Answer:
(14, 9 )
Step-by-step explanation:
Given
[tex]\frac{x}{7}[/tex] + [tex]\frac{y}{3}[/tex] = 5 ( multiply through by 21 to clear the fractions )
3x + 7y = 105 → (1)
[tex]\frac{x}{2}[/tex] - [tex]\frac{y}{9}[/tex] = 6 ( multiply through by 18 to clear the fractions )
9x - 2y = 108 → (2)
Multiplying (1) by - 3 and adding to (2) eliminates the term in x
- 9x - 21y = - 315 → (3)
Add (2) and (3) term by term to eliminate x
- 23y = - 207 ( divide both sides by - 23 )
y = 9
Substitute y = 9 into either of the 2 equations and evaluate for x
Substituting into (1)
3x + 7(9) = 105
3x + 63 = 105 ( subtract 63 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Solution is (14, 9 )
Find the Slope of the line through ( -4, 2 ) and (5, 8 )
Answer:
2/3
Step-by-step explanation:
Y2-Y1/X2-X1
8-2/5-(-4)
6/5+4
6/9
Slope: 2/3
answer: 2/3
step by step:
slope(m)=[tex]y2-y1/x2-x1[/tex]
=8-2/5+4
= 6/9
=2/3
John bought 3 pants for 25 dollars each and paid with a one-hundred-dollar bill. Write a numerical expression to represent this situation and then find how much money John gets back from the cashier?
Answer:
x-25=75
Step-by-step explanation:
ANSWER
Answer:
$ 25
Step-by-step explanation:
Let the balance amount be 'x'
Price of 3 pants = 3* 25 = $ 75
Amount paid = $ 100
x = 100 - 75
x = 25
Yolanda's age is 5 years less than twice Marco's age. If Yolanda is 15 years old, how old is Marcus? Choose the answer below that is a viable solution to this problem.
The age of marcus is 10 years old.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Yolanda's age is 5 years less than twice Marco's age. If Yolanda is 15 years old, then we have;
The reason for "5 years less", means we subtract 5, but from what exactly.
Now the next portion of the sentence says "twice Marco's Age" therefore, its 2x so we must subtract 5 from 2x.
15 = 2x - 5
Now we just solve for x.
15 = 2x - 5
Add 5 to both sides.
20 = 2x
Divide by 2 on both sides;
10 = x
Thus As a result, Marcus is 10 years old.
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Mark incorrectly solved the inequality -4(5/2+3/2x) > 8. His work is shown. Which step shows an error based on the inequality ONLY from the previous step? Help please!!
Answer : The incorrect step is, (A) step 1: -10 + 6x > 8
Step-by-step explanation :
The given expression is:
[tex]-4(\frac{5}{2}+\frac{3}{2}x)>8[/tex]
Now solving this expression step by step.
First -4 distributed over parentheses.
[tex](-4\times \frac{5}{2})+(-4\times \frac{3}{2}x)>8[/tex]
Now solving bracket term, we get:
[tex]-10-6x>8[/tex]
Now taking like terms together, we get:
[tex]-6x>8+10[/tex]
[tex]-6x>18[/tex]
[tex]-x>3[/tex]
Now multiplying this expression by (-1), we get:
[tex]x>-3[/tex]
Thus, the incorrect step is, (A) step 1: -10 + 6x > 8
Answer:
A. Step 1: -10 + 6x > 8
Step-by-step explanation:
The correct way:
Step 1: Multiply both sides by [tex]-1[/tex] (reverse the inequality)
[tex]\left(-4\left(\frac{5}{2}+\frac{3}{2}x\right)\right)\left(-1\right)<8\left(-1\right)[/tex]
Step 2: Simplify
[tex]4\left(\frac{5}{2}+\frac{3}{2}x\right)<-8[/tex]
Step 3: Divide both sides by 4
[tex]\frac{4\left(\frac{5}{2}+\frac{3}{2}x\right)}{4}<\frac{-8}{4}[/tex]
Step 4: Simplify
[tex]\frac{5}{2}+\frac{3}{2}x<-2[/tex]
Step 5: Subtract [tex]\frac{5}{2}[/tex] from both sides
[tex]\frac{5}{2}+\frac{3}{2}x-\frac{5}{2}<-2-\frac{5}{2}[/tex]
Step 6: Simplify
[tex]\frac{3}{2}x<-\frac{9}{2}[/tex]
Step 7: Multiply both sides by 2
[tex]2\cdot \frac{3}{2}x<2\left(-\frac{9}{2}\right)[/tex]
Step 8: Simplify
[tex]3x<-9[/tex]
Step 9: Divide both sides by 3
[tex]\frac{3x}{3}<\frac{-9}{3}[/tex]
Step 10: Simplify
[tex]x<-3[/tex]
Can someone please help me?
Answer:
The next number is 1 and the pattern is divide by 4.
Step-by-step explanation:
256÷4=64
64÷4=16
16÷4=4
4÷4=1
Kathy Crawford works as a freelance writer and editor. She charges $12 per page for editing services and $0.15 per word for writing. Kathy’s regular client has asked her to write a 500-word press release and edit a 12-page newsletter. what is the total pay for the job?
PLEASE HELP!! A classmate wrote the set notation for the values of the domain of a function {−5, −4, −3, −2, −1, 0} as {x | −5 ≤ x ≤ 0}. Explain the student's error.
A. The student should have listed 0 before −5
B. The set notation includes all values from −5 to 0, but the domain only includes the integer values.
C. The student should have used less than symbols rather than less than or equal to symbols.
D. The student should have used greater than or equal to symbols rather than less than or equal to symbols.
The set notation includes all values from -5 to 0, but the domain only includes the integer values
eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}
==========================================================
Further explanation:
Let's go through the answer choices one by one
A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that [tex]-5 \le x \le 0[/tex] is the correct order as well.B. This is true. A value like x = -1.2 is in the set [tex]\left\{x| -5 \le x \le 0\right\}[/tex] since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write [tex]\left\{x| x\in\mathbb{Z}, \ -5 \le x \le 0\right\}[/tex]. The portion [tex]x \in \mathbb{Z}[/tex] means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers". C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.D. This is false. Writing [tex]-5 \ge x \ge 0[/tex] would not make any sense. This is because that compound inequality breaks down into [tex]-5 \ge x \ \text{ and } \ x \ge 0[/tex]. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists. solve 3/2 + t = 1/2
t = ___
Answer:
-1
Step-by-step explanation
1/2-3/2 = -1
Answer:
-1
Step-by-step explanation:
3/2+t=1/2
T=1/2-3/2
T=(1-3)/2
=-2/2
-= - 1
Algebra Parent Functions Graph
Answer:
b. Cubic
Exponential and logarithmic graphs are the similar, logarithmic graphs just reflect exponential graphs. Cubic root is like the one shown, just horizontal.
What is an expression that represents the area of the rectangular room? How can the expression be rewritten as a polynomial in standard form? Show your work. What is an expression that represents the area of the rectangular room? How can the expression be rewritten as a polynomial in standard form? Show your work. Expression: ______________________ Expression in Standard Form (Show your work): Expression: ______________________ Expression in Standard Form (Show your work):
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, the correct question is:
The length of a rectangular room is 9 less than four times the width, w , of the room. What expression represents the area of the room? How can the expression be rewritten as a polynomial in standard form
Answer: A rectangle is a polygon that has for sides in which the opposite sides are equal. All angles in a rectangle are equal and the diagonals bisect each other. The area of a rectangle is given by the formula:
Area = Length × Width
Given that The length is 9 less than four times the width and the width is w, hence, the length is given as:
Area = 4w² - 9w
A polynomial is in standard if its terms are arranged from highest degree to lowest degree.
The polynomial in standard form is: 4w² - 9w
What is 4/10 - 2/15 simplify
A. 4/15
B. 2/5
C.8/18
D.2/3
uhm, yeah im not very good at math, i need to graduate man, someone help lol
Answer:
d=√73=8.544
Step-by-step explanation:
Find distance (d) between market (0,8) , court house(6,5) and library(6,-1)
d between two pint is :
d=√(x2-x1)²-(y2-y1)²
d between market and court house:
d=√(6-0)²+(5-8)²
d=√36+9=√45 = 6.7082 ≅6.71 rounded to the nearest hundredths
d between courthouse and the library:
d=√(6-6)²+(-1-5)²
d=√36=6
the distance that Runner A ran=6.71+6=12.71
the distance from the library to the school:
d=√(6-(-2))²+(-1-(-4))²
d=√8²+3²
d=√64+9
d=√73=8.544 ( rounded to the nearest hundredth)
Runner B went 8.544 further than Runner A before stopping at school ( which is the distance between the library and the school.
What is an equation of a line that passes through the point of (-8 2) and (-4,-3)
Answer:
y = -5/4x -8Step-by-step explanation:
[tex](-8,2)=(x_1 ,y_1)\\(-4 ,-3) = (x_2 ,y_2)\\\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-2}{x-(-8)}= \frac{-3-2}{-4-(-8)}\\ \\\frac{y-2}{x+8}= \frac{-5}{-4+8} \\ \\\\\frac{y-2}{x+8} = \frac{-5}{4}\\ \\Cross\:Multiply \\4(y-2) = -5(x+8)\\\\4y-8 =- 5x-40\\\\4y = -5x-40+8\\\\4y =- 5x-32\\\\\frac{4y}{4} = \frac{-5x}{4} + \frac{-32}{4} \\\\y = -\frac{5}{4}x-8[/tex]
A certain number is both a perfect square root and a perfect cube will its cube root and square root always be different numbers
Answer:
The exception is 1
Step-by-step explanation:
The cube root of 1 is 1, and the square root of 1 is also 1..
hence, 1 has cube root equal to square root
The blackpoll warbler migrates 2,376 miles, stops, and then flies another 3,289 miles to reach its destination. The arctic tern migrates 11,013 miles, stops, and then flies another 10,997 miles to reach its destination. How much farther is the arctic tern's migration than the blackpoll warbler's migration?
Here is a collection of dogs, mice, and cats: There are 6 dogs, 2 mice, and 4 cats. Write two sentences that describe a ratio of types of animals in this collection.
Answer:
The ratio of dogs to mice is
6 to 2; 6:2; 6/2
The ratio of cats to dogs is
4 to 6; 4:6; 4/6
Hope this helped~
Your smart local crackhead
The ratio of the dogs, mice, and cats is 3 : 1 : 2.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, there are 6 dogs, 2 mice, and 4 cats.
The ratio of the collection is:
dogs : mice : cats
6 : 2 : 4
= 3 : 1 : 2
Hence, the ratio of the dogs, mice, and cats is 3 : 1 : 2.
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What 2 consecutive whole numbers does v3 fall between?
Answer:
1 and 2
Step-by-step explanation:
√3 is ≈ 1.7
This is between 1 and 2
Carmen draws this area model to help her divide 1,800 by 9. She says the quotient is 20. Does Carmen's model make sense? Use the drop-down menus to explain.
Answer:
No shes wrong
Step-by-step explanation:
IF you divide 1800 divided by 9 you will get 200 not 20 so she is wrong.
The expression (√90 *√40) - (√8*√18) simplifies to what
Answer:
48
Step-by-step explanation:
[tex] \sqrt{90 \times 40} - \sqrt{8 \times 8} [/tex]
Answer 48
A jar holdsFraction 3 over 4 gallon of juice when it is Fraction 7 over 8 full. Which statement best describes the quotient of 3 over 4division sign 7 over 8? The maximum amount of juice the jar can hold is Fraction 7 over 6 gallons. The maximum amount of juice the jar can hold is Fraction 6 over 7 gallon. The amount of juice that can be still poured in the jar is Fraction 7 over 6 gallons. The amount of juice that can be still poured in the jar is Fraction 6 over 7 gallon.
Answer: 3/4 / 7/8
Step-by-step explanation:
= 3/4 * 8/7 = 24/28 = 6/7 gallons
This is the volume of juice when the jar is full.
Answer:
6/7
Step-by-step explanation:
If the relationship is proportional, what is the missing value from the table?
x
8
16
24
y
6
?
18
Answer:
The answer is 12.
Step-by-step explanation:
6 is 3/4 of 8 and 18 is 3/4 of 24. All you do is divide 16 by 4 which equals 4. Then multiple that answer by 3 which gives you 12.
Answer:
The answer is 12
Step-by-step explanation:
I need the answers from question 10 to 17
You don’t have to answer all of them but I would like one or maybe a couple of answers
the 4th tetm of a G.P. is 54 and the 6th term is 24. Is 64/9 a term of the G.p.?
Answer:
d
Step-by-step explanation:
Here is a pic
Hope this helps
Determine which line the point (1, -2) lies on. y = x + 5 y = 2x + 1 y = 2x - 4 y = x -2
Answer:
y = 2x - 4
Step-by-step explanation:
Given point (1, -2) so x = 1, y = -2
Just plug in and verify
y = x + 5
y = 1 + 5 = 6 ≠ -2 , noy = 2x + 1
y = 2*1 + 1 = 3≠ -2 , noy = 2x - 4
y = 2*1 - 4 = -2, yesy = x -2
y = 1 - 2 = -1 ≠ -2 , noThe sum of two numbers is five more than twice the first. The sum of the number is 45. Find the numbers
Answer:
First number is 20, second is 25
Step-by-step explanation:
x + y = 5 + 2x = 45
solve for x first
5 + 2x = 45
x = 20
then solve for y
20 + y = 45
y = 25
hope this helps
Simplfy... PLZ HELPPPP 3x^2 - 4x + 8 + 5x^2 + 9x - 10
Answer:
8x² + 5x - 2
Step-by-step explanation:
Given
3x² - 4x + 8 + 5x² + 9x - 10 ← collect like terms
= (3x² + 5x²) + (- 4x + 9x) + (8 - 10)
= 8x² + 5x - 2
You want to make a rectangular banner that is 18ft. Long with a trim around the entire border of the banner . You have no more than 48ft. Of trim of the banner. What are the possible widths of the banner?
Answer:
6 ft
Step-by-step explanation:
Given that:
Length of rectangular banner = 18 ft
Total trim of banner available = 48 ft
To find:
Possible widths of the banner = ?
Solution:
Maximum trim available of the banner around the entire border of the banner = 48 ft
i.e. we are given the total perimeter of the rectangular banner.
Formula for perimeter of a rectangle is given as:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
Putting the values of perimeter and length to find the value of width.
[tex]48 = 2 \times (18 + Width)\\\Rightarrow 48 =36+2 \times Width\\\Rightarrow 2 \times Width = 48-36\\\Rightarrow 2 \times Width = 12\\\Rightarrow \bold{Width = 6\ ft}[/tex]
So, width possible is 6ft.
Which statement comparing |−12| and |8| is true?
Answer:
[tex]\huge\boxed{|-12|\ is\ greater\ than\ |8|}[/tex]
Step-by-step explanation:
|-12| = 12
|8| = 8
So, the statement is :
|-12| is greater than |8|
In Crosby's model collection, 5/16 of the models are trains and 7/16 of the models are cars. What part of Crosby's model collection is trains and cars?
Answer:
3/4.
Step-by-step explanation:
5/16 + 7/16
= (5+7)/16
= 12/16
= 3/4.
I need help on these questions
Answer:
1. 21 hours
2. 21 hours
Step-by-step explanation:
1. If we add up all the time it takes them to build one dog house, we get 210 minutes or 3.5 hours. All we have to do is multiply this by 6 because they are building 6 of these exact dog houses. We would then get the answer 21 hours.
2. For this one, it would take Reece double the time it would take both friends. We know if they are both working it takes 3.5 hours so if it is just one of them working it would take 7 hours. So if she builds 3 it will take 21 hours.