We can use substitution to solve this system of equations. We can solve the first equation for y and get:
y = (2x + 12)/3
We can then substitute this expression for y into the second equation:
(2x + 12)/3 + 3x = -7
Multiplying both sides of this equation by 3 to eliminate the denominator, we get:
2x + 12 + 9x = -21
Simplifying this equation gives:
11x = -33
Dividing both sides by 11, we get:
x = -3
We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:
3y = 2(-3) + 12
3y = 6
y = 2
Therefore, the solution to the system of equations is x = -3 and y = 2.
To check the solution, we substitute these values back into both equations:
3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6
This equation is true, so the solution (x = -3, y = 2) checks out.
w/ solution please thanks
Answer:
x=-5, y=-2
Step-by-step explanation:
2x+4y=-18 (1)
5x-10y=-5 (2)
apply 5×(1)+2×(2)
10x+20y=-90 (3)
10x-20y=-10 (4)
by adding (3) and (4)
20x=-100
x=-5
put the value of x in (1)
we get 2×(-5)+4y=-18
⇒y=-2
After solving the given equations, the value of x and y are -5 and -2 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
So, we have the equations:
2x+4y=-18 (1)
5x-10y=-5 (2)
Apply as follows: 5×(1)+2×(2)
10x+20y=-90 (3)
10x-20y=-10 (4)
After adding (3) and (4):
20x=-100
x=-5
Insert the value of x in (1) as follows:
We obtain: 2×(-5)+4y=-18
⇒y=-2
Therefore, after solving the given equations, the value of x and y are -5 and -2 respectively.
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PLSSSSSSSSSSSSSSSSS HURRRYYYYYYYYYYYYYYYYYYYYYYY
A triangle with an area of 360 square meters was created from a triangle with an area of 2.5 square meters using a scale factor. What is the scale factor?
900:1
72:1
30:1
12:1
Answer:
Step-by-step explanation: Multiply all numbers and add all then divided by the lowest
Let x be the scale factor.
Then, the ratio of the areas of the two triangles is x².
We are given that the larger triangle has an area of 360 square meters and the smaller triangle has an area of 2.5 square meters. So we can set up the equation:
x²(2.5) = 360
Solving for x, we get:
x = sqrt(360/2.5)
x = sqrt(144)
x = 12
Therefore, the scale factor is 12:1. Answer: 12:1.
describe the key features que f the graph of the quadratic function f(x)=x^2-8-20
The graph is a parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
Define quadratic functionA quadratic function is a type of polynomial function of degree 2. It can be defined as a function in which the highest power of the independent variable x is 2.
The quadratic function f(x) = x² - 8x - 20 has a graph that is a parabola with a vertical axis of symmetry.
Vertex: The vertex of the parabola can be found using the formula x = -b/2a, where a and b are the coefficients of x² and x respectively.
In this case, a = 1 and b = -8, so the x-coordinate of the vertex is x = -(-8)/(2×1) = 4.
To find the y-coordinate of the vertex, substitute x = 4 into the equation: f(4) = 4² - 8(4) - 20 = -4. Therefore, the vertex is located at (4,-4).
Axis of symmetry: The axis of symmetry of the parabola is a vertical line passing through the vertex.
In this case, the axis of symmetry is the line x = 4.
Intercepts: To find the x-intercepts set y = 0 and solve for x: x² - 8x - 20 =0.
this quadratic equation can be factored as (x - 10)(x + 2) = 0
so the x-intercepts are x = 10 and x = -2.
To find the y-intercept, set x = 0 and evaluate f(0) = 0² - 8(0) - 20 = -20. Therefore, the y-intercept is (0,-20).
Image is attached below.
The graph is a upward-facing parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
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Find the absolute extrema of the function on the closed interval.
y = 3 cos x, [0, 2π]
The absolute extrema for the given function occurred at the critical points for Interval [0, 2π] is 3.
Explain about the absolute extrema of function?The point wherein the minimum or maximum value of the function is reached is known as the absolute extremum (also global extremum) of the function in the given interval.
The absolute extremum, or point equivalent to the highest or least value in the entire function, is frequently the interval specified, which is the domain of the function.
The given function :
y = 3 cos x,
Differentiate the function with respect to 'x'.
y' = -3 sin x
Find the critical point , by y = 0
-3 sin x = 0
x = sin ⁻¹ (0)
Interval [0, 2π]
So, critical points are: x = 0,π, 2π
Now, evaluate function by putting the critical points;
y(0) = 3 cos 0 = 3
y(π) = 3 cos π = 0
y(2π) = 3 cos 2π = 3
Thus, absolute extrema for the given function occurred at the critical points 0 and 2π that is 3.
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Find the value of z such that 0.5762
0.5762
of the area lies between −z
−
z
and z. Round your answer to two decimal places.
Answer:
z = 0.80
Step-by-step explanation:
You want the value of z such that p(-z < X < z) = 0.5762 for a normal distribution.
TailsThe area outside the region of interest will be split evenly between the two tails. That is, the lower tail will hold (1 -0.5762)/2 = 0.2119 of the area of the distribution. The required value of z will be the magnitude of the Inverse CDF function for this value.
Inverse CDFThe attached calculator shows the required value of z is about 0.80.
Katya owns two cockatoos, an older white cockatoo and a younger Galah cockatoo. At present, the sum of the cockatoos' ages is 44 years. In n years, where n > 0, the white cockatoo's age will be four times the Galah cockatoo's age. If n is an integer, determine the possible present ages of each cockatoo.
The possible present ages of each cockatoo, given the sum of the cockatoos would be Galah cockatoo is currently 10 years old and the white cockatoo would be 34 years old
How to find the ages of the cockatoos?Let's use variables to represent the present ages of the two cockatoos. Let W be the present age of the white cockatoo and G be the present age of the Galah cockatoo. We're given that the sum of their ages is 44 years:
W + G = 44 (1)
In n years, the white cockatoo will be W + n years old, and the Galah cockatoo will be G + n years old:
W + n = 4(G + n) (2)
Since n > 0, 5G - 44 must be positive. We can try different values of G to find possible integer values for n.
For G = 8:
44 - 5(8) = 4
4 = -3n
n is not an integer.
For G = 10:
44 - 5(10) = -6
-6 = -3n
n = 2
So one possibility is that the Galah cockatoo is currently 10 years old. In this case, the white cockatoo would be 34 years old (since W + G = 44).
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PLEASE HELP ASAP PLEASE!!
Answer: a/ c/ d and e
Step-by-step explanation:
100 pts answer fast and brainliest
Answer:
1 c
2 d
3 a
4 b
5 e
Step-by-step explanation:
scale factor > 1 => expansion
scale factor < 1 => contraction
scale factor = 1 => no change
scale factor is (-) => opposite site
Helena sketches a circular backyard skating pond that fits into a square section of her yard. In her sketch, what is the area of the shaded region?
Answer:
The area of the shaded region equals 21.43 sq. units.
Step-by-step explanation:
Why do we use area?When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.
Given, A circle is circumscribed in the square,
Area of shaded region = area of square - area of circle
Area of square = Side²
= 10 × 10 = 100 sq. units,
Area of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 unitsArea of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 units
Area of circle = 22/7 × 5 × 5
= 78.57 sq. units
Area of shaded region = 100 - 78.57,
Area of shaded region = 21.43 sq. units
A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
Match the events on the left with probabilities on the right.
The probabilities of the events and their values are shown below
Matching the probabilities of the eventsThe total number of marbles in the bag is 13, with 6 blue, 2 green, and 5 red.
P(Blue or Green) represents the probability of selecting a blue or green marble on the first pick.
This is calculated as follows:
P(Blue or Green) = P(Blue) + P(Green)
= 6/13 + 2/13
= 61.5%
P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, with replacement.
Therefore:
P(Blue and Green) = P(Blue) * P(Green)
= (6/13) * (2/13)
= 7.1%
P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, without replacement.
Therefore:
P(Blue and Green) = P(Blue) * P(Green)
= (6/13) * (2/12)
= 7.7%
P(Blue) represents the probability of selecting a blue marble on the first pick.
This is simply the proportion of blue marbles in the bag:
P(Blue) = 46.2%
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HELP ME PLS I LITERATELY CANT
Rewrite the following in scientific notation and calculate the answer in scientific notation. If necessary, convert your answer to scientific notation. 2,520,000/14,000
The given expression can be written in scientific notation as 1.8 x 10² To obtain this, we first divide 2,520,000 by 14,000 to get 180. Then, we express this as 1.8 x 10² by moving the decimal point two places to the left and adding an exponent of 2.
What is scientific notation?For expressing very big or very small numbers in scientific notation, the number is written as the product of a number between 1 and 10 and a power of 10
How do you convert a number to scientific notation?To convert a number to scientific notation, first express it in the form a x 10^b, where a is a number between 1 and 10, and b is an integer.
Then, move the decimal point in a to obtain a number between 1 and 10, and add an exponent to 10 that corresponds to the number of places you moved the decimal point.
