Answer:
a = 1
b = -1
Step-by-step explanation:
[tex]g(x)=ax^2-b \quad \quad \textsf{(where }\:a\:\textsf{ and }\:b\:\textsf{ are real numbers)}[/tex]
Create 2 equations with b as the subject using the given information.
Equation 1
[tex]\begin{aligned}g(2) &=-5\\\implies a(2)^2-b &=-5\\4a-b &=5\\ b&=4a-5\end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}g(-1) &=2\\\implies a(-1)^2-b &=2\\a-b &=2\\ b &=a-2\end{aligned}[/tex]
Equate the equations and solve for a:
[tex]\begin{aligned}b & =b\\\implies 4a-5 & = a-2\\3a & = 3\\a & = 1\\\end{aligned}[/tex]
Substitute the value of a into Equation 2 and solve for b:
[tex]\begin{aligned}b & =a-2\\a=1 \implies b & =1-2\\b & = -1\end{aligned}[/tex]
Answer:
a = -7/3
b = -13/3
Step-by-step explanation:
Making equations in terms of 'a' and 'b' :
g(2) = -5 = a(2)² - b ⇒ 4a - b = -5 [Equation 1]g(-1) = 2 = a(-1)² - b ⇒ a - b = 2 [Equation 2]Subtract : Equation 1 - Equation 2
4a - b - a + b = -5 - 23a = -7a = -7/3Finding b :
-7/3 - b = 2b = -7/3 - 6/3b = -13/3What is the least common multiple of 2 and 5
Answer:
10Step-by-step explanation:
We Notice that 2 and 5 are two prime numbers
Remark : the least common multiple of two prime numbers is equal to their product .
Then
LCM(2 , 5) = 2 × 5 = 10
2 * 5
= 10 ⟶ least common multiple of the number (since no common factor is there)
If we invest $5,000.00 in an investment account paying 1% interest compounded annual, how much
will the account be worth in 14 years?
A(t) = P(1+)".
n
The account in 14 years will be worth $
Answer:
5747.37
Step-by-step explanation:
5 000 ( 1 + .01) ^14
= 5747.37
Which oylinders have the same volume as the cylinder below? Cheok all that apply, height- 20m and base- 32m:
Answer:
Picture 3: A cylinder with height of 8 meters and diameter of 40 meters.
Picture 5: A cylinder with height of 128 meters and diameter of 10 meters.
Step-by-step explanation:
-------------------------------------------------------------------------------------------------------------
Given:
Which Cylinders have the same volume as the cylinder below? Cheok all that apply, height- 20m and base- 32m:
Answer choices:
picture 1: 40m and 16
picture 2: 5m and 64
picture 3: 40m and 8
picture 4: 32m and 20
picture 5: 10m and 128
Formula for Cylinders:
V=Bh or V=πr²h
-------------------------------------------------------------------------------------------------------------
Diameter = Half of Radius {Divide by 2}
Original Cylinder:
20m and 32m
20/2 = 10
V=πr2h=π·102·32≈10053.09649
V ≈ 10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Picture 1: 40m and 16
40/2 = 20
V=πr2h=π·202·16≈20106.19298
V ≈20106.19
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 2: 5m and 64
5/2 = 2.5
V=πr2h=π·2.52·64≈1256.63706
V ≈1256.64
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 3: 40m and 8
40/2 = 20
V=πr2h=π·202·8≈10053.09649
V≈10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 4: 32m and 20
32/2 = 16
V=πr2h=π·162·20≈16084.95439
V≈16084.95
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 5: 10m and 128
10/2 = 5
V=πr2h=π·52·128≈10053.09649
V≈10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
After solving each answer choices the answers are:
picture 3: 40m and 8
picture 5: 10m and 128
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Kavinsky
An amusement park issued a coupon to increase the number of visitors to the park each week. The function below represents the number of visitors at the amusement park x weeks after the issuance of the coupon. V(x) = 500(1.2)x What is the approximate average rate of change over the interval [2, 6]? A. 129 visitors per week B. 249 visitors per week C. 180 visitors per week D. 193 visitors per week
Answer:
the answer to this question is "D"
have a awesome day
simplify the ratio of 1:3¼
Answer:
[tex]\frac{4}{13}[/tex]
Step-by-step explanation:
1÷3[tex]\frac{1}{4}[/tex]=3+[tex]\frac{1}{4}[/tex], 3×[tex]\frac{4}{4}[/tex]
1÷[tex]\frac{13}{4}[/tex]
Let f(x) = 3x + 8 and g(x) = x^2 Find (f.g)(x).
