Choose the graph below that represents the solution to the system of equations
y= 3x + 2
10x + 2y = 20
Answers
Answer:
Graph 3 represents the solution to the system of equations.
Step-by-step explanation:
The given two linear equations of x and y are
y = 3x + 2 ........ (1) and
10x + 2y = 20 .......... (2)
Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).
Hence, 10x + 2(3x + 2) = 20
⇒ 16x = 16
⇒ x = 1
And from equation (1), y = 3x + 2 = 5
Therefore, the solution of the system of equations (1) and (2) are (1,5).
Therefore, graph 3 represents the solution to the system of equations. (Answer)
Related Questions
Two equivalent fractions of 4/7
Answers
Answer:
8/14 and 12/21
Step-by-step explanation:
Just multiply numerator and denominator by the same number, e.g., 2 and 3 to get above.
Answer:
8/14 and 12/21
Step-by-step explanation:
Write the quadratic equation whose roots are 3 and 4, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)
Answers
Step-by-step explanation:
equation-
(x-3) (x-4) =
[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]
Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.
Explanation:To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).
Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.
The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.
So, the requested quadratic equation is 2x^2 - 14x + 24.
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Please solve number 80
Answers
Answer:
option D. 20 cm
Step-by-step explanation:
step 1
Find the volume of the water
The volume of the water is equal to
[tex]V=LWH[/tex]
we have
[tex]L=60\ cm\\W=40\ cm\\H=50\ cm[/tex]
substitute
[tex]V=(60)(40)(50)[/tex]
[tex]V=120,000\ cm^3[/tex] ---> volume of water
step 2
Find the deep of the water, if the tank is returned to its horizontal position
we have
[tex]V=120,000\ cm^3[/tex]
[tex]L=100\ cm\\W=60\ cm\\H=?\ cm[/tex]
where
H is the deep of the water
substitute in the formula of volume
[tex]120,000=(100)(60)(H)[/tex]
solve for H
[tex]120,000=6,000)(H)[/tex]
[tex]H=20\ cm[/tex]
The scale map shows that 5 centimeters =2 kilometers.What number of centimeters on the map represents an actual distance of 5 kilometers?
Answers
Answer:
Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.
Step-by-step explanation:
Given:
The scale map shows that
5 centimeters =2 kilometers.
To Find:
What number of centimeters on the map represents an actual distance of 5 kilometers?
Solution:
Let 'x' cm be on the map to represent 5 kilometer.
Given:
5 centimeters = 2 kilometers.
Therefore,
x cm = 5 kilometer
Soon Equality of proportion we get
[tex]\dfrac{5}{x}= \dfrac{2}{5}\\ \\x=\dfrac{5\times 5}{2}=\dfrac{25}{2}=12.5\ cm\\\\\therefore x = 12.5\ cm[/tex]
Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.
The number of students enrolled at a college is 12,000 and grows 4% each year. Complete parts (a) through (e).
a) The initial amount a is
.
Answers
Answer:
48000
Step-by-step explanation:
12000 students
4%
1 =annually
12×4×1= 48000
Answer:12,000
Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p
A movie theater sells out 7 times per month. How many times will it sell out in the next 2 years?
Answers
1 year = 12 months.
2 years = 12 x 2 = 24 months.
Multiply the number of times it sells out per month by the number of months:
7 x 24 months = 168 times.
Which equation has both -3 and 3 as possible values of y?
A
y^2=6
B
y^2=8
C
y^2=9
D
y^2=64
Answers
Answer:
C. [tex]y^2=9[/tex]
Step-by-step explanation:
1. [tex]y^2 = 9[/tex]
2. [tex]y = \frac{+}{}\sqrt{9}[/tex]
3. Equation solutions:
[tex]y_{1} = 3\\y_{2} = -3[/tex]
.The sum of the digits of a two-digit number is one-fifth the value of the
number. The tens digits is one less than the ones digit. What is the two-digit
number? (Hint: Assign a different variable to the value of each digit.)
Answers
Here's how I'm assigning a different variable to the value of each digit:
10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)
The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:
x + y = (1/5)(10x + y)
Simplify
x + y = 2x + (1/5)y
The tens digit is one less than the ones digit. Using this information, we can form the equation:
x = y - 1
Adding both sides by 1 gives
x + 1 = y
Substituting this into the y's the first equation gives:
x + x + 1 = 2x + (1/5)(x + 1)
Distribute and simplify
2x + 1 = 2x + (1/5)x + 1/5
Subtract both sides by 2x
1 = (1/5)x + 1/5
Subtract 1/5 from both sides
4/5 = (1/5)x
Multiply both sides by 5
4 = x
x = 4
Use this to solve for y
x + 1 = y
4 + 1 = y
y = 5
Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.
Let me know if you need any clarifications; this was a very interesting math problem to solve!
what number is 10 times as great as 7962
Answers
To find a number that is 10 times greater than 7962, we can multiply.
7,962 * 10 = 79,620
79,620 is 10 times greater than 7,962.
Best of Luck!
Answer:
79,620
Step-by-step explanation:
7,962 (10) = 79,620
The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.
Statements Reasons
2x + 2y = 14
−x + y = 5 Given
2x + 2y = 14
y = x + 5 ?
Answers
Answer:
As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.
Step-by-step explanation:
[tex]2x + 2y = 14[/tex]
[tex]-x + y = 5[/tex] Add x in both sides (Addition Property of Equality)
[tex]2x + 2y = 14[/tex]
[tex]y = x + 5[/tex] Multiply both sides by 2
[tex]2x + 2y = 14[/tex]
[tex]2y = 2x + 10[/tex] Subtract 2x in both sides
[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex] ∵adding both equation
[tex]4y = 24[/tex] divide both sides by 4
[tex]y = 6[/tex]
Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]
[tex]-x + 6 = 5[/tex] Subtract 6 from both sides
[tex]-x = -1[/tex] Change the sign
[tex]x = 1[/tex]
Keywords: Addition property of equality, reason, proof
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4x-1=2x+11
what is the value of x and what are the steps?
Answers
Answer:
x=6
Step-by-step explanation:
4x-1=2x+11
4x-2x-1=11
2x-1=11
2x=11+1
2x=12
x=12/2
x=6
You need to isolate the variable or get x on one side of the = sign and a number on the other side.
1. Do the inverse operation and add one to each side of the equation. -1+1= 0 and 11+1=12
2. Subtract 2x from both sides. 2x-2x=0 and 4x-2x=2x.
So we are left with 2x=12 or 2 times some number “x” is equal to twelve.
3. Next we divide both sides by 2
2/2=1 and 12/2=6
So x=6
To the nearest tenth, what is the distance between the point (10, -11) and (-1, -5)
Answers
Answer:
≈ 12.5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)
d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]
= [tex]\sqrt{(-11)^2+6^2}[/tex]
= [tex]\sqrt{121+36}[/tex]
= [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )
how can you use functions to solve real world problems ??
Answers
Answer:ioj;i;
hStep-by-step explanation:
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A cat is running away from a dog. After 5 seconds it is 16 feet away from the dog and after 11 seconds
it is 28 feet away from the dog. Let x represent the time in seconds that have passed and y represent the
distance in feet that the cat is away from the dog.
Answers
Answer:
18 feet
Step-by-step explanation:
Given:
A cat is running away from a dog.
After 5 seconds it is 16 feet away from the dog
After 11 seconds it is 28 feet away from the dog.
Let x represent the time in seconds that have passed and y represent the
distance in feet, so there are two points are formed such as (5, 16) and (11,28).
We will find the distance between dog and cat. by using distance formula of the two points.
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Now we substitute the given value in above equation.
[tex]d=\sqrt{(11-5)^{2}+(28-11)^{2} }[/tex]
[tex]d=\sqrt{(6)^{2}+(17)^{2} }[/tex]
[tex]d=\sqrt{36+289}[/tex]
[tex]d=\sqrt{325}[/tex]
[tex]d=18.08\ feet[/tex]
18.08 ≅ 18
So [tex]d=18\ feet[/tex]
Therefore the distance between dog and cat is 18 feet.
To find the linear equation for the distance between the cat and the dog, we calculate the slope with the given points and use it with one of the points to establish the equation y = 2x + 6. A graph can be drawn with the points (5, 16) and (11, 28) to visualize the cat's path.
The linear equation describing the distance the cat is from the dog in relation to time can be determined using the two given points: (5, 16) and (11, 28), where 'x' is the time in seconds and 'y' is the distance in feet.
We first find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values we get:
m = (28 - 16) / (11 - 5) = 12 / 6 = 2
This means for each second that passes, the cat is 2 feet further away from the dog. Next, we use one of the points and the slope to write the equation in point-slope form. Using the point (5, 16) we have:
y - 16 = 2(x - 5)
Expanding and simplifying this equation gives us:
y = 2x + 6
This is the linear equation that describes the distance of the cat from the dog over time. To draw a graph, we plot the two points given and draw the line that passes through them, which will represent the cat's path. The slope of 2 indicates that for every 1 second, the distance increases by 2 feet.
A student spends 2200 dollars during one semester of college. They spend 325 on books. What percentage was spent on books
Answers
Answer:
Step-by-step explanation:
percentage spent on books = (325/2200) * 100
= 325/22 = 14.77%
Prove that ABCD is a square if a A(1,3) B(2,0) C(5,1) and D(4,4)
Answers
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Step-by-step explanation:
To prove ABCD a square we have to find the lengths of each side
So,
the distance formula will be used to find the lengths
The distance formula is:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now,
[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
we can see that
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Keywords: Distance formula, square
Learn more about coordinate geometry at:
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What did Tarzan like to play?
Answers
Answer:
Step-by-step explanation:
Tell whether the sequence is arithmetic. If it is, what is the common difference? -19,-11,-3,5,...
Answers
Every next number is incremented by 8 from the previous number hence the sequence is arithmetic and the common difference is 8.
Hope this helps.
Answer:
The given sequence is arithmetic and common difference is 8.
Step-by-step explanation:
Given that :
- 19, - 11, - 3, 5......
Here, a = - 19 ; a is the first term of the series.
Now, For common difference-
d = [tex]t_{2} - t_{1}[/tex] = [tex]t_{3} - t_{2}[/tex] = [tex]t_{4} - t_{3}[/tex]
Let [tex]t_{1} = - 19, t_{2} = - 11[/tex]
d = - 11 - (-19)
= -11 + 19
= 8
Let [tex]t_{3} = - 3, t_{2} = - 11[/tex]
d = - 3 -(-11)
= - 3 + 11
= 8
Let [tex]t_{4} = 5, t_{3} = - 3[/tex]
d = 5 - (-3)
= 8
In each condition common difference d is same therefore the given sequence is arithmetic and common difference d = 8.
Find the product
(-3)(8)
Answers
Answer:
-24
Step-by-step explanation:
This is a simple multiplication problem. 8 times 3 is 24, and since one of the numbers is negative, the product (answer in multiplication) will be negative.
In multiplication and division of integers (positive and negative numbers), if the numbers have the same signs, the answer is ALWAYS positive, and if the numbers have different signs, the answer is ALWAYS negative.
Answer: -24
Step-by-step explanation: To multiply (-3)(8), it is important to understand that a negative times a positive is a negative so (-3)(8) is -24.
Plz help me this isn’t that hard but I’m struggling so plz I don’t want another detention
Answers
Answer:
The length of the total 8 pieces in 0.8 meters = 6.4 meters
How many pieces there are in the remaining 0.4 meter = 6.5
Step-by-step explanation:
0.8 x 8 = 6.4
9 meters - 6.4 meters = the remaining 2.6 meters
2.6 x 0.4 = 6 1/2 pieces of ribbon in 0.4 meters.
Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]
[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]
-3x+7y=5x+2y−3x+7y=5x+2yminus, 3, x, plus, 7, y, equals, 5, x, plus, 2, y
Complete the missing value in the solution to the equation.
(-5,(−5,left parenthesis, minus, 5, comma
))
Answers
Answer:
The complete missing value in the solution to the equation is (-5,-8).
Step-by-step explanation:
Consider the provided equation.
[tex]-3x+7y=5x+2y[/tex]
We need to find the missing value of the coordinate; (-5__)
To find the missing value substitute x = -5 in above equation.
[tex]-3(-5)+7y=5(-5)+2y[/tex]
[tex]15+7y=-25+2y[/tex]
[tex]7y-2y=-25-15[/tex]
[tex]5y=-40[/tex]
[tex]y=-8[/tex]
Hence, the missing value is -8.
Thus, the complete missing value in the solution to the equation is (-5,-8).
Answer:
Step-by-step explanation:
-5, -8
a certain triangle has two 45 degree angles what type of triangle is it
Answers
Answer:
most likely isosceles
Step-by-step explanation:
due to the fact that two angles are congruent and the other angle is probably not it would make it all isosceles triangle
A triangle with two 45-degree angles is a special type of triangle known as an isosceles triangle.
In a triangle, if two angles are congruent, then the opposite sides of those angles are also congruent. In an isosceles triangle, two sides are equal in length, and the angles opposite those sides are congruent. Since two angles of the triangle are 45 degrees each, their opposite sides are also equal in length, making it an isosceles triangle.
The diameter of a circle is 4 cm. Which equation can be used to find its circumference?
OC = T2
OC= Tx4
4
Answers
Answer: OC = πx4
Step-by-step explanation:
This question is incomplete, the correct question is
The diameter of a circle is 4 cm. Which equation can be used to find its circumference?
OC = πx2
OC= πx4
4
Answer,
Since the diameter is given as 4cm
Also,
The circumference of a circle OC = π x diameter
Therefore, OC = πx4
Select the correct answer from each drop-down menu.
A 4
7
15
B 15
4
7
C 15
7
4
Answers
Answer: The correct answer is: [C]: " [tex]15^{(7/4)}[/tex] " .
____________________________________
Step-by-step explanation:
____________________________________
Note the property for square roots in exponential form:
_____________________________________
→ [tex]\sqrt[a]{(b)^ c}[/tex] ; ↔ b[tex]b^{(c/a)}[/tex] ;
{ [tex]a\neq 0[/tex] ; [tex][a^{(b/c)}]\neq 0[/tex] ; [tex]c\neq 0[/tex] .}.
_____________________________________
As such, given:
→ [tex]\sqrt[4]{(15^7)}[/tex] ;
a = 15, b = 7, c = 4 .
→ [tex]\sqrt[4]{(15^7)}[/tex] ; ↔ [tex]15^{(7/4)}[/tex] ;
→ which corresponds to:
_____________________________________
Answer choice: [C]: " [tex]15^{(7/4)}[/tex] " .
_____________________________________
Hope this helps!
Wishing you well in your academic endeavors!
_____________________________________
when a positive number is multiplied by itself, the result is equal to 3 more than twice the original amount. What is the value of that number?
Answers
Hope it helps u..........
Evaluate f(1) using substitution:
f(x) =2x^3 -3x^2-18x+8
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Substitute 1 in everywhere you see 'x'
2(1)^3 - 3(1)^2 - 18(1) + 8
Solve:
f(1) = -11
Have A Nice Day ❤
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Final answer:
To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.
Explanation:
The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.
So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.
Thus, f(1) evaluates to -11.
evaluate 81/36 x^2 - y^2/25
Answers
Answer:
Step-by-step explanation:
Final answer:
To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Explanation:
The given expression is:
[tex]81/36 * x^2 - y^2/25[/tex]
To simplify this expression:
Multiply 81/36 which equals 9/4.
Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.
Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Solve the following system of equations.
3x + 2y - 5 = 0
x = y + 10
Make sure there are NO SPACES in your answer. Include a comma in your answer.
ANSWER: {(
)}
Answers
Answer:
The solution is the point (5,-5)
Step-by-step explanation:
we have
[tex]3x + 2y - 5 = 0[/tex] -----> equation A
[tex]x = y + 10[/tex] -----> equation B
Solve the system by substitution
substitute equation B in equation A
[tex]3(y+10) + 2y - 5 = 0[/tex]
solve for y
[tex]3y+30 + 2y - 5 = 0[/tex]
[tex]5y=-25[/tex]
[tex]y=-5[/tex]
Find the value of x
[tex]x=5+ 10[/tex]
[tex]x=5[/tex]
therefore
The solution is the point (5,-5)
A man gained rs. 3000 by selling a mobile set allowing 15 % discount on the marked price the loss would be rs. 8000. Find the marked price and cost price of a mobile set
Answers
Answer:
Marked price is Rs. 53333.33 and the cost price is Rs. 42333.33.
Step-by-step explanation:
Let Rs. x and Rs. y are the cost price and marked price of the mobile set respectively.
Now, the man has a loss of Rs. 8000 after giving a 15% discount on the marked price.
Therefore, 15% of y is 8000 i.e. [tex]8000 = \frac{y\times 15}{100}[/tex]
⇒ y = Rs. 53333.33
Now, the man gained Rs. 3000 by selling the mobile set allowing 15% discount on the marked price.
Therefore, the mobile set has the cost price = x = Rs. [(53333.33 - 8000) - 3000] = Rs. 42333.33 (Answer)