Answer:
[tex]\frac{XM}{4y}=u[/tex]
Step-by-step explanation:
First, multiply both sides by M.
X M = 4uy
Now, divide both sides by 4y.
[tex]\frac{XM}{4y} =\frac{4uy}{4y}[/tex]
Therefore,
[tex]\frac{XM}{4y}=u[/tex]
If f(x) = -3 and g(x) = 4x² + x − 4, find (ƒ+ g)(x).
Answer:
4x² + x - 7
Step-by-step explanation:
Given f(x) = -3 and g(x) = 4x² + x - 4, solve for (f + g)(x).
Step 1: Replace the function designators with the actual functions in f(x) and g(x); that gives us 4x² + x - 4 - 3.
Step 2: Simplify; that gives us the answer 4x² + x - 7.
Please mark me as Brainliest! Thanks :)Complete the steps to factor the polynomial by grouping. p(x) = x3 5x2 – x – 5 p(x) = x2 (x ) – (x 5) p(x) = (x2 – )(x 5) p(x) = (x – )(x 1)(x )
The polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
The given polynomial to us is p(x) = x³ + 5x² - x - 5.
We are asked to factor the polynomial by grouping.
We can do this by following these steps:
p(x) = x³ + 5x² - x - 5.We group the first two terms and the next two terms to get p(x) = (x³ + 5x²) + (-x -5).Now, we take x² common from the first group and -1 common from the second group to get p(x) = x²(x + 5) -1(x + 5)Now, we take (x + 5) common from both the terms to get, p(x) = (x + 5)(x² - 1).Now, we right (x² - 1) as (x + 1)(x - 1). to get the polynomial as, p(x) = (x + 5)(x + 1)(x - 1).Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
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Which of the following appear in the diagram below?
Answer:
Step-by-step explanation:
Comment
The one you can pick out that is true is D. The others you have to be careful with. C is a line and it has two arrowheads in the symbol above the two letters which makes it correct as well. A is not correctly marked, so it is not there the way it is marked. One would think ZX is a ray the way it is marked.
Answer: C and D
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answer:
A) 3%
B) Product A
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Part A
Product A
Assuming the function for Product A is exponential:
[tex]f(x) = 0.69(1.03)^x[/tex]
The base (b) is 1.03. As b > 1 then it is an increasing function.
To calculate the percentage increase/decrease, subtract 1 from the base:
⇒ 1.03 - 1 = 0.03 = 3%
Therefore, product A is increasing by 3% each year.
Part B
[tex]\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]
To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:
[tex]\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%[/tex]
Check using different two consecutive values of f(t):
[tex]\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%[/tex]
Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.
Although the question has not asked, we can use the given information to easily create an exponential function for Product B.
Given:
a = 10,100b = 1.01n = t - 1 (as the initial value is for t = 1 not t = 0)[tex]\implies f(t) = 10100(1.01)^{t-1}[/tex]
To check this, substitute the values of t for 1 through 4 into the found function:
[tex]\implies f(1) = 10100(1.01)^{1-1}=10100[/tex]
[tex]\implies f(2) = 10100(1.01)^{2-1}=10201[/tex]
[tex]\implies f(3) = 10100(1.01)^{3-1}=10303.01[/tex]
[tex]\implies f(4) = 10100(1.01)^{4-1}=10406.04[/tex]
As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
Answer:
(A). y - 4 = 3 ( x - 1 )
Step-by-step explanation:
Slope "m" and ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) ⇒
Slope-point form of linear equation is y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~
m = 3 and point with coordinates ( 1 , 4 )
y - 4 = 3 ( x - 1 )
Given: NQ is the bisector of ZMNP and ZNMQ
ZNPQ
Prove: Δ MNQ =ΔΡΝΟ
M
N
Q
P
1) [tex]\overline{NQ}[/tex] is the bisector of [tex]\angle MNP[/tex] and [tex]\angle NMQ \cong \angle NPQ[/tex] (given)
2) [tex]\angle MNQ \cong \angle QNP[/tex] (a bisector splits an angle into two congruent angles)
3) [tex]\overline{NQ} \cong \overline{NQ}[/tex] (reflexive property)
4) [tex]\triangle MNQ \cong \triangle PNQ[/tex] (AAS)
If = 12 –3 a,find the value ofxwhen a= 8
Answer:
-12
Step-by-step explanation:
x = 12-3a
When a=8:
x = 12-3(8)
x = 12 - 24
x = -12
The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Who had the largest dollar amount in sales for the month of December?
a.
The salary plus commission employee.
b.
The straight commission employee.
c.
The graduated commission employee.
d.
They each had the same dollar amount in sales.
The answer to the person with the largest dollar sales in December is d. They each had the same dollar amount in sales.
What were the sales amounts in December?The sales of the salary + commission employee is:
= (4,400 - 2,000) / 3%
= $80,000
The sales of the straight commission employee is:
= 5,600 / 7%
= $80,000
The sales of the graduated commission employee is:
The amount earned on the first $40,000 is:
= 5% x 40,000
= $2,000
The rest of the sales is therefore:
= (5,200 - 2,000) / 8%
= $40,000
The total sales for this employee is:
= 40,000 for 5% commission + 40,000 for 8%
= $80,000
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m²æ + m²æ² - 6m²a 2
Answer:
m2ae+hs72;(27£+£73-££:£7£To show - 7 on the number line, from zero, we have to move 7 units in which direction?
Answer:
7 units to the left.
Step-by-step explanation:
On the number line , the number will always decrease when we move towards the left, and likewise will always increase when we move towards the right. In this case since the number is moving from 0 to -7, it is definitely decreasing therefore we will move 7 units to the left.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
An expression is defined as a set of numbers, variables, and mathematical operations.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are given below,
If the given expression 2.3p – 10.1 = 6.5p – 4 – 0.01 is simplified, then the expression can be written as,
2.3p – 10.1 = 6.5p – 4 – 0.01
2.3p – 10.1 = 6.49p – 4
Thus, Option A is one of the option.
Using the multiplication property of Equality, if we multiply both the sides of the equation by 100, then we will get,
230p – 1010 = 650p – 400 – p
Thus, c is one of the option.
Hence, the correct options are A and C.
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The sum of the series: -2+(-8) + (-32)++ (-2048) equals
I really neeed help!!! Please I’m begging you!!!!!!
Answer:
-2090
Step-by-step explanation:
1) Remove parentheses.
-2 -8 -32 -2048
2) Simplify - 2 - 8 to -10.
-10 - 32 - 2048
3) Simplify -10-32 to -42.
-42 - 2048
4) Simplify.
-2090
A response variable, Price, is defined as the selling price of a used car. Three predictor variables include, Age, the age of the car in years, Mileage, the mileage of the car in thousands of miles, and Cylinders, the number of engine cylinders. The estimated regression equation is: Price
The estimated regression equation is Price = bo +b1Age+ b2Mileage + b3Cylinders
How to determine the regression equation?We have:
Predictor variables = 3Variable 1 = AgeVariable 2 = MileageVariable 3 = CylindersThe regression equation is estimated using:
Price = bo +b1 * Variable 1+ b2 * Variable 2 + b3 * Variable 3
Substitute the variable parameters
Price = bo +b1Age+ b2Mileage + b3Cylinders
Hence, the estimated regression equation is Price = bo +b1Age+ b2Mileage + b3Cylinders
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pls help with age problem.
Answer:
John is 19 and his sister is 23.
Step-by-step explanation:
See attached image.
the number of sides of regular polygon if the measure of its interior angle is 150 degree
Answer:
12 sides
Explanation:
[tex]\sf interior \ angle = \dfrac{(n-2) \times 180}{n} \quad (where \ n \ denotes\ number \ of \ sides)[/tex]
Solving Steps:
[tex]\sf \dfrac{(n-2) \times 180}{n} = 150[/tex]
[tex]\sf (n-2) \times 180} = 150n[/tex]
[tex]\sf 180n-360 = 150n[/tex]
[tex]\sf 180n-150n = 360[/tex]
[tex]\sf 30n = 360[/tex]
[tex]\sf n = 12[/tex]
What is the mean absolute deviation of Patrick’s scores? Show your work
f(x) = 4x² + 7x-3
g(x) = 6x³ – 7x² - 5
-
Find (f + g)(x).
Answer:
(f + g)(x) = 6x³ - 3x² + 7x - 8
Step-by-step explanation:
Another way of writing (f + g)(x) is f(x) + g(x). So, this question is asking you to combine both of the functions.
f(x) + g(x)
(4x² + 7x - 3) + (6x³ - 7x² - 5) <----- Insert functions
-3x² + 7x - 3 + 6x³ - 5 <----- Combine 4x² and -7x²
-3x² + 7x - 8 + 6x³ <----- Combine -3 and -5
6x³ - 3x² + 7x - 8 <----- Rearrange
write 5 rational numbers between 1 and 2
Answer:
1.1, 1.2, 1.3, 1.4, 1.5 or 11/10, 12/10, 13/10, 14/10, 15/10
Explanation:
Rational numbers can be expressed as fractions (p/q), decimals, whole numbers, natural numbers, integers.
Some rational numbers between 1 and 2 are: -
1.05, 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.95, 1.97
Five rational numbers are
1.5=15/101.05=105/1001.007=10007/10001.3=13/101.03=103/100_______________ is the value of the best alternative given up when a choice is made.
What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner shown?
The probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be 1/4 or 0.25.
The complete question is given below.
I rolled a number cube and spun a spinner. The number cube is numbered 1 to 6. The spinner has 4 equal parts: red, blue, yellow, and green. What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner?
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Then the probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be
The probability of getting even number on dice will be
Total event = 6 {1, 2, 3, 4, 5, 6}
Favorable events = 3 {2, 4, 6}
P₁ = 3/6
P₁ = 1/2
The probability of getting red or yellow will be
Total event = 4 {red, blue, yellow, green}
Favorable events = 2 {red, yellow}
P₂ = 2/4
P₂ = 1/2
Then the both event occur simultaneously, then we have
P = P₁ × P₂
P = 1/2 × 1/2
P = 1/4
P = 0.25
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Hope this helps, have a great day!
Raphael is ordering a scoop of ice cream. For the flavor, he is given the option of chocolate, strawberry, vanilla, cookies ‘n cream, or peanut butter. For the size, he is given the option of small, medium, or large. For the cone, he is given the option of a sugar cone, waffle cone, or cup. How many possible order combinations are there?
Answer: 165
Step-by-step explanation: If you calculate the 3 different choices and the total of 11 different objects, you get 165 total combinations.
Answer:
45 possible combinations
Step-by-step explanation:
since there are 5 options of flavour (chocolate, strawberry, vanilla, cookies 'n' cream, and peanut butter) then you must multiply your flavours by your next option.
the size options come in 3 options (small, medium, and large) therefore we multiply the flavours (5) by sizes (3)
5 * 3 = 15
then multiply the result (15) by the cup options (3)
15 * 3 = 45
your answer is 45
hope this helps:)
N
O O
What is the slope of the line represented by the equation y = --- 5x?
0-5
4 ~/m ~/m
+
O 5
O
suppose your household income increased to $2,000.00 and your energy bill came from $180.00 how many percent of your household income is being spent on electricity?
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
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[tex]\large \bold {ANSWER}[/tex]
[tex]\implies \boxed{\underline{\huge{\tt{\orange{\: \: 9\% \: \: }}}}}[/tex]9% of the family income is being spent to pay the energy bill.
[tex]\large \bold {SOLUTION}[/tex]
HOW TO FIND OUT THE PERCENTAGE?If your income is now $2,000.00 and you have withdrawn $180.00 from the value, then we say that the $2,000.00 is equivalent to 100% of the value, that is, the total amount. And the amount that was withdrawn will be X because we still don't know how much percent is equivalent to $ 180.00 of this value.
To solve, we will use the simple rule of three like this:
[tex]\frac{2000}{180} = \frac{100}{x}[/tex]With this we will multiply the denominator of one with the numerator of the other, being:
2000 * X and 180 * 100Where: 2000 * x is equal to 2000xAnd 180 * 100 is equal to 18,000Knowing this, we will solve it this way:
2000x = 18,000To start we will isolate the unknown(x) from the values taking the 2000 to the other side of the equality turning it into the denominator of 18,000.
[tex]x = \frac{18000}{2000}[/tex]And to finish, we cut the 3 zeros of the numerator with the d 3 zeros of the denominator getting 18 / 2. Now it's just dividing.
[tex]\begin{gathered}x = \frac{18}{2} \\ \\ x = 9\end{gathered}[/tex]We can conclude that the amount spent to pay the energy bill is equivalent to 9% of the family income.
whats the answer for this
Answer:
a) Angle X = 108°
C). Vertically opposite anglesas AD is parallel to EH both the angles are equal
Answer:
108 degrees, vertical angles
Step-by-step explanation:
Angle x is 108 degrees because angle x and angle EFB are vertical angles, meaning that they are equal since opposite angles have the same measures.
Brainliest, please :)
3.
The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.
Answer:
x = 5.00 cm
Step-by-step explanation:
• area of the rectangle = [tex]x[/tex] x [tex](x + 1)[/tex]
= [tex]x^2 + x[/tex]
• area of the circle = π r²
= [tex]\frac{22}{7}[/tex] x [tex](x + 2)^2[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4)[/tex]
∴ [tex]x^2 + x[/tex] + [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4) = 184[/tex]
⇒ [tex]x^2 + x[/tex] + [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]
⇒ [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]
• Using quadratic formula, where
a = [tex]\frac{29}{7}[/tex]
b = [tex]\frac{95}{7}[/tex]
c = [tex]\frac{-1200}{7}[/tex] ,
[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]
[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]
[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]
As length (x) cannot be a negative number,
x = 5.00 cm
How is a perfect square trinomial similar to a perfect square number? Is it possible to have a perfect square binomial? Explain.
Yes, it is possible to have a perfect square binomial. The detailed information is given below.
What is the perfect square binomial to trinomial?In trinomial, there are three terms and in binomial, there are two terms.
Let the perfect square of the binomial will be given as
⇒ (a + b)²
There are only two terms a and b and has a square on it. So the expression (a + b)² is a perfect square binomial.
Open the bracket, then we have
(a + b)² = a² + b² + 2ab
There are only three terms a², 2ab and b² and derived from a perfect binomial square. So the expression a² + b² + 2ab is a perfect square trinomial.
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Directions:
Sarah is going to the movies and she has $10 to spend on snacks. Smoothies are $3
and candy bars are $1 each. She will be spending all of the $10.
Budget: $10
Smoothies: $3
Candy bars: $1
Draw a line graph that represents the budget constraints and possible purchasing
options that Sarah has with her $10.
The attached graph represents the graph of the equation 3x + y = 10
How to determine the line graph?The given parameters are:
Budget: $10Smoothies: $3Candy bars: $1Represent the number of smoothies with x and the number of candy bears with y.
So, the equation is:
3x + 1y = 10
This gives
3x + y = 10
Next, we plot the graph of the above equation
See attachment for the graph of 3x + y = 10
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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.
Let's suppose the number of smoothies is x and the number of candy bars is y:
Then, we can frame a linear equation in one variable:
3x + y = 10
Drawing the above the line on the coordinate plane:
Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
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the area of square ABCD is 10cm2 show that x^2+6x=a where a is a constant to be found
The value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The question is incomplete.
The question is:
The area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant to be found.
The missing figure is attached; please refer to the picture.
As we can see in the figure we have given a rectangle.
Area of rectangle = (3 + x)(3 + x)
10 = (3 + x)(3 + x)
or
10 = (3 + x)²
10 = 9 + 6x + x²
After rearranging:
x² + 6x = 1
We have equation:
x² + 6x = a
After comparing:
a = 1
Thus, the value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
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can someone please help mee
For the graphed function we can see:
domain = set of all real numbersrange = set of all real numbers.How to get the range and domain?For a function y = f(x), the domain is the set of the possible inputs "x" and the range is the set of the possible outputs "y".
In this case, we can see that in the right side we have a parabola, and on the left side a linear equation which increases up to the left (so it has a negative slope).
Then the domain will be the set of all real numbers.
Similar for the range, as we can see that on the left side, the line goes upwards, while on the right side, the parabola goes downwards. So this function has a range of all real numbers.
Then:
domain = set of all real numbers
range = set of all real numbers.
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Which sign should be used for the following equation? 0.452 _______ 0.712 < > ≤ ≥
Answer:
<
Step-by-step explanation:
0.4<0.7
4 is smaller than 7 so the sighn points to 0.7
