Answers
Answer:
(7, - 2 )
Step-by-step explanation:
Given the 2 equations
x = - 3y + 1 → (1)
- 3x - 3y = - 15 → (2)
Substitute x = - 3y + 1 into (2)
- 3(- 3y + 1) - 3y = - 15 ← distribute and simplify left side
9y - 3 - 3y = - 15
6y - 3 = - 15 ( add 3 to both sides )
6y = - 12 ( divide both sides by 6 )
y = - 2
Substitute y = - 2 into (1) for corresponding value of x
x = - 3(- 2) + 1 = 6 + 1 = 7
solution is (7, - 2 )
Related Questions
Find the maximum or minimum value of the product of two numbers whose difference is 14.
Answers
The maximum value of the product of two number whose difference is 14 is 49.
What is the maximum or minimum value of a function?The maximum or minimum value of a function is the highest or lowest value of that function.
How to determine the maximum or minimum of the product of two numbers?Let the numbers be x and y
Their product f(x,y) = xy
Since their difference is 14, x - y = 14
So, x = 14 - y
Substituting x into f(x,y), we have
f(x,y) = xy
= (14 - y)y
= 14y - y²
To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.
So, f(x,y) = f(y) = 14y - y²
df(y)/dy = d(14y - y²)/dy
df(y)/dy = d(14y)/dy - dy²/dy
df(y)/dy = 14 - 2y
Equating to zero, we have
df(y)/dy = 0
14 - 2y = 0
14 = 2y
y = 14/2
y = 7
To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again
So, df'(y)/dy = d(14 - 2y)/dy
= d14/dy + d(-2y)/dy
= 0 - 2
= -2 < 0.
Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)
So, since y = 7,
x = 14 - y = 14 - 7 = 7
So, f(x,y) is maximum at x = 7 and y = 7
So, f(7,7) = 7 × 7
= 49
So, the maximum value of the product of two number whose difference is 14 is 49.
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Hi having a bit of trouble.
Answers
Answer:
P = 160/A
Step-by-step explanation:
For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.
Inversely proportionalTwo quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:
y = kx
They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:
y = k(1/x) = k/x
In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...
P = k/A
You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:
P = 160/A
what is the volume of the sphere shown below with a radius of 9
Answers
Answer:
972π or 3052.08 if π=3.14(remember to label the answer with your units)
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}\\[/tex]π[tex]r^{3}[/tex]. So, just plug the radius into the formula. [tex]r^{3}[/tex] in this case is [tex]9^{3}[/tex] which is 729. For, [tex]\frac{4}{3}[/tex]×729, the 3 and 729 cancel out to create 4×243 which is 972. Just add π to this and you get 972π. If π is 3.14 just multiple 972 and 3.14 to get 3052.08.
5x=3125 how do i solve that
Answers
Answer:
just divide 3125 by 5 and your answer is 625
Step-by-step explanation:
Using division, 3125 by 5 and get answer 625.
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, a / b = a divided in b equal parts.
We have been given 5x = 3125
Divide by 5 each sides;
x = 3125/5
x = 645
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The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)
The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.
Answers
The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.
Which conclusion is true about the quadrilaterals?Given that,
vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)
vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)
(x,y) ; (x, y-8)
ABCD is reflected across the line y=4 to get the quadrilateral EFCD.
Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.
Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.
Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).
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1 1/5 · x/3 = 9/10
solve for x
Answers
The value of x in the equation 1 1/5 - x/3 = 9/10 is 9/10
Fraction1 1/5 - x/3 = 9/10
- x/3 = 9/10 - 1 1/5
- x/3 = 9/10 - 6/5
-x/3 = 9-12 / 10
-x/3 = -3/10
divide both sides by - 1/3x = -3/10 ÷ - 1/3
= -3/10 × -3/1
x = 9/10
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(08.01)Angela wants to know how many families in her neighborhood plan to attend the parade. She puts all 120 of the neighborhood addresses in a hat and draws a random sample of 30 addresses. She then asks those families if they plan to attend the parade. She finds that 40% of the families plan to attend the parade. She claims that 40% of the neighborhood families would be expected to attend the parade. Is this a valid inference?
A) Yes, this is a valid inference because the 30 families speak for the whole neighborhood
B)Yes, this is a valid inference because she took a random sample of the neighborhood
C)No, this is not a valid inference because she did not take a random sample of the neighborhood
D) No, this is not a valid inference because she asked only 30 families
Answers
Using sampling concepts, the correct option regarding the validity of the inference is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.
In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
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1/2a+2/3b=50 when b=30?
Answers
The given equation is (1/2)a + (2/3) b = 50
and b = 30
Substituting the given value of b is above the equation we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]
Therefore, a = 60 and b = 30 is a solution of the given equation.
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https://brainly.com/question/12950748What addition/subtraction equation should I put?
Answers
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
What is the value of the function at x=−2? y=−4 y equals negative 4 y = 0 y, = 0 y = 2 y = 2, y = 3
Answers
Based on the graph which models the function at x = -2 (see attachment), the corresponding y-value is y = 3.
What is a function?In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.
In this scenario, there are several values (points) on the given linear graph expressed as a coordinate (x, y). Hence, the x-values on the x-axis is directly proportional to the y-values on the x-axis.
By critically observing the graph which models the function at x = -2 (see attachment), we can logically deduce that the corresponding y-value is three (3).
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Answer:
Ik im late but yea
Step-by-step explanation:
I took the test :O
A linear expression does not have a squared variable.
Answers
it is true that a linear expression does not have a squared variable.
How to determine the true statement?The following are the forms of a linear expression
y = mx + c
Ax + By = C
x = a
Notice that none of the above expressions have a squared variable
This means that, a linear expression does not have a squared variable.
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In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.
Answers
VARIABLE is a symbol which is used for representation in a math.
According to the statement
we have to explain about the what is a variable.
So, VARIABLE is a symbol which is used for representation in a math.
It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.
A variable may also be called a data item.
It is used to represent a data like country name, name, age, date of birth etc.
we know that the every thing is changeable. So, like ther things variables are also changeable.
The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.
So, VARIABLE is a symbol which is used for representation in a math.
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Please help! I'm giving 25 points!!
The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
Answers
1. The number of gallons of water produced is 460 gallons
2. The amount in cm the sea would increase after 6 years is 392 cm
1. How to determine the number of gallons producedWe'll begin by by converting 1.9 m³ to cm³. This is illustrated below:
1 m³ = 1×10⁶ cm³
Therefore,
1.9 m³ = 1.9×10⁶ cm³
Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:
From the question given,
1 cm³ of ice = 0.92 cm³ of water
Therefore,
1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92
1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water
Finally, we shall determine the number of gallons produced. This is illustrated below:
From the question given,
3800 cm³ of water = 1 gallon
Therefore,
1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800
1.748×10⁶ cm³ of water = 460 gallon
Thus, 460 gallons were produced
2. How to determine the amount in cm the sea would increase to after 6 yearsFrom the question given above,
1000 Km³ = 364 cm
Therefore,
179.4 Km³ = (179.4 × 364) / 1000
179.4 Km³ = 65.3016 cm per year
To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:
65.3016 × 6 = 392 cm
Thus, the sea will increase 392 cm after 6 years
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If the width of a rectangle can be represented by x and the length by x + 10, write an expression that can be used to represent the area of the rectangle. Simplify the expression as much as possible.
Answers
Answer:
The expression for area is (x)(x+10).
Step-by-step explanation:
Area=(w)(l)
Area=(x)(x+10)
(Note: This expression can be expanded, but then it wouldn't be fully simplified)
Hope this helps!
What is the size of exterior angle of regular polygon which has interior angle of 120 degree?
Answers
Answer: 60 degrees
Step-by-step explanation:
An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits, we say the process is
Answers
The process is Capable.
According to statement
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits
and when these conditions are fulfilled then the process is to be called CAPABLE.
So, The process is Capable.
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(17,-13),(17,8) finding slope from two points
Answers
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
There are really two ways to solve this problem. One of them is the slope formula. You can familiarise yourself with this formula
[tex]\sf{\dfrac{y2-y1}{x2-x1}}[/tex]
SUBSTITUTE the values
[tex]\sf{\dfrac{-13-8}{17-17}}[/tex]
[tex]\sf{\dfrac{-21}{\bf{0}}[/tex] (notice the zero was in bold-face)
Dividing by zero is an operation we cannot do.
So the slope of this particular line is not defined.
The other way is looking at the first co-ordinates of the points given
Notice that they are exactly the same. Whenever that happens, the slope of that line is not defined.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{\tt{calligraphy}}\star[/tex]
What number is represented by point B? A number line going from 1 to 2 with 5 equal spaces between 1 and 2. Point B is one mark to the left of 2. StartFraction 4 Over 5 EndFraction 1 and StartFraction 4 Over 5 EndFraction 1 and StartFraction 5 Over 4 EndFraction 2 and StartFraction 1 Over 5 EndFraction
Answers
Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅
The question has to deal with proportion
What is proportion?Proportion is the measure of a variable or quantity relative to another.
How to calculate which number represents point B?Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is
= 1/5
So, each sub-unit measure 1/5
Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5
= 9/5
= 1⁴/₅
So, the number represented by point B is 1⁴/₅
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mean of four consecutive even numbers is 15. Enter each number separated by a comma
Answers
Therefore second number is (x+2).
Therefore third number is (x+4).
Therefore forth number is (x+6).
Hence,
(x+x+2+x+4+x+6+x+8)/4 = 15
(4x+12)/4 = 15
x+3 = 15
x = 12
So,
The number is 12, 14, 16, 18.
Hope it helps : )
Answer:
12, 14, 16, 18
Step-by-step explanation:
(x + (x+2) + (x+4) + (x+6))/4 = 15
^ solve algebraically
you'll get (4x+12)/4 = 15
then: 4x + 12 = 60
then 4x = 60-12
then 4x = 48
then x = 12
x is 12 so then do substitution
so you get
12 + (12+2) + (12+4) + (12+6)
12, 14, 16, 18
Someone do this please
Answers
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees
can someone please help mee
Answers
Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
60÷8 explained well and not in a decimal form
Answers
Answer: 15/2
Step-by-step explanation: if you fraction it, it'll be 60/8 so you can simplify it by 4. So 60÷4/8÷4 will be 15/2. So the answer is 15/2
Answer:
15/2 or 7 1/2.
Step-by-step explanation:
60 / 8 divide top and bottom by 4:-
= (60/4) / (8/4)
= 15/2.
Denise wants to enlarge her prom photo. She wants to increase the
size 4 times the original photo. If the original photo is 6 inches by 8 inches,
how many times larger is the new photo?
4
40
16
8
Answers
After enlargement, the new photo would be 16 times larger. The answer is C: 16.
What is an Enlargement?An enlargement can be described as a type of dilation in transformation which involves increasing the dimensions of an original image by a given scale factor, so that the new image is similar to the original image. Their sizes would be different while their shapes remain the same. Also, the ratio of their corresponding dimensions would be the same.
Given the following:
Dimension of original photo = 6 inches by 8 inches
Scale factor = 4
To find the new dimensions of the new photo, multiply the corresponding dimensions of the original photo by 4, thus:
6 × 4 = 24 inches
8 × 4 = 32 inches
New dimensions = 24 by 32
Area of original photo = 6 × 8 = 48 in.²
Area of new photo = 24 × 32 = 768 in.²
768/48 = 16
This means that the new photo is 16 times larger than the original photo.
The answer is: C. 16.
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Solve the equation: √2 + 4 - 1 = 2
A) ±x= √5
B) ±x = √13
OC) x= 3
D) x = 5
Answers
Answer:
Step-by-step explanation:
1) Separate terms with roots from terms without roots.
[tex]x^2+4=\sqrt[\frac{1}{2} ]{4+1}[/tex]
2) Simplify 4 + 1 to 5.
[tex]x^2+4=\sqrt[\frac{1}{2} ]{5}[/tex]
3) Invert and multiply.
[tex]x^2+4=5^2[/tex]
4) Simplify [tex]5^2[/tex] to 25.
[tex]x^2+4=25[/tex]
5) Subtract 4 from both sides.
[tex]x^2=25-4[/tex]
6) Simplify 25 - 1 to 24.
[tex]x^2=21[/tex]
7) Take the square root of both sides.
[tex]x=\pm\sqrt{21}[/tex]
Answer:
A
Step-by-step explanation:
[tex]\sqrt{x^{2}+4}-1=2\\\sqrt{x^{2}+4}=3\\x^{2}+4=9\\x^{2}=5\\x=(plus/minus) \sqrt{5}[/tex]
5 roses in a vase 12 flowers what is the ratio of all flowers in the vase of daisies
Answers
The ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.
The number of flowers in the vase = 12 flowers
The number of roses in the vase = 5 roses.
Therefore, the number of daisies in the vase = The number of flowers in the vase - The number of roses in the vase,
or, the number of daisies in the vase = 12 - 5 = 7.
Thus, the number of daisies in the vase = 7.
We are asked to find the ratio of the total number of flowers in the vase, to the number of daisies in the vase.
Thus, the ratio = The number of flowers in the vase/The number of daisies in the vase,
or, the ratio = 12/ = 12:7.
Thus, the ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.
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Identify the perimeter of a rectangle in which h = 8 ft and a = 144x ft^2. please help asap
Answers
Here, Given
h= 8ft
a=144 * ft^2
then,
A=L*H
144=L*8 or 144/8 =L
L=18
now, P=2(L+H)
P=2(18+8)
P=52m
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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PLEASE ANSWER WILL GIVE YOU ALOT OF POINTS
Answers
The theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.How to prove lines are parallel?Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
Theorems that prove that lines are parallel includes:
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Find the circumference of a circle with diameter, d = 8.92m. give your answer rounded to 2 dp.
Answers
Answer:
Step-by-step explanation:
circumference is 2πr
r=d/2
r=4.46m
C=2π(4.46)=28.02
If x = false and y = false, is the statement: not x or not y
a) true
b) false
Answers
Answer:
false
Step-by-step explanation:
X is equal to Y
therefore,
X = Y
X= false
Y = false
so,
false = false
Which answer represents the following conditional statement in shorthand?
if megan is swimming, then it is warm outside.
Answers
The expression which represents the given conditional statement in shorthand is: S → W.
What is a conditional statement?A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
If Megan is swimming = S
It is warm outside = W
Therefore, if Megan is swimming, then it is warm outside is represented by S → W.
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