Answer:
The system has infinitely many solutions when a = 3/4 and b = 1/2Given
System of linear equations
ax +by = 163x+2y=64To find Values of a and b that leads to infinitely many solutionsSolutionThe linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.
We can solve it in two different ways
1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.
4ax + 4by = 643x + 2y = 64When compared it gives us:
4a = 3 ⇒ a = 3/44b = 2 ⇒ b = 2/4 = 1/22. Convert both equations from standard to slope-intercept form and compare:
ax + by = 16by = -ax + 16y = - (a/b)x + 16/b3x + 2y = 642y = - 3x + 64y = - (3/2)x + 32Work out values of a and b:
16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2- (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4The first term of an arithmetic progres- sion is 3 and the last term is 9. Find the number of terms in the progression if the common difference is 3/2
Answer:
5 terms
Step-by-step explanation:
The numbers will be 3, 4 1/2, 6, 7 1/2, and 9.
please help i dont know how to do this
PLEASE HELP PLEASEEEE!! 100 PTS!
Answer:
R
H
S
= cos
2
x
Step-by-step explanation:
Hope this helped!
Pleaseeeeee helpppppp
They are both factors of 15x-10 because 5(3x-2)=15x-10
factor x factor=product.
In this case 15x-10 is the product
WILL GIVE BRAINLIEST!!!
For science class, Cora observed the growth of a pepper plant over time. Below is her log. How much taller was the pepper plant at the end of 4 weeks?
Growth of Plant
Start 3 inches
Week 1 5 inches
Week 2 7 inches
Week 3 9.5 inches
Week 4 11 inches
A. 6.75 inches
B. 7.5 inches
C. 8 inches
D. 10 inches
Answer:
c
Step-by-step explanation:
week 4 = 11
start = 3
11 - 3 = 8
answer is c
The correct Answer is: C. 8 inches
Step-by-step explanation:
If the plant started out at 3 inches and finished after 4 weeks at 11 inches, we can do 11-3 to find how much growth the pepper plant had.
11 - 3 = 8, therefore our answer is
C. 8 inches
Determine the measure of each indicated angle. Show all necessary steps!
a)
We know that a 4-sided polygon's angles add up to 360 degrees
so to find x:
360-(69+118+84)=89 degrees
b)
For a 4-sided polygon we also know that the outside angles add up to 360 degree.
so to find p:
360-(100+62+106)=92 degrees
Hope it helps!
y = 2x² - 9x + 10
solve the following quadratic function by factoring
What is the area of Jack’s patio?
Answer:
62m^2
Step-by-step explanation:
From the figure above, we have two rectangles
For one rectangle,
Lenghts= 7m
Width = 6m
Area = lenght× width = 7×6= 42m^2
For the sect rectangle
Lenght = 5cm
Width = 4cm
Area = 5×4 = 20cm^2
Area of jack patio = 42+20= 62m^2
Carly will be going to college in 3 years. she anticipates that she will need $12,000 to pay for the first year. she currently has $2,900 in a savings account. without including any interest earned, what is a reasonable estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college? $150 $250 $350 $450
The estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college is $250
SavingsAmount needed = $12,000Amount available = $2,900Number of months in three years = 12 × 3 = 36Amount of savings per week = x12,000 = 2900 + 36x
12,000 - 2900 = 36x
9,100 = 36x
x = 9100 / 36
x = 252.777777777777
Approximately,
$250
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Answer:
The answer is B. $250
Step-by-step explanation:
What is the rate of change of the amount earned with respect to hours worked for this function?
Answer:
72
Step-by-step explanation:
I got to get some bread for you guys
Answer:
I'll do it the answer is truthfully 72 if you don't think go check my page
Find the common difference and the SIMPLIFIED general term formula.
3) a 14=1322 and a 38 = 3722
I reallyyyy need help!!! ASAP PLEASE!!!!!
Answer:
[tex]a_{n}[/tex] = 100n - 78
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₄ = 1322 and a₃₈ = 3722 , then
a₁ + 13d = 1322 → (1)
a₁ + 37d = 3722 → (2)
subtract (1) from (2) term by term to eliminate a₁
24d = 2400 ( divide both sides by 24 )
d = 100
substitute d = 100 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 13(100) = 1322
a₁ + 1300 = 1322 ( subtract 1300 from both sides )
a₁ = 22
then nth term formula is
[tex]a_{n}[/tex] = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78
Describe the transformations of the graph of y=5 times 2^x-2+3 as compared to the graph of y=2^x
the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
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What can each term of the equation be multiplied by to eliminate the fractions before solving?
1/2x-5/4+2x=5/6+x
Answer:
12
Step-by-step explanation:
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
? Question The point (x, y) is first rotated 180° clockwise about the origin, translated 6 units to the left, and then reflected across the line y = x. Write a function S to represent the sequence of transformations applied to the point (x, y).
The function S to represent the sequence of transformations applied to the point (x, y) is (-y, -x - 6)
Transformation of coordinatesTransformation is a technique used to change the position of an object on an xy-plane.
Given the coordinate (x, y)
Rotation of the coordinate by 180° clockwise about the origin will given;
(x, y) - > (-x, -y)
If the result is translated 6 units to the left, then;
(-x, -y) -> (-x-6, -y)
If it is then reflected across the line y = x, we will switch the coordinates to have:
(-x-6, -y) -> (-y, -x - 6)
The function S to represent the sequence of transformations applied to the point (x, y) is (-y, -x - 6)
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If x+y=4 and x-y=k, what does x equal?
If x+y-z=8 and x-y+z=12 then x=
If x=3b and y=2/6b+4, what is x in terms of y?
The values of x are (4+k)/2 and 10. The value of the variable x in terms of y is x = y -4
System of equationsThese are equations that contains several equations and unknowns.
Given the following system of equation
x+y=4
x-y=k
Add both equation
x + x = 4 + k
2x = 4+k
x = (4+k)/2
For the equation
x+y-z=8
x-y+z=12
Add both equations
2x = 8 + 12
2x = 20
x = 10
The value of x from the equation is 10
Given the equations
x=3b
y = 2/6b+4,
______________
b = x/3
Substitute
y = 2/6(x/3)+4
y = x + 4
x = y - 4
Hence the value of the variable x in terms of y is x = y -4
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Hii! would anyone mind helping me out?
Find the center of this hyperbola
[tex]\large\boldsymbol{9x^2-y^2-72x+8y+119=0}[/tex]
[tex]\bigstar[/tex]
[tex]\underbrace[/tex]
Answer:
(4, 4)
Step-by-step explanation:
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Match the values in this hyperbola to those of the standard form. The variable h represents the x-offset from the origin, k represents the y-offset from origin, a.
a = 1
b = 3
k = 4
h = 4
Thus,
[tex](x-4)^2 - \frac{(y-4)^2}{9} = 1[/tex]
The center of a hyperbola follows the form of (h, k). Substitute in the values of h and k.
= (4, 4)
A student is trying to solve the system of two equations given below:
Equation P: x+y=8
Equation Q: 2x + 5y = 24
Which of the following steps can be used to eliminate the x term?
02(x+y=8)
O-2(x+y=8)
O-1(2x + 5y = 24)
O-2(2x + 5y = 24)
Step-by-step explanation:
as the following pic answer should be × -2
Answer:
O -2(x+y=8)
Step-by-step explanation:
If you put the problems beside each other, they look like this;
2x + 5y = 24
x + y = 8
So you are trying to find a way to simplify the x's
Step 1;
See if there are any numbers that you could multiply to the bottom problem that would help you get rid of the x specifically.
In this case, -2 would cancel out that other 2 right? Because if you added them, they cancel each other out; 2 -2 = 0
Step 2:
if you multiply, you have to do it to the entire problem;
-2(x + y = 8) (-2 times x, -2 times y, -2 times 8)
-2x + -2y = -16
Step 3:
Go back to your original problem and work it out;
2x + 5y = 24
-2x + -2y = -16
2x and -2x cancel each other out so now you only have;
5y = 24
-2y = -16
Step 4:
Combine like terms;
5y = 24
-2y = -16
3y = 8
Divide by 3
y = 2.6
Here is a rectangle.
A (-3,0)
D(-2,-3)
B (3,2)
C (4,-1) What is CD unit number?
Step-by-step explanation:
Let the area of rectangle with given points are as follows :
A(-3,3)
B(3,2)
C(4,-1) = C( x1,y1)
D(-2,-3) = D( x2, y2)
Now,
The distance of CD = root under(x2-x)^2 +( y2 - y1)^2
= root under (-2-4)^2 + ( -3+1)^2
= root under (-6)^2 + (-2)^2
= root under 36 + 4
= root under 40
= 2root 10
Therefore; the unit number if CD is 2 root 10.
Which solution set matches the equation on the graph?
Answer: C, {(1, -4), (4, -1)}
Step-by-step explanation: Where the two graphs meet are their solutions, and the points where they meet are {(1, -4),(4,-1)}.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
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Select the true statement about triangle ABC.
13
5
12
A. sin C = sin A
B. sin C = cos B
C. sin C = tan A
D. sin C = cos A
Answer:
sin C = cos A
Step-by-step explanation:
sinC = opp/hyp
=12/13
cosA = adj/hyp
12/13
Which sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent?A)reflection and dilationB)reflection and rotationC)rotation and reflectionD)translation and rotation help please
The sequence of transformations will be relection and dilation. Then the correct option is A.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.
The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.
Reflection does not change the size and shape of the geometry.
Rotation does not change the size and shape of the geometry.
Translation does not change the size and shape of the geometry.
Dilation does not change the shape but changes the size of the geometry.
Then the correct option is A.
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Find the half line in days of Co-60. ROUND YOUR ANSWER TO THE NEAREST TENTH
The half life in days is 1924.0245 days.
What is half life?Half life is the time taken for the radioactivity of a substance to fall to half its original value.
Given:
N= 8
N[tex]_0[/tex]= initial mass
t= in days
So, N= [tex]N_0e^{-kt}[/tex]
Putting the values we get
half value = 5.2713 years or 1924.0245 days
Hence, the half-life is 1924.0245 days.
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The average monthly temperature of a city can be modeled by a
cosine graph. Melissa has been living in Phoenix, Arizona, where the
average annual temperature is 75°F. She would like to move, and live
in a location where the average annual temperature is 62°F. When
examining the graphs of the average monthly temperatures for
various locations, Melissa should focus on the
The average monthly temperature of a city can be modeled by a cosine graph, Melissa should focus on the Midline. This is further explained below.
What is Melissa's focus on the Midline.?Generally, The average temperature would be indicated somewhere along the curve, most likely near the middle.
In conclusion, Melissa should concentrate on the Midline, which can be used to model the average monthly temperature of a city.
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A man of height 1.5 m is standing in front of a tower of height 81.5 m. At what angle should he observe the top of the tower from the distance of 80 m?
The angle at which the man should observe is 45 degrees.
To solve the question :Given :
height of man = 1.5m
height of tower = 81.5 m
distance between tower and man = 80 m
Since, ABCD is a rectangle, AD = BC = 80m
Similarly, AB = CD = 1.5m
EC = ED + CD
81.5 = ED + 1.5
ED = 80m
Now, in order to find the angle EAD, we use trigonometric functions,
tan ∅ = perpendicular / base = ED / AD
tan ∅ = 80 /80 = 1
∅ = [tex]tan^{-1} (1)[/tex]
∅ = 45°.
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Where would 1.84 be on a number line?
Answer:
It is located to the right of the 0 on the line,
Step-by-step explanation:
the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.
Which exponential equation is equivalent to this logarithmic equation? (2)
Answer:
A. e⁴=xStep-by-step explanation:
Log x=4 ➡️ e⁴=x or x= e⁴
Hope it helps
NEEP HELP ASSAP IF YOU COULD PLEASE
Find the greatest common factor of these two expressions.
28y^7x^2 and 8y^8v^4x^6
Answer:
4y⁷x²
Step-by-step explanation:
Finding GCF:Prime factorize each expression.
28y⁷x² = 2 * 2 * 7 * y⁷ * x²
8y⁸v⁴x⁶ = 2 * 2 * 2 * y⁸ * v⁴ * x⁶
GCF = 2 * 2 *y⁷*x²
= 4y⁷x²
