Answer:
A pastry shop has fixed costs of
$
280
per week and variable costs of
$
9
per box of pastries. The shop’s costs per week in terms of
x
,
the number of boxes made, is
280
+
9
x
.
We can divide the costs per week by the number of boxes made to determine the cost per box of pastries.
280
+
9
x
x
Notice that the result is a polynomial expression divided by a second polynomial expression. In this section, we will explore quotients of polynomial expressions.
Simplifying Rational Expressions
The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let’s start with the rational expression shown.
x
2
+
8
x
+
16
x
2
+
11
x
+
28
We can factor the numerator and denominator to rewrite the expression.
(
x
+
4
)
2
(
x
+
4
)
(
x
+
7
)
Then we can simplify that expression by canceling the common factor
(
x
+
4
)
.
x
+
4
x
+
7
Answer:
Step-by-step explanation:
Use the identity : a² - b² = (a + b )(a - b)
25 and 36 should be written in the form raised to power 2
25 = 5 * 5 = 5²
36 = 6 * 6 = 6²
[tex]\frac{e^{2}}{25}-\frac{f^{2}}{36}=\frac{e^{2}}{5^{2}}-\frac{f^{2}}{6^{2}}\\\\=(\frac{e}{5})^{2}-(\frac{f}{6})^{2}\\\\=(\frac{e}{5}+\frac{f}{6})(\frac{e}{5}-\frac{f}{6})[/tex]
Find the value of x.
Answer:
6
Step-by-step explanation:
The two small triangles are congruent by SAS.
By CPCTC, x = 6.
Answer: 6
what is 7.266435 986 159 17 to the nearest integer?
Answer:
7
Step-by-step explanation:
Rounding rules. Anything below 5 will round down
Kristin
spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost
$15. If she bought a total of 7 then how many of each kind did she
buy?
tell whether the ordered pair is a solution of the system of liner equation (3,2)x+y=5 y-2x=-4
Given:
The two linear equations are:
[tex]x+y=5[/tex]
[tex]y-2x=-4[/tex]
To find:
Whether the ordered pair (3,2) is a solution of the given system of liner equations.
Solution:
We have,
[tex]x+y=5[/tex] ...(i)
[tex]y-2x=-4[/tex] ...(ii)
If both the equations are satisfy by the point (3,2), then this point is the solution of the given system of equations.
Putting [tex]x=3,y=2[/tex] in (i), we get
[tex]3+2=5[/tex]
[tex]5=5[/tex]
This statement is true. It means the point (3,2) satisfies the equation (i).
Putting [tex]x=3,y=2[/tex] in (ii), we get
[tex]2-2(3)=-4[/tex]
[tex]2-6=-4[/tex]
[tex]-4=-4[/tex]
This statement is true. It means the point (3,2) satisfies the equation (ii).
Since both the equations are satisfy by the point (3,2), therefore the point (3,2) is the solution of the given system of equations.
1. x+1 when x=10
2. 5y-8 when y=6
3. 6t-9m when t=5 and m=3
4. 62/2 when x=10
5. 5h3-3j2+20 when h=4 and j=5
Answer:
1
X is equal to 10
10 plus 1 equals 11
2
y is equal to 6
30 minus 8
is equal to 22
3
m equals 3 and t equals 5
30 minus 27
is equal to 3
4 not written properly
5 not written properly
A scientist used a microscope to count the number of bacterial cells in a petri dish every hour. The graph shows the data collected.
Which function most accurately represents this data, where n is the number of bacteria and t is the time elapsed, in hours?
n = 2t
n = 2^t
n = t^2
n =
how many minutes will it take for a plane altitude to change by -5,400 meters
Answer:
I believe it will be 5 minutes for it to reach that.
Identify the slope and y-intercept of the following equation:
3x - 2y = -10
Answer:
m=3/2,y-int=5
Step-by-step explanation:
y=mx+b is the slope equation. since -10 is at the end of the equation and it does not have a variable next to it yk it is the y-intercept. if you want you draw this on a graph and you can see that you go up 3 and over 2
A student simplified the expression (3x^2+2)-(2x^2+4) as x^2+^6 Explain what the student did incorrectly and state the correct answer.
Answer:
x^2 - 2
Step-by-step explanation:
The correct procedure would have been to distribute the negative to the +4 also, so you would have +2 - 4 = -2 so the final answer should have been
x^2 - 2
(3x²+2)-(2x²+4)
write in a different form, remove parentheses
3x²+2-2x²-4
calculate the value of the corresponding terms
x²-2
Answer: Yes, he made a mistake.
A simplified expression would look like this x²-2 and not like this x²+^6.
Can someone help me slove this plss. :-)
Answer:
Step-by-step explanation:
.
Please help me I will give brainlest if right
What is the complete factorization of the polynomial below?
x^2 + 4x^2 + 16x + 64
O A. (x-4)(x + 4i)(x + 4i)
B. (x + 4)(x + 4i)(x + 4i)
C. (x + 4)(x + 4i)(x-4i)
O D. (x-4)(x + 4i)(x-4i)
Given:
Consider the given polynomial is:
[tex]x^3+4x^2+16x+64[/tex]
To find:
The complete factorization of the given polynomial.
Solution:
We have,
[tex]x^3+4x^2+16x+64[/tex]
Using grouping method, we get
[tex]=(x^3+4x^2)+(16x+64)[/tex]
[tex]=x^2(x+4)+16(x+4)[/tex]
[tex]=(x+4)(x^2+16)[/tex]
[tex]=(x+4)(x+4i)(x-4i)[/tex] [tex][\because x^2+y^2=(x+iy)(x-iy)][/tex]
Therefore, the correct option is C.
In the sequence: 20, 25, 23, 28, 26, …, what number should come next?
a) 24
b) 31
c) 21
d) 28
Answer:
b) 31
Step-by-step explanation:
20 + 5 = 25
25 - 2 = 23
23 + 5 =28
28 - 2 = 26
pattern: add 5 then subtract 2
since we subtract last, we would add 5 on 26:
26 + 5 = 31
Answer:
31
Step-by-step explanation:
In the sequence they are adding 5 and taking away 2. So if they start with 20, they added 5 and took away 2, it was 23. Then they added 5 again and it was 28, they took away 2 and it was 26. If they add 5, the next number would be 31.
Hope it helped :)
what two number multiply to make -36 as well as add to make 16
-12 x 3 = -36
-6 x 6 = 36
-8 x 2 = -16
-4 x 4 = -16
The mapping diagram shows a relation. A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2). What is the domain of the relation? {x| x = –4 , 0, 1, 2}. {x| x = –7, –6, 2, 11, 3}. {y| y = –4, 0, 1, 2}. {y| y = –7, –6, 2, 11, 3}.
Answer:
b
Step-by-step explanation:
The domain is a set of input values so {x| x = –7, –6, 2, 11, 3} will be the domain of the relation therefore option (B) will be correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
The domain is the set of all input values where the function is defined.
Since in the given relation ;
All input values have an output so all input values will be the domain of the given relation.
Hence "{x| x = –7, –6, 2, 11, 3} will be the domain of the relation".
For more details about the range and domain of the function,
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2020-2021-T-Math-Gr05-T10
Question: 1-5
Lia cut a long piece of string into 2 pieces. one piece of the string is 24 inches long, and the other place of the string is 12 inches long How many feet long was the piece of string before a cut it?
Answer:
36 inches.
Step-by-step explanation:
If one piece of string is 12 inches
and the second piece = 24 inches
Then the total is 12 + 24 = 36 inches.
1. How long does it take running at a rate of 12m/s over a distance of 360m?
Step-by-step explanation:
T=D/S
D=360m
S=12m/s
360m÷12m/s
Time=30s
Help me out , plzzzzz
Answer:0.14%
Step-by-step explanation:
Andy buys a new car for $23,540. He estimates that the new car will decrease in value by about 5% each year. Which of the following functions best models this situation?
f(x)=23,540(1.05)xf of x is equal to 23 comma 540 times 1 point 0 5 to the x th power
f(x)=23,540(0.95)xf of x is equal to 23 comma 540 times 0 point 9 5 to the x th power
f(x)=−23,540(1.05)xf of x is equal to negative 23 comma 540 times 1 point 0 5 to the x th power
f(x)=−23,540(0.95)x
The function that best models the situation is f(x) = 23540(0.95)ˣ, where x is the number of years.
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, Andy buys a new car for $23,540. He estimates that the new car will decrease in value by about 5% each year.
The depreciation rate =
A = P(1-r)ⁿ
Where, A = amount final
P = initial amount
r = rate and n = number of the years
Therefore,
The depreciation rate =
f(x) = 23540(1-0.05)ˣ
f(x) = 23540(0.95)ˣ
Hence, the function that best models the situation is f(x) = 23540(0.95)ˣ, where x is the number of years.
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3
Carl's baseball team is selling
trash bags to raise money for
uniforms and equipment. Each
player starts with a credit of $50
towards their sales, and each roll of
trash bags sells for $8. Determine
how many rolls of trash bags each
person must sell to make $300.
Answer:
32
Step-by-step explanation:
One member would make 250$ by selling 31.25 rolls. Which if you round up you get 32. You can't sell a quarter of a roll so you must go up one therefore the answer is one person must sell 32 rolls in order to make 300$ including the 50$ already towards his credit.
Winston earns $140.00 by selling 56 hot dogs at a concession stand at school. Using the same rate for the cost of one hot dog, how many more hot dogs would winston need to sell to earn a total of 185.00?
Complete the following table for f(x) = -2.4"
-2
-1
0
1
2
-2
[
Choose
- 1
Choose)
0
Choose!
1
Choose
2
Choose
Answer:
3
Step-by-step explanation:
Expand and simplify
2(m - 3) + 3(m + 4)
Answer:
5m+6
Step-by-step explanation:
Hello There!
We can simplify the given expression using distributive property
We can distribute the 2 to the m and - 3
2 * m = 2m
2 * -3 = -6
Now lets distribute the 3 to the m and the 4
3 * m = 3m
3 * 4 = 12
we´re left with
2m - 6 + 3m +12
our final step would be to combine like terms
2m + 3m = 5m
-6 + 12 = 6
so the simplified version would be
5m+6
4. What is the slope-intercept equation of the
line that goes through the points (1, 5) and
(2,8)?
A. y = 2x - 3
B. y = x + 1
C. y = 3x + 2
D. y =- 1.5x – 2
Answer:
Answer C: y=3x+2 because the y-intercept is positive 2 if you graph it
Derek's car has run out of gasoline. He walks 24 km west and then 10 km south looking for a gasoline station. If he is now h km directly from his starting point, find the value of h
Answer:
the value of h is √676km
Step-by-step explanation:
The computation of the value of h is shown below
Here we apply the Pythagoreus theorem
= 24^2 + 10^2
= 576 + 100
= √676
Hence, the value of h is √676km
We simply determine by using the Pythagoreus theorem
Please help me with this i will give brainliest
Answer:
i think it's 10%
Step-by-step explanation:
How do you graph it ?
Answer:
It should look like this
Step-by-step explanation:
hope it helps
Find the value of 3p2 – 4p -5, if p= -3
Answer:
-11
Step-by-step explanation:
3 x (-3) x 2 - 4 x (-3) - 5
= -18 + 12 - 5
= -11
Can someone please answer this for me.
Answer:
[tex]\huge\boxed{\sf Slope = \frac{9}{7}}[/tex]
Step-by-step explanation:
The top and bottom points of the line are
(3,0) and (10,9)
[tex](x_1,y_1) = (3,0)\\\\(x_2,y_2) = (10,9)[/tex]
So,
[tex]\sf Slope = \frac{y_2-y_1}{x_2-x_1}\\\\Slope = \frac{9-0}{10-3} \\\\\boxed{\sf Slope = \frac{9}{7} }\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH180720 Points!!!! PLEASE help!! Math!! Due soon!!
Answer:
the first one is true, the third one is true, the fourth one is true, the fifth one is true
Step-by-step explanation:
the second one is false
Anyone know the answer to this ?
Answer:
no srry
Step-by-step explanation: