Answer:
[tex]1296 = 6 \times 6 \times 6 \times 6 = {6}^{4} = {2}^{4} \times {3}^{4} [/tex]
Given f(x) and g(x) = k•f(x), use the graph to determine the value of k.
Step-by-step explanation:
the slope of f(x) = 1
for every increase of x by 1 also y increases by 1.
the slow of g(x) = -2
for every increase of x by one y decreases by 2.
so, we see, as
g(x) = k × f(x)
k = g(x) / f(x) = slope g / slope f = -2/1 = -2
why ? because both functions are linear functions (lines).
they look like
y = ax + b
with a being the slope of the line.
so, when multiplied by k, this is kax + kb, and we see k as factor already in the slope of the line itself.
What is the solution to this system of equations? 2x + 2y = 8 and 4x + 3y = 16
Answer:
y=0, x=4
Step-by-step explanation:
2x+2y=8 --- (1)
4x+3y=16 --- (2)
Multiply the coefficient of x in equation (1) across the variables in equation (2), and multiply the coefficients of x in equation (2) across the variables in equation (1).
8x+8y=32 ---- (3)
8x+6y=32 ---- (4)
Subtract equation (3) from (4)
2y=0, y=0/2, y=0.
Substitute the solution for y=0 into equation (1)
2x+2(0)=8
2x=8
x=4
The volume of this rectangular prism is 48,608 cubic centimeters. What is the value of b?
Answer:
b = 49 cm
Step-by-step explanation:
Volume of a rectangular prism = width × length × height
Given:
volume = 48,608 cm³width = 16 cmlength = bheight = 62 cmSubstituting the given values into the formula and solving for b:
⇒ 48608 = 16 × b × 62
⇒ 48608 = 992 b
⇒ b = 48608 ÷ 992
⇒ b = 49
Answer:
b = 49 cm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 48,608 cm³l = b cmw = 16 cmh = 62 cmSubstitute the values above and solve for b:
48,608 = b × 16 × 62
48,608 = 992b
48,608/992 = 992b/992
49 = b
Final answer: 49 cm
Hope this helps!
A container is shaped like a triangular prism. The height of the container is 15 centimeters, and the volume of the container is 180 cubic centimeters. What is the area of the base of the container in square centimeters?
a. 10 cm2
b. 12 cm2
c. 18 cm2
d. 20 cm2
Explain what the following statement means:
Polynomials are closed under the operations of addition and subtraction.
Provide one addition example and one subtraction example to demonstrate.
a set is closed under certain operation if the operation performed on two elements of the set gives an element of the same set
addition,subtractio sa well as multiplication of polynomials result into another polynomial.Therefore,the set of polynomials is closed under addition,subtraction and multiplication.
division of a polynomial need not be a polynomial (sometimes it is ,but not always).Therefore,the set of polynomials is not closed under division.see the example in the box beside.
Sample Response: If you add two polynomials, the sum is always a polynomial. Example: (2x2 + 3x) + (8x2 - 4x) = 10x2 - x If you subtract two polynomials, the difference is always a polynomial. Example: (2x2 + 3x) - (8x2 - 4x) = -6x2 + 7x
Compare your response to the sample response above. Did your response …
… explain what closure means for addition and give an example?
… explain what closure means for subtraction and give an example?
Polynomials are the algebraic expressions that consist of variables and coefficients.
How to explain the polynomial?
The Closure property of addition states that in a defined set, for example, the set of all positive numbers is closed with respect to addition since the sum obtained adding any 2 positive numbers is also a positive number which is a part of the same set.
Closure property of subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will be a real number as well. For example, 9 - 4 = 5.
Learn more about polynomial on:
https://brainly.com/question/2833285
#SPJ1
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
The graph shows a curve with an end point at 2 comma 3 that increasing to the right
The graph shows a curve with an end point at 3 comma 2 that increasing to the right
The graph shows a curve with an end point at negative 3 comma negative 2 that increasing to the right
The graph shows a curve with an end point at negative 2 comma negative 3 that increasing to the right
The obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis. None of the option is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
The given equation of the function is;
[tex]y = -(x+2)^{1/3}+5[/tex]
Hence,the obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis.
To learn more about the function refer:
https://brainly.com/question/5245372
#SPJ1
Answer:
The function f(x) = sqrt(x - 2) + 3 represents a square root function that is shifted 2 units to the right and 3 units up from the parent function f(x) = sqrt(x).
The endpoint of the function occurs when the radicand (x - 2) is equal to zero, which means x = 2. So, the function has an endpoint at (2, 3).
Since the function involves a square root, the value of y cannot be negative. Therefore, the function is increasing to the right.
The correct graph that represents the function f(x) = sqrt(x - 2) + 3 is the one that shows a curve with an endpoint at (2, 3) that increases to the right.
Therefore, the answer is: The graph shows a curve with an endpoint at 2 comma 3 that increases to the right. A.
write the equation of the line that passes through (-3,6) with a slope of -2
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the equation of the line that passes through (-3, 6) and has a slope of -2?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]
First, we need to write the equation of the line in point-slope form:-
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Replace y1 with 6, m with -2, and x1 with -3:-
[tex]\sf{y-6=-2(x-(-3)}[/tex]
On simplification,
[tex]\sf{y-6=-2(x+3)}[/tex]
On further simplification,
[tex]\sf{y-6=-2x-6}[/tex]
Add 6 on both sides:-
[tex]\it{y=-2x}[/tex]
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
I was confused on how to write the quadratic in standard form
Answer:
3x² + 4x + 8 = 0
Step-by-step explanation:
Standard form of quadratic equation is
ax²+bx+c=0
standard form of quadratic equation 3x²+4x+7=-1 is
3x² + 4x + 7 = -1
3x² + 4x + 7 + 1 = 0
3x² + 4x + 8 = 0
Find the center and radius of the circle represented by the equation below.
x² + y²- 6x - 12y +29=0
Answer:
radius 4
center (3,6)
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
coordinates of the center (h, k) and the radius is (r)
x² + y²- 6x - 12y +29=0
x² - 6x + y²- 12y +29=0
(x² - 6x) + (y²- 12y) +29=0
complete the square
(x² - 6x) + 9 + (y²- 12y) +36 +29= + 9 +36
(x² - 6x + 9) + (y²- 12y + 36) = + 9 +36 -29
(x-3)^2 + (y-6)^2 = 16
(x - h)^2 + (y - k)^2 = r^2
coordinates of the center (h, k) and the radius is (r)
center (3,6)
radius 4
cuemathcom
varsitytutors
Answer: Center: (3,2) Radius: 5
Step-by-step explanation:#x^2 - 6x +y^2 - 4y = 12
Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides.
#x^2 -6x + 9 + y^2 - 4y + 4 = 12 + 9 + 4
(x - 3)^2 + (y -2)^2 = 25
Circle centered at (3,2) with radius = 5
pls help asap The scatter diagram shows the grades and number of missing assignments for students in a grade 8 math class
In a company's first year in operation, it made an annual profit of $247,500. The
profit of the company increased at a constant 16% per year each year. How much
total profit would the company make over the course of its first 10 years of operation,
to the nearest whole number?
To calculate this sort of problem:
⇒ involves calculating the total profits over each year
⇒ with a constant increase periodically
⇒ need to use the Compound Interest Equation
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
A: total amount after t yearsP: initial amount in accountr: rate per periodn: number of times the profit increases per yeart: number of yearsLet's fill in some variables:
P: $247500r: 16% increase (in equation form, we plugin 0.16)n: 1 time per yeart: 10 yearsWhat do we want to know:
A: total amount after 10 yearsLet's solve:
[tex]A= 247500*(1+\frac{0.16}{1} )^{1*10}=\\A=247500*(1+0.16)^{10}\\A=247500*(1.16)^{10} \\A= 1,091,830.18[/tex]
To the nearest whole number
Answer: $1,091,830Hope that helps!
Using the points ( 6.4, 117) and (6.6, 120), what is the slope of the trend line?
a. -15
b. -12
c. 12
d. 15
Answer:
d 15.
Step-by-step explanation:
Slope = (difference in y values)/ (corresponding difference in x values)
So we have:
Slope = (120-117) / (6.6-6.4)
= 3 / 0.2
= 30/2 = 15.
20 points
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 216, 36,6 Find the 8th term.
Answer:
0.001
Step-by-step explanation:
Given (or we can find) :
First term : 216
Common ratio : 36/216 = 1/6
To find 8th term :
a₈ = ar⁸⁻¹
a₈ = (216)(1/6)⁷
a₈ = 216/279936
a₈ = 6³/6⁷
a₈ = 1/6⁴
a₈ = 1/1296
a₈ = 0.000771604938
a₈ = 0.001 (nearest thousandth)
what is the probability tho computer will select a point in the shaded region?
Please help me with my math please?
Answer:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Line passes through (2, -1) and slope of 1/3
Step 1y = mx + b, Identify: x = 2, y = -1, slope: [tex]\sf \frac{1}{3}[/tex]
insert following values
[tex]\rightarrow \sf -1 = \dfrac{1}{3} (2) + b[/tex]
multiply
[tex]\rightarrow \sf -1 = \dfrac{2}{3} + b[/tex]
switch sides
[tex]\rightarrow \sf b = -1 - \dfrac{2}{3}[/tex]
subtract
[tex]\sf \rightarrow b = -\dfrac{5}{3}[/tex]
convert to mixed fraction
[tex]\sf \rightarrow b = -1\dfrac{2}{3}[/tex]
Step 2y = mx + b, m = [tex]\sf \frac{1}{3}[/tex], b = [tex]-1\frac{2}{3}[/tex]
insert following values
[tex]\rightarrow \sf y = \dfrac{1}{3} x -1\dfrac{2}{3}[/tex]
7829y[tex]\frac{-69}{56x}[/tex] Find the exact value!
[tex]\\ \rm\Rrightarrow 7829y\times \dfrac{-69}{56x}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{7829(69)y}{56x}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{540201y}{56x}[/tex]
[tex]\\ \rm\Rrightarrow 9646.4y/x[/tex]
Question Write an equation in slope-intercept form of the line that passes through (6, −2) and (12, 1)
Answer:
[tex]y = \dfrac 12x -5[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (6,-2)~ \text{and}~ (x_2,y_2) = (12,1)\\\\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{1+2}{12-6}= \dfrac{3}{6} = \dfrac 12\\\\\text{Equation of line,}\\\\~~~~~~~~y-y_1 =m(x-x_1)\\\\\implies y+2=\dfrac 12 (x-6)~~~~~~~~~~~~~~;[\text{Point -slope form}]\\\\\implies y = \dfrac 12 x -3 -2\\\\\implies y = \dfrac 12x -5~~~~~~~~~~~~~~~~~~~~~;[\text{Slope-intercept form.}][/tex]
Given that l is the centroid of triangle CDE, find CH.
A. 3
B. 4
C. 8
D. 12
Answer:
D. 12.
Step-by-step explanation:
As I is the centroid G is the midpoint of CE, so
2x + 5 = 5x - 4
5+4 = 5x - 2x
3x = 9
x = 3.
x + 5 = 2/3 * CH (Properties of the centroid of a triangle).
So as x = 3
2/3 CH = 3 + 5
CH = 8 * 3/2
CH = 12.
Solve the math:
Elsa is 2 years older than Bella. Emma is twice as old as Elsa. So, what will be the sum of their ages in 1 years time. And then also find out what was the summation of their ages before 5 years from now.
Answer:
Step-by-step explanation:
Let Emma's age be 2x years, then:
Elsa's age is x years, also:
Bella's age is x - 2 years.
In one years time the sum of their ages
= 2x + 1 + x + 1 + x - 2 + 1
= 4x + 1 where x = Elsa's age now.
5 years before now
Sum of their ages
= 2x -5 + x - 5 + x - 2 - 5
= 4x - 17 where x = Elsa's age now,
Question 39 of 40
The circle below has a radius of 8 centimeters. What is the area of the shaded
region?
X
120°
8 cm
OA. 32 square centimeters
B. 8 square centimeters
64
3
square centimeters
square centimeters
O C.
O D.
16
3
Convert angle to radians
120=2π/3So
Area
r²Ø/28²(2π/3)(1/2)64π/3cm²Answer:
[tex]\textsf{C.} \quad \dfrac{64 \pi}{3} \: \sf square\:centimeters[/tex]
Step-by-step explanation:
Formula
[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]
Given:
[tex]\theta[/tex] = 120°r = 8 cmSubstitute the given values into the formula and solve for Area:
[tex]\large \begin{aligned}\implies \textsf{Area} & =\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \pi (8)^2\\\\& =\left(\dfrac{1}{3}\right) \pi (64)\\\\& =\dfrac{64}{3} \pi \: \sf cm^2\end{aligned}[/tex]
What is the probability that the manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this? a. 0.2975 b. 0.0525 c. 0.0975 d. 0.5525 e. 0.6325
The conditional probability that the carbon emission is beyond the permissible emission level and the test predicts this is given by:
a. 0.2975.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, we have that the events are as follows:
Event A: Carbon emission beyond the permissible emission level.Event B: Test predicts this.We have that 35% of the units have carbon emission beyond the permissible emission level, and the test is 85% accurate, hence:
[tex]P(A) = 0.35, P(B|A) = 0.85[/tex]
Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]0.85 = \frac{P(A \cap B)}{0.35}[/tex]
[tex]P(A \cap B) = 0.85(0.35) = 0.2975[/tex]
Which means that option a is correct.
More can be learned about conditional probability at https://brainly.com/question/14398287
#SPJ4
The surface areas of two similar solids are 169 m2 and 81 m2. the volume of the larger solid is 124.92 m3. which proportion correctly shows how to solve for the volume of the smaller solid, x? = = = =
By finding the scale factor, we will see that the volume of the smaller solid is 86.75 m³.
How to get the volume of the smaller solid?If the solids are similar, then there is a scale factor between the two. Then the relation between the areas is equal to the scale factor squared, and the relation between the volumes is equal to the scale factor cubed.
This means that if the areas are 169 m² and 81 m², then we can write:
169 m² = (k²)*81 m²
Solving for k, we get:
k = √(169 m²/81 m²) = 1.44
Then if the volume of the large solid is 124.92m³ we can write:
124.92m³ = k³*V
Replacing k and solving for V we get:
124.92m³ = (1.44)³*V
(124.92m³/ (1.44)³) = V = 86.75 m³
If you want to learn more about scale factors:
https://brainly.com/question/3457976
#SPJ4
Answer: Its C
Step-by-step explanation: Just did it
Please help don’t understand radical
Simplified
[tex]x\sqrt[3]{x}[/tex]
help with practice problem
Answer:
i think the answer is r=0.5 or r=−3/2−x^2
Step-by-step explanation:
-4r^2-4r=6
step 1. -4r(-4r)= 16r
16r-4r=6
step 2. 16r-4r=12r
12r=6
step 3. /12 on both sides
r= 0.5
Need help please answer ASAP!
(20-21)
#20
1/2x+3<2x-61/2x-2x<-6-3-3/2x<-93/2x>9x>9(2/3)x>6#21
Find LCD of 2,7x,x
x is most commonSo
LCD is 2(7x)(x)=14x²Answer:
20. (4) x > 6
21. (3) 14x
Step-by-step explanation:
Question 20
[tex]\begin{aligned}\dfrac{1}{2}x+3 & < 2x-6\\\dfrac{1}{2}x+3-3 & < 2x-6-3\\\dfrac{1}{2}x & < 2x-9\\\dfrac{1}{2}x-2x & < 2x-9-2x\\-\dfrac{3}{2}x & < -9\\-\dfrac{3}{2}x \cdot 2 & < -9 \cdot 2\\-3x & < -18\\-\dfrac{3x}{3} & < -\dfrac{18}{3}\\-x & < -6\\\dfrac{-x}{-1} & < \dfrac{-6}{-1}\\x & > 6\end{aligned}[/tex]
Question 21
Rewrite all three fractions so that their denominators are the same:
[tex]\dfrac{1}{2}=\dfrac{1 \times 7x}{2 \times 7x}=\dfrac{7x}{14x}[/tex]
[tex]\dfrac{2}{7x}=\dfrac{2 \times 2}{7x \times 2}=\dfrac{4}{14x}[/tex]
[tex]\dfrac{5}{x}=\dfrac{5 \times 14}{x \times 14}=\dfrac{70}{14x}[/tex]
Therefore, the least common denominator is [tex]14x[/tex]
BRAINLIEST For the fastest answer
Hello I need help on this math question
Answer:
B
Step-by-step explanation:
B: $303.75
I hope this helps you and I hope you do well.
which term describes where the three angle bisecters of a a triangle intersect
Answer:
The incenter....
Step-by-step explanation:
The point at which all three of the angle bisectors of a triangle meet is known as the incenter
dont confuse it with the circumcenter and the centroid.
i hope this helps!!!
Graph the line 2x – 3y = 12.
Answer:
-6, -4
Step-by-step explanation:
I got it right
A map has a scale of 1 cm: 10 km. If Centerville and Greenwood are 40 km apart, then they are how far
apart on the map?
(Pls answer quick)
Answer:
4 cm
Step-by-step explanation:
1 cm : 10 km (given)-> 1*4 cm = 10*4 km (Multiply both sides by 4)-> 4 cm = 40 kmScale
1cm:10kmScale factor=10
Distance of Greenwood=40km
Now apart in map
40/104cmQuestion is in the picture (I got it wrong)
Answer:
(B) 38.4 m³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the height.
__
The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...
V = Bh = (24 m²)(1.6 m) = 38.4 m³
The volume of the prism is 38.4 cubic meters.
