When we have dependent and independent variables we will have a linear relationship.
Let x be the independent variable and y be the dependent variable.
To write the relationship we will have :
y = kx + c
Where k and c are constants.
In the case of a line the constant k is the gradient.
A multiplicative change is a log form and it is given by :
Y = Ck^x
The relationship is not linear but exponential.
The correct answer is thus :
Additive rate of change.
Answer:
A
Step-by-step explanation:
F(x)=3x+1 and g(x)= x^2-6 find (f•g)(x)
Answer:
Step-by-step explanation:
It never occurred to me that the closed circle meant multiplication. The most common symbol for multiplication here is *. If that is what is meant (closed circle = multiplication) then my answer is wrong.
f(x) = 3x + 1
g(x) = x^2 - 6
f(x)(g(x)) = (3x + 1)(x^2 - 6)
f(x)(g(x)) = 3x^3 - 18x + x^2 + 6 or more properly
f(x)(g(x)) = 3x^3 + x^2 - 18x - 6
[tex](f\cdot g)(x)=(3x+1)(x^2-6)=3x^3-18x+x^2-6=3x^3+x^2-18x-6[/tex]
for questions 5-6 the functions are
f(x)=5x^2+3
g(x)=x^2-7
Answer:
see explanation
Step-by-step explanation:
Note that
(f + g)(x) = f(x) + g(x) and
(f - g)(x) = f(x) - g(x)
5
f(x) + g(x)
= 5x² + 3 + x² - 7 = 6x² - 4
6
f(x) - g(x) = 5x² + 3 - (x² - 7) ← distribute parenthesis
= 5x² + 3 - x² +7 ← collect like terms
= 4x² + 10
7
f(x) + g(x) = [tex]4^{x}[/tex] + 3x + 2x - 5 = [tex]4^{x}[/tex] + 5x - 5
Simplify remove all the perfect squares from inside the square root 45
Answer:
3[tex]\sqrt5}[/tex]
The square root of 45 can be simplified by removing perfect square factors. In this case, the number 9 is a perfect square factor of 45, resulting in the simplification √45 to 3√5.
Explanation:To simplify the square root of 45 by removing perfect squares, we first need to identify the factors of 45 that are perfect squares. In this case, the number 9 is a factor of 45 and is a perfect square. Therefore, we can simplify √45 to √9*5 or 3√5. Simplifying square roots is a basic principle of Mathematics one should know as it is often applied in various middle school, high school, and even college math problems.
Learn more about Simplifying Square Roots here:https://brainly.com/question/1441039
#SPJ2
Which of the fractions listed below are equal to 2⁄3?
Check all that are true.
6⁄9
1⁄3
3⁄2
4⁄6
1⁄6
A 12-volume numbered set of books is placed randomly on a shelf. What is the probability that the books will be numbered in the correct order from left to right?
Answer:
Step-by-step explanation:
There is a 1/12 probability that volume 1 will be correctly put in position 1.
If we assume that volume 1 is right, then since there are then only 11 books left to choose from, there is then a 1/11 prob that volume 2 will be in position 2. And so on. By the same reasoning there is 1/10 prob that volume 3 is then right, 1/9 prob for volume 4, 1/8 prob for volume 5, and 1/7 prob for volume 6,
and 1/6 prob for volume 7,and 1/5 prob for volume 8,and 1/4 prob for volume 9,and 1/3 prob for volume 10,and 1/2 prob for volume 11,and 1/1 prob for volume 12.
So the probability is 1 /(12*11*10*9*8*7*6*5*4*3*2*1) = 1 / 479,001,600 ....
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? A] The test contains 4 three-point questions and 20 five-point questions. B]The test contains 10 three-point questions and 14 five-point questions. C]The test contains 14 three-point questions and 10 five-point questions. D]The test contains 20 three-point questions and 8 five-point questions.
Answer:
B. The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
Let us first find the solution to the system of equations.
x+y= 24
3x+5y= 100
We use substitution method.
x=24-y
Replacing the value of x in the second equation.
3(24-y)+5y=100
Then solve for y.
72-3y+5y=100
2y=100-72
2y=28
y=14
To find x let us replace the value of y in x=24-y
x=24-14
x=10
This means that the test has 14 five-point questions and 10 three point questions.
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11
Answer:
10
Step-by-step explanation:
First convert the fractions.
9 1/6 to 55/6 and 1 1/11 to 12/11
With these fractions, you can cross out 11 and 6.
55 times 12 5 × 2
6 11 1 × 1
This equals 10/1 or 10
Final answer:
To multiply 9 1/6 by 1 1/11, first convert them to improper fractions, 55/6 and 12/11 respectively. Multiply the numerators together to get 660, and the denominators together to get 66. Simplify by dividing both by their greatest common divisor, which is 66, to get the simplest form, which is 10.
Explanation:
The question asks to multiply 9 1/6 by 1 1/11 and express the answer in simplest form. First, we will convert these mixed numbers to improper fractions. For the first number, 9 1/6, we multiply the whole number part by the denominator of the fractional part and add the numerator: (9 × 6) + 1 = 54 + 1 = 55, thus we get 55/6. For the second number, 1 1/11, we follow the same process: (1 × 11) + 1 = 11 + 1 = 12, resulting in 12/11.
Next, we multiply the resulting improper fractions. The numerators are multiplied together, and the denominators are multiplied together yielding 55 × 12 over 6 × 11 which equals 660/66. Simplifying by common factors, we notice that both the numerator and denominator have a common factor of 66. Dividing the numerator and denominator by 66 gives us the simplest form, which is 10/1 or simply 10.
What is the surface area of the figure?
314 in.2
792 in.2
628 in.2
546 in.2
Answer:
628 n.2 is the correct answer
Need some help ya plz
Answer:
C. (-5, 3)
Step-by-step explanation:
Point C is currently (5,3).
If it is reflected over the y-axis, that means while the y-coordinate stays the same, the x- coordinate is negative of what is was before.
C is the only answer that keeps the y-coordinate constant, so just by looking at that, we can say that the answer is C.
Answer:
C
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Hence
C(5, 3 ) → C'(- 5, 3 ) → C
Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.
weekly pay; hours worked; 30 to 35 hours; $360 to $420
hours worked; weekly pay; 30 to 35 hours; $0 to $420
hours worked; weekly pay; 30 to 35 hours; $360 to $420
weekly pay; hours worked; $360 to $420; 30 to 35 hours;
Answer:
See below.
Step-by-step explanation:
The independent variable is the number of hours worked and the dependent variable is the weekly pay.
The domain is 30 to 35.
The range is $360 to $420.
{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?
A. one-to-many
B. many-to-many
C. one-to-one
D. many-to-one
Answer:
B. Many-to-many
Step-by-step explanation:
We have the following ordered pairs:
(1,2)(-2,3)(1,3)(-2,2)First let's define the following concepts:
One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.Many-to-one: If there are y values that have more than one x value mapped onto them.One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.
Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.
The given relation is a many-to-one relationship.
The given relation {(1,2), (-2,3), (1,3), (-2,2)} is an example of a many-to-one relationship. In a many-to-one relation, multiple elements in the domain map to a single element in the range. Each x-value has a unique y-value.
I really need help with 9 and 10 please.
Answer:
9) The equation that represents our monthly bill is y=20+0.05m.
10) The equation that gives us the cost for the month is y=5+0.1m.
Step-by-step explanation:
9) So if we are trying to find how much our monthly bill is where the monthly fee is 20 and we are charged $.05 per minute, then:
For 0 minutes, we spend 20 dollars in the month.
For 1 minute, we spend 20+.05=20.05 dollars in the month.
For 2 minutes, we spend 20+.05+0.05 or 20+2(.05)=20+.1=20.10 dollars in the month.
For m minutes, we spend 20+.05m.
The equation that represents our monthly bill is y=20+0.05m.
They gave us the y-intercept (the initial amount=20) and the rate (the slope=.05).
Remember: slope-intercept form is y=mx+b.
10) I'm going to shorten number 10.
They give us the rate=$.1/min and the initial cost=5 dollars.
The equation that gives us the cost for the month is y=5+0.1m.
Q: Which best describes the demand for consumer goods in the 1920's.
Select one:
a. people were less likely to buy new goods.
b. the demand for consumer goods declined during the 1920's.
0 C. all of these are correct
d. people began buying more than they had the cash to pay for becaus
could access loans and buy things on credit.
NE
Answer:
d. people began buying more than they had the cash to pay for because they
could access loans and buy things on credit.
Step-by-step explanation:
In the 1920's, it was a period of prosperity and people in the middle class began to have more income available to purchase products. Also, there were more products available because of the assembly line production and the credits expanded which resulted in people being able to buy things that they couldn't purchase paying the full price. According to this, the answer is that the statement that best decribes the demand for consumer goods in the 1920's is that people began buying more than they had the cash to pay for because they could access loans and buy things on credit.
Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.
J = 90° J' = 90°
K = 65° K' = 65°
L = 25° L' = 25°
Which statement is true about this transformation?
Answer:
It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.
Step-by-step explanation:
Answer:C
Step-by-step explanation:
I know
A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water. 7 liters of yellow tint is added to the original mixture. What percent of yellow tint is in the new mixture? Answer must be correct to 1 decimal place.
Final answer:
To find the percent of yellow tint in the new mixture, we need to consider the original mixture and the additional 7 liters of yellow tint that was added. The new mixture has a percent of yellow tint of 38.6%.
Explanation:
To find the percent of yellow tint in the new mixture, we need to consider the original mixture and the additional 7 liters of yellow tint that was added.
The original mixture contains 30% yellow tint, which is equivalent to 30% of 50 liters, or 0.3 * 50 = 15 liters of yellow tint.
When the 7 liters of yellow tint is added, the total amount of yellow tint in the new mixture is 15 liters + 7 liters = 22 liters.
The new mixture has a total volume of 50 liters + 7 liters = 57 liters.
To find the percent of yellow tint in the new mixture, we divide the amount of yellow tint (22 liters) by the total volume (57 liters) and multiply by 100:
Percent of yellow tint = (22 liters / 57 liters) * 100 = 38.60% (rounded to 1 decimal place).
Final answer:
After adding 7 liters of yellow tint to the mixture, the new total volume of yellow tint is 22 liters, and the total volume of the mixture is 57 liters. Calculating the percentage, the mixture now consists of 38.6% yellow tint.
Explanation:
To calculate the new percentage of yellow tint in the mixture after adding 7 liters, we first need to determine how much of each component there was in the original mix.
Original amount of red tint: 25% of 50 liters = 12.5 litersOriginal amount of yellow tint: 30% of 50 liters = 15 litersOriginal amount of water: 45% of 50 liters = 22.5 litersAfter adding 7 liters of yellow tint, the new total amount of yellow tint becomes 15 liters + 7 liters = 22 liters. The total volume of the mixture is now 50 liters + 7 liters = 57 liters.
The new percentage of yellow tint is calculated as follows:
(Amount of yellow tint / Total volume) × 100 = (22 liters / 57 liters) × 100
This calculation gives us the new yellow tint percentage in the mixture:
(22 / 57) × 100 ≈ 38.6%
Therefore, the mixture now contains 38.6% yellow tint.
Please help me solve this problem !
[tex]f(3)=2^3=8[/tex]
Answer:
D. 8
Step-by-step explanation:
The value of f(3) in f(x)=2x is 8.
f(3)=2^3=8
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
Answer:
7z^3+6z^2-27z+22
Step-by-step explanation:
The given question is of subtraction:
So,
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
=7z^3+42z^2-15z+1-36z^2-12z+21
Combining alike terms to simplify
=7z^3+42z^2-36z^2-15z-12z+1+21
=7z^3+6z^2-27z+22
So the answer in simplified form is:
7z^3+6z^2-27z+22 ..
Answer:
7z³ + 6z² - 27z + 22
Step-by-step explanation:
It is given an expression in variable z,
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
To find the simplified form
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
= (7z³ + 42z² - 15z + 1 - 36z² - 12z + 21)
= 7z³ + 42z² - 36z² - 15z -12z + 1 + 21
= 7z³ + 6z² - 27z + 22
Therefore the simplified expression is = 7z³ + 6z² - 27z + 22
Which expression has the same value as -18-(-9)?
0 -18+2
9 -12-(-3)
-10-5
Answer:
None of the given option is correct.
Step-by-step explanation:
The expression given is:
-18-(-9)
= -18+9
= -9
Now checking the options, which will have -9 as answer
1) 0 -18+2
= -18+2
= -16
As answer is not -9, so this is not a correct option
2) 9 -12-(-3)
= 9 - 12 + 3
= 0
As answer is not -9, so this is not a correct option
3) -10-5
= -10-5
= -15
As answer is not -9, so this is not a correct option
So, None of the given option is correct.
The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants
Answer:
13
Step-by-step explanation:
If you look at where $5 crosses the line of best fit, you see it between 12 and 14 ounces. The answer is 13.
Answer:
13 oz
Step-by-step explanation:
The blue line here is the trend line of the function between cost and size.
The trend line is the linear equation approximation of the function
So, for predicting the size when $5 is paid we need to take the corresponding x axis value and the corresponding y axis value on the trend line.
Hence, the Size of frozen yogurt is between 12 and 14 oz which means the size is 13 oz.
Indicate which property is illustrated in step 8. A. Subtraction property of equality B. Simplification C. Distributive property D. Division property of equality
step 8: -3x/-3 = -7/3
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex]-3x=7[/tex]
After Step 8 it becomes,
[tex]\dfrac{-3}{-3}=\dfrac{-7}{3}[/tex]
It indicated the Division property of equality.
To find the value of x, we need to divide the left hand side and right hand side by -3.
So, this property is known as "Division property of equality":
Hence, Option 'D' is correct.
Answer:
Option D - Division property of equality
Step-by-step explanation:
Given : Step 8 - [tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
To find : Indicate which property is illustrated in step 8 ?
Solution :
Step 8 - [tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
In step 8 we have seen that -3 is divided both side,
So, The division property of equality is applied to get the result.
[tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
[tex]x=-7[/tex]
Therefore, Option D is correct.
Division property of equality
what is 2% out of 3000
Answer:
It would be 60.
Answer:
Step-by-step explanation:
(3000×2)/100 = 6000/100 = 60
which decimal is equivalent to forty and seventy six thousands ? a.40.076 b 40.76 C 47.006 D 47.06
Answer:
A. 40.076
Step-by-step explanation:
Because B is forty and seventy six hundredths. C is forty-seven and six thousandths. D is forty-seven and six hundredths.
Seventy-six thousandths is written as .076, making the final answer 40.076.
The decimal equivalent to forty and seventy six thousandths is 40.076. This is because seventy-six is in the thousandths place after the decimal point.
The decimal equivalent to forty and seventy six thousandths is 40.076. To write this out, you place the decimal point after the whole number forty, then you need to ensure that seventy-six is in the thousandths place. When writing decimal numbers, the first place to the right of the decimal is the tenths place, the second is the hundredths place, and the third is the thousandths place. Therefore, seventy-six thousandths is written as .076, making the final answer 40.076.
solve the equation
log(5x)-log(x-3)=1
Answer:
x = 6
Step-by-step explanation:
Using the rules of logarithms
• log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
log(5x) - log(x - 3) = 1
log ( [tex]\frac{5x}{x-3}[/tex] ) = 1, then
[tex]\frac{5x}{x-3}[/tex] = [tex]10^{1}[/tex] = 10 ( cross- multiply )
10(x - 3) = 5x
10x - 30 = 5x ( subtract 5x from both sides )
5x - 30 = 0 ( add 30 to both sides )
5x = 30 ( divide both sides by 5 )
x = 6
Answer:
x =6
Step-by-step explanation:
log(5x) - log(x - 3) = 1
Recall that the logarithm of a fraction is the difference of the logarithms,
so, the difference between two logarithms is logarithm of the fraction. Then,
[tex]\begin{array}{rcll}\\\\\log \dfrac{5x}{x-3} & = & 1 &\\\\\dfrac{5x}{x - 3} & = & 10 & \text{Took the antilogarithm of each side}\\\\5x & = & 10(x - 3) & \text{Multiplied each side by x - 3}\\5x & = & 10x - 30 & \text{Distributed the 10}\\-5x & = & -30 & \text{Subtracted 10 x from each side}\\x & = & \mathbf{6} & \text{Divided each side by -5}\\\end{array}[/tex]
Check:
[tex]\begin{array}{rcl}\log(5\times6) - \log (6 - 3) & = & 1\\\log 30 - \log 3 & = &1\\\\\log \dfrac{30}{3} & = & 1\\\\\log 10 & = & 1\\1 & = & 1\\\end{array}[/tex]
OK.
which statements must be true about ru reflection of xyz across mn? select 3 options
Answer:BZ congruent to BZ'
XY congruent to X'Y'
X'Z'Y' 90 degrees
Step-by-step explanation:
Answer:
(1). m∠X'Z'Y'=90°
(2). m∠MCY=90°,
(3). Line segment BZ'≅ line segment BZ
Step-by-step explanation:
Line MN is reflecting line for ΔXYZ. Triangle X'Y'Z' is formed after reflection of ΔXYZ about a line MN. Therefore the line MN works like a symmetric axis of the given figure.
Hence
(1). m∠X'Z'Y'=90°, because ∠XYZ=90° and figure are symmetric about line MN.
(2). m∠MCY=90°, because figure is symmetric ,so line segment YY'⊥ line MN.
(3). Line BZ' ≅line BZ, because figure is symmetric about about symmetric axis line MN and Line BZ'= line BZ.
Which of the following is the correct notation for the complex number
Answer:
1-4i
Step-by-step explanation:
[tex]i=\sqrt{-1}[/tex]
We have [tex]1-\sqrt{-16}[/tex].
Let's look at the [tex]\sqrt{-16}[/tex] part.
Since it has a negative inside the square root, it is imaginary. This is our imaginary unit [tex]i=\sqrt{-1}[/tex].
So [tex]\sqrt{-16}[/tex]
[tex]=\sqrt{16} i [/tex]
[tex]=4i[/tex]
So [tex]1-\sqrt{-16}=1-4i[/tex]
Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay 4.5% interest, and stocks pay 10.4% interest. Country days invests $70000 more in bonds than CDs. If the annual income from the investments is $8555, how much was invested in stocks, bonds, and CDs?
Answer:
CDs — $10,000bonds — $80,000stocks — $45,000Step-by-step explanation:
Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:
c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested
0.0275c +.045b +0.104s = 8555 . . . . . total income earned
-c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs
Using the third equation to write an expression for b, we can substitute into the other two equations.
b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b
c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation
2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify
.0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn
.0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify
Using [eq4], we can write an expression for s that can be substituted into [eq5].
s = 65000 -2c . . . . . . . expression we can substitute for s
0.0725c +0.104(65000 -2c) = 5405
-0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify
c = 1355/.1355 = 10,000
s = 65000 -2×10000 = 45,000
b = 70000 +10000 = 80,000
The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.
_____
Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...
[tex]\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right][/tex]
What type of function is represented by the table of values below?
8
12
16
20
Answer:
To be precise, I think it's a pattern question, where you have to add 4 to each number. I'm not very sure though.
Which expression is equivalent to the following complex fraction?
2-1/y / 3+ 1/y
Answer:
[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] is equivalent to [tex]\frac{2y-1}{3y-1}[/tex]
Step-by-step explanation:
The given expression is :[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex].
We collect LCM in both the numerator and the denominator to obtain:
[tex]\frac{\frac{2y-1}{y} }{\frac{3y-1}{y} }[/tex]
Change to the normal division sign;
[tex]\frac{2y-1}{y} \div \frac{3y-1}{y}[/tex]
Multiply by the reciprocal of the second fraction:
[tex]\frac{2y-1}{y} \times \frac{y}{3y-1}[/tex]
Cancel out the common factors
[tex]\frac{2y-1}{3y-1}[/tex]
Therefore [tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] is equivalent to [tex]\frac{2y-1}{3y-1}[/tex]
PLEASE HELP ME 20 POINTS !! tyvm
ASAP
Answer:
[tex]\large\boxed{m\angle S=78^o}[/tex]
Step-by-step explanation:
[tex]\text{If}\ \triangle MNP\cong\triangle QST,\ \text{then corresponding angles}\\\text{and corresponging sides are congruent.}\\\\\angle M\cong\angle Q\\\angle N\cong\angle S\\\angle P\cong\angle\\\\m\angle N=78^o,\ \text{therefore}\ m\angle S=78^o[/tex]
how many 1/4s fit in 1/2
Answer:
2
Step-by-step explanation:
1/4+1/4=1/2