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Triangle WXY with W(0, 1), X(-4, 4), Y(0, 2)
in y-axis
(x, y) ⇒ (x − 1, y — 4)
a) Reflection
b) Translation
(a)The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
(b)The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
What is reflection ?a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.
The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
The reflected triangle would be W'X'Y'.
b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.
The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
The translated triangle would be W'X'Y'.
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your mom got 20 cupcakes in you got 1 plate how the 1 and 20
Answer:
Step-by-step explanation:
explain you question more i cant understand if i could i would help
Solving Systems of Quadratic Equations
5. Solve this nonlinear system of equations. Show your work.
a. Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point)
b. Factor your equation from Part a. (1 point)
c. Identify the x-values of the solutions. (1 point)
d. Identify the solutions to the system. (1 point)
Using equations,
A: y=-x²+6x-5
y=3
3=-x²+6x-5
y=0
B: (x-2) (x-4) =0
C: x-2=0 OR x-4=0
D: x=2 OR x=4
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.
Y=-x²+6x-5
Y=3
Using substitution:
3 = - x²+6x- 5
x²- 6x+8 = 0
Now factor your equation:
x²- 6x+8 = 0
⇒ x² -2x - 4x + 8 = 0
⇒ x (x-2) -4(x-2) = 0
⇒ (x- 2) (x-4) =0
Identify the x-values of the solutions:
x-2=0 or x-4 =0
x=2 or x=4
Identify the solution to the system:
x=2 y=3 and
x=4 y=3
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solve using substitution method y = -3x 4x+y = 2
[tex]\Large\textbf{Please give complete questions}[/tex]
PLEASE HELP LATE HOMEWORK
The number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
What is meant by intersection?
In mathematics, the intersection of two sets A and B is a new set that contains all the elements that are common to both sets. In symbols, the intersection of A and B is denoted by A ∩ B, and it is defined as:
A ∩ B = {x : x ∈ A and x ∈ B}
Let A represent the set of students who have a cell phone, and B represent the set of students who have a tablet. The intersection of A and B, denoted by A ∩ B, represents the set of students who have both a cell phone and a tablet. Therefore, we want to find the cardinality (or size) of the set A ∩ B.
From the frequency table, we know that the total number of seventh graders surveyed is 100. We also know that there are 32 students who have a cell phone (i.e., |A| = 32) and 70 students who have a tablet (i.e., |B| = 70). We are given that 19 students who have a cell phone do not have a tablet, which means that there are 32 - 19 = 13 students who have both a cell phone and a tablet (i.e., |A ∩ B| = 13).
Therefore, the number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
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The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten.
The volume of the solid with a hole in the shape of a rectangular prism passing through the center of a cylinder with a radius of 10 yards is approximately 1410 cubic yards, rounded to the nearest ten.
The cylinder with the hole can be viewed as the difference of two solids: the cylinder and the rectangular prism. The volume of the cylinder is given by the formula V_cyl = π[tex]r^2h[/tex], where r is the radius and h is the height.
The height of the cylinder is equal to the height of the rectangular prism that passes through its center. The height of the rectangular prism is given as 12 yards, which is also the diameter of the cylinder. Therefore, the height of the cylinder is h = 12/2 = 6 yards.
The volume of the cylinder is therefore V_cyl = π[tex](10)^2(6)[/tex] = 600π cubic yards.
The rectangular prism has a length of 20 yards, a width of 10 yards, and a height of 12 yards. Therefore, its volume is V_prism = 20 × 10 × 12 = 2400 cubic yards.
The volume of the solid with the hole is then:
V = V_cyl - V_prism = 600π - 2400 = 600(π - 4) ≈ 1412.2 cubic yards.
Therefore, the volume of the solid is approximately 1410 cubic yards.
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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
__ __
Answer:
[tex]13 < \sqrt{181} < 14[/tex].
Step-by-step explanation:
We have been given an inequality ___[tex]< \sqrt{181} <[/tex]___. We are asked to fill in the blank with two consecutive integers to complete the given inequality.
We know that square root of 181 is not an integer. We can see that 181 is greater than square root 169 and and square root of 196.
[tex]\sqrt{169} < \sqrt{181} < \sqrt{196}[/tex]
We know that [tex]\sqrt{169}=13[/tex] and [tex]\sqrt{196}=14[/tex].
Therefore, our required inequality would be [tex]13 < \sqrt{181} < 14[/tex]
A house is advertised for sale. If the sale price
is $140,000. Calculate the mortgage of the deposit is 25% of the cash price
Answer: $105,000
Step-by-step explanation:
$140,000-25%deposit =$105,000
Malinda wants to rent a compact car for eight days. Ace Rental rents these cars for $48 per day or $312 per week. Compute the cost of each plan for her. Which plan is more economical?
a) The total cost for renting a compact car for eight days is as follows for each plan:
Daily rental = $384Weekly rental = $360.b) It is more economical to take the weekly rental plan than the daily rental plan.
How is the total cost determined?Each plan's total rental cost is determined using multiplication or addition.
For instance, the total cost for the daily plan is a product of the daily rental cost and the number of days the car is rented.
The total cost for the weekly plan is an addition operation since the car is rented for 7 days (weekly cost) and 1 day (daily cost).
Day Week
Rental cost per $48 $312
1 week = 7 days
Total rental cost for
8 days $384 ($48 x 8) $360 ($312 + $48)
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In a survey by the Pew Research Center, adult members of the Church of Jesus Christ of Latter-day Saints in the U.S. were asked how important religion is in their life. 558 adults said religion is “very important” in their lives, 79 adults said religion is “somewhat important” in their lives, 20 adults said religion is “not too important” in their lives, and 7 adults said religion is “not at all important” in their lives. Which of the following columns (A, B, C, D, or E) correctly shows the responses to this question as a probability model? (A) (B) (C) (D) (E) Very important 63.5% 84% 84% 12% 77% Somewhat important 22.5% 12% 14% 84% 21% Not too important 2% 3% 5% 1% 5% Not at all important 1% 1% 3% 3% 3%
The correct column is (A), which correctly represents the responses as probability.
Define probabilityProbability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The sum of all the responses is 558 + 79 + 20 + 7 = 664.
To represent the responses as a probability model, we need to divide each response by the total number of respondents, 664.
The correct column is (A), which correctly represents the responses as probabilities:
(A)Very important 558/664 = 0.841
Somewhat important 79/664 = 0.119
Not too important 20/664 = 0.030
Not at all important 7/664 = 0.011
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i need the answers please
Answer:
(7) AB is a tangent , (8) AB is not a tangent
Step-by-step explanation:
the angle between a tangent and the radius is 90°
if AB is a tangent then Δ ABC is right with hypotenuse AC
using Pythagoras' identity
the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
if AC² = AB² + BC² , then AB is a tangent to the circle
(7)
AC² = 34² = 1156
AB² + BC² = 30² + 16² = 900 + 256 = 1156
since AC² = AB² + BC² , then AB is a tangent to the circle
(8)
AC² = 28² = 784
AB² + BC² = 21² + 20² = 441 + 400 = 841
since AC² ≠ AB² + BC² , then AB is not a tangent to the circle
Pat listed all the numbers that have 15 as a multiple. What’s the numbers in Pats list
Answer:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735...
Step-by-step explanation:
PLSSS HELPPP QUICK
What is the product of the monomial x and the
trinomial 2x² -5x+1?
Dario walks from his house to a comic book store along the route shown. Distances in the coordinate plane are in units of miles. How many miles does Dario walk to reach the comic book store
The distance walked by Dario from to reach comic book store is 1.4 miles.
What is distance?Displacement and distance are two terms that, while they appear to imply the same thing, have quite different definitions and meanings. Displacement is the measurement of "how much space an item has covered while it has been in motion," whereas distance is the indication of "how much ground an object has covered during its motion." Let's examine the distinction between displacement and distance in this essay.
For the given route we have:
House to jewelry store:
0.2 - (-0.5) = 0.2 + 0.5 = 0.7 miles.
Jewelry store to bank:
0.6 - 0.2 = 0.4 miles.
Bank to comic book store:
-0.5 -(-0.8) = -0.5 + 0.8 = 0.3 miles.
House to comic book store:
0.7 + 0.4 + 0.3 = 1.4 miles.
Hence, the distance walked by Dario from to reach comic book store is 1.4 miles.
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The complete question is:
what is the length of tr?
Answer:
12
Step-by-step explanation:
The graph of a proportional relationship contains the point (-12, 3).
What is the corresponding equation?
(A) y = 1/4x
(B) y = - 1/4x
(C) y = - 4/1x
(D) y = 4/1x
____
The variables x and y have a proportional relationship, and y=3 when x=4
Which equation represents this relationship?
(A) y = −12x
(B) y = 4/3x
(C) y = 7x
(D) y = 3/4x
____
correct answers gets brainliest
Determine f(3) for f(x)
A. 9
B. 19
C. 22
D. 27
I js need help with this question
Answer: D. y=-x+7
Step-by-step explanation: For example,
(-1,8)
x= -1
y=8
-(-1) = 1
1 + 7 = 8