Answer:
3x^2 +8
Step-by-step explanation:
f.g(x) = f(x^2) = 3(x^2) + 8 = 3x^2 +8
The difference betneen x ond 4, where 4 is greater than x
This can be written as,
x - 4 > 10Why?✓ We use the operation of subtraction since the terms used is difference. Difference is the result when you subtract numbers.
✓ The symbol for greater than is >. Therefore, you'll have x - 4 > 10 as an answer.
Baby Caden wants to arrange 11 blocks in a row. How many different arrangements can he make?
Explanation:
Start with 11, and count down until you reach 1. Multiply everything along the way.
11*10*9*8*7*6*5*4*3*2*1 = 39,916,800
Or a shortcut would be to say
11! = 39,916,800
The exclamation mark means factorial. It tells the calculator to follow the instructions mentioned above.
The number 39,916,800 is a little over 39.9 million, or you could say it's a bit smaller than 40 million.
c(d), when c = 7 and d= 34?
Answer:
[tex]238[/tex]
Step-by-step explanation:
Step 1: Input the values and solve
c(d) just basically means c * d
If we just multiply 7 (for c) and 34 (for d) we get 238 which is our answer.
Answer: [tex]238[/tex]
Answer:
238
Step-by-step explanation:
c(d), when c = 7 and d= 34
7 * 34
= 238
Simplify the expression 3(7x).
help
Answer:
21x
Step-by-step explanation:
7x is one term. With parenthesis, you have to multiply whatever is on the outside, inside. So that's 3*7x, or 21x.
Hope this helps!
Hey there!
3(7x)
= 3 * 7x
= 7x * 3
= 7x + 7x + 7x
= 14x + 7x
= 21x
Therefore, the answer should be: 21x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
solve for absolute value: 3(r+1)+2>-7
Answer:
[tex]\huge\boxed{\bf\:r > -4 }[/tex]
Step-by-step explanation:
[tex]3(r+1)+2 > -7[/tex]
Use the distributive property to solve 3 (r + 1).
[tex]3r+3+2 > -7 \\3r + 5 > -7[/tex]
Now, bring 5 to the right hand side of the inequality .
[tex]3r > -7-5 \\3r > -12[/tex]
Divide both sides of the inequality by 3.
[tex]r > \frac{-12}{3} \\\boxed{\bf\:r > -4 }[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Identify the maximum or minimum value, domain, and range of the graph of the quadratic function.
Answer:
See below ~
Step-by-step explanation:
Details of the graph
Maximum = 4 [highest value past which no values are part of the graph]Domain : all real numbers [graph is vertical, so it will be all possible real numbers]Range : y ≤ 4 [all y values are less than or equal to 4 according to the graph]Select the correct answer.
What is the approximate solution to this equation?
15(3)2+ = 90
=
2log
a = log3
O
210g3
t = log 6
O
log 6
210g3
=
log3
2log 6
Answer:
C) [tex]x=\frac{\log(6)}{2\log(3)}[/tex]
Step-by-step explanation:
[tex]15(3)^{2x}=90\\\\3^{2x}=6\\\\2x=\log_3(6)\\\\2x=\frac{\log(6)}{\log(3)}\\\\x=\frac{\log(6)}{2\log(3)}[/tex]
Remember to use the change of base formula, which states that [tex]\log_a(b)=\frac{\log(b)}{\log(a)}[/tex] so that everything has the same base of 10
Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 40, 33, 26, ...
The nth term of the Sequence: 40, 33, 26, .... is 47 - 7n.
What is Arithmetic Progression?An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.
Here, we know nth term of the Arithmetic Sequence is
Aₙ = A + (n - 1)D
where, A is first term and D is common difference
A = 40 and D = 33 - 40 = -7
Now, Aₙ = 40 + (n - 1) (-7)
Aₙ = 40 - 7n + 7
Aₙ = 47 - 7n
Thus, the nth term of the Sequence: 40, 33, 26, .... is 47 - 7n.
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In a basketball game, Jacob gets 4/9 of the rebounds and Adam gets 3/8 of the rebounds for their team. What fraction of the rebounds did the rest of the team get?
Answer:
The fraction of the rebounds the rest of the team get was 13/72 (13 out of the 72 total)
Step-by-step explanation:
Jacob gets 4/9
Adam gets 3/8
Since the given fraction provided doesn't have common denominator we would need to do thos first...
4/9 x 8/8 = 32/72
3/8 x 9/9 = 27/72
combining Adam and Jacob rebounds...
32/72 + 27/72 = 59/72
so the remaining, uncounted rebounds are...
72 - 59 = 13
Elly is a self-employed financial advisor. Last year her income was $57,000.How much does she owe in SECA taxes?
The SECA taxes for the income $57000 will be $7068.
What is SECA?SECA stands for Self Employed Contributions Act. These taxes are computed from the net earnings, which in this case is $57000.
The basic rate for SECA taxes is 6.2% for employeer and 6.2% for employee. In the case of people who are self employed, the taxes are double, because they are employee and employeer at the same time.
So, Doug have to pay 12.4% taxes, which is equivalent to:
[tex]\rm SECA=57000\times 12.4\%= $7067[/tex]
Therefore, the SECA deduction for Doug is $7068.
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(64 / 8 + 2 - 10) + (9 x 9 + 19) = 2 points 100 90 99
Answer:
Answer is 100
Step-by-step explanation:
(64/8+2-10) + (81+19)
(8+2-10) + (81+19)
(10-10) + (100)
(0) + (100)
0+100
100
A parachutist's speed during a free fall reaches 50 meters per second. What is this speed in feet per second? At this speed, how many
feet will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round
your answers.
Speed:
0
Х
5
?
Distance fallen in 10 seconds:
50m ≅164 ft (3s.f.)
50m/s≅164 ft/s
distance after 20s:
d=164 ft/s ⋅20s
=3280ft
Hope This Helps!
Find the size of the angle marked a and b on the diagram
Answer:
Step-by-step explanation:
we know that the total angles around the big triangle are 180° so, we know the right angle is 90° and we are told that one of the angles is 52° so just find the last angle by
180 = 90 + 52 + X
180 - 90 - 52 = X
38 = X
b = 38°
a = 52°
Answer:
a = 52°b = 38°Step-by-step explanation:
We know:
Angles in a triangle sum to 180°.
Therefore:
52° + 90° + b = 180°
142° + b = 180° |-142°
b = 38°(look at the picture)
a + b = 90° ⇒ a + 38° = 90° |-38°
a = 52°or
Angles 52° and a, are alternate interior angles. Therefore they are congruent.
a = 52°Maribel was approved for a 7-year private student loan at 6.8% to cover her college costs of $10,900. (Round monthly payment calculations to 2 decimal places.)
Using it's formula, it is found that her monthly payment for the loan will be of $163.45.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 10900, r = 0.068, n = 7 x 12 = 84.
Hence:
r/12 = 0.068/12 = 0.005667.
Hence the monthly payment will be given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 10900\frac{0.005667(1 + 0.005667)^{84}}{(1 + 0.005667)^{84} - 1}[/tex]
A = 163.45.
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1 × 10^ − 4 ) + ( 2 × 10^ − 2 )
Answer:
[tex]2.01 *10^{-2}[/tex]
Step-by-step explanation:
this is the correct answer
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
6 m
7 m
9 m
Answer:
378 M -small 3 that goes on on top right side of the M.
Step-by-step explanation:
you multiply the 6m x 7m x 9m = 378 m to the 3rd power
An isosceles trapezoid with bottom base 26.5 decimeters, top base 8.5 decimeters, and height 9 decimeters. Find the area. a. 238.5 dm2 c. 157.5 dm2 b. 257.5 dm2 d. 315 dm2 Please select the best answer from the choices provided A B C
Answer:
the answers c 157.5
Step-by-step explanation:
on edg 2022
The area of given isosceles trapezoid is c. 157.5 decimeters².
What is an area of a trapezoid?The area of a trapezoid is = (1/2*sum of the two parallel sides *height). The area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The surface area of a solid object is a measure of the total area that the surface of the object covers.⇒ (1/2*sum of the two parallel sides *height)
⇒ 1/2*(26.5+8.5)*9
⇒ 157.5 decimeters².
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X= 1/8 y^2
The directrix of the parabola is
y=-2
x=-2
x= 2
Consider the
equation
S=Ut+ 2gt²
The formula s= ut + 1/2gt^2
Represents the total distance "s" travelled by an object in time "t" which has an initial speed of "u" and is accelerating at the uniform rate of "g". It is customary to use the symbol "g" for acceleration due to gravity. However this equation is valid for any value of uniform acceleration.
We can derive the equation as follows.
The total distance travelled by a uniformly accelerating object is equal to average speed multiplied by time
That is: s = (average speed)*t ... (1)
And, average speed = (initial speed + final speed at the end of period t)/2
And final speed = u + gt
Therefore: Average speed = (u + u + gt) = 2u + gt
Substituting this value of average speed in equation (1) we get:
s = (2u + gt)/2]*t = ut +1/2gt^2
hope it helps...!!!
what is c
5a-b+c= -10
a-3b-c= -4
2a+4b-2c= 12
Answer:
{5a-b+c=10}
{a-3b-c=-4
[2a+2b-c=6
Step-by-step explanation: so it's 6 hope this helps. Let me know if it helps and give brainliest.
Brainliest to the correct answer, but answer ASAP
ONLY answer if you are 100% sure so don't say "I think" or "It might be"
Answer:
B
Step-by-step explanation:
[tex] \frac{25}{8} = 3.125[/tex]
π = C/d = 25/8 = 3.125
1 of 9
2.
4
5
6
Solve each addition or subtraction problem with its corresponding answer.
a.
11
b. 6
c. 4
d. 1
e.
1. 3
F=-=-= = = = = = =
2. 6
T +
Elo Elm En = 100
3.
5
4. 10
5.
2
11
Check Answer
Imad and Amra are butterflies. Imad drinks 3 grams of nectar a week. Amra drinks 2 grams of nectar a week. How many grams of nectar do they drink all together after 4 weeks?
Answer:
20 grams
Step-by-step explanation:
3+2=5 grams for 1 week
5x4=20
Write the equation of the circle graphed below.
Answer:
Your equation is [tex](x - 1)^2 + (y +1)^2 = (\frac{1}{2} )^2[/tex]
Step-by-step explanation:
Well, the center origin of the circle is given (h,k) = (1,-1).
We have to find our radius as they gave us a point. from origin to the edge of the circle.
Using the formula: (x - h)^2 + (y - k)^2 = r^2
Plug in our (h,k) = (1,-1) and (x,y) = (0.5,-1) to solve for radius.
(x - h)^2 + (y - k)^2 = r^2
(0.5 - (1))^2 + (-1 - (-1))^2 = r^2
(-0.5)^2 + (0)^2 = r^2
1/4= r^2
r^2 = 1/4
r = 1/2