Answer:
y = -2x
Step-by-step explanation:
Some points are (1,-2) , (2, -4), and (3,-6).
From these three points, we can try each of the equations to see what is correct.
If y = -2x
-2 = (-2)1
-4 = (-2)2
-6 = (-2)3
If y = x
-2 ≠ 1
-4 ≠ 2
-6 ≠ 3
If y = 2x
-2 ≠ 2(1)
-4 ≠ 2(2)
-6 ≠ 2(3)
You spend 1/5 of your income on car payment. You spend 3/8 of the remainder of your income on rent. What fraction of income is spent on rent?
Answer:
3/10
Step-by-step explanation:
1/5 of total income - spent on car
remainder income = 4/5
3/8 of remainder = 3/8 ×4/5 = 3/10(of total income spent on rent)
the word "of" means you can find it by multiplication
e.g. 2 of 1/2 means 2 × 1/2 which is 1
Jan is solving the equation shown below. Which of the following represents the solution to Jan’s equation?
a. x = 3
b. x = -3
c. x = 27
d. x = -33
Answer:
C. X=27
Step-by-step explanation:
-11+1/3x+9=7
1/3x=7+11-9
1/3x=9
x=9x3
x=27
The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.
Answer:
The rhombus ABCD has an area of 22 square units.
Step-by-step explanation:
The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:
[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]
[tex]AC = 15.620[/tex]
[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]
[tex]BD \approx 2.828[/tex]
The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])
[tex]A = \frac{AC\cdot BD}{2}[/tex]
[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]
[tex]A = 22.087[/tex]
The rhombus ABCD has an area of 22 square units.
Answer:
22 units
Step-by-step explanation:
What is the range of the function for the given domain? y = 2x − 5 D: {-2, 0, 2, 4}
Answer:
Range of Function : { - 9, - 5, - 1, 4 }
Step-by-step explanation:
We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.
{ - 2, 0, 2, 4 }
y = 2( - 2 ) - 5 = - 9,
y = 2( 0 ) - 5 = - 5,
y = 2( 2 ) - 5 = - 1,
y = 2( 4 ) - 5 = 4
We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.
pls asap its not 128......In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer:
hope it helps
this is my best
please tell me if I'm wrong
What’s the slope for this graphed?
A.1/2
B.-2
C.2
D.-3
Answer:
the answer is just 2
Step-by-step explanation:
start at the -3 and move right 3 and up 6 this is a inclined line so the answer will be positive the fraction put the numbers into a rise over run fraction which will be 6/3 which will reduce to 2/1 which is 2.
In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answer:
HIG=28°
Step-by-step explanation:
HI is a diameter therefore it's measure is 180°
HI-IG=HG
180-128=HG
52°=HG
HIG=1/2HG
HIG=1/2(56°)
HIG=28°
Please hurry!!!
The fraction bars represent which equation?
A fraction bar is labeled 1. Underneath the bar, 4 boxes are labeled 1/4. Underneath the 4 boxes, boxes are labeled 1/8. 6 of those boxes are circled.
A. 1/4 ÷ 1/8 = 6
B. 3/4 ÷ 1/8 = 6/8
C. 1/4 ÷ 1/8 = 6/8
D. 3/4 ÷ 1/8 = 6
Answer:
Answer- 3/4 divided by 1/8 = 6/8
Mark scored an 89 on his first
test, an 85 on his second test, a
95 on his third test, and an 83 on
his fourth test. What is Mark's
average test score for all 4 tests?
Answer:
88
Step-by-step explanation:
89+85+95+83= 352,
352/4 = 88
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 22 and 15
Answer:
7 < (third side length) < 37
Step-by-step explanation:
Add these two side lengths together. We get 37. Unless the 3rd side is LESS than 37, we cannot form a triangle.
Next, subtract 15 from 22, obtaining 7. The 3rd side has to be GREATER than 7 in order for the sides 7+, 15 and 22 to form a triangle.
7 < (third side length) < 37
Answer:
26.63 ??
Step-by-step explanation:
I think you use pythagorean theorum to solve.
do 22^2 and 15^2 and get 709.1569
sqrt of that is 26.63
-----------------> 10x - 3 - 2x = 4
Answer:
[tex]x=\frac{7}{8}[/tex]
Step-by-step explanation:
[tex]10x-3-2x=4[/tex]
First, collect and rearrange the like terms.
[tex]10x-3-2x=4[/tex]
[tex]8x-3=4[/tex]
[tex]8x=4+3[/tex]
Then, solve the equation:
[tex]8x=4+3[/tex]
[tex]8x=7[/tex]
[tex]x=\frac{7}{8}[/tex]
So, the answer is [tex]x=\frac{7}{8}[/tex]. Hope my solution and explanation can help you. Thank you!
If you still cannot get the point, you can ask me anytime.
Answer:
x=7/8
Step-by-step explanation:
10x-3-2x=4
collect like term
8x-3=4
move constant to the right-hand side and change its sign
8x-3=4 into 8x=4+3
add up the number : 8x=4+3
8x=7 divide both sides of the equation by 8
x = 7/8
Suppose that f(x)=4x+5. What is f^-1 (f^-1(9)) ?
Step-by-step explanation:
the inverse of the inverse of a function is the function itself
It's like going and coming back
f^-1(f^(-1)9) = f(9) f(9) = 4*9+5f(9) = 36+5 f(9) = 41Answer:
9
Step-by-step explanation:
The inverse of the inverse is the input
f^-1 (f^-1(9)) = 9
As a proof
f(x) = 4x+5
y = 4x+5
Exchange x and y
x = 4y+5
Solve for y
(x+5) = 4y
(x+5)/4 = y
f^-1 (x) = ( x-5)/4
Then find the inverse of this function
y = ( x-5) /4
Exchange x and y
x = (y-5)/4
4x = y-5
4x+5 = y
Which gives us the original function back
f^-1( input) = 4x+5
Using the value given
f^-1 (9) = ( 9-5)/4=4/4 =1
Using the 1 from the previous part as the input
f^-1( 1) = 4*1+5 = 4+5 = 9
Experiment consist of drawing one card from a standard 52 card deck. What is the probability of drawing a black 10?
Answer:
2/52 or 1/26 or 0.0385 or 3.85%
Step-by-step explanation:
There are 2 black 10's in a standard 52 card deck.
2/52 or 1/26 or 0.0385 or 3.85% (depending on how your teacher wants it expressed)
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answer:
72cm2 (2 means squared)
Step-by-step explanation:
you add all the sides once you get the are for each side. To do that you multiply l(w)
Answer:
The surface area of the rectangular prism is [tex]136cm^{2}[/tex]
Step-by-step explanation:
What is surface area?
Surface area is the amount of space covering the outside of a three-dimensional shape.
What is rectangular prism?
A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.
Given, length l= 7cm
breadth b=6cm
height h=2cm
The surface area of the cuboid is,
=2(lb+bh+lh)
=2(7*6+6*2+2*7)
=2(42+12+14)
=2*68
=136 [tex]cm^{2}[/tex]
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[tex]solve for x if 4 x+1-9(2 ^{2} +2=0[/tex]
Answer:
mark my answer as the brainliest
Step-by-step explanation:
x = 53/4
Answer:
4×+1-9 (2^)+2)=0
4×+1-9 (4+2)=0
4×+1(-36-18)=0
4×+1 (-54)=0
4×-54=0
4×=54
×=54÷4
×=13.5
Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2).
Answer:
(-6,6), (0,12), (4,8)
Step-by-step explanation:
To dilate an object, we need to multiply the x and y values by the given scale factor.
In this case the scale factor is 2 --> 2(x, y)
Before-> After dilation
2(-3,3) = (-6,6)
2(0,6) = (0,12)
2(2,4) = (4,8)
Please leave a 'thanks' if this helps!
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice. How many servings can David make with the current amount of spice he has
Answer:
8 servings
Step-by-step explanation:
At the ratio of 15:1, the 75 grams of rice in one serving will require 75/15 = 5 g of spice. David's inventory of 40 g of spice is enough for ...
40 g/(5 g/serving) = 8 servings
Only 8 servings can be made with the available spice.
Rice to spice ratio = 15 : 1
Number of grams per serving = 75 grams
Grams of spice available = 40 grams
Grams of rice, r required for available spice :
15 grams of rice = 1 gram of spice
r grams of rice = 40 grams of spice
Cross multiply :
r = (40 × 15)
r = 600 grams
The grams of rice which can go with the available spice :
Number of servings = grams of rice / grams per serving
Number of serving = 600 grams / 75 grams
Number of grams per serving = 8
Hence, The number of servings which can be made with the available spice is 8 servings
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which equation is correct?
arccsc(x)=1/cos(x)
Answer:
arccsc(x)=1/cos(x)
Step-by-step explanation:
Answer:
the answer to your question is D
Step-by-step explanation:
Find the.equation of the line through point (-4,1) and parallel to y=-1/2x -2
Answer: y = -1/2x -1
Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation
y-y1=m(x-x1)
y-1=-1/2(x+4)
y-1=-1/2x -2
y=-1/2x-1
If the perimeter of a square is 32 meters, then what is
the area of the square, in square meters?
Answer:
The awnser is 64
Step-by-step explanation:
It is 64 because you devide the perimiter (32) by 4, to get all sides, and then multiply 1 side by the other to get 64
THIS METHOD ONLY WORKS FOR A SQUARE
For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
A. (5+1/2 x)^6
B. (Y- 1/2 x) ^6
C. (5- 1/2 x) ^6
D. (-5 + (- 1/2 x))^6
Answer:
C. [tex](5-\frac{1}{2})^6[/tex]
Step-by-step explanation:
Given
[tex]15(5)^2(-\frac{1}{2})^4[/tex]
Required
Determine which binomial expansion it came from
The first step is to add the powers of he expression in brackets;
[tex]Sum = 2 + 4[/tex]
[tex]Sum = 6[/tex]
Each term of a binomial expansion are always of the form:
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
Where n = the sum above
[tex]n = 6[/tex]
Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion
[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
Substitute 6 for n
[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
[Next is to solve for a and b]
From the above expression, the power of (5) is 2
Express 2 as 6 - 4
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
By direct comparison of
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
and
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
We have;
[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]
Further comparison gives
[tex]^nC_r = 15[/tex]
[tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]b^r= (-\frac{1}{2})^4[/tex]
[Solving for a]
By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]a = 5[/tex]
[tex]n = 6[/tex]
[tex]r = 4[/tex]
[Solving for b]
By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]
[tex]r = 4[/tex]
[tex]b = \frac{-1}{2}[/tex]
Substitute values for a, b, n and r in
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
Solve for [tex]^6C_4[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]
Check the list of options for the expression on the left hand side
The correct answer is [tex](5-\frac{1}{2})^6[/tex]
PLEASE HELPPPP Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years. Number of years 1 2 3 House 1 (value in dollars) 253,980 259,059.60 264,240.79 House 2 (value in dollars) 256,000 263,000 270,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points) (10 points)
Part A
House 1: we make exponential can be used to describe the
value of house 1. After 1 year, 253480 = 249000 x 1.02
After 2 years, 259059.6 = 25398×1.02. After 3 years 264240.79 =259059.60x1.02.
House 1: we make linear. 256000=249000 + 1000.263000 = 256000 +7000.270000=263000 + 1000.
Part B.
House 1: f(x)=249000 1.02x [genometic sequence]
House 2: f(X) = 24900 + 1000x [arithmetic progression]
Part C
House 1: f(45)=249000×1.02 45 = 607025.697
House 2: f(45) = 249000 +7000x45 = 564000
"House 1 is an arithmetic sequence that increases in price each year while House 2 is an arithmetic sequence that only increases by 1000 per year.
What are word problems in mathematics?
In computational mathematics, a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
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Solve on the interval [0,2pi)
4 CSC x + 1 = -3
Answer:
[tex]$\frac{3\pi }{2}$[/tex]
Step-by-step explanation:
Solve for the interval: [tex][0, 2\pi)[/tex]
[tex]4 \csc(\theta)+1=-3[/tex]
[tex]4 \csc(\theta)=-4[/tex]
[tex]\csc(\theta)=-1[/tex]
[tex]$\frac{1}{\sin(\theta)} =-1 \Rightarrow \sin(\theta)=-1$[/tex]
We have [tex]\sin(\theta)=-1[/tex] for coterminal angles [tex]$\frac{3\pi }{2}+2\pi n$[/tex]
Once we just want the interval [tex][0, 2\pi)[/tex]
The solution is [tex]$\frac{3\pi }{2}$[/tex]
Which of the following functions represent exponential growth? f(x)=.0001(1.77)^x f(x)=2(1.5)^x/2 f(x)=5(0.5)^-x f(t)=5e^-t
Answer:
Hello There. ☆~\《`°---_●£●__---`°》\~☆
An exponential growth function is represented by
f(x)=a(b)^{x},a>0,b>1.
The given functions can be written as,
A)f(x)=.001(1.77)^x,0.001>0,1.77>1
B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1
C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1
D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.
So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), (C).
Hope It Helps!~ ♡
ItsNobody~ ☆
The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.
What is exponential growth?Exponential growth is the process of gradual increase of quantity over time.
An exponential growth function is represented by
[tex]\rm f(x)=a(b)^{x}[/tex], a>0,b>1
The given functions can be written as,
A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1
B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex] 2>0, [tex]\sqrt{1.5}[/tex] >1
C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex], 5>0, 2>1
D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex], 5>0, 1/e.
So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), and (C).
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15 POINTS!!!!!!!!!!
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. "Graph of f of x and g of x. f of x equals 1 over 3 x minus 3 and g of x equals 1 over 3 x plus 1. "
a.) 2
b.) 3
c.) 4
d.) 5
Answer: B.
k=3
Step-by-step explanation:
g(x) is 3 units higher than f(x)
so k must be equal to 3
Answer:
it is b i think
k=3
Step-by-step explanation:
Make a 3-by-3 logic grid on your own paper. Use it to help you solve the logic
puzzle and answer the question given below.
Tina, Jewel, and Amy have three different pets (dog, goldfish, and ferret).
• Tina is allergic to dogs.
• Jewel does not have the ferret.
• The dog belongs to Amy.
Who owns the ferret?
Answer:
Tina
Step-by-step explanation:
Since Amy owns the dog, she doesn't have the ferret and we know that Jewel doesn't have the ferret so the answer is Tina.
Write ln (4∕9) in terms of ln 2 and ln 3. Question 13 options: A) 3(ln 2 – ln 3) B) 2ln 2 – 2ln 3 C) 4ln 2 – 4ln 3 D) ln2 2 – 4ln 3
Answer:
The answer is option B
Step-by-step explanation:
2ln 2 - 2ln3
= ln ( 2²/3²)
= ln (4/9)
Hope this helps you
Answer:
B) 2ln 2 – 2ln 3
Step-by-step explanation:
please solve these questions for me. i am having a difficult time understanding.
Answer:
1) AD=BC(corresponding parts of congruent triangles)
2)The value of x and y are 65 ° and 77.5° respectively
Step-by-step explanation:
1)
Given : AD||BC
AC bisects BD
So, AE=EC and BE=ED
We need to prove AD = BC
In ΔAED and ΔBEC
AE=EC (Given)
[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)
BE=ED (Given)
So, ΔAED ≅ ΔBEC (By SAS)
So, AD=BC(corresponding parts of congruent triangles)
Hence Proved
2)
Refer the attached figure
[tex]\angle ABC = 90^{\circ}[/tex]
In ΔDBC
BC=DC (Given)
So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)
So,[tex]\angle CDB=\angle DBC=x[/tex]
So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)
x+x+50=180
2x+50=180
2x=130
x=65
So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]
Now,
[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]
So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]
In ΔABD
AB = BD (Given)
So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)
So,[tex]\angle BAD=\angle BDA=y[/tex]
So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)
y+y+25=180
2y=180-25
2y=155
y=77.5
So, The value of x and y are 65 ° and 77.5° respectively
The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence 2, -6, 18, -54, ...? an = 2 · 3n - 1 an = 2 · (-3)n - 1 an = 3 · 2n - 1 an = -3 · 2n - 1
Answer:
The second choice
Step-by-step explanation:
So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.
Answer:
option 2
Step-by-step explanation:
First term [tex]a_{1} = 2\\[/tex]
common ratio = r = second term ÷ first term
= -6 ÷2 = -4
Plug in the values of [tex]a_{1}[/tex] & r in the formula
[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]
Solve for x: 4x - 2 > 6x + 8. (5 points)
x<-5
x>5
x<5
x>-5
Answer:
x<-5 is the correct answer
Answer:
x<-5 is the answer
Step-by-step explanation: