Answer:
15x^2y+20xy^2+28xy-9x
Step-by-step explanation:
15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x
First distribute the -4 to all the terms in the parentheses
15x²y +8xy² + 36xy + 12xy² - 8xy - 9x
Now combine like terms
15x²y +8xy² + 12xy² + 36xy - 8xy - 9x
15x^2y+20xy^2+28xy-9x
Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answer:
[tex]y = -2x + 5[/tex]
m = -1
b = 5
Step-by-step explanation:
Hello!
Slope - Intercept Form: [tex]y = mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how the graph changes in y as it changes in x.
Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).
Calculate Slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{5 - (-3)}{0 - 4}[/tex][tex]m = -\frac{8}{4}[/tex][tex]m = -2[/tex]The slope is -2.
Y-interceptThe y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.
The intersection happens at point (0,5), so the y-intercept is 5.
EquationWe found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.
Equation: [tex]y = -2x + 5[/tex]
Solve for x. Round to the nearest tenth, if necessary.
X
H
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!A line that includes the points (-8, f) and (-6, 4) has a slope of 6. What is the value of f?
f =?
Answer:
-8
Step-by-step explanation:
Slope = (y1-y2) / ( x1-x2)
= ( f-4) / (-8 - -6) = 6
(f-4) / -2 = 6
f-4 = -12
f = - 8
Answer:
f = -8
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given:
points: (-8, f), (-6, 4)slope : 6Inserting into slope formula:
[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]
[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]
[tex]\sf \rightarrow 4-f = 12[/tex]
[tex]\sf \rightarrow -f = 12-4[/tex]
[tex]\sf \rightarrow -f =8[/tex]
[tex]\sf \rightarrow f =-8[/tex]
a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the current model's battery is 671.0 minutes, in how many months will the latest model's battery life reach 1,008.9 minutes?
The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months
How to solve geometric progression?
Each month, there is an increase by a factor of 0.06 of the previous months model.
From geometric sequence formula of aₙ = ar^(n - 1),
where;
a is first term
r is common ratio
aₙ is nth term
we have;
1,008.9 = 671 * 1.06^(n - 1)
1008.9/671 = 1.06^(n - 1)
In 1.504 = (n - 1) In 1.06
0.408 = (n - 1) * 0.058
n - 1 = 0.408/0.058
n = 7.03 + 1
n ≈ 8 months
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What is the equation for the line of reflection
X=6
Y=6
Y=x
Y=2
Answer: x = 6
Step-by-step explanation:
B(7,3) maps onto B'(5,3).
The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.
Answer:
x = 6
Step-by-step explanation:
Taking test as we speak
median mark of 3,2,0,1,9,12,3,5
Answer: 3
Step-by-step explanation:
Median is a statistical measure that determines the middle value of a dataset listed in ascending order.
arranged data is 0,1,2,3,3,5,9,12
number of data terms=8
if data is even then
median=(3+3)/2=3
Which figure shows a line of reflectional symmetry for the letter T?
A letter T is folded at the horizontal line.
A letter T is folded diagonally.
A letter T is folded vertically through the middle.
A letter T is folded diagonally through its center.
Mark this and return
The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, it means that two mirror images will be created.
Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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Simplify √3. √21
√24
√63
O 3√7
09√7
Answer:
•3✓7
✓3.✓21
=✓3×✓3✓7
=3✓7
Answer:
3rd answer is correct
Step-by-step explanation:
√3 × √21
√3 × √(7 × 3)
√( 3 × 3 × 7 )
√ ( 3 × 3 ) × √7
3√7
Which equation is equivalent to 162 - 32+³?
=
=
O 84 - 84+3
O 84-84+12
O 28 - 25p+15
=
O 28P = 25p+3
[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]
Step-by-step explanation:
I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]
The value of 16^2 = 256.
Also, the answer of 2^5 is 32. i.e.,
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]
Find the sum of the first 5,000 odd numbers
Step-by-step explanation:
this is an arithmetic sequence :
a1 = 1
an = an-1 + 2 = a1 + (n-1)×2
the sum of n terms of an arithmetic sequence is
S = n×(a1 + an)/2
n = 5000
an = a1 + 4999×2 = 9999
S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000
e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?
Answer:
Step-by-step explanation:
the objects which have less density than water will float
and the objects which have more density than the density of liquid will sink in liquid or will not float.
MATH: GRAPHING PIECE-WISE...HELP! 15 PTS
Answer:
Step-by-step explanation:
4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x)
= x - 90.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
Answer: The base graph has been shifted down 90 units.
Step-by-step explanation:
See attached image.
What is the determinant of K =
[6 8
0 3]
When you start your career, you decide to set aside $250 every month to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 9.0% compounded monthly. Assuming this to be true, how much money will your account be worth after 20 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
After 20 years of depositing and investing there will be 168474.01 dollars in your account.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:
P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]
A = 1502.287 + 166971.717
A = $168474.01
Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.
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QUESTION 1 -
If f(x)=3x²-5x+4, then f(-2)=
a.) - 18
b.) 26
c.) 2
d.) 6
Question 2 -
For an ordered pair (x, y) in a relation, the y element represents the _____
a.) input
b.) range
c.) domain
d.) function
Need help urgently! Will give brainliest.
Given: f(x) = 3x² -5x + 4
To find f(-2), simply substitute x = -2 in function f(x).
f(-2) = 3(-2)² -5(-2) + 4
f(-2) = 12 + 10 + 4
f(-2) = 26
Answer: 26
#2For an ordered pair (x, y) in a relation, the y element represents the range.
Answer: range
(07.01 MC)
The picture shows a triangular island:
Island
Z
O x sin 50°
O
Which expression shows the value of z? (1 point)
cos 50°
O x cos 50°
O
sin 50°
y
50
Answer:
Option (2)
Step-by-step explanation:
cos 50° = y/z
z = y/cos 50°
A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coin are there?
There are 5 nickels, 3 dimes, and 9 pennies.
Let d = The number of dimes
Let n = number of nickels
Let p = The number of pennies
As given, there are two more nickels than dimes and three times as many pennies as dimes:
d+2=n
3d=p
0.10d+0.05n+0.01p=0.64
Plug in the value to find d
[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]
[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]
[tex]0.18d=0.64[/tex]
[tex]d=3[/tex]
What is the value of p?The value of p is equal to 3d
p=3(3)=9
n=d+2
n=3+2
n=5
Hence, there are 5 nickels, 3 dimes, and 9 pennies.
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Find an equation of the line. Write the equation using function notation.
Through (8,8); perpendicular to 5y = x - 10
Answer:
f(x) = -5x +48
Step-by-step explanation:
A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.
Swapped coefficientsIn this instance, we find it convenient to leave the coefficient of y as positive.
5y = x -10 . . . . . . original equation
y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated
New constantAt the given point, the equation becomes ...
8 = -5(8) +c
48 = c . . . . . . . add 40
Equation of the perpendicular lineThe equation of the line is then ...
y = -5x +48
f(x) = -5x +48 . . . . . . in functional notation
find x and y
pls help
Step-by-step explanation:
(3x+6)= 48(Alternate angles)
3x=48-6
3x=42
x=14
2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)
48+9=5y-2y
57=3y
y=19
What is the factored form of 8x² + 12x?
O 4(4x² + 8x).
O 4x(2x + 3)
O8x(x + 4)
O 8x(x² + 4)
Answer:
Step-by-step explanation:
Solution
The factored form is going to be the HCF (highest common factor)
The fest way to do this is to turn this into primes.
8x^2 + 12x
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
Now bold the HCF.
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
The HCF = 2*2*x
Divide that into the original question to determine the second factor.
8x^2 / 4x = 2x
12x / 4x = 3 Notice how the x-s cancel
Answer
4x (2x + 3)
find the lowest common multiple ( L.C.M. ) of the (a² - 4), (a³ - 8), ( a + 2 ) ²
Answer: according to my work i got
LCM - Lowest Common Factor
HCF - Highest common factor
Step-by-step explanation:
please mark brainlest!!
yw! =^.^=
PLS HELP ME Solve the following equation: five eighths plus two eighths equals
three eighths,
seven sixteenths,
seven eighths,
or eight sevenths.
The bisection method is being used to calculate the zero of the following function between x = 0 and x = 1.
The bisection method will converge to the solution after three iterations.
How to illustrate the information?It should be noted that after one iteration, x1 will be:
= (1 + 9)/2
= 10/2
= 5
Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.
After the second iteration, x2 will be:
= (1 + 5)/2
= 3
Also, this is greater than 0. The third iteration will be:
m= (1 + 3)/2
= 2.
Now, f(2) = 2⁴ -2³ - 2² - 4
= 0
Therefore, the method converges exactly to the root in 3 iterations.
Complete question:
The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.
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Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answer:
(x+2)²+(y-4)²=36
Step-by-step explanation:
1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);
2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];
3) to make up the required equation according to the scheme:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.
4) finally, (x+2)²+(y-4)²=6².
PS. for more details see the attachment.
Deepak stacked 14 copies of the
same book. Each book is 13 inches
thick. How high is the stack of books?
8
inches
Answer:
182 inches
Step-by-step explanation:
1 book is 13 inches thick.
So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),
Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches
= 182 inches
0,2,14,36,68,?
Find the next number in the sequence
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Geometric sequenceGeometric sequence are sequence that increase in an exponential manner.
Given the recursive sequence 0, 2, 14, 36, 68
From the sequence
0 + 2 = 2
2 + 12 = 14
14 + 22 = 36
36 + 32 = 68
68 + 42 = 110
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
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The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
B.
C.
D.
The slope is m=6 and length of line is 3.5√37.
What is slope?The slope of a line is a measure of its steepness.
Given:
endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5
slope= 8-2/3-2= 6
Now, using distance formula,
d= √(3-2)² + (8-2)²
d= √1+ 36
d= √37
As, Line AB is dilated by a scale factor of 3.5.
So, new d= √37*3.5
new d= 3.5√37
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Least common multiple of 35 and 70
Answer:
70
Step-by-step explanation:
【Answer】The least common multiple of 35 and 70 is 70.
[tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]
To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]
{ Pisces04 }Whats the correct answer answer asap for brainlist
Answer:
option A: West Europe, East Europe, and Asia
Explanation: Europe and Asia as a whole are called Eurasia.
hope that helps...