The total purchase price is $ 357.75
Solution:
Joanna buys a table and 2 chairs
Cost of table = $ 250
Cost of 1 chair = $ 100
Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450
Thus, cost price = $ 450
She receives a 25% discount for being a preferred customer
Therefore, discount = 25 % of cost price
[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]
Thus, amount after discount = cost price - discount
amount after discount = 450 - 112.5 = 337.5
Thus, amount after discount is $ 337.5
Then pays 6% sales tax on the discounted purchase price
Sales tax = 6 % of 337.5
[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]
Thus, total purchase price is given as:
total purchase price = Amount after discount + sales tax
total purchase price = 337.5 + 20.25 = 357.75
Thus total purchase price is $ 357.75
What is the solution to this system of linear equations? Y-x=6 y+x=-10 (-2,-8) (-8,-2) (6,-10) (-10,6)
Answer:
x=-8, y=-2. (-8, -2).
Step-by-step explanation:
y-x=6
y+x=-10
--------------
2y=-4
y=-4/2=-2
-2-x=6
x=-2-6=-8
Answer:
x=-8, y=-2. (-8, -2).
Step-by-step explanation:
The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.
Answer:
The two numbers are 15 and 6.
Step-by-step explanation:
Given:
The difference between two numbers is 9.
The first number plus twice the other number is 27.
Now, to find the two numbers.
Let the first number be [tex]x.[/tex]
And the other number be [tex]y.[/tex]
So, the difference between two numbers is 9.
[tex]x-y=9[/tex]
[tex]x=9+y[/tex] ............(1)
As, given the first number plus twice the other number is 27.
According to question:
[tex]x+2y=27[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex](9+y)+2y=27\\9+y+2y=27\\9+3y=27[/tex]
Subtracting both sides by 9 we get:
[tex]3y=18[/tex]
Dividing both sides by 3 we get:
[tex]y=6.[/tex]
The other number = 6.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=9+y\\x=9+6\\x=15.[/tex]
The first number = 15.
Therefore, the two numbers are 15 and 6.
please help What is the domain of the following function?
Answer:
Let's use these two sets given to explain what is the domain.
Each value from the left set is x, and from the right is f(x).
If we plug any x from the left set in the function, we'll get f(x) that corresponds to it and that's exactly what the arrows are showing.
Domain of the function is, basically, a set of all values x can have.
In this case, it's easy to see, those are all members of the left set (-6, 1, 5, 8), but sometimes this set can have lots and lots of members, even infinity.
8y-x. When x=20 and y=4
Answer:
12
Step-by-step explanation:
8(4)-20
32-20
12
How many solutions does this equation have?
9c − 10 = –10c − 10
The equation has only one solution, c = 0.
Explanation:To determine the number of solutions for the given equation, we need to solve it and see if there is a unique solution, infinitely many solutions, or no solution at all.
First, we can simplify the equation by combining like terms:
9c - 10 = -10c - 10
Adding 10c to both sides, we get:
19c - 10 = -10
Adding 10 to both sides, we have:
19c = 0
Finally, dividing both sides by 19, we find the value of c:
c = 0
The equation has only one solution, c = 0.
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Two expressions are below.
M = 4(2x + 6)
N = 8x + 10
Part A:
Apply the distributive property to write an expression that is equivalent to expression M.
Part B:
Explain whether or not expressions M and N are equivalent for any value of x.
Label your answers to both parts of the problem in the response box.
Answer:
part A:
M = 4(2x + 6)
= 8x + 24
part B:
option 1) i think the x value is equal for both M and N since they have the value 8.
option 2) If you meant to solve M and N with an EQUATION then here's your answer:
8x+24 = 8x+10
24≠10 (you subtract 8x when taken to the other side)
So, the answer would be NO SOLUTION
Final answer:
To apply the distributive property to expression M, multiply each term inside the parentheses by 4, resulting in M = 8x + 24. Comparing this to expression N, which is N = 8x + 10, one can see that M and N are not equivalent because their constant terms differ.
Explanation:
Part A: Equivalent Expression for M
To find an equivalent expression for M, we use the distributive property which states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Therefore:
M = 4(2x + 6)
Apply the distributive property to get:
M = (4 × 2x) + (4 × 6)
M = 8x + 24
Part B: Are M and N Equivalent?
To determine if M and N are equivalent expressions, we must compare the expressions that we have for M and N:
M = 8x + 24
N = 8x + 10
Since the coefficients of x are the same but the constant terms are different, the two expressions are not equivalent for any value of x.
I need help with filling in first y variable please
Answer: 5
Step-by-step explanation:
)$;&&;:)&!;$:!:&:?($;!:!::99
Answer:
In the given equation : y= 128-4x (select the coordinate and plug in the x and y)
y= 128-4(0)
y= 128-0
y= 128
Therefore, the value for y is 128
One of two or more Expressions that are multiplied together to get a product
Answer:
factor
Step-by-step explanation:
We assume this is a vocabulary question and you want the word that has the definition you have supplied.
Such an expression is called a factor.
Please answer will mark as brainliest
Answer:
ANSWER
Step-by-step explanation:
Are the ratios 3:7 and 1:2 equivalent
Answer:
Step-by-step explanation:
no they are not equivalent
Answer:
No
Step-by-step explanation:
3 divided by 3 gives you 1, whatever you do on top you have to do in the bottom .
7 divided by 3 does not give you 2. Since you cant apply the same rule of divided by 3 and getting a whole number. They are not the same.
15 is 37.5 of what number
Answer:
40
Step-by-step explanation:
15 / 37.5% = 40
A puppy finds a rawhide bone and begins to pull it with a force, Ft. The free-body diagram is shown. A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline = negative 8 N. The second vector is pointing right, labeled F Subscript t Baseline = 6 N. The third vector is pointing upward, labeled F Subscript N Baseline = 8 N. The fourth vector is pointing left, labeled F Subscript f Baseline = negative 4 N. The up and down vectors are the same length. The right vector is longer than the left vector. Which describes what happens to the bone? It begins to move toward the right. It stays in static equilibrium. It stays in dynamic equilibrium. It begins to move toward the left.
Answer:
It begins to move toward the rightExplanation:
The given information can be summarized in this way:
First force vector: Fg = - 8N (vertical down)Second force vector: Ft = 6N (horizonal right)Third force vector: FN = 8N (vertical up)Fourth vector: Ff = - 4N (horizontal left)Following Newton's second law, net force equal mass times acceleration:
Net force = mass × accelerationTo predict the motion, you apply Newton's second law in each direction (vertical and horizontal)
Vertical force balance:Net vertical force = 8N - 8N = 0. This means there is not motion in the vertical direction.
Horizontal force balance:Net horizontal force = 6N - 4N = 2N. This means there is a net force of 2N to the right, which lets you predict that the bone starts to accelerate to the right; this is, the bone begins to move toward the right.
Answer:
A. It begins to move toward the right.
Step-by-step explanation:
2X plus 8Y minus 3X +9+2y
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
minated when you add them?
4x - 2y=7
3x - 3y=15
Answer:
Below.
Step-by-step explanation:
You could multiply the first equation by 3 and the second one by -2 so that the 2 y terms would be -6y and 6y:
12x - 6y = 21
-6x + 6y = -30
Adding these will eliminate the y variable.
The variable is directly proportional to the variable . If y = 10 when x = 6, what is the value of y when x = 15?
Answer:
y = 25
Step-by-step explanation:
Given that the quantities are proportional then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 10 when x = 6
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x ← equation of proportion
When x = 15, then
y = [tex]\frac{5}{3}[/tex] × 15 = 5 × 5 = 25
6 1/4 % of $3,875.00
Answer:
$242.19
Step-by-step explanation:
6 1/4 as a percent: 25/400
25*3,875= 96,875
96,875^400=242.1875, rounded is equal to $242.19
The value of Peter's house has risen 30% a year for the last 3 years. If the value of Peter's home 3 years ago was $120,000.00, what is the value now? A. $156,000.00 B. $228,000.00 C. $202,800.00 D. $263,640.00
Step-by-step explanation:
The price has gone up by 30% each year so each year it is 130% compared to last year. that means a price rate of 1.3^n, with n as number of years gone by. In this case n=3 so 1.3^3=2.197. $120,000.00×2.197=$263,640.00, which is D
_y =-2x +7
Do any of y’all know the y intercept
y=0
y=2x+7
x= 7/2 =3.5
- 2×3.5+7 =0
0=- 2×3.5+7
y. x
The Skittles jar has a radius of 3.5 cm and a height of 11.5 cm. Using the two given boxes for reference what would be a good estimate for the number of jelly beans in the jar?
Answer:
1052
Step-by-step explanation:
The two given boxes for reference are presented below.
Since we know the dimensions of the first container, we can calculate its volume.
[tex]V_1= 5 \text{cm} \cdot 4 \text{cm} \cdot 4 \text{cm} = 80 \text{cm}^3[/tex]
The first container held 192 skittles. Using that fact, now that we know the volume of the first box, we can calculate the volume of a single skittle.
[tex]v = \frac{80}{192} = 0.416 \approx 0.42 \text{cm}^3[/tex]
The second container held 258 skittles.
The volume of the second box is:
[tex]V_2 = 12 \text{cm}\cdot 3 \text{cm} \cdot 3 \text{cm} = 108 \text{cm}^3[/tex]
Using this facts, the volume of a single skittle would be
[tex]v = \frac{108}{258} = 0.418 \approx 0.42 \text{cm}^3[/tex]
Therefore, the volume of single skittle is around to 0.42 cm³.
A skittle jar is a cylinder. Its volume is calculated by the formula
[tex]V = r^2h \pi[/tex],
where [tex]r[/tex] is the radius and [tex]h[/tex] is the height. From the given data, we have [tex]r = 3.15 \text{cm}[/tex] and [tex]h = 11.5 \text{cm}[/tex]. Hence, the volume of the jar is
[tex]V = 3.5^2 \cdot 11.5 \cdot 3.14 = 442 \text{cm}^3[/tex]
Now, we can determine the number of skittles in the jar. Let [tex]n[/tex] be the number of skittles in the jar. Then,
[tex]n = \frac{\text{volume of the jar}}{\text{volume of a skittle}} = \frac{V}{v} = \frac{442}{0.42} = 1052.38 \approx 1052\\[/tex]
Final answer:
The best estimate for the number of jelly beans in the jar is approximately 1,000 beans, calculated based on linear dimensions and volume estimation.
Explanation:
The best estimate for the number of jelly beans in the jar would be approximately 1,000 beans.
To estimate this, we first look at linear dimensions and consider a rectangular jar. Assuming the jar is about 10 beans deep, 10 beans wide, and 10 beans high, the volume would be around 10 x 10 x 10, giving us ~ 1,000 beans inside.
Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4•2^8
To use the product of powers rule, the powers must have the same base. In this expression, the bases are 3 and 2, which are different, so the rule does not apply.
A square and a circle are used as sample designs for a tiling project. The length of an edge of a square is two times the length of the radius of a circle.
Find the ratio of the area of the circle to the area of square using the given radii.
Select either Choice 'A' or Choice 'B'
For radius x, Choice 'A' π/4 is the correct answer.
For radius 10x, Choice 'B' π/4 is the correct answer.
For radius 100x, Choice 'B' π/4 is the correct answer.
Step-by-step explanation:
The Area of the circle = πr^2, where "r" is the length of the radius.
The Area of square = a^2, where "a" is the length of an edge of a square.
CASE 1 :
Substitute radius r = x and edge length a = 2x,
Area of circle = π*x*x = πx^2
Area of square = 2x*2x = 4x^2
The ratio of the area of the circle to the area of square = πx^2 / 4x^2 = π/4
Choice 'A' π/4 is the correct answer.
CASE 2 :
Substitute radius r = 10x and edge length a = 20x,
Area of circle = π*10x*10x = 100πx^2
Area of square = 20x*20x = 400x^2
Ratio of the area of the circle to the area of square = 100πx^2 / 400x^2
= π/4
Choice 'B' π/4 is the correct answer.
CASE 3 :
Substitute radius r = 100x and edge length a = 200x,
Area of circle = π*100x*100x = 10000πx^2
Area of square = 200x*200x = 40000x^2
Ratio of area of the circle to the area of square = 10000πx^2 / 40000x^2
= π/4
Choice 'B' π/4 is the correct answer.
What is the simplified value of the expression below rounded to the nearest hundredth?
3.5x2+9
10.4-14X2
0 0.28
0.89
1.91
02.11
Answer:
The correct answer is D. 2.11
Correct statement and question:
What is the simplified value of the expression below rounded to the nearest hundredth?
(3.5x2+9)/(10.4-1.4x2)
Source: Previous question that can be found at brainly
Step-by-step explanation:
Let's solve and simplify, this way:
(3.5 x 2 + 9)/(10.4 - 1.4 x 2)
=(7 + 9)/(10.4 - 2.8)
= 16/7.6
= 2.11 (Rounding to the next hundredth)
The correct answer is D. 2.11
Answer:
its d
Step-by-step explanation:
Deposits of gold can be found in the deep ocean.
Please select the best answer from the choices provided
OT
OF
The given statement, "Deposits of gold can be found in the deep ocean" is true.
Explanation:
According to the report of National Ocean service, oceans have nearly 20 million pounds of gold that are suspended in normal sea water to the tune of parts per trillion. Deep down the ocean floor, larger amount of gold are encased in rocks that could be mined. But mining in the deepest part of the ocean is not much cost efficient and would not bring any profits. Moreover, since gold will not get decomposed by salt water, it stays undisturbed on the ocean floor.
Answer:
ture!!!!!
Step-by-step explanation:
Use algebra tiles to find (8x2+4)-(8x2+2)
Answer:
2
Step-by-step explanation:
(8x^2+4)-(8x^2+2)
8x^2+4-8x^2-2
4-2
2
The sum of four consecutive even integers is 28
Answer:
The four consecutive even integers are 4, 6, 8 and 10.
Step-by-step explanation:
Let the four consecutive even integers be [tex]x, x+2, x+4, x+6[/tex]
It is provided that the sum of these consecutive even integers is 28.
Solve for x as follows:
[tex]x+ x+2+ x+4+ x+6=28\\4x+12=28\\4x=16\\x=4[/tex]
The four consecutive even integers are:
[tex]x=4\\x+2=4+2=6\\x+4 = 4 +4 =8\\x+6=4+6=10[/tex]
Thus, the four consecutive even integers are 4, 6, 8 and 10.
For what value of the variable the value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x)?
The value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x) for x=2
Step-by-step explanation:
We have to write the given problem mathematically to solve it
So,
[tex]4(5x-8) = 2(4-x)+4[/tex]
First of all, distributive property will be applied
[tex]20x-32 = 8-2x+4\\20x-32 = 12-2x[/tex]
We have to isolate the variable on one side of the equation
Adding 2x on both sides of equation
[tex]20x-32+2x = 12-2x+2x\\22x-32 = 12[/tex]
Addition property of equality with 32
[tex]22x-32+32 = 12+32\\22x = 44[/tex]
Division Property of Equality (22)
[tex]\frac{22x}{22} = \frac{44}{22}\\x = 2[/tex]
Hence,
The value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x) for x=2
Keywords: Linear equation, variables
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What is 3(n+1)= 3+1=4
Answer:
n = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
3(n+1) = 4
distributive property means multiply every term in the parentheses by the number on the left and add the new terms.
(3*n) + (3*1) = 4
3n + 3 = 4
-3 -3 subtract 3 from both sides.
3n = 1
/3 /3 divide by 3 on both sides.
n = [tex]\frac{1}{3}[/tex]
What is the answer to, - (-x - 3)?
Step-by-step explanation:
[tex](+)(+)=(-)(-)=(+)\\(+)(-)=(-)(+)=(-)\\\\-(-x-3)=-1(-x-3)\qquad\text{use the distributive property}\\\\=(-1)(-x)+(-1)(-3)=x+3[/tex]
1) 6x + 5y = -6
y = 2x – 14
On average, seawater in the world oceans has a salinity of about 3.5%.
How much seawater need to have evaporated to leave 100g salt?
Find it in Grams
i suppose that 3.5% means every 100g of water there is 3.5g if salt...so...
3.5g ->100g
1g ->100/3.5
100g->(100/3.5)*100
=10000/3.5
2857.1428g
=2.857kg
Answer:
3.5 grams
Step-by-step explanation:
100g x 3.5% = 3.5 grams