 2.5
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 6000(1 + \frac{0.05}{1})^{1 \cdot 2.5}[/tex]Simplify: [tex]\displaystyle A = 6000(1.05)^{2.5}[/tex]Evaluate: [tex]\displaystyle A = 6778.36[/tex]i need help A S A P!
Answer:
ewfwefwfewfwfwe
Step-by-step explanation:
What is [tex]\pi r^2[/tex] ?
Answer:
The formula to determine the area of the circle.
Step-by-step explanation:
↔
The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?
PLS HELP WILL GIVE BRAINLIEST
Answer:
-6
Step-by-step explanation:
2n can be the smallest integer, and 2n + 18 will be the largest integer.
The sum of this, divided by two, will result in the average/mean.
(2n + 2n + 18)/2 = 3
Multiply each side by 2:
(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2
2n + 2n + 18 = 6
Combine the like terms:
4n + 18 = 6
Subtract 18 from both sides:
4n + 18 - 18 = 6 - 18
4n = -12
Divide each side by 4:
4n/4 = -12/4
n = -3
Since we decided to go by 2n:
2n = 2(-3) = -6
HELP ME WITH THIS PROBLEM PLEASE!!
Answer:
w ≈ 33.9 in
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
w² + w² = 48²
2w² = 2304 ( divide both sides by 2 )
w² = 1152 ( take the square root of both sides )
w = [tex]\sqrt{1152}[/tex] ≈ 33.9 in ( to the nearest tenth )
Rewrite the expression in the form a^n.
1/a^-5/6
Step-by-step explanation:
here's the answer to your question
Answer:
[tex]\frac{1}{a^{\frac{-5}{6} } }[/tex]
[tex]\frac{1}{a^{-n} }[/tex][tex]\frac{1}{a^{-5/6} } =a^{5/6}[/tex][tex]ans: a^{5/6}[/tex]OAmalOHopeO
what would be the u to usub and what would be the steps to solving this integral?
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
Please solve this question 3(n+4)=5n?
Answer:
6=n
Step-by-step explanation:
Hi there!
We are given this equation:
3(n+4)=5n
And we need to solve it for n
To do that, we need to isolate n on one side
But we need to open up the parentheses on the left side by doing the distributive property
Multiply both n and 4 by 3
3n+12=5n
Now subtract 3n from both sides to remove it from the left side
12=2n
Divide both sides by 2 to change the coefficient on n from 2 to 1
6=n
n is now isolated on one side
Hope this helps!
Answer:
n=6
Step-by-step explanation:
Using the distributive property, we distribute 3 to n and 4. In case if you don't know what that means, it means we multiply 3 to the variables inside the parentheses. So we get (3×n)+(3×4)=5n, and we simplify it so we get 3n+12=5n. Now, we can subtract 3n from both sides and get 12=2n, and divide 2 from both sides and get n=6.
Javier jogs & of a -
mile in 8 minutes
how many minutes will
it take him to jog
1 mile?
Answer:
It will take him 10 minutes to jog 1 mile.
Step-by-step explanation:
can i have brianliest please
The perimeter of a rectangle is 24 cm. If the length is 7 cm, find it width
Answer:
The width is 5 cm
Step-by-step explanation:
The perimeter of a rectangle is
P = 2(l+w)
Substitute what we know
24 = 2(7+w)
Divide each side by 2
24/2 = 2/2(7+w)
12 = 7+w
Subtract 7 from each side
12-7 = 7+w-7
5 =w
The width is 5 cm
The formula for perimeter = 2 x length + 2 x width
Fill in the known dimensions:
24 = 2 x 7 + 2 x width
Simplify:
24 = 14 + 2 x width
Subtract 14 from both sides:
10 = 2 x width
Divide both sides by 2:
Width = 5 cm
Answer: Width = 5 cm.
The slope of a line is 5/9 and the slope of another line is -975. The two lines
are
Answer:
the third option - they are perpendicular to each other.
Step-by-step explanation:
for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.
and that is exactly what happened here.
Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP
Answer:
5.1 cm
Step-by-step explanation:
(Probable) Question;
Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP
The given parameters are;
The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm
The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm
The length of OP = Required
By Pythagoras's theorem, we have;
[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²
∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01
[tex]\overline{OP}[/tex] = √26.01 = 5.1
The length of OP = 5.1 cm
Does this graph show a function? Explain how you know.
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
What is the surface area of the cone?
Answer: C
Step-by-step explanation:
To find the surface area of a cone, you use the formula [tex]A=\pi r(r+\sqrt{h^2+r^2} )[/tex]. Since we are already given the height and radius, all we have to do is plug in the values and solve.
[tex]A=9\pi (9+\sqrt{41^2+9^2} )[/tex] [solve inside of square root]
[tex]A=9\pi (9+\sqrt{1762} )[/tex] [parenthesis]
[tex]A=9\pi (50.976 )[/tex] [multiply]
[tex]A=458[/tex]
Therefore, the closest answer is C.
how can the graph of g(x) =x2+4 be obtained from the graph of f(x) =x2
Answer:
see explanation
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
The graph of g(x) is the graph of f(x) shifted up by 4 units
which algebraic expression represents this word description?
the product of two and the difference between eleven and a number
a. 2(11-x)
b. 11-2x
c. 2x-11
d. 2(x-11)
Step-by-step explanation:
c. 2x-11 this is the answer
hope this helps you
have a nice day:)
Ah(t)
1800-
A ball is dropped from a height of 1296 ft. Its height h,
in feet, after t seconds is given by h(t) = 1296 - 1612.
After how long will the ball reach the ground?
0 0
1296
0-
0
12
The ball will reach the ground in seconds.
(Type an integer or a simplified fraction.)
Can someone please help me out with a small explanation thank you :)
Step-by-step explanation:
1 . when we collect like terms we only focus on the variables and the power of the variable I f exist so in this question the answer is 8x^2 because both have the same variable and same power or exponent.
2. one term is monomial
two terms is binomial
3. b
4. -9
5. c
if the sum of an angle measures of a polygon with sides s is 2340, what is s
Answer:
polygon is 15 side
Step-by-step explanation:
Here sum of interior angels is 2340 degrees. Therefore, the polygon is 15 side
Please help, explain too and I will give brainliest :)
Answer:
c
Step-by-step explanation:
Answer:
C. 37 degrees
Step-by-step explanation:
27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.
I'm sure you can do it with an actual formula, but i can't recall. Cheers
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
x – 4
x – 2
x + 2
x + 4
The answer for (a) is 28 and the answer for (b) is 13 but I don’t know how to get the answer
Answer:
Step-by-step explanation:
If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):
[tex]x=\frac{4}{5}(35)[/tex] 35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.
For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.
If the point A at (5, 3) is rotated clockwise about the origin through 90°, what
will be the coordinates of the new point?
Answer:
(5,-3) in the 4th quadrant
Step-by-step explanation:
What is the standard form of the ellipse equation
25x2 - 150x + 9y2 = 0?
O
(x - 3)2
32
y
1
+
52
0 (x - 5)
1
y2
22
(y - 3)2
22
0x2
+
14
1
O
x2
32
(y - 3)2
22
= 1
Answer: The correct answer is in the first option.
Step-by-step explanation:
Equation of an Ellipse
[tex]\dfrac{x^{2} }{a^{2} } +\dfrac{y^{2} }{b^{2} } =1\\\\25x^{2} - 150x + 9y^{2} = 0\\\\\text {Let's \: perform \: the \: transformations:}\\\\\dfrac{25x^{2} }{25 \cdot 9} -\dfrac{150x}{25 \cdot 9} +\dfrac{9y^{2} }{25 \cdot 9} =0\\\\\dfrac{x^{2} }{3^{2} } -\dfrac{6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } =0\\\\\dfrac{x^{2} -6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } +\dfrac{3^{2} }{3^{2} } -\dfrac{3^{2} }{3^{2} } =0\\\\\dfrac{x^{2} -6x+3^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =\dfrac{3^{2} }{3^{2} }[/tex]
[tex]\dfrac{(x-3)^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =1[/tex]
pls help me solve this multiplication fractions. (show work)
Answer:
32:3/4
33:4/3
34:40
35:48
Hellllllllp plsss!! Due in very soon maths
Answer: 23, 27,29
Those im absolutely positive about.
Im not sure abt the rest
Step-by-step explanation:
geometry help translations
Answer:
A' (9,4)
B' (8,-1)
C' (5,1)
Answered by GAUTHMATH
Answer:
A' = 9,4
B' = 8,-1
C' = 5,1
Step-by-step explanation:
