Answer:
The quantity sold by Annette was $600
The quantity sold by Barb was $480
The quantity sold by Carlita was $400
Step-by-step explanation:
Let
x ----> quantity sold by Annette
y ---> quantity sold by Barb
z ---> quantity sold by Carlita
we know that
[tex]x+y+z=1,480[/tex] ----> equation A
[tex]x=y+120[/tex] ----> equation B
[tex]y+z=x+280[/tex] ----> equation C
substitute equation C in equation A and solve for x
[tex]x+(x+280)=1,480[/tex]
[tex]2x=1,480-280[/tex]
[tex]2x=1,200[/tex]
[tex]x=\$600[/tex]
Find the value of y
[tex]x=y+120[/tex]
[tex]600=y+120[/tex]
[tex]y=600-120=\$480[/tex]
Find the value of z
[tex]x+y+z=1,480[/tex]
[tex]600+480+z=1,480[/tex]
[tex]1,080+z=1,480[/tex]
[tex]z=\$400[/tex]
therefore
The quantity sold by Annette was $600
The quantity sold by Barb was $480
The quantity sold by Carlita was $400
The solution involves setting up a system of three linear equations based on the given problem. By solving these equations methodically, we find that Barb, Annette, and Carlita sold $400, $520, and $560 of clothing respectively.
Explanation:The problem involves setting up and solving a system of linear equations. Here's how we approach it:
Let's denote Barb's sales as B, Annette's sales as A, and Carlita's sales as C.The total sales are given to be $1480, so we have our first equation as A + B + C = 1480.The problem states that Annette sold $120 more than Barb. This gives us another equation: A = B + 120.It is also said that Barb and Carlita combined sold $280 more than Annette, hence the third equation: B + C = A + 280.Now we have a system of three equations which we can solve step-by-step. Firstly, substitute A from the second equation into the first and third one, providing us with two new equations: B + 120 + B + C = 1480 and B + C = B + 120 + 280. These simplify to 2B + C = 1360 and B = 400. Substituting B = 400 into the equation 2B + C = 1360 gives C = 560.Last, we substitute B = 400 into the second equation A = B + 120, which simplifies to A = 520.So, Barb sold $400 of clothing, Carlita sold $560, and Annette sold $520.
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if log x - log(2x-1)=1 find x
Answer:
x = 10/19
Step-by-step explanation:
[tex]log(x)-log(2x-1) = 1\\log\frac{x}{2x-1}=log(10)\\\frac{x}{2x-1}=10\\x = \frac{10}{19}[/tex]
The solution to the equation log x - log(2x-1) = 1 is x = 10/19.
We have,
To solve the equation log x - log(2x-1) = 1, we can use logarithmic properties to simplify the equation.
First, we can apply the quotient rule of logarithms, which states that
log a - log b = log(a/b).
Applying this rule to the equation, we get:
log(x / (2x-1)) = 1
Next, we can rewrite the equation in exponential form, using the definition that log base a of b is equivalent to a raised to the power of the logarithm equals b.
In this case, the base is 10 since we are using common logarithms (log base 10):
[tex]10^1[/tex] = x / (2x-1)
Simplifying the left side, we have:
10 = x / (2x-1)
To eliminate the denominator, we can multiply both sides of the equation by (2x-1):
10(2x-1) = x
Expanding the left side:
20x - 10 = x
Now, we can isolate the variable x:
20x - x = 10
19x = 10
Dividing both sides by 19:
x = 10/19
Therefore,
The solution to the equation log x - log(2x-1) = 1 is x = 10/19.
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Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function?
A.
D: 10 ≤ b ≤ 12
R: 0 ≤ W(b) ≤ 120
B.
D: 0 ≤ b ≤ 120
R: 0 ≤ W(b) ≤ 10
C.
D: 0 ≤ b ≤ 10
R: 12 ≤ W(b) ≤ 120
D.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120
Each birdhouse uses 12 sq ft of wood.
He has enough to build 10 birdhouses, so he has 120 sq ft of wood.
The function has an input of the number of birdhouses, b, and has an output of the amount of wood needed, W. b is the input or the domain, and W is the output or the range. The domain is 0 to 10. The range is 0 to 120.
Answer: B. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
Enjoy! Hope this helped you! :)
What is the answer ? Explain.
Answer:
152
Step-by-step explanation:
4(3x + 5)
4(3(11) + 5)
4(33 + 5)
4(38)
152
c.
5 tomatoes for $3.10. What was the cost per tomato?
The cost per tomato is $0.63.
Answer:
The cost of each tomato is $0.62
Step-by-step explanation:
Consider the provided information.
5 tomatoes for $3.10.
We need to determine the cost per tomato.
To find this divide the number of tomatoes from the cost of tomatoes.
[tex]\frac{3.10}{5}=0.62[/tex]
Hence, the cost of each tomato is $0.62
What is the coefficient of b in the expression b + 10? Explain.
Answer:
The coefficient of b is 1
Step-by-step explanation:
we know that
In a mathematical equation, a coefficient is a constant by which a variable is multiplied
so
A coefficient is a constant multiplied by a variable.
In this problem we have
b+10
Rewrite'
b+10=(1)b+10
therefore
The coefficient of b is 1
How do cows buy gifts
Answer:they dont
Step-by-step explanation:
given the domain (-2,2,4) what is the range for the relation 3x-y=3
Final answer:
The range for the relation 3x - y = 3 with the domain (-2,2,4) is calculated by substituting each domain value into the equation, resulting in the range (-9, 3, 9).
Explanation:
To find the range for the relation 3x - y = 3 given the domain (-2,2,4), we need to substitute each value from the domain into the equation and solve for y. Here's how you do it step by step:
For x = -2: 3(-2) - y = 3; -6 - y = 3; y = -6 - 3; y = -9.For x = 2: 3(2) - y = 3; 6 - y = 3; y = 6 - 3; y = 3.For x = 4: 3(4) - y = 3; 12 - y = 3; y = 12 - 3; y = 9.The range for the given domain is (-9, 3, 9).
One number is five less than three times another number. If the sum of the numbers is 3, find the numbers.
Answer:
First number 2
Second number 1
Step-by-step explanation:
Let the first number = x
Let the second number = 3x - 5
Equation
x + 3x - 5 = 3
Solution
x + 3x- 5 = 3 Combine
4x - 5 = 3 Add 5 to both sides
4x - 5 + 5 = 3 + 5 Combine
4x = 8 Divide by 4
4x/4 = 8/4 Combine
x = 2
3x -5 = 3(2)- 5 = 1
Write 5.48 as a mixed number in simplest form.
5.48=
Answer:
5 12/25
Step-by-step explanation:
The first step is to separate the whole number number from the decimal.
that would be 5
Next would to see in which place the decimal number is in. .48 is in the hundredths place so we put 48 over 100 like this 48/100
So now we have the whole number 5 and the fraction 48/100
Lastly we simplify the fraction. 48 divided by 2 and 100 divided by 2
This equals 24/50
This can be simplified even more
24 divided by 2 and 50 divided by 2
This equals 12/25
Then we put the whole number in front and your final answer is
5 12/25
what is the answer to 5 over 35 simplalifying
Answer:
1/7
Step-by-step explanation:
Divide each number by 5.
5/5=1
35/5=7
Answer:
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 5 and 35 is 5
Divide both the numerator and denominator by the GCD
5 ÷ 5
35 ÷ 5
Reduced fraction:
1
7
Which expression is equivalent to (2r2+r - 1) – (3r2+48 - 5)?
-p2 – 3r+4
°-p2 + 58 - 6
5r²+5r-6
5r2 - 3r + 4
The specified expression simplifies to -r² + r - 44. Steps to find equivalent expressions include gathering like terms and utilizing the distributive property.
Explanation:
The expression (2r²+r-1) – (3r²+48-5) can be rewritten as 2r²+r-1 - 3r² - 48 +5. For the r² terms, combine 2r² and -3r² to get -r². For the constant terms, combine -1, -48 and +5 to get -44. And there's only one r term which is r. Together, these give the equivalent expression as -r² + r - 44.
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The expression equivalent to (2r2 + r - 1) - (3r2 + 48 - 5) is -r2 + r - 44.
Explanation:To find the equivalent expression, we need to distribute the negative sign into the second set of parentheses.
Then, combine like terms.
The expression becomes: (2r2 + r - 1) - 3r2 - 48 + 5.
Combining like terms further, we have: 2r2 + r - 1 - 3r2 - 48 + 5
Now, combine the like terms again: (2r2 - 3r2) + r + (-1 - 48 + 5). Simplifying this gives us: -r2 + r - 44
Therefore, the expression equivalent to (2r2 + r - 1) - (3r2 + 48 - 5) is -r2 + r - 44.
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Barry and Lou entered a hot dog eating contest. The winner of the contest is the person who can eat the most hot dogs in the allotted amount of time. Barry can eat 12 hot dogs in 9 minutes. Lou can eat 20 hot dogs in 16 minutes. Barry thinks with his rate he will win the contest.
Is Barry correct?
Answer:
Yes
Step-by-step explanation:
If you divide 12 by 9, you get 1.33... and if you divide 20 by 16, you get 1.25 so Barry can eat more hot dogs in less amount of time than Lou can.
Answer:
yes
Step-by-step explanation:
Julias text messaging plan costs $8 for the first 400 messages and 20e for each additional text message. If she owes $24.00 for text messaging in the month of
September, how many text messages did she send that month?
Julia sent 401 text messages in the month of September.
Explanation:To find the number of text messages Julia sent, we can set up an equation using the given information.
Let's assume she sent x additional messages.
The cost of the additional messages would be 20x.
Since her total cost is $24, we can write the equation:
8 + 20x = 24
Subtracting 8 from both sides gives:
20x = 16
Dividing both sides by 20 gives:
x = 0.8
Since x represents the additional messages sent, we can round it to the nearest whole number.
Therefore, Julia sent 1 additional text message.
In order to find the total number of messages sent, we can add the initial allowance of 400 messages to the additional message:
Total messages sent = 400 + 1 = 401 text messages.
Final answer:
Julia sent a total of 401 text messages in September.
Explanation:
Julia's text messaging plan costs $8 for the first 400 messages and $20 for each additional text message. To find out how many text messages she sent in September, we need to determine the number of additional text messages she sent beyond the first 400. Let's assume she sent x additional text messages. The additional cost for these text messages would be 20 * x. We can set up an equation to solve for x:
$8 + 20x = $24
Subtracting $8 from both sides gives:
20x = $16
Dividing both sides by 20, we get:
x = $16 / 20 = 0.8
Since we cannot have a fraction of a text message, Julia must have sent 1 additional text message beyond the first 400. Therefore, she sent a total of 401 text messages in September.
How many solutions does this problem have? 3(y+41)=3y+123
Answer:
The answer is many solutions
Answer:
infinite
Step-by-step explanation:
3 x 41 = 132 so
3y +132 =3y +132
3. After hiking to the top of a mountain, Raul starts to descend at the rate of 350
feet per hour. What real number represents his vertical change after 1 1/2 hours?
Answer: 525 ft
Step-by-step explanation:
350 = 1 hour
350 / 2 = 175 in half an hour
350 + 175 = 525 ft
What is the least common multiple of 15 and 90
Answer:
90
Step-by-step explanation:
Divide the larger number by the smaller number
If the remainder is zero then the larger number is the LCM
If not repeat with multiples of larger number
90 ÷ 15 = 6 remainder 0
Since remainder is 0 then 90 is the LCM of 15 and 90
How many packs of DVD's can you buy with 180 dollars if one pack costs 12 dollars?
Final answer:
With $180 and each pack costing $12, you can buy 15 packs of DVDs.
Explanation:
Calculating the Number of DVD Packs
To determine how many packs of DVDs you can buy with $180 when one pack costs $12, you need to perform a simple division operation. You divide the total amount of money you have by the cost of one pack of DVDs:
$180 ÷ $12 per pack = 15 packs.
Therefore, with $180, you can buy 15 packs of DVDs.
To solve this equation: d/5 + 12 = -15, which step will be performed last?
Let's go through the steps.
d/5 +12 = -15
1. Multiply both sides by 5.
Doing this we get:
d + 60 = - 75
2. Subtract 60 from both sides.
d = - 75 - 60
d = -135
Step 2 above is the final step taken to find the value of d.
Find the area of the parallelogram that has a base of 2 1/2 ft and a height of 1 1/4ft
Answer:
The area of the parallelogram is [tex]3\frac{1}{8}ft^{2}[/tex]
Step-by-step explanation:
Remember that a mixed fractions are composed for a whole number, a numerator and a denominator. For example in the mixed fraction [tex]2\frac{1}{3}[/tex]: 2 is the whole number, 1 is the numerator and 3 is the denominator.
If you want to convert to a improper fraction you need to multiply the whole number by the denominator and add to the numerator. The result will be the numerator of the improper fraction. The denominator remains the same.
[tex]2\frac{1}{3}=\frac{(2*3)+1}{3} =\frac{7}{3}[/tex]
1. Convert the mixed fractions in the improper fraction type, as follows:
[tex]Base= 2\frac{1}{2}=\frac{5}{2} \\ \\Height= 1\frac{1}{4}=\frac{5}{4}[/tex]
2. Replace the data in the equation of a parallelogram
[tex]Area= Base*Height[/tex]
[tex]Area= Base*Height\\Area=\frac{5}{2}ft *\frac{5}{4}ft\\Solve...\\Area=\frac{25}{8}ft^{2}[/tex]
3. Convert the improper fraction in a mixed fraction
[tex]Area=\frac{25}{8}ft^{2}=3\frac{1}{8}ft^{2}[/tex]
The area of the parallelogram is [tex]3\frac{1}{8}ft^{2}[/tex]
A man was surprised when he found an old bank account statement in his mother’s attic. Money had been left for 30 years in a bank account paying simple annual interest. The statement showed that originally $500 had been put into the account. When he called the bank, he found that there is now $1550 in the account! What is the annual interest rate?
Answer:
7%
Step-by-step explanation:
Answer:
7% is the correct answer
Evaluate the expression if x = 3 and y = 11. 3x + 2y
Answer:
31
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
3(3)+2(11)=31
what is the simplified form of the following expression? 3 sqrt 4x/5
Final answer:
The simplified form of the expression [tex]3 \sqrt(4x/5) \ is\ 6 \sqrt(5x) / 5[/tex]after performing the square root separately on the numerator and denominator, and then rationalizing the denominator.
Explanation:
The expression given is [tex]3 \sqrt(4x/5)[/tex]. To simplify this expression, we observe that the square root of 4 is a perfect square and equals 2. The square root of the fraction can be taken by applying the square root to the numerator and the denominator separately. Therefore, we have:
[tex]3 \times \sqrt(4) \times \sqrt(x) / \sqrt(5)[/tex]
Upon simplifying, we get:
[tex]3 \times 2 \times \sqrt(x) / \sqrt(5)[/tex]
This simplifies further to:
[tex]6 \sqrt(x) / \sqrt(5)[/tex]
However, it's not common to leave a square root in the denominator, so we can multiply both the numerator and the denominator by sqrt(5) to rationalize the denominator.
The final simplified form is:
[tex]6 \sqrt(5x) / 5[/tex]
Simplify the expression (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2. Assume a not-equals 0, b not-equals 0.
Answer:
The simplest form of the expression is 16 a²b²
Step-by-step explanation:
* Lets explain how to solve the problem
- To simplify any fraction with exponent you must put it with positive
exponent
- Ex: the fraction [tex](\frac{2}{3})^{-1}[/tex] not in the simplest form
because it has negative exponent
- To change the negative exponent to positive exponent reciprocal the
fraction, [tex](\frac{3}{2})^{1}[/tex] and this is the simplest form of the fraction
* Now lets solve the problem
∵ The expression is [tex](\frac{1}{4ab})^{-2}[/tex], where a and b ≠ 0
- At first reciprocal the fraction
∴ [tex](\frac{1}{4ab})^{-2}=(\frac{4ab}{1})^{2}[/tex]
- Then solve the power
∵ 4² = 16
∵ (ab)² = a²b²
∴ (4ab)² = 16 a²b²
* The simplest form of the expression is 16 a²b²
Answer:
16 a²b² is option D on e2020
Step-by-step explanation:
100% on test
43tens×3tens=how many hundreds
Answer:
129 hundreds
Step-by-step explanation:
List the angles of rotation, separated by commas, less than 360° if the figure has rotational symmetry. If
the figure does not have rotational symmetry, enter the number zero.
The list of angles of rotation is
Answer:
The list of angle of rotation is zero
Step-by-step explanation:
* Lets revise some definitions about isosceles trapezoid
- An isosceles trapezoid is a trapezoid with congruent base angles
- An isosceles trapezoid has congruent legs
- An isosceles trapezoid has 1 axis of symmetry
- An isosceles trapezoid has no rotational symmetry
* Lets solve the problem
- From the attached figure:
∵ The figure is quadrilateral
∵ The quadrilateral has only a pair of parallel sides
∵ The parallel side not equal in length
∵ The other two sides of the quadrilateral are equal in length
∴ The quadrilateral is an isosceles trapezoid
∵ The isosceles trapezoid has no rotational symmetry
∴ There is no angle of rotation
∴ The list of angle of rotation is zero
Answer:
the answer is 0
Step-by-step explanation:
Add. 4 7/12+2 3/4+7 5/12
A.13 3/4
B.14 1/4
C.14 3/4
D.15 1/4
Add.
4/5+3 1/10
Enter the sum in the box as a mixed number in simplest form.
Answer:
C.14¾
3 9⁄10
Step-by-step explanation:
[tex] \frac{4}{5} + 3 \frac{1}{10} = \frac{8}{10} + 3 \frac{1}{10} = 3 \frac{9}{10} [/tex]
[tex]4 \frac{7}{12} + 2 + \frac{3}{4} + 7 \frac{5}{12} = 13 \frac{12}{12} + \frac{3}{4} = 14 + \frac{3}{4} = 14 \frac{3}{4} [/tex]
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3 1/4 yards of fabric costs $27.95. what is the cost per yard
Answer:
8.6
Step-by-step explanation:
because 27.95 divided by 3.25=8.6
Martin paid $6 for 4 avocados at a farm stand. He wants to know what the price would be for buying different numbers of avocados? What is the price of 2 avocados?
Answer:
$3
Step-by-step explanation:
4/$6 = 2/$3
Answer:
3
Step-by-step explanation:
ywwwwww
a ^-4 / a ^-6 please simplify and show your work if possible <:D
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^{-4}}{a^{-6}}\implies a^{-4}\cdot a^6\implies a^{-4+6}\implies a^2[/tex]
Can some help me pleaseeee.
Answer:
I cant answer it because it blocked the equation can you show the details on text?
Step-by-step explanation: