The function is f (x) = 3/4 x - 1.
What is Linear equation?
A linear equation is an algebraic equation with slope m is defined as,
y = mx + b
Where, b is the y - intercept.
Given that;
Slope of function (m) = 3/4
f (-12) = -10
Now,
A linear equation with slope m is defined as,
f (x) = mx + b
Substitute m = 3/4,
f (x) = 3/4 x + b
Apply the condition f (-12) = -10 we get,
f (-12) = 3/4 * (-12) + b
- 10 = 3 * (-3) + b
- 10 = - 9 + b
b = - 10 + 9
b = - 1
Substitute value of m and b in linear equation we get;
The function is,
⇒ f (x) = 3/4 x - 1.
Hence, The function is f (x) = 3/4 x - 1.
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Solving a Real-World Problem Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?
Answer:4/ 1/5=20 or 4/.20=20
Step-by-step explanation: brainliest?
help plsssssssssss tyyy
Answer:
Associative property of addition!
Step-by-step explanation:
You have to add the numbers a lot!!
Commutative property is the answer Bec of addition says that the change in order of numbers in addition will not change the result.
Therefore, for variable x and y the commutative property of addition is x+y=y+x.
Please helpppppp now ASAP
Answer:
units 6.0 I think good luck brother
James is looking at rectangular pools. He wants to calculate the volume of water in each pool.
Which pool will hold more water: a pool with dimensions 6 feet deep by 11 feet by 11 feet, or a pool with dimensions 2 yards deep by 3 yards by 5 yards?
Responses
The pool with dimensions 6 feet by 11 feet by 11 feet will hold more water.
The pool with dimensions 6 feet by 11 feet by 11 feet will hold more water.
It cannot be determined from the given information.
It cannot be determined from the given information.
Both pools hold the same amount of water.
Both pools hold the same amount of water.
The pool with dimensions 2 yards by 3 yards by 5 yards will hold more water.
The pool with dimensions 2 yards by 3 yards by 5 yards will hold more water.
Answer:
2 yards by 3 yards by 5 yards
Step-by-step explanation:
6 times 11 times 11 = 726
3(2*3*5) = 6*9*15 = 810
*Please mark brainliest answer
What is the equation of the line that passes through the point (3,-7) and has a slope of -2?
Answer:
y=-2x-1
Step-by-step explanation:
y=mx+b
-7=-2(3)+b
-7=-6+b
-1=b
y=-2x-1
Solve each equation. Check for extraneous solutions. 2(x-1)³/₄=16
Answer:
[tex]x = 17[/tex].
Step-by-step explanation:
Simplify the given equation:
[tex]2\, (x - 1)^{3/4} = 16[/tex].
[tex](x - 1)^{3/4} = 8[/tex].
[tex]((x - 1)^{1/4})^{3} = 8[/tex].
Take the cubic root of both sides to eliminate the numerator of the exponent. Only roots of even degree could introduce alternative solutions. Since the degree of this root is an odd number, this step would not create extraneous solutions.
[tex]\sqrt[3]{((x - 1)^{1/4})^{3}} = \sqrt[3]{8}[/tex].
[tex](x - 1)^{1/4} = 2[/tex].
Raise both sides to the fourth power to eliminate the denominator of the exponent:
[tex](x - 1) = 2^{4}[/tex].
[tex]x - 1 = 16[/tex].
[tex]x = 17[/tex].
Substitute the solution [tex]x = 17[/tex] into the equation:
[tex]\begin{aligned}& 2\, (17 - 1)^{3/4} \\ =\; & 2\times (16^{1/4})^{3} \\ =\; & 2 \times 2^{3} \\ =\; & 16\end{aligned}[/tex].
Thus, [tex]x = 17[/tex] isn't an extraneous solution since setting [tex]x[/tex] to [tex]17[/tex] satisfies the original equation.
Could someone help me find how to extract the root from this equation?2y ^ 2 - 8 = 6 - 2y ^ 2
Answer:
y = ± √ 7/2
Step-by-step explanation:
2*y^2-8-(6-2*y^2)=0
(2 • (y2)) - 8) - (6 - 2y2) = 0
(2y2 - 8) - (6 - 2y2) = 0
Pull out like factors :
4y2 - 14 = 2 • (2y2 - 7)
4.2 Factoring: 2y2 - 7
difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
2 • (2y2 - 7) = 0
5.1 Solve : 2 = 0
5.2 Solve : 2y2-7 = 0
Add 7 to both sides of the equation :
2y2 = 7
Divide both sides of the equation by 2:
y2 = 7/2 = 3.500
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
y = ± √ 7/2
Someone that knows algebra 1 please help me
Go ahead and ask the question!! <3
how do you simplify this expression? can you explain it step step by step
Answer:
-4
Step-by-step explanation:
-12+3(-8+(-4)^2-6)+2
first the -4^2
-12+3(-8+16-6)+22
now everything in the parenthesis
-12+3x2+2
now the multiplying.
-12+6+2
now calculate this all together.
-4
Add. Write your answer in scientific notation.
(2.4×10^8) + (4.87×10^8)
Answer: = 7.27 × 108
(scientific notation)
with calculate significant figures = 7.3 × 108
(scientific notation)
Step-by-step explanation: hope this helps
Write the word sentence at an inequality. n plus 3.9 is less than or equal to 16. An inequality is What?
Answer:
n + 3.9 ≤ 16
An inequality is a mathematical expression represented by less than, greater than, or equal to symbols to compare values or to measure and solve complex equations.
Zoe says that 2³.42 can be rewritten as 86. Juana says that it can be rewritten as 85. Danladi says that it cannot be rewritten as either of these expressions. Who is correct? Explain.
Danladi says that it cannot be rewritten as either of these expressions. He is correct.
How to calculate the value?It should be noted that 2³ × 42 will be:
= 2³ × 42
= 8 × 42
= 336
Therefore, Zoe says that 2³.42 can be rewritten as 86 and Juana says that it can be rewritten as.85. They're both wrong.
In the other hand, Danladi says that it cannot be rewritten as either of these expressions. Therefore, he is correct.
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What is the rational expression in simplest form? State any restrictions on the variables.
c. 12-4 x / x²-9}
According to the question, the given rational expression can be simplified which is as shown below:
Rational expression = [tex]\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}[/tex]
For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.
Rational expression = [tex]\frac{-4}{(x+3)}[/tex]
The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.
Therefore, the final expression is [tex]\frac{-4}{(x+3)}[/tex]
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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question in image thank you!
Using proportions, it is found that:
1. a) 1/5 of the marbles are red.
b) 40% of the marbles are yellow.
c) 60% of the marbles are not yellow.
d) 11/20 of the marbles are green or yellow.
2) Event A, B and C are the most likely, each with equal probabilities.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For the first problem, we have that there are 3 + 4 + 5 + 8 = 20 marbles, hence:
a) 4/20 = 1/5 of the marbles are red.
b) 8/20 x 100% = 0.4 x 100% = 40% of the marbles are yellow.
c) 12/20 x 100% = 0.6 x 100% = 60% of the marbles are not yellow.
d) 3 are green and 8 are yellow, hence 11/20 of the marbles are green or yellow.
A die has 6 possible outcomes, numbered 1 to 6, hence the probabilities(number of desired outcomes divided by number of total outcomes) are given as follows:
Event A: 3/6 = 1/2.Event B: 3/6 = 1/2.Event C: 3/6 = 1/2.Event D: 2/6 = 1/3.Event A, B and C are the most likely, each with equal probabilities.
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Find the inverse of each function.
y=log₂2 x
The inverse of the function y = log₂(2x) is f ⁻¹(x) = 2ˣ⁻¹.
Given the function is :y = log₂ 2x
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.
To get x = ay + b from the equation y = ax + b, replace x with y and y with x.
Here, find y and solve for x = ay + b.
Then we get y = (x - b/a).
Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.
now interchange the positions of x and y in the function.
x = log₂ 2y
the next step is to isolate the dependent variables.
f ⁻¹(x) = 2ˣ ⁻ 1
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Solve by factoring. Check your answers. 4 x²=-8 x+5
The factoring of the expression 4 x²=-8 x+5 is (2x-1) (2x+5)
By ordering the values, we get:
4 x² + 8 x - 5
To solve this exercise, we have to follow the rules of factoring:
1. Factor 8 from 8x:
4 x² + 8 x - 5
4 x² + (-2 + 10) x - 5
2. Apply the distributive property:
4 x² - 2x + 10x - 5
3. Groups the first two terms and the last two terms:
(4 x² - 2x) + 10x - 5
4. Factorize the greatest common denominator (GCM) of each group:
2x(2x - 1) + 5(2x-1)
5. Factor the polynomial by factoring the greatest common denominator, (2x-1):
(2x-1) (2x+5)
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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Consider the diagram and proof below.
Given: WXYZ is a parallelogram, ZX ≅ WY
Prove: WXYZ is a rectangle
Parallelogram W X Y Z with diagonals is shown.
Statement
Reason
1. WXYZ is a ▱; ZX ≅ WY 1. given
2. ZY ≅ WX 2. opp. sides of ▱ are ≅
3. YX ≅ YX 3. reflexive
4. △ZYX ≅ △WXY 4. SSS ≅ thm.
5. ∠ZYX ≅ ∠WXY 5. CPCTC
6. m∠ZYX ≅ m∠WXY 6. def. of ≅
7. m∠ZYX + m∠WXY = 180° 7. ?
8. m∠ZYX + m∠ZYX = 180° 8. substitution
9. 2(m∠ZYX) = 180° 9. simplification
10. m∠ZYX = 90° 10. div. prop. of equality
11. WXYZ is a rectangle 11. rectangle ∠ thm.
What is the missing reason in Step 7?
triangle angle sum theorem
quadrilateral angle sum theorem
definition of complementary
consecutive ∠s in a ▱ are supplementary
The missing step 7 in the two column proof is; Consecutive ∠s in a ▱ are supplementary
How to carry out a two column proof?
We are told that WXYZ is a parallelogram in which we have to prove that: WXYZ is a rectangle. The two column proof is as follows;
Statement Reason
1. WXYZ is a parallelogram, 1. Given
ZX ≅WY
2. ZY ≅ WX 2. Opposite sides of parallelogram
are congruent.
3. YX≅YX 3. Reflexive property of congruence
4. ΔZYX ≅ Δ WXY 4. SSS congruence postulate
5. ∠ZYX ≅ ∠WXY 5. CPCTC
6. m∠ZYX ≅ m∠WXY 6. definition of congruence.
7.m∠ZYX + m∠WXY = 180° 7. Consecutive ∠s in a ▱ are
supplementary
8.m∠ZYX + m∠ZYX = 180° 8. By substitution
9. 2(m∠ZYX) = 180° 9. By simplification
10.m∠ZYX = 90° 10. Division property of equality
11. WXYZ is a rectangle 11. Rectangle angle theorem.
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(-9 6) and (0 1) in slope intercept form
what is the exprssion -2 (3x+5) +1+4x written in simplest form
3m^2+2p^2-15 what the answer kinda got stuck
Answer:
212.
Step-by-step explanation:
Given: 3m^2 + 2p^2 - 15
When m = 3 and p = 10
Substituting the values
= 3(3)^2 + 2(10)^2 - 15
By further calculation
= 3(9) + 2(100) - 15
So we get
= 27 + 200 - 15
= 212
Therefore, the value of the expression is 212.
Describe the difference between direct variation and inverse variation.
When two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y, direct variation occurs, whereas indirect or inverse variation occurs when an increase in the value of X results in a decrease in the value of Y and vice versa.
Difference between direct variation and inverse variation:To give the reader a hint, direct variation equations use the same phrase. The phrase is either "directly proportional" or "directly varies." The area of a square, for example, varies directly from the square of its side. Direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y.Inverse variation is a relationship between two variables in which the value of one increases while the value of the other decreases. Indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.
Therefore, direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y whereas indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.
