Let,
[tex]\begin{gathered} 12x+5y=-24\ldots(1) \\ 13x-5y=14\ldots(2) \end{gathered}[/tex]Perform the operation (1)+(2),
[tex]\begin{gathered} 12x+5y+(13x-5y)=-24+(14) \\ 12x+13x+5y-5y=-10 \\ 25x+0y=-10 \\ 25x=-10 \\ x=\frac{-10}{25} \\ x=\frac{-2}{5} \end{gathered}[/tex]Substitute the value of x=-2/5 in the expression (1).
[tex]\begin{gathered} 12\times\frac{-2}{5}+5y=-24 \\ 5y=-24+\frac{24}{5} \\ 5y=\frac{-96}{5} \\ y=\frac{-96}{5\times5} \\ y=\frac{-96}{25} \end{gathered}[/tex]Thus, the value of x is -2/5 and value of y is -96/25.
Create a quadratic inequality with the roots -5 and 2.
Answer:
y=x^2+3x-10
Step-by-step explanation:
.........
(3,-8) with a slope of -1
Answer:
See below
Step-by-step explanation:
Point slope form
y - - 8 = (-1)(x -3) re-arrange
y + 8 = -x+3
y = -x - 5
ABC is rotated 90° counterclockwise around the origin to form A'B'C'. Then
AA'B'C' is dilated using a scale factor of with a center of dilation at vertex A'
to form A"B"C". What are the coordinates of A"B"C"? Show your work.
The coordinates of A"B"C" are as follows :
A = 1 1/2,3
B = 1 1/2,0
C = -4 1/2, 3.
What are coordinates?Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. a group of numbers representing a precise place. On graphs, there are typically two numbers: the first one indicates the length along, and the second one indicates the length up or down. For instance, the value of the point (12,5) is 12 units. In general, alphanumeric characters are used to express GPS coordinates, which are a distinctive identifier of a certain geographic location on the globe. Points of intersection in a grid system are referred to as coordinates in this context. Typically, the latitude and longitude coordinates are used to represent GPS coordinates.
Five units up and along.
90degrees clockwise is x, y, y, -x.
A = 1,2
B = 1,0
C = -3, 2.
Times everything by 3/2 now.
A = 1 1/2,3
B = 1 1/2,0
C = -4 1/2, 3.
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Dracula needs to mix 4 quarts of liquid iced tea concentrate with 5.5
quarts of water to make iced tea. He wants to make 66.5 quarts of
iced tea. How much iced tea concentrate will he need?
Use the table to answer the question. HELP PLS
Number of cases ordered
1
3
5
10
Number of rolls of paper towels
12
36
60
120.
A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair.
The constant of proportionality when the restaurant is placing an order for paper towels is 12.
How to calculate the value?It should be noted that the constant of proportionality simply means the ratio that is important to show the proportional relationship between the two given values.
This will be illustrated as:
y = kx
y = Number of paper roll
x = Number of cases ordered
From the table, this will be:
y = kx
12 = k × 1
k = 12
Therefore, the constant of proportionality is 12.
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write the polynomial in standard given the following zeros: x=0,i\sqrt(2),-i\sqrt(2)
The polynomial is x³ + 2x
If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.
That is, a, b and c are roots of the polynomial, then the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.
Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc
Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.
So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).
Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x
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Allison's math teacher asked her to write an irrational and rational number. She wrote the following numbers √46 Rational and 5.25 Irrational. Explain if you agree with Allison's identification of rational and irrational numbers.
If you disagree, provide an example of an irrational and rational number.
3=british paintings
t=painting from 2th century
b=british paintings
a painting is chosen at random
work out the probability that it is british
The probability of choosing a painting random and it is British is 0.50.
Given,
The total number of paintings = 30
Then,
x (x - 2) + x + (2x - 8) + 10 = 30x = 3T = Painting from 20th century
B = British paintings
We have to find the probability of choosing a painting random and it is British.
Here,
Probability = British/ Its from 20th century
Probability = n (B and T) / n(T)
= x / (x + x(x-2))
= 3 / (3 + 3(3 - 2))
= 3 / (3 + 9 - 6)
= 3 / 6 = 1/2 = 0.5
Here, the probability of choosing a painting random and it is British is 0.50.
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Find the distance between each pair of points.
M(-4,9) N(-5,3)
Helpppp please , fast
The coordinates of the orthocenter of triangle DEF are given as follows:
(6.67, -2).
How to find the orthocenter of a triangle?The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.
Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.
The midpoint of segment DE is:
(6, 1).
Which is the mean of the coordinates.
Vertex F is at point (8, -8), hence the slope of the line with these two points is:
m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.
Hence:
y = -4.5x + b.
When x = 6, y = 1, hence we can find b as follows:
1 = -4.5(6) + b
b = 28.
Hence one line is:
y = -4.5x + 28.
The midpoint of segment EF is:
(8, -1.5).
Which is the mean of the coordinates.
Vertex D is at point (4, -3), hence the slope of the line with these two points is:
m = (-1.5 - (-3))/(8 - 4) = 0.375.
Hence:
y = 0.375x + b.
When x = 8, y = -1.5, hence we can find b as follows:
-1.5 = 0.375(8) + b
b = -4.5.
Hence the two lines that we have to find the intersection point is:
y = -4.5x + 28.y = 0.375x - 4.5.Then the x-coordinate of the orthocenter of the triangle is:
-4.5x + 28 = 0.375x - 4.5
4.875x = 32.5
x = 32.5/4.875
x = 6.67.
The y-coordinate of the orthocenter of the triangle is:
y = 0.375(6.67) - 4.5 = -2.
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Given f(x) = -x - 1, find ƒ (1).
Answer:
You've gotta be kidding me...It's easy come on
-2 is the answer
Step-by-step explanation:
f(x)= -x-1 JUST SUBSTITUTE 1 FOR X
f(1)= -(1)-1
f(1)= -2
A store owner mixes 2 lbs of candy that cost x dollars pound with 3 lb of candy that costs $1.50 per pound. she sells the mix for $2.50 per pound. how much did the 3lb of the second type cost the owner?
Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.
The cost of 2 pounds(lb) of the first type of candy is $8
Note that: x represents the cost per pound (lb) of the first type of candy
The Algebraic equation for the above statement is given as:
2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)
2x + 4.5 = 12.5
Collect like terms
2x = 12.5 - 4.5
2x = 8
Divide both sides by 2
2x/2 = 8/2
x = 4
The cost of the 1 pound of first type of candy is $4
The cost of 2 pounds(lb) of the first type of candy is calculated as:
2 x $4
= $8
hope it will be helpful
C is the center of the circle with a diameter whose endpoints are the points A(-2, 1) and B(6, 9).
What is the equation of circle C?
well, the midpoint of segment AB is the center of the circle, so
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]
now since we know AB is the diameter, so half that distance AB is its radius, so
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]
[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]
Plot the intercepts to graph the equation.
2x-3y=6
Answer:
y - intercept is (0,2)
x - intercept is (3,0)
Step-by-step explanation:
This is standard form.
Let x = 0
2x + 3y = 6
2(0) + 3y = 6
3y = 6 Divide both sides of the equation by 3
y = 2
The y intercepts is (0,2)
Let y = 0
2x + 3(0) = 6
2x = 6 Divide both sides of the equation by 2
x = 3
The x intercept is (3,0)
Answer:
x-intercept (3, 0)
y-intercept (0, -2)
Step-by-step explanation:
Finding the intercepts:At x-intercept the y = 0. The line passes the x-axis.
2x -0 = 6
2x = 6
x = 6 ÷ 2
x = 3
x-intercept (3, 0)
At y-intercept, x = 0 . The line passes y-axis.
0 - 3y = 6
-3y = 6
y = 6 ÷ (-3)
y = (-2)
y-intercept (0 , -2)
Plot these two points in the graph and join the points.
Aiden is preheating his oven before using it to bake. The initial temperature of the oven is 70° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 13 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
HURRY PLEASE!
What is the x ponet of y
;-;
The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.
Which number sentence is true?
A.1/3x(-2/5)=-2/15
B.-1/3x2/5=2/15
C.-1/3x(-2/5)=-2/15
D.1/3x2/3=-2/15
The number sentence that is true is 1/3 x (-2/5)=-2/15 . Option A
What is a fraction?A fraction is simply defined as the subset of a whole set or the part of a whole element.
The several types of fractions includes;
Simple fractionsProper fractionsMixed fractionsImproper fractionsComplex fractionsExamples of simple fractions: 1/2, 1/8
Examples of proper fractions: 3/4, 8/10
Examples of mixed fractions: 3 1/6, 2 1/8
Examples of improper fractions: 7/4, 8/5
Given the fraction;
a. 1/3 x (-2/5)
The product of the fraction is = - 2/15
b. -1/3 x 2/5 = 2/15
The product is = -2/15
c. -1/3 x (-2/5)
The product is 2/15
d. 1/3 x 2/3
The product is 2/9
Hence, the sentence is option A
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X=
/////////////////////
Answer:
x = 60
Step-by-step explanation:
(2x + 15)° and 135° are corresponding angles and are congruent , then
2x + 15 = 135 ( subtract 15 from both sides )
2x = 120 ( divide both sides by 2 )
x = 60
Answer:
x = 60
Step-by-step explanation:
The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!
find x
please and thank you
Answer: x = 65
Step-by-step explanation:
1) First find the mini triangles, left and right angles
We will be calling the left one A and the right one B.
2) Next use triangle sum to find B.
62 + 50 + b = 180
b = 68
3) Use triangle sum again to find A.
53 + 80 + a = 180
a = 47
4) Use triangle sum to find the top mini angle.
47 + 68 + c = 180
c = 65
5) Since x is in the vertical angle of c, they are equal
c = x
65 = x
The cost of Sara’s Cell Phone is $200 plus $45 per month.
How much will she spend on the cell phone in 3 years?
…. If Sara spent $1500, how long would she have had the phone?
(Use Cost ((y=mx+b))
Answer: The cost of her phone is $1,820.
45*12=540 per year
540*3=1,820 every 3 years.
She would have had the phone between 2 and 3 years if she had spent 1,500.
Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:
What is the direct variation equation that represents this situation? (worth 2
points)
How much will Eric spend if he buys 12 pizzas? (worth 2 points)
Explain how you calculated his total cost for pizzas. (worth 2 points)
Answer:
The answer would be 7 times 12
Eric will spend $84
I calculated it by seeing how much each of the pizzas cost-$7 the I figure out how many pizzas he need-12 Now what we need to do is multiply 7 and 12 because if one pizza is $7 (Stated in the written problem) then I know that it would be 7+7+7+7+7+7+7+7+7+7+7+7 12 times, one time for each pizza needed. The simpler version would be 7 time 12 which then we would get a value of $84.
Step-by-step explanation:
Hope this helps!!
Answers to all the subparts using equations are:
(A) Equation: 7x = C(B) Cost of 12 pizzas: C = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.So, the answers to all the subparts are as follows:
(A) Equation that can be formed is:
Let, the cost be C.x be the number of pizza buying.Equation: 7x = C(B) Cost of 12 pizzas:
Let, x = 12.
Then,7x = C7(12) = CC = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.
Therefore, answers to all the subparts using equations are:
(A) Equation: 7x = C(B) Cost of 12 pizzas: C = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.Know more about equations here:
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Correct question:
Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:
(A) What is the direct variation equation that represents this situation? (worth 2
points)
(B) How much will Eric spend if he buys 12 pizzas? (worth 2 points)
(C) Explain how you calculated his total cost for pizzas. (worth 2 points)
55
1. Given the sequence: 10, 5,
10,5, 2'4"
(a) Write the explicit formula for the sequence.
(b) Generate the next 3 terms. Label appropriately.
81 PI 01
3 1 1 / 5 + 1 /
2 =
Answer:
5 7/10
Step-by-step explanation:
first you multiply five by the three, then add the eleven. so now you have a improper fraction, 26/5 plus 1/2. find the Least common denominator which is 10, and whatever you do to the denominator you do to the numerator which makes 57/10 simplify and you'll get 5 7/10
Answer:
Step-by-step explanation:
1. Find the lcm(least common denominator)
(5 x 2 = 10)
2. Multiply the numerators by the same number as the denominator(you multiplied 5 by 2 to get 10 so you multiply 311 by 2. You multiplied 2 by 5 to get 10 so you multiply 1 by 5.)
311 x 2 = 622
1 x 5 = 5
3. Add
622/10 + 5/10 = 627/10
4. Simplify
627 ÷ 10 = 62 [tex]\frac{7}{10}[/tex] (it can also be written as: 62.7)
10. Find the area of the shaded region.
17 yd
5 yd
7 yd
6 yd
7 yd
4 yd
Answer:
176 yd
Step-by-step explanation:
UNSHADED REGION (white rhombus): A=(s1+s2)/2 * H
s1=7
s2=1+7=8
H=6
A=(7+8)/2*6=45
SHADED + UNSHADED REGION (big parallelogram): area of parallelogram A=B*H
B=17
H=7+6 = 13
A=17*13=221
SHADED REGION: big parallelogram area - rhombus area
221 - 45 =176 yd
What is the
range?
Help meeeeeee
20$ startup fee and a $5 monthly fee write an equation in slope intercept form that models
The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months
What is slope intercept form?The slope intercept form of an equation is y = mx + c
where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.
Let the total fee after x months be y
Then y is sum of startup fee and sum of all month's fee
For x months total monthly fees = 5(x)
Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c
when x= 0 ⇒ y = 20 , startup fee
Thus, the equation in slope intercept form is y = 5x +20 ,where y is total fee and x is number of months.
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What is the y-intercept of f(x) = -2 (1/2)^x?
Answer:
-2
Step-by-step explanation:
f(x) = -2 (1/2)^x
you find the y-intercept where x = 0
= -2 (1/2)^0
= -2 *1
= -2
Question 4 of 5
Compare -2 and 5. Which statement is not true?
OA. 5 is farther to the right on a number line.
OB. 151>1-21
C. -2 has a greater absolute value.
O D. 5 is farther from zero on a number line.
Which graph represents the solution set for p − 3.6 < −5.8?
The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.
Graph of linear inequalitiesFrom the question, we are to determine the graph for the solution set for the given inequality
The given inequality is p - 3.6 < -5.8
First, we will solve the inequality
Solving the inequality
p - 3.6 < -5.8
Add 3.6 to both sides
p - 3.6 + 3.6 < -5.8 + 3.6
p < -2.2
The solution is p < -2.2
The graph of the inequality is shown below
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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left
Step-by-step explanation:
If this guy is correct
Can someone please help me
In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.
What is the equation for a line shown on a graph?
Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.
Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:
b = - 6 (1)
4 · m + b = - 7 (2)
By (1) in (2):
4 · m - 6 = - 7
4 · m = - 1
m = - 1 / 4
The equation that represents the line is y = - (1 / 4) · x - 6.
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