Answer:
see explanation
Step-by-step explanation:
A
(f + g)(x)
= f(x) + g(x)
= x² + 3x + 2x + 2 ← collect like terms
= x² + 5x + 2
B
(f - g)(x)
= x² + 3x - (2x + 2)
= x² + 3x - 2x - 2 ← collect like terms
= x² + x - 2
A student took SAT (mean = 500 and standard deviation = 100) and got a score of 550. ACT is known to have a mean of 20 and a standard deviation of 5. What would this student’s score be on the ACT metric?
106 would be student's score on ACT metric.
What is mean and standard deviation?The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. It demonstrates how different things are from the standard.
Given Data
Mean = 500
Standard deviation = 100
ACT metric
Mean = 20
Standard deviation = 5
Score = [tex]\frac{550-20}{5}[/tex]
Score = [tex]\frac{530}{5}[/tex]
Score = 106
106 would be student's score on ACT metric.
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Help Please!!
A. 3
B. 1/2
C. 2
D. 1
Answer:
B is the answer
Step-by-step explanation:
The functions r and s are defined as follows.r(x)=– 2x-2s(x)=x²+2Find the value of s (r(4)).s(r(4)) = 006ХŚ
The given functions are
r(x) = - 2x - 2
s(x) = x^2 + 2
To find s(r(4)), the first step is to substitute x = - 2x - 2 into s(x) = x^2 + 2. Thus, we have
s(r(x)) = (- 2x - 2)^2 + 2
s(r(x) = (- 2x - 2)(- 2x - 2) + 2
s(r(x) = 4x^2 + 4x + 4x + 4 + 2
s(r(x)) = 4x^2 + 8x + 6
Finally, we would substitute x = 4 into s(r(x) = 4x^2 + 8x + 2. Thus, we have
s(r(4)) = 4(4)^2 + 8(4) + 6
s(r(4)) = 64 + 32 + 6
s(r(4)) = 102
this week Linda got a promotion at work that came with a 4% pay increase. If now her monthly salary is $2,496, how much was he making before the raise?
We will say that x is the salary before the raise, to calculate how much the salary grows, we just have to take the given percent from x, in this case, the payment increased by 4% (0.04 expressed in decimal form) then the increased amount would be x times 0.04.
Salary increase = x*0.04 = 0.04x
Adding 0.04 x to the original salary x (before applying the increase) we get the actual monthly salary, $2,496, then we can formulate the following expression:
Current salary = original salary + salary increase
2,496 = x + 0.04x
From this equation, we can solve for x like this:
1. Factoring x on the right side of the equation:
2,496 = x(1+0.04)
2. making the sum inside the parentheses:
2,496 = x*1.04
3. Dividing both sides by 1.04:
2,496 / 1.04 = x * 1.04 / 1.04
2400 = x
x = 2400
Then, Linda was making $2400 before the pay increase
OS 11.9 (a) 5X + OVC (c) At - 7 - 21 (e) Vmx + 5 (0) Ax + By = 0 the characterizing property for each family of lines. (1) ] = f Lan 50° + b live x-intercep(2.0) • (b) 6x + By = 24 (d) y = 4x + b (1) kx + kyk (h) m(x + 2) = y- (1) x=4
Family of lines characteristics
b) 6x + By = 24
find x-intercept
24/6 = 4. = C/A
y= 0
Then ANSWER IS
x- intercept= (4,0)
2nd part
c) Ax - 7y= 21
Find y- intercept
C/B= 21/-7 = -3
Also
x=0
Then. ANSWER IS
y-intercept is = ( 0,-3)
Identify the law illustrated by the following 0 + 12 m is the same as 12 m
The law that was illustrated by the following 0 + 12 m is the same as 12 m is addition of zero.
What is the addition of zero law?The addition of zero law can be described as the law that says that whenever a particular number is been added to zero then the result of that addition will be that particular number.
It should be noted that this Identity Law of Addition can be seen in the given example where zero is added to 12m which gives the result of 12m which implies that the particular number 12m is added to zero and it gives the particular number 12m as the answer.
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Store A sold a total of 36 cups and plates. Store B sold twice as many cups and half as many plates for a total of 39 cups and plates. How many cups did store A sell?
By solving a system of equations we will see that 8 cups were sold on store A.
How many cups did store A sell?Let's define:
c= cups sold on store A.
p = plates sold on store A.
pᵇ = plates sold on store B
cᵇ = cups sold on store B.
For "Store B sold twice as many cups and half as many plates"
We can write:
pᵇ = 0.5*p
cᵇ = 2*c
We can write the system of equations:
c + p = 36
0.5*p + 2*c = 39
We want to solve this for c, so we isolate p on the first equation and replace that in the second one.
p = 36 - c
0.5*(36 - c) + 2c = 39
18 + 1.5*c = 30
1.5*c = 30 - 18
1.5*c = 12
c = 12/1.5 = 8
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=Initial Knowledge CheckEpitaxian is a cutting edge technology company based in Florida. The company has just finisheddeveloping a prototype of a product it is calling the X-13. According to the company'sdocumentation, the X-13 must be operated in a room that is kept at a temperature of -3.8 °F.What is this temperature in degrees Celsius (°C)?Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.°CX3Question 7?Formulas:C = = (F-32)5995F== 30C+32
The given temperature in degrees Celcius is -19.89°.
What is temperature?Temperature is a numerical expression of how hot a substance or radiation is.There are three different types of temperature scales: those that are defined by the average translational kinetic energy per freely moving microscopic particle, like an atom, molecule, or electron, in a body, like the SI scale; those that rely only on macroscopic properties and thermodynamic principles, like Kelvin's original definition; and those that are not defined by theoretical principles but rather by useful empirical properties of particulate matter.So, the formula for conversion from Celsius to Fahrenheit:
C = 5/9(F-32)F given is -3.8°.
Now, insert the value in the formula to find the temperature in Celcius.
C = 5/9(F-32)C = 5/9(-3.8 -32)C = 5/9(-35.8)C = -179/9C = -19.88888After rounding off: 19.89Therefore, the given temperature in degrees Celcius is -19.89°.
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Homework: 3.410 of 15 (10 complete)Score: 0 of 1 ptX 3.4.34A certain lottery has 27 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)There are different ways the numbers can be selected.(Simplify your answer.)Enter your answer in the answer box and then click Check AnswerClear Allshowing
Which lines best fit the data graphed below?ABCNone of the lines fit the data
Given the graph, we can find the line of best fit by its definition.
A line of best fit is a straight line drawn through the maximum number of points on a scatter plot balancing about an equal number of points above and below ...
e caun use this idea above alongside survey the graph and see which lines fall into place.
By observation,
Answer: Line B is the line of best fit.
If f(x)and f−1(x)
are inverse functions, which of the following must be true? Select all that apply.
Group of answer choices
The graphs are reflections of each other across the line y=x.
f(x)= f−1(x)
f−1(f(x))=x
f(f−1(x))= x
Both functions are base graphs.
The option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the b is related to exactly one value in the range.
The functions f(x) and f⁻¹(x) are inverses of each other.
As we know, the graph of the function and inverse function are reflections of each other about y = x.
From the property of the inverse of function:
f(f⁻¹(x)) = x
Thus, the option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.
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The formula that represents the image is:
ANSWER:
[tex]2p+5=21[/tex]STEP-BY-STEP EXPLANATION:
Let p be the figure of the pentagon.
We can establish the following equation:
[tex]\begin{gathered} 2p+5=10+10+1 \\ 2p+5=21 \end{gathered}[/tex]Therefore, the correct answer is the 4th option a) 2p + 5 = 21
There sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three
times the age of the oldest is five less than five times the middle sister's age.
(a) If x represents the age of the youngest child, then write an equation that models this scenario.
(b) Determine the ages of the three sisters.
If x represents the age of the youngest child, then the equation that models this scenario is x+3(x+4) = 5(x+2)-5 and the ages of the three sisters are 7, 9 and 11 years respectively.
According to the question,
We have the following information:
There sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age.
Age of youngest sister = x years
Middle sister = (x+2) years
Oldest sister = (x+4) years
Now, the equation according to the given situation is:
(a) x+3(x+4) = 5(x+2)-5
(b) Now, we can solve this equation:
x+3x+12 = 5x+10-5
4x+12 = 5x+5
12-5 = 5x-4x
x = 7
Middle sister = 7+2 = 9 years
Oldest sister = 7+4 = 11 years
Hence, the equation is x+3(x+4) = 5(x+2)-5 and their ages from the youngest to the oldest are 7, 9 and 11 years respectively.
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Please help I’ll mark you as brainliest if correct!!
Answer: The answer is 5
Step-by-step explanation:
(c) If sand and cement are mixed in the ratio of 2:5,find the part of them in fraction
Answer:
The sand is 2/5 and the cement is 5/7
Step-by-step explanation:
You need to get the total parts of both by adding the numerator and the denominator, and then divide the amount of parts by the total amount of parts.
The graph shows a linear relationship between x and y. What is the rate of change of
y with respect to x for this function?
The rate of change of y with respect to x for this function is equal to: C. 2.
How to calculate the rate of change (slope) of a line?In Mathematics and Geometry, the rate of change (slope) of any straight line can be determined by using this mathematical equation;
Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope) = rise/run
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the rate of change (slope) of a line, we have the following;
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope) = (5 - 1)/(2 - 0)
Rate of change (slope) = 4/2
Rate of change (slope) = 2.
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mark is trying to remeber is account number his account has 6 digits he knows that the 6 digit are 2,3,5,7,8 and 9 but he cant rember the sequen in the correct order how many possible ways are there for mark to find the correct order
Answer:
720
Step-by-step explanation:
Formula: P (n,r) = n! ÷ (n - r)!
n = Total number of objects in a set
r = The number of items you choose
Mark knows the account number includes the numbers 2,3,5,7,8, and 9. There are obviously 6 numbers in total in this set and 6 he must choose in order to have a 6 digit account number, which the problem also directly states he has.
That means P(n,r) = P(6,6)
!/Factorial = Product of all positive numbers less than or equal to the given positive number
Therefore, 6! = 1 x 2 x 3 x 4 x 5 x 6
P (n,r) = P(6,6) = 6! ÷ (6-6)! = 720
find the number such that when 3/4of it is added to 3 whole number 1/2 the sum is the same as when 2/3 of it is subtracted from 6 whole number 1/2
The number such that when 3/4of it is added to 3 whole number 1/2 the sum is the same as when 2/3 of it is subtracted from the 6 whole number 1/2 is 36/17
What is a fraction?A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as the one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) the line on which the numerator is shown. Compound fractions, complicated fractions, and the mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.
The numerator and denominator of the positive common fractions are both natural integers. The denominator tells how many of those equal parts make up single unit or fraction, whereas the numerator represents the number of equal parts. Since a whole can never be made up of zero parts, denominator cannot be zero.
3/4 of it is added 3 1/2 sum is the same way as when 2/3 of it is subtracted from 6 1/2
The way I see it is
[tex]\frac{3}{4} x+3\frac{1}{2} = 6\frac{1}{2}-\frac{2}{3} x[/tex]
[tex]\frac{17}{12} x= 3[/tex]
[tex]x=\frac{36}{17}[/tex]
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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
What is a function?
A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variablegiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
We possess
P/64 = 64d/64
d = P/ 64
P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
The value is 10.5 feet.
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
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There are about 146 million sheep in China and 101 million sheep in Australia. The number of sheep in Australia is what percent less than the number of sheep in China?
Answer: 4500% i think
Step-by-step explanation: no explanations pls
7th grade math please help!
Answer:
B
Step-by-step explanation:
Percentages represent the fraction over 100.
2:5:4=n:8 so please do this for me
The mismatch in the number of variables in the ratio, implies that the ratio is undefined
How to evaluate the ratio?The ratio expression is given as:
2 : 5 : 4 = n : 8
In the above ratio expression, we have the following observations:
Right-hand side: Two variablesLeft-hand side: Three variablesIf the ratio expression is to represent an equivalent expression, then the number of variables on both sides of the expression must be the same
This in other words implies that
When the number of variables on either sides of the ratio expression, then the ratio is either incorrect or undefined
In this case, we can conclude that the ratio is undefined
Hence, the value of n in the ratio given as 2 : 5 : 4 = n : 8 is undefined
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Which expression shows the distance on the number line between 2 and −7?
Responses
∣∣2−(−7)∣∣
open absolute value 2 minus open parenthesis negative7 close parenthesis close absolute value
∣∣−7+2∣∣
open absolute value negative 7 plus 2 close absolute value
∣∣2+(−7)∣∣
open absolute value 2 plus open parenthesis negative 7 close parenthesis close absolute value
|2−7|
pls help quick
The correct expression to show the distance between 2 and -7 is :
∣∣2−(−7)∣∣
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
2x + 3 is an example of a variable mathematical expression. Every variable must have a coefficient, which is a number multiplied by the variable. The coefficient of x in the formula 2x + 3 is the number 2, and it signifies 2 times x plus 3.
The expression that shows the distance on the number line between 2 and −7 is |2−(−7)|. If we solve the given expression to calculate the distance then it can be solved as,
||2−(−7)||
= ||2 + 7||
= ||9||
= 9
Hence, the expression that shows the distance on the number line between 2 and −7 is 9 units.
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
THE FIRST SHAPE LOOKS LIKE A PARALLELOGRAM IN A PARALLELOGRAM OPPOSITE SIDES ARE EQUAL.
THE LAST SHAPE IS A RECTANGLE OPPOSITE SIDES OF ARECTANGLE ARE EQUAL
FOR THOSE OTHER TWO(TRAPEZIUM AND THE OTHER THEY ARE SHAPED SUCH THAT OPPOSITE SIDES ARE NOT EQUAL.
THE FIRST AND LAST SHAPE BEST FIT AS THE SOLUTION OF THE QUESTION.
help fill in the blanks on the second problem i have the answer already
Given equation is,
[tex]g(x)=x^2+3x-10[/tex]Then,
[tex]\begin{gathered} g(f(x))=\lbrack f(x)\rbrack^2+3\lbrack f(x)\rbrack-10 \\ =(x+4)^2+3(x+4)-10 \\ =x^2+8x+16+3x+12-10 \\ =x^2+11x+18 \end{gathered}[/tex]So in the first blank, it will be,
[tex]=(x+4)^2+3(x+4)-10[/tex]And in the second blank it will be,
[tex]undefined[/tex]I have an algebra question, no rush, please explain if you can, if not that is okay.
Answer:
a) [tex]6x^2 + 17x + 31 + \frac{70}{x-2}[/tex]
Step-by-step explanation:
(see attachments for explanation)
If a person shoots a basketball overhand from a position 8 feet above the floor, then the path of the basketball 2 through the hoop can be modeled by the parabola y = +1.15x+8, where v is the initial velocity of the ball in 0.434v ft/sec, y is the height of the ball and x is the distance away from the person. (a) If the basketball hoop is 10 ft high and 11 ft away, what initial velocity v should the basketball have?
Basketball should have 20.64 ft/s initial velocity.
What is velocity?When an object is moving, its velocity is the direction at which it is moving as a measure of how quickly its location is changing as seen from a certain point of view and as measured by a specific unit of time. velocity. It is the quickness, swiftness, or speed of movement, action, or operation. A measurement of a body's rate of motion in physics is the rate at which its location changes over time in a certain direction.
Given Data
The parabola y=(-16x2/0.434v2)+1.15x+8 can be used to represent the ath of a basketball through a hoop, where v is the ball's speed in feet per second, y is the hoop's height, and x is the distance from the hoop. When the basketball hoop is 10 feet high and 17 feet away, the following is true:
y = (-16x⁰.434v²)+1.15x+8
10 = [-16(17)⁰.434v²] + 1.15(17) + 8
v = 24.64 ft/s
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equations help me please
Solve the equation and check
___________________
-89 = 11 - 4x
4x = 89 +11
x = 100/ 4
x= 25
________________
Can you see the updates?
___________________
Verifying
if x= 25
so then
-89 = 11- 4*(25)
-80
50 points!
Find the acceleration of the two blocks. The is system is initially at rest and the friction coefficient are as shown in Fig.
Given mA = mB = 10Kg.
__________________◇~
I have solution available , due to less explanation unable to understand . So please provide PROPER EXPLANATION!
DON'T SPAM CAUSE ANSWER WILL BE FOR SURE REPORTED.
Thankyou in advance! :)
Answer:
Here is a suggestion I hope I helped
A movie theater sells tickets for $12 for adults and $7 for children.
On one weekend, 267 people visited and the total ticket sales was $2379
How many adults attended?
Answer:
102 adults, 165 children
Step-by-step explanation:
Let a be the number of adults, and let c be the number of children. We set up and solve this system of equations:
a + c = 267---------> 7a + 7c = 1869
12a + 7c = 2379------->12a + 7c = 2379
-----------------------
5a = 510
a = 102, c = 165