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Expand each logarithm.
log x³ y⁵
The answer to this question is: og(x³y⁵) = 3log(x) + 5log(y)
In mathematics, the logarithm is that the function to exponentiation. which means the logarithm of a given number x is that the exponent to which another fixed number, the base b, must be raised, to supply that number x. within the simplest case, the logarithm counts the amount of occurrences of the identical consider repeated multiplication
To solve this question, we need only 2 identities, i.e.,
log(a*b) = log(a) + log(b) ...(1)
log(aⁿ) = nlog(a) ...(2)
Using 1, we can expand log x³ y⁵ as: log x³ y⁵ = log(x³) + log(y⁵) ...(3)
Using 2, we can expand both the terms as: log(x³) = 3log(x)log(y⁵) = 5log(y)
Putting them in equation 3, we get:3log(x) +5log(y)
Therefore, log(x³y⁵) = 3log(x) + 5log(y)
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HELP MEEE plsssssss
Answer:
18.84 inches
Step-by-step explanation:
Use the formula.
2πr
Use 3.14 for π.
Use 3 for r.
2(3.14)(3)
Multiply.
2(3.14)(3)=18.84
Hope this helps!
Please mark as brainliest if correct!
One half + four fifths vertical
Answer:
1 1/2+4/5 and the vertical would be graphed?
Simplify the expression. (3.65u − 11) − (−5 + 8.7u)
The expression is simplified to -5. 05u - 6
What is an algebraic expression?An algebraic expression can be defined as a mathematical expression made up variables, coefficients, terms, factors and constants.
These algebraic expressions are also made up of arithmetic operations, such as;
AdditionMultiplicationDivisionBracketParenthesesSubstraction, etcFrom the information given, we have the expression;
(3.65u − 11) − (−5 + 8.7u)
Now, expand the bracket, we get;
3. 65u - 11 + 5 - 8. 7u
collect like terms
3. 65u - 8. 7u - 11 + 5
Add/substract the values
-5. 05u - 6
Hence, the expression is -5. 05u - 6
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A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.
A graph titled Customer Rewards. The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11. A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.
Which statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt?
The required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.
What is a statement?
A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11.\
A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.
According to given question we have
In the analysis of the given options, the most likely answer to this question is A rewards customer earns 2 free ounces of yogurt because total amount paid for 10 ounces and 12 ounces is the same.
Also 9 dollars spent at 20 ounces.
Therefore, the required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.
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Answer:
A
Step-by-step explanation:
A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa’s age and her sister’s age? (if you see this question pls answer) ty!
None of these
(x − 4) − x
x − (x − 4)
(x + 4) − x
Answer:
i say it would be "None of these"
Step-by-step explanation:
because say x=sisters age so, x=12 if lisa if 4 years youger, than x-4=8 (x-4)-x=(-2) x-(x-4)=4 (x+4)-x=4 so therefore it would be none.
Answer:
none of these
Step-by-step explanation:
because we don't know her sisters age we'll use "x" and Lisa is 4 years younger so you deduct 4 from x and the equation will be '4-x'
Question 6 (5 points)
(01.04)
Solve the following for y: 2x + 2y = 8 (5 points)
O a
Ob
Oc
Od
y = -x + 4
y = x + 4
y = 3x
y = -3x
We get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.
We are given an equation:
2 x + 2 y = 8
Divide both the sides by 2, we get that:
2 x / 2 + 2 y / 2 = 8 / 2
x + y = 4
Now, we will subtract x from both the sides, so, we get that:
x + y - x = 4 - x
y = 4 - x
Therefore, we get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.
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HELP IMMEDIATELY PLEASE
use the couple of lines for #4
Answer:
#2 Alternate interior angles: 4 & 5 and 3 and 6
#4 :
m∠6 = 55°
m∠3 = 55°
m∠1 = 125°
Reasons: See below
Step-by-step explanation:
Angles 6 and 8 are supplementary angles since they are on the same straight line intersected by another straight line.
So m∠6 + m∠8 = 180
m∠6 + 125 = 180
m∠6 = 180-125= 55°
Angles 3 and 6 are alternate interior angles and equal to each other
m∠3 = m∠6 = 55°
Angles 1 and 3 are supplementary angles whose sum of measures should add up to 180°
m∠1 + m∠3 = 180
m∠1 + 55 = 180
m∠1 = 180-55 = 125°
-8/2x-5/ = 16
slash is absolute value
Answer:
No solution
Step-by-step explanation:
-8l2x -5l =16 When I divide both sides by -8
l2x - 5l = -2
The absolute value cannot equal a negative number.