Answer:
C. (4y -1)(3y+2)
Step-by-step explanation:
12 y^2 + 5 y - 2
12 y^2 + (-3+8) y - 2
12 y^2 - 3y + 8y - 2
3y(4y-1)+2(4y-1)
(4y-1)(3y+2)
Which of these sentences is always true for a parallelogram? A. All sides are congruent.
B. All angles are congruent.
C. The diagonals are congruent.
D. Opposite angles are congruent.
Answer:
The correct option is D.
Step-by-step explanation:
A paralellogram is a flat shape with 4 straight sides and opposite sides are parallel.
There are six important properties of a parallelogram.
1) Opposite sides are congruent.
2) Opposite angels are congruent.
3) Consecutive angles are supplementary.
4) If one angle is right, then all angles are right.
5) The diagonals of a parallelogram bisect each other....
Answer:
its D
Step-by-step explanation:
please
simplify 7^6 √ 7^2
Answer:
Step-by-step explanation:
The tough part of this question is figuring out what to do with √(7^2). You could do it by expanding the square. √(7^2) = √49
Now what is the square root of 49? Is it not 7?
√49 = 7
7^6 * 7^1
7 ^(6 + 1)
7 ^ 7
Answer:
49
Step-by-step explanation:
PLS ANSWER THESE QUESTIONS. I WILL GIVE 20 POINTS AD BRAINLIEST.
1. Write an expression to represent the sum of three consecutive even numbers. Let x equal the first number.
2. Find the circumference of a circle that has a diameter of 1 4/5 inches. Use 22/7 for pi.
3. Divide. Write the quotient in simplest form. 1/7 divided by -2/7 = ?
THANK YOU
Answer:
1. 3x + 6
2. [tex]\frac{99}{14}[/tex] or 7.071
3. [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
1. 3 consecutive even integers
If the first is x, the 2nd is x+2, and the 3rd is x+4
x + (x+2) + (x+4)
= 3x + 6
2. The equation for circumference is
[tex]C=2\pi r[/tex]
If the diameter is [tex]1\frac{4}{5} = \frac{9}{5}[/tex]
The the radius is half of that.
So the circumference is
[tex]\pi * \frac{9}{4} *\frac{1}{2} * 2\\= \pi * \frac{9}{4}\\=\frac{22}{7} * \frac{9}{4}\\= \frac{198}{28}\\ =\frac{99}{14} \\=7.071[/tex]
3. To divide we multiply by the reciprocal. So flip the fraction that we are dividing by.
[tex]\frac{1}{7} / -\frac{2}{7}\\ = \frac{1}{7} * -\frac{7}{2} \\= -\frac{1}{2}[/tex]
the rational roots of a polynomial function f(x) can be written in the form p/q where p is a factor of the leading corfficient of the polynomial and q is a factor of the constant term true or false
False.
The Rational Root theorem states that P is a factor of the constant term and q is a factor of the leading coefficient.
(6x^2-2x)+(5x-7)
Add and/or simply
Answer:
6x^2 + 3x - 7.
Step-by-step explanation:
(6x^2 - 2x) + (5x - 7)
= 6x^2 - 2x + 5x - 7 Adding like terms we get:
6x^2 + 3x - 7.
Final answer:
To simplify the algebraic expressions (6x²-2x)+(5x-7), you combine like terms to get the final expression 6x² + 3x - 7.
Explanation:
The student's question involves adding and simplifying algebraic expressions. To add the expressions (6x²-2x)+(5x-7), you need to combine like terms. Like terms are those terms that contain the same variable raised to the same power. Here is the process step-by-step:
Identify like terms in both expressions.Combine like terms by adding their coefficients. For the terms, 6x² and 0x² (the second expression doesn't have an x² term, so it's 0x²), add 6 + 0 = 6. For the terms -2x and 5x, add -2 + 5 = 3.Finally, the constant terms -7 and 0 (again, no constant term in the first expression) are combined by adding -7 + 0 = -7.The resulting simplified expression is 6x² + 3x - 7.
What is the solution to the equation ? 1/2n =8 ? = 4 n = 6 n = 10 n = 16
Answer:
n = 16
Step-by-step explanation:
1/2 n = 8 (multiply both sides by 2)
(1/2) (2) n = 8 (2)
n = 8 (2)
n = 16
What is the length of the side of a right triangle that has a side length of 12 ft and hypotenuse that measures 15 ft
Answer:
9 ft
Step-by-step explanation:
The Pythagorean theorem states
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
Substituting in what we know (one leg is 12 and the hypotenuse is 15)
12^2 +b^2 = 15^2
144+ b^2 = 225
Subtract 144 from each side
144-144 +b^2 = 225-144
b^2 =81
Take the square root of each side
sqrt(b^2) = sqrt(81)
b = 9
What is cos -1 ( -1/2) in quadrant 1 ?
Answer:
[tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
So here they are asking for one angle that gives you the cosine value is equal to -1/2 while being in quadrant 2.
So you look in quadrant 2 and find x=-1/2 which is at [tex]\frac{2\pi}{3}[/tex].
[tex]\cos^{-1}(\frac{-1}{2})=\frac{2\pi}{3}[/tex] while being in quadrant 2.
consider the polynomial p(x)=32x^5y-2xy^5
part a: What is the complete factorization of p(x)=32x^5y-2x^5 over the integers?
part b: what methods are used to factor p(x)=32x^5y^5?
Select 1 answer for a and one for b.
a- 2xy(2x-y)^2 (2x+y)^2
a-2xy(2x-y)(2x+y)(4x^2+y^2
a-2xy(4x^2-y^2)(x^4-4x^2y^2+y^4
b-repeated differences of squares
b- difference of cubes
b-greatest common factor
b-grouping
Answer:
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²) ⇒ 2nd answer
b- repeated differences of squares ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
∵ p(x) = 32x^5y - 2xy^5
- The coefficients of the two terms are 32 and 2
∵ 2 is a common factor in 32 and 2
∵ 32 ÷ 2 = 16 and 2 ÷ 2 = 1
∴ p(x) = 2(16x^5y - xy^5)
* Now lets find the common factors of the variables x and y
∵ The common factor is x^5 and x is x
∵ The common factor in y and y^5 is y
∴ the common factors in 16x^5y - xy^5 are xy
∵ 16x^5y ÷ xy = 16x^4
∵ xy^5 ÷ xy = y^4
∴ p(x) = 2xy(16x^4 - y^4)
- Remember that a² - b² is called difference of two squares we
factorize it by distributed into two polynomials have same terms
with different middle sign (a + b)(a - b)
∵ 16x^4 - y^4 is a different of two squares because √(16x^4) = 4x²
and √9y^4) = y²
∴ The factorization of 16x^4 - y^4 is (4x² + y²)(4x² - y²)
∴ p(x) = 2xy[(4x² + y²)(4x² - y²)]
- The bracket 4x² - y² is also different of two squares because
√(4x²) = 2x and √(y²) = y
∴ The factorization of 4x² - y² is (2x - y)(2x + y)
∴ p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
b- The methods used to factor p(x) are:
greatest common factor and repeated differences of squares
- But you ask to chose one answer of b so chose repeated
differences of squares
Find four consecutive even integers with a sum of -52
Final answer:
To find four consecutive even integers with a sum of -52, we denote the smallest integer as x and use the equation x + (x+2) + (x+4) + (x+6) = -52 to find that these integers are -16, -14, -12, and -10.
Explanation:
To find four consecutive even integers with a sum of -52, let's denote the smallest of these integers as x. Consequently, the next three integers can be represented as x+2, x+4, and x+6. The sum of these four integers can be expressed as the equation x + (x+2) + (x+4) + (x+6) = -52.
Combining like terms gives us 4x + 12 = -52. Subtracting 12 from both sides gives 4x = -64, and dividing both sides by 4 yields x = -16. Therefore, the four consecutive even integers are -16, -14, -12, and -10.
The four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.
Let's denote the four consecutive even integers as [tex]\( x \), \( x+2 \), \( x+4 \), and \( x+6 \)[/tex].
According to the problem, their sum is -52. So, we can set up the equation:
[tex]\[ x + (x + 2) + (x + 4) + (x + 6) = -52 \][/tex]
Now, let's solve for \( x \):
[tex]\[ 4x + 12 = -52 \][/tex]
Subtract 12 from both sides:
[tex]\[ 4x = -52 - 12 \][/tex]
[tex]\[ 4x = -64 \][/tex]
Divide both sides by 4:
[tex]\[ x = \frac{-64}{4} \][/tex]
[tex]\[ x = -16 \][/tex]
Now that we've found the value of \( x \), we can find the consecutive even integers:
- First even integer: [tex]\( x = -16 \)[/tex]
- Second even integer: [tex]\( x + 2 = -16 + 2 = -14 \)[/tex]
- Third even integer: [tex]\( x + 4 = -16 + 4 = -12 \)[/tex]
- Fourth even integer: [tex]\( x + 6 = -16 + 6 = -10 \)[/tex]
So, the four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.
complete question given below:
Find four consecutive even integers with a sum of -52.Find the four integeres
What is the solution to the equation? 305p equals 1,525
Answer:
Step-by-step explanation:
305p=1,525
305 305
p=5
The solution of the linear equation 305p = 1525 will be 5.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear equation with one variable is given below.
305p = 1525
On simplifying, we have
305p = 1525
p = 1525 / 305
p = 5
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Which point is on the graph of f(x) = 3 • 4x? A. (0, 12) B. (0, 0) C. (1, 12) D. (12, 1)
Answer:
(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].
Please correct if I'm wrong about your expression.
Step-by-step explanation:
I think you mean [tex]f(x)=3 \cdot 4^x[/tex].
Let's test the point and see.
A. (0,12)?
(0,12)=(x,y)
What happens when x equals 0? Is the result 12?
[tex]3 \cdot 4^0[/tex]
[tex]3 \cdot 1[/tex]
[tex]3(1)[/tex]
[tex]3[/tex]
Yep that isn't 12 so (0,12) is not on the graph of f.
B. (0,0)?
(0,0)=(x,y)
What happens when x equals 0? Is the result 0?
[tex]3 \cdot 4^0[/tex]
We already this and got 3 so (0,0) is not on the graph of f.
C. (1,12)?
(1,12)=(1,12)
What happens when x equals 1? Is the result 12?
[tex]3 \cdot 4^1[/tex]
[tex]3 \cdot 4[/tex]
[tex]12[/tex]
The result is 12 so (1,12) is on the graph of f.
C. (12,1)
(12,1)=(x,y)
What happens when x equals 12? Is the result 1?
[tex]3 \cdot 4^{12}[/tex]
This will result in a really big number that isn't 1 so (12,1) is not on the graph of f.
(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].
Answer:
(1,12)
Step-by-step explanation:
ape x
Select the expressions that are equivalent to 6r + 5r.
For this case we have the following expression:
[tex]6r + 5r[/tex]
We can rewrite the expression in different ways.
Form 1:
Adding similar terms:
[tex]6r + 5r = 11r[/tex]
Form 2:
Making common factor we have:
[tex]6r + 5r = (6 + 5) r[/tex]
Answer:
Some equivalent expressions are given by:
[tex]6r + 5r = 11r\\6r + 5r = (6 + 5) r[/tex]
The expression 6r + 5r simplifies to 11r by combining like terms. In this case, the 'like term' is 'r'. When we add the coefficients of the like terms, we get 11r.
Explanation:The student's question involves simplifying the expression 6r + 5r. This is an addition problem in algebra where we are adding like terms. Like terms are terms in an algebraic expression that has the exact same variable(s) to the same power(s). In the given expression '6r + 5r', the like terms are '6r' and '5r' because they both have the same variable 'r'.
To simplify, we add the coefficients of the like terms. The coefficient of 'r' in '6r' is 6 and in '5r' is 5. When we add 6 and 5, we get 11. Therefore, the equivalent expression of '6r + 5r' is '11r'.
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The sum of two numbers is 10 the larger number is four times the smaller number this is the system of equations used to represent the scenario is Y equals negative X +10 and Y equals 4X what is the larger number
Answer:
The larger number is 8
Step-by-step explanation:
Let
x -----> the smaller number
y ----> the larger number
we know that
x+y=10
y=10-x -----> equation A
y=4x -----> equation B
Solve by substitution
substitute equation B in equation A and solve for x
4x=10-x
4x+x=10
5x=10
x=2
Find the value of y
y=4x-------> y=4(2)=8
therefore
The smaller number is 2 and the larger number is 8
To find the larger number where the sum of two numbers is 10 and the larger is four times the smaller, the system of equations y = -x + 10 and y = 4x is used, and through solving, the larger number is determined to be 8.
The question entails finding the larger number when two numbers sum to 10, and the larger number is four times the smaller number. The system of equations representing the scenario is y = -x + 10 and y = 4x. To find the larger number, set these two equations equal to each other since they both equal y:
4x = -x + 10
Now, solve for x by adding x to both sides:
5x = 10
Then, divide both sides by 5:
x = 2
Since x is the smaller number, and y is four times larger, compute y:
y = 4x = 4(2) = 8
The larger number (y) in this case is 8.
What is the common difference or common ratio of the sequence 2,5,8,11...? A. 1 B. 3 C. 5 D. 7
Answer:
B. 3
Step-by-step explanation:
A common difference in an arithmetic sequence is the value the terms in the sequence vary from one to another.You can find one term to another by adding or subtracting the common difference.
In this case, the terms are 2,5,8,11,.....
From the first term to the second term, the difference is, 5-2=3
From the second term to the third term, the difference is, 8-5=3
From the third term to the fourth term the difference is=11-8=3
Hence the common difference in this arithmetic sequence is 3
[tex]\huge{\text{Hey there!}}[/tex]
[tex]\huge\text{We could use the word {difference} in this equation}[/tex]
[tex]\huge\text{The\ difference usually means subtract in math}}[/tex] [tex]\huge\text{terms!}[/tex]
[tex]\huge{\text{So, we subtract the terms to find your answer!}}[/tex]
[tex]\huge\text{5 - 2 = 3. So we know that 3 could be a possible}[/tex] [tex]\huge\text{answer.}[/tex]
[tex]\huge\text{11 - 8 = 3 }[/tex]
[tex]\huge\rightarrow\text{8 - 5 = 3}[/tex]
[tex]\huge\text{The ratio difference = 3!}[/tex]
[tex]\boxed{\boxed{\huge{\text{Answer: B. 3}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:}[/tex]
Which of the following would be the most logical first step to solving this
quadratic equation?
x2 - 4x + 16 = 2
A. Take the square root of both sides.
B. Subtract 2 from both sides.
ESTATE
C. Factor the left side into a perfect square.
D. Divide both sides by x
Answer:
The correct option is B:
Subtract 2 from both sides
Step-by-step explanation:
We have the equation x²-4x+16=2
The first step to solve this equation is:
Subtract 2 from both sides
We get;
x²-4x+16=2
x²-4x+16-2=2-2
x²-4x+14=0
Now this is the quadratic equation. You can use quadratic formula to solve this equation....
Find the range of 2,7,3.1,4.2,1.9,2.4,and 2.7
Answer:2244.23136
Step-by-step explanation:
The range is the difference between the highest term and the lowest term.
The range of the numbers is 1.1.
GivenThe numbers are 2, 7, 3.1, 4.2, 1.9, 2.4, and 2.7.
What is the range?
The range is the difference between the highest term and the lowest term.
[tex]\rm Range = Highest \ Term - Lowest \ Term[/tex]
Here, the highest term in the numbers = 3.1
And the lowest term = 2
Therefore,
The range is given by,
[tex]\rm Range = Highest \ Term - Lowest \ Term\\\\Range = 3.1-2\\\\Range = 1.1[/tex]
Hence, the range of the numbers is 1.1.
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Factor the polynomial completely.
Find a GCF: –2x2 + 2 + 5x3 – 5x
GCF = –2 GCF = 5x
Factor out the GCF: –2(x2 – 1) + 5x(x2 – 1)
Which product of prime polynomials is equivalent to the original polynomial?
(–2 – 5x)(x2 – 1)
(–2 + 5x)(x2 – 1)
(–2 – 5x)(x – 1)(x + 1)
(–2 + 5x)(x – 1)(x + 1)
Answer:
Option D is correct
Step-by-step explanation:
The original polynomial is:
–2x2 + 2 + 5x3 – 5x
Arranging in decreasing power of x:
[tex]5x^3 - 2x^2 -5x+2[/tex]
Factoring the given polynomial by grouping:
[tex]5x^3 - 2x^2 -5x+2\\=5x^3-5x- 2x^2+2\\=5x(x^2-1)-2(x^2-1)\\=(5x-2)(x^2-1)[/tex]
Now, (x^2-1) can be further solved using formula:
(a^2-b^2)=(a-b)(a+b)
Solving:
[tex]=(5x-2)(x^2-1)\\=(5x-2)(x-1)(x+1)[/tex]
So, [tex](5x-2)(x-1)(x+1)[/tex] represents the factors of [tex]-2x2 + 2 + 5x3-5x[/tex]
Hence Option D is correct.
Answer: the answer is D
Step-by-step explanation:
the screen has proof it is correct... also please STOP deleting my answers its all ways the same person and its getting really annoying when im giving you the correct answer, im just trying to help :(
Edgar accumulated $5,000 in credit card debt. If the interest is 20% per year and he does not make any payment for 2 years. How much will he owe on this debt in 2 years by compounding continously?
Answer:
$7,434.57
knewton alta 2023
Step-by-step explanation:
Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.
Explanation:To calculate the amount Edgar will owe on his credit card debt in 2 years with continuous compounding, we can use the formula for compound interest:
A = P*e^(rt)
Where:
A is the final amountP is the initial principal (the amount Edgar owes)e is Euler's number (approximately equal to 2.71828)r is the interest rate per year in decimal formt is the time in yearsPlugging in the values, we have:
A = $5,000 * e^(0.20*2)
Calculating this expression gives the approximate value of $6,360.92. Therefore, Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.
Solve y over negative 2 + 5 = 13
Answer: y=-16
Step-by-step explanation:
Y/-2+5=13
Y/-2=8
Y=-16
Plutonium-240 decays according to the function L where o
represents the quantity remaining after t years and k is the decay constant,
0.00011... How long will it take 24 grams of plutonium-240 to decay to 20
grams?
Answer:
[tex]\boxed{\textbf{1700 yr}}[/tex]
Step-by-step explanation:
[tex]-\dfrac{\text{d}L}{\text{d}t} = kL\\\\\dfrac{dL}{L}=-kdt\\\\\ln L = -kt + C\\\text{At t = 0, L = L$_{0}$, so C = $\ln L_{0}$}\\\ln L = -kt + \ln L_{0}\\\ln L_{0} - \ln L = kt\\\\\ln \dfrac{L_{0}}{L} =kt[/tex]
Data:
L₀ = 24 g
L = 20 g
k = 0.000 11 yr⁻¹
Calculation:
[tex]\ln \dfrac{24}{20} =0.000 11t\\\\\ln 1.2 = 0.000 11t\\\\0.1823 = 0.000 11t\\\\t = \dfrac{0.1823}{0.000 11} = \textbf{1700 yr}\\\\\text{It will take } \boxed{\textbf{1700 yr}}\text{ for the polonium to decay to 20 g}[/tex]
What is the measure of angle ABC in the circle shown in the picture?
Answer:
45°
Step-by-step explanation:
I think you meant m<ACB, and from what I see here, I took half of 90°, which is 45°.
The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?\
Answer:
The rate of change determines the average speed of the ball when it is dropped from the building.
Step-by-step explanation:
d(t) = 16t^2
when t = 2
d(t) = 16 (2)²
d(t) = 64
when t = 5
d(t) = 16 (5)²
d(t) = 400
Average speed/rate of change = distance/time = 64/2 = 32 feet
Average speed/rate of change = distance/time = 400/5 = 80 feet
The rate of change determines the average speed of the ball when it is dropped from the building.
!!
The average rate of change of d(t) from [tex]\( t = 2 \) to \( t = 5 \)[/tex] represents that the ball traveled at an average rate of 112 feet per second during this time interval.
The average rate of change of a function over a given interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing by the difference in the independent variable values. In this case, we want to find the average rate of change of the function [tex]\( d(t) = 16t^2 \) from \( t = 2 \) to \( t = 5 \).[/tex]
First, we find the values of the function at the endpoints of the interval:
- At [tex]\( t = 2 \), \( d(2) = 16(2)^2 = 64 \)[/tex] feet.
- At [tex]\( t = 5 \), \( d(5) = 16(5)^2 = 400 \)[/tex] feet.
Then, we calculate the difference in the function values:
[tex]\[ \text{Difference in } d(t) = d(5) - d(2) = 400 - 64 = 336 \text{ feet} \][/tex]
Next, we calculate the difference in the independent variable values:
[tex]\[ \text{Difference in } t = 5 - 2 = 3 \text{ seconds} \][/tex]
Finally, we find the average rate of change by dividing the difference in d(t) by the difference in t:
[tex]\[ \text{Average rate of change} = \frac{\text{Difference in } d(t)}{\text{Difference in } t} = \frac{336}{3} = 112 \text{ feet/second} \][/tex]
what are terms? how do you combine them? can you give me an example?
A term is any number, variable or combination of a number and a variable in an equation.
Examples:
In 2x + 5y + 8, 2x is one term, 5y is a second term and 8 is a 3rd term.
In the equation 2x + 3 + 5x -2
Combine the like terms 2x and 5x are like terms because they both have x as a variable, there is a plus sign in fron of the 5x, so you would have 2x +5x = 7x
Then 3 and 3 are like terms, because they are just numbers, there is a subtraction sign in front of the 2, so you have 3-2 = 1
The equation then becomes: 2x + 3 + 5x -2 : 7x + 1
Which shows a perfect square trinomial?
502-4x2
100-36x?y
16x2+24 xy +9y2
49x2 - 70 xy +10y
Answer:
Third choice.
Step-by-step explanation:
Trinomial means you have 3 terms.
You don't have 3 terms in first two choices so let's not look at them.
Anything of the form [tex]a^2x^2+2abxy+ b^2y^2[/tex] is a perfect square trinomial because it can be written as [tex](ax+by)^2[/tex].
Let's this this:
[tex](ax+by)^2[/tex]
[tex](ax+by)(ax+by)[/tex]
Now foil!
First=ax(ax)=a^2x^2
Outer=ax*by=abxy
Inner=by*ax=abxy
Last=by*by=b^2y^2
Add together and this gives you a^2x^2+2abxy+b^2y^2.
So looking at third choice you can write it as 4^2x^2+24xy+3^2y^2.
Is 2*4*3 equal to 24? If it is then you have your answer. It is.
We have our answer.
Neeeed help noww please
Answer:
6
Step-by-step explanation:
f(n+1) = f(n) -2
We know f(1) = 10
Let n=1
f(1+1) = f(1) -2
f(2) = 10-2 =8
We now know f(2)
Let n=2
f(2+1) = f(2)-2
f(3) = 8 -2=6
f(3) =6
The system of equations 3x – 6y = 20 and 2x – 4y = 3 is
A. consistent.
B. inconsistent.
C. independent.
D. dependent.
Answer:
The system is inconsistent because there is no solution.
Step-by-step explanation:
I'm going to put both of these in slope-intercept form (y=mx+b where m is slope and b is y-intercept).
3x-6y=20
Solve for y.
3x-6y=20
Subtract 3x on both sides:
-6y=-3x+20
Divide both sides by -6:
y=(-3/-6)x+(20/-6)
Reduce:
y=(1/2)x+(-10/3)
The slope is 1/2 and the y-intercept is -10/3.
2x-4y=3
Solve for y.
2x-4y=3
Subtract 2x on both sides:
-4y=-2x+3
Divide both sides by -4:
y=(-2/-4)x+(3/-4)
Reduce:
y=(1/2)x+(-3/4)
The slope is 1/2 and the y-intercept is -3/4.
The lines are parallel so they have no intersection. I know they are parallel because they have the same slope and different y-intercept.
The system is inconsistent because there is no solution.
Answer:
B) Inconsistent
Step-by-step explanation:
Step 1: Write both equations
3x - 6y = 20
2x - 4y = 3
Step 2: Find x in terms of y
3x - 6y = 20
x = 20+6y/3
Step 3: Substitute x in one of the equations to find y
2x - 4y = 3
2(20+6y/3) - 5y = 3
40 + 12y - 12y = 9
0 ≠ -31
Therefore, these system of equations have no solution.
Step 4: Choose the option
A) consistent- A consistent system of equations has at least one set of equations. Therefore, this option is incorrect.
B) inconsistent- An inconsistent system of equations has no solution. Therefore, this option is correct.
C) Independent- An independent system of equations has one solution. Therefore, this option is incorrect.
D) Dependent- A dependent system of equations have infinite solutions. Therefore, this option is incorrect.
Option B is the right answer
!!
Terry has 2 more quarters than fines and has a total of $6.80. How many quarters and dimes does Terry have?
Answer:
Terry has 20 quarters and 18 dimes
Step-by-step explanation:
Let
x -----> the number of quarters
y ----> the number of dimes
Remember that
1 quarter=$0.25
1 dime=$0.10
we know that
x=y+2 ----> equation A
0.25x+0.10y=6.80 -----> equation B
Substitute equation A in equation B and solve for y
0.25(y+2)+0.10y=6.80
0.25y+0.50+0.10y=6.80
0.25y+0.10y=6.80-0.50
0.35y=6.30
y=18 dimes
Find the value of x
x=y+2 -----> x=18+2=20 quarters
therefore
Terry has 20 quarters and 18 dimes
To determine the number of quarters and dimes Terry has, set up two equations based on the information provided, solve one of the equations for one variable, and substitute this into the second equation. Solve the equation to get the number of dimes and substitute it into the first equation to get the number of quarters.
Explanation:To solve this, we can use algebra, setting up equations to represent the problem and then solve it.
Let F represent the number of dimes (since a dime is worth $0.10) and let Q represent the number of quarters (since a quarter is worth $0.25). We have two key pieces of information:
Terry has 2 more quarters than dimes: Q = F + 2The total amount of money Terry has equals $6.80: 0.10F + 0.25Q = 6.80From the first equation, we can substitute F + 2 for Q in the second equation: 0.10F + 0.25(F + 2) = 6.80.
Solve this equation to find the value of F, representing the number of dimes, Terry has. Then, substitute the value of F into the first equation to determine the number of quarters Terry has.
Learn more about Algebra here:https://brainly.com/question/24875240
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If y = x+ 5 were changed to y = x + 9, how would the graph of the new
function compare with the first one?
O
A. It would be shifted down.
O
B. It would be shifted up.
O
C. It would be shifted right.
O
D. It would be steeper.
Answer: B. It would be shifted up.
Step-by-step explanation: We are changing the last number only. This number determines where the y-intercept is, which is on the vertical axis. Since the number increases by 4, the y-intercept would be shifted up by 4, without changing the slope. Therefore, the answer would be B. It would be shifted up.
Find the measure of the third angle of a triangle given that the first two angles are 44º and 72º.
Show your work.
The sum of the three angles of a triangle need to equal 180
To find the third angle subtract the two known angles from 180.
Third angle = 180 - 44 - 72 = 64 degrees.
Answer:
All angles of a triangle add up to 180. Just subtract. -72 --> 108 - 44. 64