Final answer:
Without knowing the individual prices of small and large candles, we cannot solve for the exact numbers of each type sold. A system of equations would normally be used, but in this case, essential price information is missing.
Explanation:
You sell small and large candles at a craft fair and collect $144 selling a total of 28 candles. To solve how many of each type of candle you sold, let's set up a system of equations with two variables. Let x represent the number of small candles and y represent the number of large candles.
The first equation comes from the total number of candles:
x + y = 28
The second equation involves the total amount of money collected:
ax + by = 144
where a and b are the prices of small and large candles respectively.
Unfortunately, the question does not provide the individual prices of the small and large candles, so we cannot continue without that information. To solve this system correctly, you would need to know the price of at least one type of candle.
With the missing price information, we cannot define a and b and therefore cannot provide a numerical solution to this question.
Which expression is equivalent to 4x -7-4y + 18-x-y
Answer:
3x-5y+11
Step-by-step explanation:
4x-7-4y+18-x-y
4x-x-4y-y-7+18
3x-5y+11
8 divided by 709 long division show work
Answer:
0.011 (taking till hundredth decimal value)
Step-by-step explanation:
Given: 8 divided by 709.
Lets solve it by using long division.
[tex]8\div 709[/tex]
Divisor is 709 and dividend is 8.
Now, while solving we will get quotient and remainder, if any.
As in this case 709 (divisor) is smaller number than 8 (dividend).
So, we need to take decimal in quotient to add zero with the dividend, which is again smaller than divisor, therefore we will take 0 also in quotient after decimal to add more zero with dividend, now dividend have value "800".
∴[tex]800\div 709= 0.0[/tex]
In the next step, we will divide 800 by 709.
As we know, [tex]709\times 1= 709\\709\times 2= 1418[/tex]
As 709 is lesser than 800 and we don´t have value equal to 800 in the multiple of 709, therefor we will quotient as "1" .
∴ [tex]800\div 709=0.01[/tex]
Now, we have remainder [tex]800-709= 91[/tex]
we cannot divide 91 by 709, so we add zero to the dividend as we have already taken decimal.
∴ with remainder 91 and adding zero to it, make it [tex]910\div 709[/tex]
Now, we have [tex]910\div 709= 0.011[/tex]
As we know, [tex]709\times 1= 709\\709\times 2= 1418[/tex]
As 709 is lesser than 910 and we don´t have value equal to 9100 in the multiple of 709, therefor we will quotient as "1" .
∴ We have result as 0.011 (taking till hundredth decimal value)
Sarah is buying a pair of jeans that regularly cost $60. They are on sale for 40% off. What is the sales price of the jeans?
Aliyah has 75 candy canes and 45 holiday cookies. She wants to divide them into gift bags, so that each bag has an equal number of candy canes and each bag has the same number of cookies as all the other bags. What is the greatest number of gift bags that Aliyah can make? How many candy canes will be in each bag? How many cookies will be in each bag?
Answer:
1) 15 gift bags2) 3 holiday cookiesExplanation:
1) Find the greatest number that divides exactly both 75 (candy canes) and 45 (holiday cookies).
That is, find the GCF (greatest common factor) of 75 and 45.
45 = 3² × 575 = 3 × 5²GCF = common factors each raised to its least exponent: 3×5 = 15Then, the greatest number of gift bags, so that each bag has an equal number of candy canes and same number of cookies that Aliyah can make is 15.
2) How many cookies will be in each bag?
To find the number of cookies that will be in each bag, you divide the number of holiday cookies by the number of gift bags:
45 holiday cookies / 15 gift bags = 3 holiday cookies per bag.Thus, each bag will contain 3 holiday cookies.
-5 * 1/-7 * 4/8
........................
Answer:
5/14
Step-by-step explanation:
-5*-1/7*4/8=5/7*4/8=20/56=5/14
Imagine you were shopping in the city of Los Angeles and purchased the following:
Shoes: $64.99
Shirt: $34.99
Bag: $45.50
What would the subtotal be BEFORE taxes? (Be sure to use $ sign and a decimal.)
Answer:
Subtotal = $145.48
Step-by-step explanation:
Products purchased:
Shoes, Shirt and bag.
Cost of shoes = $64.99
Cost of shirt = $34.99
Cost of bag = $45.50
The subtotal of the the products purchased before taxes can be calculated by finding the sum of all the costs.
[tex]Subtotal = \textrm{Cost of shoes + Cost of shirt + Cost of bag}[/tex]
[tex]Subtotal =\$64.99+\$34.99+\$45.50 [/tex]
[tex]Subtotal = \$145.48[/tex] (Answer)
What is the domain and range of the function y = 2x2 - 4x - 10?
Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
[tex]2(x^2-2x)=10[/tex]
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
[tex]2(x^2-2x+1)=10+2[/tex]
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
[tex]x^2-2x+1=(x-1)^2[/tex] and on the right we will just add 10 and 2:
[tex]2(x-1)^2=12[/tex]
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
[tex]2(x-1)^2-12=y[/tex]
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}
how many seconds are in a day?
Answer:
86400 seconds
Step-by-step explanation:
1 year consists of 365 days. 1 day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. 1 day = (24 hours/day) × (60 minutes/hour)(60 seconds/minute) = 86400 seconds
HOPE THIS HELPED ;3
6.3 - 9.5 wroten as a fraction in simplest form
Answer:
-3 2/4
Step-by-step explanation:
I calculated so I am correct and it's not -32
its 3 2/4
2 tanx/1 - tan2x + 1/ 2 cos2x -1= cosx + sinx/ cosx - sinx
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex] is proved
Solution:
Given that,
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
Let us first solve the L.H.S
[tex]\text { L. H.S }=\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}[/tex] --- (1)
By trignometric identities,
[tex]\tan 2 x=\frac{2 \tan x}{1-\tan ^{2} x}[/tex]
[tex]\cos 2 x=2 \cos ^{2} x-1=\cos ^{2} x-\sin ^{2} x[/tex]
By using these in (1) we get,
[tex]\text { L. H.S }=\tan 2 x+\frac{1}{\cos 2 x}[/tex]
By definition of tan,
[tex]tan x = \frac{sinx}{cosx}[/tex]
Therefore,
[tex]L. H.S =\frac{\sin 2 x}{\cos 2 x}+\frac{1}{\cos 2 x}\\\\L. H . S=\frac{1+\sin 2 x}{\cos 2 x}$[/tex] --- (ii)
By trignometric identities,
[tex]\cos 2 x=2 \cos ^{2} x-1=\cos ^{2} x-\sin ^{2} x[/tex]
[tex]\begin{aligned}&\sin 2 x=2 \sin x \cos x\\\\&\cos ^{2} x+\sin ^{2} x=1\end{aligned}[/tex]
By using these in (ii)
[tex]\text { L. H.S }=\frac{\cos ^{2} x+\sin ^{2} x+2 \sin x \cos x}{\cos ^{2} x-\sin ^{2} x}[/tex] ----- (iii)
We know that,
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
Similarly,
[tex](cosx + sinx)^2 = cos^2x + 2cosxsinx + sin^2x[/tex]
Also,
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Similarly,
[tex]cos^2x - sin^2x = (cosx+sinx)(cosx-sinx)[/tex]
Therefore apply these in (iii)
[tex]\begin{aligned}&\text { L. } H . S=\frac{(\cos x+\sin x)^{2}}{\cos ^{2} x-\sin ^{2} x}\\\\&\text { L. H.S }=\frac{(\cos x+\sin x)(\cos x+\sin x)}{(\cos x+\sin x)(\cos x-\sin x)}\end{aligned}[/tex]
Cancel out (cos x + sin x) on numerator and denominator
[tex]\text { L. H.S }=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
Thus L.H.S = R.H.S
Thus proved
Which shows the expression x^2-1/x^2-x in simplest form
Answer:
[tex]\large\boxed{\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2-1}{x^2-x}=(*)\\\\x^2-1=x^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(x-1)(x+1)\\\\x^2-x=(x)(x)-(x)(1)\qquad\text{use the distributive property}\\=x(x-1)\\\\(*)=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]
The expression x^2-1 / x^2-x in its simplest form is 1 + 1/x.
How to simplify a given expression?The given expression can be simplified by eliminating the common terms from the denominator and numerator. By doing this, the expression can be simplified.
The given expression is:
[tex]\frac{x^{2}-1 }{x^{2}-x}[/tex]
It can be simplified as shown below:
[tex]\frac{x^{2}-1 }{x^{2}-x} = \frac{(x+1)(x-1 )}{x(x-1)}[/tex]
The numerator is split using the identity :
[tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]
It can be further simplified as follows:
[tex]\frac{x^{2}-1 }{x^{2}-x} = \frac{(x+1)(x-1 )}{x(x-1)}\\= \frac{x+1}{x} \\=\frac{x}{x} +\frac{1}{x} \\= 1+\frac{1}{x}[/tex]
We have simplified the given expression into 1 + 1/x.
Thus, the expression x^2-1 / x^2-x in its simplest form is 1 + 1/x.
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What is the percent of change if 40 is increased to 50?
Answer:
25%.
Step-by-step explanation:
As a fraction it will be (50 - 40)/ 40 = 10/40 = 1/4.
% change 1/4 * 100 = 25%.
What does [tex]4![/tex] equal?
Answer:
4! = 24
Step-by-step explanation:
The "!" in math is a factorial.
A product in a four factorial is the product of all the numbers from one to 4.
[tex]4!= 1*2*3*4=24[/tex]
Ethan borrowed $1,200 from a loan company at 15% simple interest for 6 months. How much did he have to pay each month on the installment plan?
Answer: 1080
Step-by-step explanation: pls mark
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1/4d + 5 Please show work too
Answer:
5 1/4
Step-by-step explanation:
add 1/4 to 5 and you get 5 1/4
Show My Work:
1/4 + 5 =
5 1/4
Answer:
1/4(d+20)
Step-by-step explanation:
1/4d+5=1/4(d+20)
-4 (2x+9) + 3x = 6 - 4 (x-3)
Answer:
x=-54
Step-by-step explanation:
-4(2x+9)+3x=6-4(x-3)
Reorder the terms in parentheses
+(-8x-36)+3x=6-4*(x-3)
Remove unnecessary parentheses
-8x-36+3x=+6-4+*(+x-3+)
Reorder the terms in parentheses
-8x-36+3x=6+(-4x+12)
Remove unnecessary parentheses
-8x-36+3x=+6-4x+12
move all terms containing x to the left and all other terms to the right.
-8x+3x+4x=+6+12+36
simplify left and right side of the equation.
-1x=+54
finally, divide both sides of the equation by -1 to get x.
x=-54
-4 (2x+9) + 3x = 6 - 4 (x-3)
Simplifying
-4(2x + 9) + 3x = 6 + -4(x + -3)
Reorder the terms:
-4(9 + 2x) + 3x = 6 + -4(x + -3)
(9 * -4 + 2x * -4) + 3x = 6 + -4(x + -3)
(-36 + -8x) + 3x = 6 + -4(x + -3)
Combine like terms: -8x + 3x = -5x
-36 + -5x = 6 + -4(x + -3)
Reorder the terms:
-36 + -5x = 6 + -4(-3 + x)
-36 + -5x = 6 + (-3 * -4 + x * -4)
-36 + -5x = 6 + (12 + -4x)
Combine like terms: 6 + 12 = 18
-36 + -5x = 18 + -4x
Solving
-36 + -5x = 18 + -4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4x' to each side of the equation.
-36 + -5x + 4x = 18 + -4x + 4x
Combine like terms: -5x + 4x = -1x
-36 + -1x = 18 + -4x + 4x
Combine like terms: -4x + 4x = 0
-36 + -1x = 18 + 0
-36 + -1x = 18
Add '36' to each side of the equation.
-36 + 36 + -1x = 18 + 36
Combine like terms: -36 + 36 = 0
0 + -1x = 18 + 36
-1x = 18 + 36
Combine like terms: 18 + 36 = 54
-1x = 54
Divide each side by '-1'.
x = -54
Simplifying
x = -54
table
Camillo is making gourmet peanut butter and jelly sandwiches for a food challenge. What is the unit price of a loaf of bread at each store?
Store A:
Store B:
Store C:
Store D:
Answer:
Store A:
$1.98 per loaf
Store B:
$1.95 per loaf
Store C:
$2.01 per loaf
Store D:
$2.02 per loaf
Step-by-step explanation:
5.94 divided by 3 = 1.98
7.80 divided by 4 = 1.95
10.05 divided by 5 = 2.01
12.12 divided by 6 = 2.02
Answer:
Store A:
$1.98 per loaf
Store B:
$1.95 per loaf
Store C:
$2.01 per loaf
Store D:
$2.02 per loaf
Step-by-step explanation:
:)
The melting point of the chemical bromine is -7.2 C. The boiling point of bromine is 58.8 C. Write and solve an equation to find how much greater the boiling point of bromine is than the melting point. Hurry answers NOW!!!
Answer:
58.8- -7.2= 51.6
Step-by-step explanation:
Because it asked for how much greater, I subtracted.
Answer:
7.2-58.8=51.6
Step-by-step explanation:
The average of five weights is 13 grams. This set of of five weights is then increased by another weight of 7 grams. What is the average of the 6 weights?
Answer:
the answer is 12
Step-by-step explanation:
You just find the total weight and divide it by the number of weights
hope this helped ;3
Answer:
12 g
Step-by-step explanation:
Recall that
Average Weight = Sum of All weights ÷ Number of Weights
in the first case we are given that average of 5 weights is 13g
i.e Average weight (of 5 weights) = 13g and number of weights = 5
or, using the formula above,
13 = sum of 5 weights ÷ 5 (rearranging)
sum of 5 weights = 13 x 5 = 65 g
we are subsequently told that one more weight of 7 g is added,
hence, new number of weights = 6
and,
sum of 6 weights = sum of original 5 weights + sum of 6th weight
= 65 g + 7 g = 72 g
once again using the first formula
Average Weight (of 6 weights) = Sum of All weights ÷ Number of Weights
= 72 ÷ 6
= 12g
Use the equation below to answer the question.
y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?
Answer:
The signa notation to represent the first five ten f(x) is given by [tex] f(x)=\sum\limits^{5}_{n=1}a_n[/tex]
Step-by-step explanation:
Given sequence is -5, -9, 13...
Let f(x) be the given sequence and is denoted by
[tex]f(x)=\{-5,-9,-13,...\}[/tex]
Let the first term be [tex]a_1, 2^{\textrm{nd}}[/tex] term be [tex]a_3,...[/tex]
ie, [tex]a_1=-5,a_2=-9, a_3=-13,...[/tex]
To find the common difference d:
[tex]d=a_2-a_1[/tex]
[tex]=-9-(-5)[/tex]
[tex]=-9-(+5)[/tex]
[tex]d=-4[/tex]
[tex]d=a_3-a_2[/tex]
[tex]=-13-(-9)[/tex]
[tex]=-13+9[/tex]
[tex]d=-4[/tex]
Therefore the common difference d is -4 for given sequence f(x) with [tex]a_1=-5[/tex] and d=-4, the seqence f(x) is an arithmetic sequence
By defintion of arithmetic sequence
[tex]a_n=a+(n-1)d\hfill(1)[/tex]
Now to find [tex]a_4, a_5[/tex]:
put n=4 in equation (1)
[tex]a_4=a+(4-1)d[/tex]
[tex]a_4=-5+(3)(-4)[/tex] [since a=-5, d=-4]
[tex]=-5-12[/tex]
[tex]a_4=-17[/tex]
in equation (1)
[tex]a_5=a+(5-1)d[/tex]
[tex]a_5=-5+(4)(-4)[/tex] [since a=-5, d=-4]
[tex]=-5-16[/tex]
[tex]a_5=-21[/tex]
Therefore [tex]a_4=-17[/tex] and [tex]a_5=-21[/tex]
Therefore [tex]f(x)=\{-5,-9,-13,-17,-21,...\}[/tex]
Now to represent the sum of the first five terms of f(x) using sigma notation as below
[tex]f(x)=\sum_{n=1}^5 a_n[/tex]
where [tex]\sum_{n=1}^5 a_n=a_1+a_2+a_3+a_4+a_5[/tex]
[tex]-5-9-13-17-21[/tex]
[tex]\sum_{n=1}^5 a_n=-65[/tex]
Priya Wants to buy three tickets for a concert she has earned 135 and each ticket cost 50 she borrows the rest of the money she needs from a bank and buys the tickets how can you represent them out of money that Priyahas after buying the tickets
Answer:
y=50x-135
Step-by-step explanation:
If each ticket costs 50 then for three tickets, Priya needs 3*50=150
However, since she earned 135, then she's less 150-135=15
The best way to present the money she borrowed is
y=50x-135
Where x is the number of tickets bought
Given the info, Priya needs to borrow $15 from the bank to afford all 3 tickets, so after purchasing, she's out of her own money and in debt to the bank.
Explanation:Essentially the question asks us how much money Priya has left after buying three concert tickets. Each ticket is priced at $50. She has earned $135 herself, so let's subtract the cost of the tickets from what she has earned.
We find that Priya needs to borrow $15 from the bank in order to purchase all three tickets (because $50 * 3 - $135 = $15).
So after buying the tickets, she would be out of her own money and $15 in debt to the bank.
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A concrete patio is
[tex]5 \frac{2}{3} [/tex]
feet wide. It has an area of
[tex]36 \frac{2}{3} [/tex]
square feet. is the concrete slab long enough to fit a 7-foot picnic table without placing the table along the diagonal of the patio? Explain.
The length of concrete patio is 6.5 feet which is less than given 7 foot picnic table. So the concrete slab is not enough to fit a 7 foot picnic table
Solution:
Given that concrete patio is [tex]5\frac{2}{3}[/tex] feet wide
Area of concrete patio = [tex]36\frac{2}{3}[/tex] square feet
Therefore,
[tex]\texttt{Width of concrete patio = }5\frac{2}{3}=\frac{5\times 3+2}{3}=\frac{17}{3}feet\\\\\text{Area of concrete patio = }36\frac{2}{3}=\frac{36\times 3+2}{3}=\frac{110}{3}feet^2[/tex]
Let us find the length of concrete patio
Concrete patio is usually of shape rectangle
Area of concrete patio = length x width
[tex]\frac{110}{3} = length \times \frac{17}{3}\\\\length = \frac{110}{3} \times \frac{3}{17}\\\\length = \frac{110}{17} = 6.4705 \approx 6.5[/tex]
Therefore length of concrete patio is 6.5 feet
So it cannot fit the 7 foot picnic table. Since the length of concrete patio is 6.5 feet which is less than given 7 foot picnic table
Two trains leave Stations 396 miles apart at the same time and travel towards each other. One train travels at 95 mph while other travels 85 mph. How long will it take two trains to meet?
It will take 2.2 hours for the trains to meet.
Step-by-step explanation:
Given,
Distance between two trains = 396 miles
Speed of one train = 95 mph
Speed of other train = 85 mph
Combined speed of trains = 95+85 = 180 mph
Distance = Speed * Time
Time = [tex]\frac{Distance}{Speed}[/tex]
Time = [tex]\frac{396}{180}[/tex]
Time = 2.2 hours
It will take 2.2 hours for the trains to meet.
Keywords: speed, distance
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The two trains will take approximately 2.2 hours to meet.
Explanation:To find the time it takes for the two trains to meet, we can use the formula:
Time = Distance/Speed
In this case, the distance between the two trains is 396 miles. The combined speed of the two trains is 95 mph + 85 mph = 180 mph. Substituting these values into the formula, we get:
Time = 396/180 = 2.2 (rounded to the nearest tenth)
So it will take approximately "2.2 hours" for the two trains to meet.
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Please help me this is urgent.!
Answer:
V = 314 mm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
Here diameter = 10, hence r = 10 ÷ 2 = 5 and h = 4, thus
V = π × 5² × 4
= 3.14 × 25 × 4 = 3.14 × 100 = 314 mm³
Is anyone good with this? I need help finding the answer.
Look at the following numbers
-6 0 6 12
Which pair of numbers has a sum of 0?
Answer:
-6, 6
Step-by-step explanation:
-6+6=0
What is the volume of the triangular prism?
Answer:
A
Step-by-step explanation:
The volume of the triangular prism is
[tex]V=A_{base}\cdot h,[/tex]
where
h = height
Base = triangle.
In your case,
[tex]A_{base}=\dfrac{1}{2}\cdot 4\cdot 4=8\ ft^2\\ \\h=1\ ft,[/tex]
then
[tex]V=8\cdot 1=8\ ft^3[/tex]
Find the volume of a right circular cone that has a height of 10.4 m and a base with a
radius of 6.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
16327.1 m^3
Step-by-step explanation:
V=13pi*r^2*h
V=13pi*(6.2)^2*(10.4)
V=16327.1
$) Craig is selling apple cider at the fall festival. He prepared 5 gallons of cider, which is equal
to 20 quarts. He sold 18 quarts. Craig wants to know the amount of cider he sold in gallons.
quarts
gallons
How many quarts are in I gailon?
The unit rate is
quarts per gallon
Answer:
Step-by-step explanation:
5 gallons to 20 qts = x gallons to 18 qts
5 x
------ = ------ cross multiply
20 18
(20)(x) = (5)(18)
20x = 90
x = 90/20
x = 4.5 <==== 18 qts is equal to 4.5 gallons
====================
20 qts to 5 gallons = 20/5 = 4 qts per gallon <==
Answer: The unit is “4” quarts per gallon
Step-by-step explanation:
what is the y intercept pf y=5
Answer:
The y-intercept is the point (0,5)
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
In this problem the value of y is a constant for all values of x
so
For x=0
The value of y=5
therefore
The y-intercept is the point (0,5)