What is the solution to the equation 9(w-4)-7w=5(3w-2)
Answer:
2
Step-by-step explanation:
true or false. If f is a function, the f(s+t) = f(s)+f(t). ...?
The statement is true for linear functions, but not in general for all functions.
Explanation:The statement is true if f(x) is a linear function.
However, it is not true in general for all functions, so the statement is false.
An example of a linear function where the statement is true would be f(x) = 2x.
If we substitute s + t into the function, we get f(s + t) = 2(s + t) = 2s + 2t.
On the other hand, if we substitute f(s) + f(t) into the function, we get f(s) + f(t) = 2s + 2t.
Therefore, the equality holds and the statement is true for linear functions.
Part 1 : When solving systems of equations, how do you determine what method to use?
Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.
–y + 3x = 6
y = –6x + 12
6x – 4y = 54
–9x + 2y = –69
2y = x + 1
–2x – y = 7
...?
To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).
Explanation:When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.
Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:
Substitute the expression for y from the second equation into the first.So –(–6x + 12) + 3x = 6.Simplify to get 6x – 12 + 3x = 6.Combine like terms to get 9x – 12 = 6.Add 12 to both sides to get 9x = 18.Divide by 9 to find x = 2.Plug x back into the second equation to get y = –6(2) + 12, hence y = 0.Our solution is (x, y) = (2, 0).
Simplify.
5√7+√7-2√7
3√7
3√21
4√21
4√7
Answer: 4 sqrt 7
Step-by-step explanation:
He is correct, the answer is the one above.
Option (D) To simplify the expression 5√7 + √7 - 2√7, combine like radicals by adding their coefficients to get the simplified form, which is 4√7.
The student is asked to simplify the expression 5√7 + √7 - 2√7. To simplify an expression that involves like radicals, combine them by adding or subtracting their coefficients, just as you would combine like terms in algebra.
The expression simplifies as follows:
Combine the terms with like radicals: (5 + 1 - 2)√7
Simplify the coefficients: 4√7
Therefore, the simplified form of the expression is 4√7.
Algebra 2 Word Problem: Set up using 3 variables & 3 equations:
"A friend e-mails you the results of a recent high school swim meet. The e-mail states that 24 individuals placed, earning a combined total of 53 points. First place earned 3 points, second place earned 2 points, and third place earned 1 point. There were as many first-place finishers as second and third-place finishers combined."
A: Write a system of THREE equations that represents how many people finished in each place.
B: How many swimmers finished in first place, second and third?
Final answer:
To solve the word problem, we define three variables representing the number of first-, second-, and third-place finishers, respectively. We set up three linear equations based on the information provided, and by solving the system, we determined that 10 swimmers finished in first place, 8 in second, and 6 in third.
Explanation:
Setting Up the Equations
Let's denote the number of first-place finishers as x, second-place finishers as y, and third-place finishers as z. According to the information provided:
Total number of individuals placed: x + y + z = 24
Total points earned: 3x + 2y + z = 53
The number of first-place finishers equals the number of second and third-place finishers combined: x = y + z
This is our system of three equations.
Solving the System of Equations
To solve for the number of swimmers in each place, use the substitution or elimination method:
Since x = y + z, substitute x in the first two equations.
You'll get two equations with two variables (y and z).
Solve these equations to find the values of y and z.
Finally, substitute the found y and z back into x = y + z to get the value of x.
By solving this system, we find that 10 swimmers finished in first place, 8 swimmers finished in second, and 6 swimmers finished in third.
A baker bought some flour. he used 2/5 of the flour to make bread and used the rest to make batches of muffins. if he used 16ib. of flour making bread and 2/3ib.for watch batch of muffins,how many batches of muffins did he make?
Answer:
The baker made 36 batches of muffins.
Step-by-step explanation:
Let the total amount of flour be x
We know he used 2/5 of the flour for bread, we also know he used 16 pounds for bread.
We can write this as :
[tex]\frac{2}{5}\times x=16[/tex]
Solving this we get;
[tex]2x=80[/tex]
So, x = 40
Means total amount of flour was 40 pounds and he used 16 pounds for bread, so the remaining is for batches of muffins, which is [tex]40-16=24[/tex] pounds
As each batch of muffin uses 2/3 pounds, so 24 pounds of flour will be used to bake :
[tex]\frac{24}{\frac{2}{3} }[/tex]
= [tex]\frac{24\times3}{2} =36[/tex]
Hence, the baker made 36 batches of muffins.
Each set of ordered pairs represents a function. Write a rule that represents the function.
1. (0,0),(1,4),(2,16),(3,36),(4,64)
2. (0,0),(1,0.5),(2,2),(3,4.5),(4,8)
Student earned a 70% on a test with 50 questions how many questions were correct
Bruno uses a piece of wrapping paper with dimensions 1 and 1/4 feet by 3 feet to wrap a gift. What is the total area of the paper used to wrap the gift?
Area is determined by using the formula A=lw Area= Length x Width
A= 1 1/4 x 3 convert to an improper fraction
A= 5/4 x 3/1 multiply
A=15/4 divide
A=3 3/4 square feet
Answer: [tex]A=3\dfrac{3}{4}\ ft^2[/tex]
Step-by-step explanation:
Given: The dimensions of the wrapping paper :
[tex]1\text{ and}\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }1+\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }\dfrac{5}{4}\text{ feet }\text{ by 3 feet}[/tex]
Now, we know that the area of a rectangle is given by :-
[tex]A=length*width[/tex]
Now, the area of the wrapping paper is given by :-
[tex]A=\dfrac{5}{4}\times3=\dfrac{15}{4}=3\dfrac{3}{4}\ ft^2[/tex]
The number of students at marita's school decreased to 98% of last year's number currently there are 1170 students how many students were there last year round to the nearest whole number
There were about 1194 students at Marita's school last year.
To find the number of students last year when the current number is 1170 and represents 98% of last year's number, you can set up a simple equation.
Let "x" represent the number of students last year.
According to the given information, the current number of students is 98% of last year's number, which can be expressed as:
1170 = 0.98x.
To find the value of "x," you need to divide 1170 by 0.98:
[tex]\(x = \frac{1170}{0.98} = 1193.877\).[/tex]
Rounding to the nearest whole number, last year's number of students was approximately 1194.
So, there were about 1194 students at Marita's school last year.
To calculate the unit price of an item, divide the total number of units by the total price.
True or False?
Answer:
Its really false!!!!!
Step-by-step explanation:
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
Answer:
D isn't the correct answer. It's "It shrinks the graph vertically to 1/2 its original height."
Step-by-step explanation:
I'm not sure why though this is right because I graphed it, and I don't see how that could be the right answer.
Answer:
Option A - It shrinks the graph vertically to 1/2 its original height.
Step-by-step explanation:
Given : In the function [tex]y=\frac{1}{2} x^2[/tex]
To find : What effect does the number [tex]\frac{1}{2}[/tex] have on the graph, as compared to the graph of the function [tex]y=x^2[/tex] ?
Solution :
The parent function is [tex]y=x^2[/tex]
We have given that [tex]\frac{1}{2}[/tex] number is multiply to the parent function.
When the unit is multiply to the function gives you vertical stretch or compression
i.e, f(x)→ bf(x), o<b<1 then the function is vertically compressed.
[tex]y=\frac{1}{2} x^2[/tex] As [tex]0<\frac{1}{2}<1[/tex] means there is vertical compression or shrinks.
Therefore, Option A is correct.
It shrinks the graph vertically to 1/2 its original height.
What multiplies to make 12 and adds up to 16
Write two equations in standard form that are equivalent to the given equation.
1.5x+10y=15
2.-9x-12y=6
3.-2x+4y=-5
Equivalent equations can be created by multiplying or dividing the original equation by any nonzero constant. Lifting the coefficients of the given equations accordingly can create multiple equivalent equations.
Explanation:To create two equations that are equivalent to the given equation 1.5x + 10y = 15, we can multiply the entire equation by a nonzero constant. By multiplying by 2, we obtain 3x + 20y = 30. Conversely, dividing the original equation by 3 gives us 0.5x + 3.3333y = 5.
Applying the same concept to the second equation -9x - 12y = 6, multiplying by 2 gives us -18x - 24y = 12, and dividing by 3 gives us -3x - 4y = 2.
For the third equation -2x + 4y = -5, multiplying by any nonzero constant yields an equivalent equation. Multiplying by 2, we get -4x + 8y = -10, and dividing by 2 gives us -1x + 2y = -2.5.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?
A. P
B. Q
C. T
D. U
the answer is A my good sir/madam
Mae currently has a balance of $8,484.79 in an account earning simple interest. Seventeen years ago she opened the account with an initial deposit of $4,854. What is the interest rate on the account?
4.4%
2.5%
10.3%
5.9%
find the quotient -8b^2-26b+24/-8b+6
Use parallelogram JKLM to find the measure of Angle KLM.
A regression model in which more than one independent variable is used to predict the dependent variable is called
? a simple linear regression model
? a multiple regression model
? an independent model
? none of the above
Angle P is an acute angle.
Which could be the measure of angle P?
A.
80°
B.
100°
C.
90°
D.
180°
Answer
A
Step-by-step explanation:
4 pairs of jeans, 3 shirts, and 2 pairs of running shoes. how many combinations can you make
If 85% of a number is 17, then what is 60% of that number
Can you help me find the value of X?
Answer:
x ≈ 4.1 cm
Step-by-step explanation:
The side (z) opposite the 42° triangle can be found from the relation ...
z/(3.6 cm) = tan(42°)
z = (3.6 cm)·tan(42°) ≈ 3.2415 cm
The relationship between z and x is ...
z/x = cos(38°)
x = z/cos(38°) ≈ 4.1135 cm
x ≈ 4.1 cm
Is the coordinate (-2,-4) a solution to the equation y= 3x-2.
PLEASE HELP!!!
Lena is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges
$115
and allows unlimited mileage.
Company B has an initial fee of
$55
and charges an additional
$0.80
for every mile driven.
For what mileages will Company A charge less than Company B?
Use
m
for the number of miles driven, and solve your inequality for
m
.
Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.
a. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal.
b. How many cans are needed to meet or surpass your goal?
Change the fraction 3/4 into a fraction
Answer:
Step-by-step explanation:
6/8
A cone has a diameter of 10 inches. If its height is twice its radius, about what is the volume of the cone in cubic inches? Use 3.14 for π.
Answer with Step-by-step explanation:
The volume of cone is given by:
V=[tex]\dfrac{1}{3}\times \pi r^2h[/tex]
Where r is the radius of cone and h is height
r=d/2 where d is the diameter
Hence, here r=5 in.
height is twice its radius ⇒ h=10 in.
V=[tex]\dfrac{1}{3}\times 3.14\times 5^2\times 10[/tex]
V=261.66 in³
Hence, Volume of cone is:
261.66 in³
Use linear approximation to estimate 15^.25 ...?
at the party 2/5 of the pizzas ordered had pepperoni .The kids ate only 1/3 of the pepperoni pizzas, while the parents ate all of the remaining pizza. How much of all the pizza ordered was eaten by the kids ? ...?