Answer:
a = 10/3 and b = -196/51.
Step-by-step explanation:
4a + 2b - 12ax + 15b = -40x - 52
Equating coefficients of x:
-12ax = -40x
-12a = -40
a = 40/12
= 10/3.
Equating constants:
4a + 2b + 15b = -52
4a + 17b = -52
Substituting a = 10/3:
40/3 + 17b = -52
17b = -52 - 40/3
b = (-52 - 40/3) / 17
= (-156/ 3 - 40/3) / 17
= -196 / 51
question is attached to image
question 9a
pls help
Answer:
(x-2y){5-(x-2y)}
=(x-2y)(5-x+2y)
If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?
Answer: Answer is 16 new releases and 22 classic movies.
Step-by-step explanation:
He'll buy 16 new releases and 22 classic movies.
Let x = number of new releases
Let y = number of classics.
The equation to solve the question will be:
20x + 8y = 500
When x= 16 and y = 22, thus will be:
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, since this is the number closest to $500, therefore this will be the appropriate number of movies that he can buy.
In conclusion, he'll buy 16 new releases and 22 classic movies.
Learn more about Algebra here brainly.com/question/28504118
#SPJ10
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
Using exponent properties, the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
What is the equivalent expression?The original expression is:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]
When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]
The negative exponent at the numerator goes to the denominator, hence:
[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]
The negative outer exponent means that we have to exchange the numerator and denominator, hence:
[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
More can be learned about exponent properties at https://brainly.com/question/11975096
#SPJ1
Answer:
y^18/x^18
Step-by-step explanation:
The parent graph for a linear function and an absolute value function are shown below. Compare and contrast the two functions. Please include information about the characteristics of each graph, including, but not limited to domain/range, shape of the graph, etc.
From the left, the first graph's characteristics is as follows
v shaped representing two straight line graphIt has two slopes, one is negative the other is positive slopeThe intercept is 0The domain is - 10 to 10The range is - 10 to 10The graph passed through the originThe second graph characteristics is as follows
The shape represents a single straight line graphThe graph has one positive slopeThe intercept is zeroThe domain is - 10 to 10The range is - 10 to 10This graph passed through the originWhat is a graph?A graph is a pictorial representation of values used in data presentation. A graph is very useful in research as the values can help show the relationship between the data obtained. Graphs can also be used to predict events and can have multiple other uses depending on the type of graph and the nature of data plotted.
A graph has so many features that varies by the type of graph and the information it is representing. The graph treated here is a straight line graph and the equation is: y = mx + c
where m is the slope , and c is the intercept
Read more on graphs here: https://brainly.com/question/19040584
#SPJ1
What is the difference between 0.2 and 0.2 repeating? How can you operate with both 0.2 and 0.2 repeating? Will the results from operating with the two rational numbers be the same or different? Provide Justification and examples to prove your reasoning.
The difference between 0.2 and 0.2 repeating is that 0.2 is that rational number and 0.2 repeating is the rational number.
What is defined as the rational and irrational numbers?Irrational numbers are real numbers that can't be depicted as a ratio-like fraction, p/q, where q and p are integers. In other words, irrational numbers are real numbers which are not rational numbers.Rational numbers are written in the form p/q, where p and q are any integer and q 0 respectively.Q represents the set of rational numbers. A rational number is one that can be demonstrated as a fraction with both the numerator and denominator being integers.For the two given values;
0.2 is the rational number as it can written in the fraction form as;
0.2 = 2/10
0.2 = 1/5 which is in the p/q form.
For the value of 0.2... repeating is also the rational number as it can be also written in the form of p/q.
0.2... = 0.2 bar is the correct representation.
Therefore, the number 0.2 and 0.2 repeating are the rational numbers.
To know more about the rational number, here
https://brainly.com/question/12088221
#SPJ9
Eleri has 97 cents credit on her phone it costs 6 cents to send a message. How many people can eleri send a message to? Explain how you worked it out.
please and thank you.
25 points plus brainliest
Answer: y-3 = 3(x+4)
Step-by-step explanation:
See attached
sam is 6 years older than mia. mia is 3 years younger than alice. if sam is 19 years old, how old is alice?
a) 17
b) 16
c) 10
d)18
e) 15
9. If h(x)=√x-3 +5, then for what value(s) of 10
x does h(x) = 3?
Answer:
There are no values of x that make this equation true.
Step-by-step explanation:
We know h(x)=[tex]\sqrt{x-3} +5[/tex]
So lets substitute h(x) for 3
3=[tex]\sqrt{x-3}+5[/tex]
We are going to then subtract 5 from each side leaving us with
-2=[tex]\sqrt{x-3}[/tex]
We then need to get rid of the square root, so we will square both sides. which gives us
4=x-3
We then need to subtract 3 from both sides which leaves us with
x=1
However, when you substitute 1 for x into the original equation, you get
h(x)=[tex]\sqrt{-2}+5[/tex]
Which is not equal to 3
Therefore, there are no values of x that make this equation true.
Find the area of the shaded region. All angles are right angles.
5m
30 m
20m
5m
if [tex]i = \sqrt{-1}, what is i^3[/tex]i^3 equal to?
(a-b)(a+b)-c(c-2b) help me guys
Answer:
a^2-b^2+2bc-c^2
Step-by-step explanation:
We multiply a with a and negative b with b. Then multiply negative c with c and multiply negative c with negative 2b. After all add/ subtract like terms
The cost of pumpkins is shown in the table. Determine whether the cost of a pumpkin is proportional to the number bought by graphing the relationship on the coordinate
plane. Explain.
Number of Pumpkins: 0 1 2 3 4
Cost: ($) 0 4 8 12 16
Cost of pumpkins
y
16
12
8
4
0 2 4 6 8 x
Pumpkins
Yes, it is true the cost of a pumpkin is proportional to the number bought.
What is the Proportional Relationship?
We are given the table showing cost of each number of pumpkins. Now, let us analyze the table values;
1) When number of pumpkins is 1, then cost is $4. Thus;
Cost per pumpkin = 4/1 = $4 per pumpkin
2) When number of pumpkins is 2, then cost is $8. Thus;
Cost per pumpkin = 8/2 = $4 per pumpkin
3) When number of pumpkins is 3, then cost is $12. Thus;
Cost per pumpkin = 12/3 = $4 per pumpkin
4) When number of pumpkins is 4, then cost is $16. Thus;
Cost per pumpkin = 16/4 = $4 per pumpkin
In all these rates, we see that the cost rate for pumpkins remains the same. Thus, we can conclude that it is true the cost of a pumpkin is proportional to the number bought.
Read more about Proportional Relationship at; https://brainly.com/question/12242745
#SPJ1
Which factor provides the basis for the grading of newly diagnosed malignant tumors? size of the tumor x number of metastases degree of differentiation of the cells number of lymph nodes involved
The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.
What is the degree of differentiation?The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.
The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.
To know more about degree of differentiation, visit:
https://brainly.com/question/28104656
#SPJ4
what is the MAD for 3,4,5,5,5,6,6,6,7,8
Answer:
1.1
Step-by-step explanation:
Find the mean of the data:(3+4+5+5+5+6+6+6+7+8)/10 = 5.5Step 2: Find the difference between each data and mean:Difference between 3 and 5.5 is 2.5Difference between 4 and 5.5 is 1.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 7 and 5.5 is 1.5Difference between 8 and 5.5 is 2.5Step 3: Add all the differences:2.5+1.5+0.5+0.5+0.5+0.5+0.5+0.5+1.5+2.5 = 11Step 4: Divide it by the number of data:11/10 = 1.1So, the MAD = 1.1
The records of four baseball teams are shown below. Which team had the greatest percent of wins?
Rattlers won 95 and lost 65. Cobras Won 92 and lost 58. Boas Won 94 and lost 66. Pythons won 96 and lost 64.
the Boas
the Cobras
the Pythons
the Rattlers
Answer:
The Cobras
Step-by-step explanation:
I just took the test
Answer:the Cobras
Step-by-step explanation:
Pls help me im not that smart !!
Work Shown:
5 times 2 = 10
5 times 13 = 65
5 times 2.13 = 10.65
This rounds to 10.7 when rounding to the nearest tenth, i.e. one decimal place.
Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he earn, m, when he shows up to your house to do a job that takes h hours?
Answer:
50 + 20h
Step-by-step explanation:
Select the correct answer.
Simplify the following expression.
4 -11/3 divided by 4 -2/3
A 12
B. 1/64
C. 64
D. 12
The correct value of the expression is 4/5.
How to calculate the fraction?The question is about simplifying 4 -11/3 divided by 4 -2/3.
It should be noted that 4 - 1 1/3 = 2 2/3
Also, 4 - 2/3 = 3 1/3
We will divide
2 2/3 ÷ 3 1/3
= 8/3 ÷ 10/3
= 8/3 × 3/10
= 4/5
Note that the correct option wasn't given.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Answer: The correct value of the expression is 4/5.
How to calculate the fraction?
The question is about simplifying 4 -11/3 divided by 4 -2/3.
It should be noted that 4 - 1 1/3 = 2 2/3
Also, 4 - 2/3 = 3 1/3
We will divide
2 2/3 ÷ 3 1/3
= 8/3 ÷ 10/3
= 8/3 × 3/10
= 4/5
Note that the correct option wasn't given.
Step-by-step explanation:
which value is an irrational number? a. 4/19 b. the square root of 200 c. the square root of seven over the square root of seven d. -0.58 repeated
Answer:
B. √200
Step-by-step explanation:
An irrational number is a number that excludes single-point decimals but includes integers and fractions. A square root is a repeating decimal(Most of the time), therefore, this is an irrational number.
the number of triangles is 1/3 the number of sides
Answer:
y=(1/3) or y=1/3x
Step-by-step explanation:
Without the parenthesis, your equation can be interpreted as Y = one over 3x
The equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
Let's denote the number of sides of a polygon as "s" and the number of triangles that can be formed within the polygon as "t."
The equation for the number of triangles being 1/3 the number of sides is:
t = (1/3) × s
This equation states that the number of triangles (t) is equal to one-third of the number of sides (s) in a given polygon.
Hence, the equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
To learn more on Triangles click:
https://brainly.com/question/29083884
#SPJ3
Complete question:
Write an equation for the number of triangles is 1/3 the number of sides.
A truck can be rented from Company A for $90 a day plus $0.40 per mile. Company B charges $60 a day plus $0.70 per mile to rent the same truck.
Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same will be 10 miles.
How to calculate the value?Let the number of miles be represented by x.
Therefore the equation for the first company will be 90 + 0.4m
The equation for the second company will be 60 + 0.7m
Therefore, we will equate them. This will be:
90 + 0.4m = 60 + 0.7m
Collect like terms
90 - 60 = 0.7m - 0.4m
0.3m = 30
m = 30/0.3
m = 10
The number of miles will be 10 miles.
Learn more about equations on:
brainly.com/question/4291546
#SPJ1
.How many gallons of hydrochloric acid must be added to
12 gallons of a 30% solution to obtain a 40% solution
Answer:
5.6
Step-by-step explanation:
.30*12+x=.40(12+x)
3.6+x=4.8+.40x
x-.40x=4.8-3.6
.6x=1.2
x=1.2/.6
x=2 gallons of acid needs to be added.
Proof:
.30*12+2=.4(12+2)
3.6+2=.4*14
5.6=5.6
If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
The different ways can a student check off one answer to each question is 1024.
It is required to find the different ways can a student check off one answer to each question.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
If a multiple choice test consists of 5 questions each with 4 possible answers of which only one is correct,
,To find how many different ways can a student check off one answer to each question we have,
: 4^5 = 2^10
= 1024
Therefore, the different ways can a student check off one answer to each question is 1024.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Find the area of a circle with a 15inch diameter in terms of pie
Answer:
56.25π in²
Step-by-step explanation:
The area of a circle is given by πr², where r is the radius of the circle.
Given that the diameter is 15 inch, let's calculate the radius.
Diameter= 2 ×radius
Radius
= 15 ÷2
= 7.5 in.
Applying the formula for area of circle,
area of circle
= π(7.5)²
= 56.25π in²
Since the question requires for the answer to be in terms of π, we have arrived at our answer.
For more about area of circle, do check out: https://brainly.com/question/19168464?utm_source=android&utm_medium=share&utm_campaign=question
A television uses 1 unit of electricity every 10 hours.
A unit of electricity costs 9.8 p.
Calculate the cost of having a television turned on for 24 hours.
Answer:
Step-by-step explanation:
9.8 p = 10 hours
24 hours = ?
= 24 hours (9.8p)
10 hours
=23.92p
find the midpoint of the line segment with the given points.
Answer:
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
Step-by-step explanation:
We will use the midpoint formula to solve.
[tex]\displaystyle (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )[/tex]
[tex]\displaystyle (\frac{0+-5 }{2}, \frac{3+5}{2} )[/tex]
[tex]\displaystyle (\frac{-5 }{2}, \frac{8}{2} )[/tex]
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
If the radius of a circle is 16 inches find the diameter area and circumference
diamater:
[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]
circumference:
[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]
Hope that I helped you!
Find the GCF 1.16,60 2.52,84 3.32,89,144 4.48,96,108 5.144,176,1
Answer:
The GCF is 1.
Step-by-step explanation:
The factors of 1 are: 1
The factors of 1 are: 1
The factors of 2 are: 1, 2
The factors of 3 are: 1, 3
The factors of 4 are: 1, 2, 4
The factors of 5 are: 1, 5
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 89 are: 1, 89
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 176 are: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
Then the greatest common factor is 1.
What is the standard deviation and its meaning given this population of customer ages? 45, 76, 30, 22, 51, 40, 63, 66, 41
The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}[/tex]
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
N is the number of observations in the data set.
It is given that:
The data set:
45, 76, 30, 22, 51, 40, 63, 66, 41
From the formula:
∑(x(i) - X)² = 2463.55
N = 9
SD = √(2463.55/9)
SD = 16.54
Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
Learn more about the standard deviation here:
brainly.com/question/12402189
#SPJ4