Final answer:
To solve this problem, we set up a system of equations representing the amount of oil in each tank. Using the fact that all three tanks end up with the same amount of oil, we determine that Tank A must have started with 1000 litres of oil.
Explanation:
You need to find the value of n which represents the amount of oil initially in Tank A, given that 500 litres are pumped from Tank A to Tank C, and that Tanks A, B, and C eventually contain the same amount of oil.
After transferring 500 litres from Tank A to Tank C, Tank A will have n - 500 litres left. Since tank C was empty and now has 500 litres, Tank B must also transfer enough oil to Tank C such that both B and C have the same amount of oil. Tank B started with n + 150 litres and must end up with the same amount as tank C, which we will refer to as x.
Therefore, we need to solve the following system of equations:
Tank A: n - 500 = x
Tank B: n + 150 - x = x
Tank C: 500 = x
From Tank C's equation, we know that x = 500. Substituting this into the equations for Tanks A and B gives us:
Tank A: n - 500 = 500
Tank B: n + 150 - 500 = 500
From Tank A's equation, we see that n = 1000 litres.
A florist needs to make 25 centerpieces for a large wedding reception. Each
centerpieces requires 7 roses. If the florist can only buy roses by the dozen,
what is the least number of roses that the florist must buy?
HELP ME ASAP !!!
Answer:
57
Step-by-step explanation:
when you multiply 7x25 you get 675 then divide by 12 you get 56.25 meaning you need one more so you get 57
A car travels for 18 minutes at an average of 72km/h.
How far will the car travel in 18 minutes?
Answer:
21.6 Kilometers
Step-by-step explanation:
We know that every hour has 60 minutes, so the car travels at [tex]\frac{72}{60}[/tex] kilometers per minute. Multiplying this by 18 gives [tex]18*\frac{72}{60}=21.6[/tex] kilometers.
Monica is buying a new dress for her
job interview at Amazon. The total
(without tax) is $65.49.
If she is shopping in Pearland, where
the sales tax rate is 8.25%, what will
be the AMOUNT OF SALES TAX for
her dress (remember to round to two
decimal places since it's money)?
What’s the answer
Answer: Sales tax would be $5.40
Step-by-step explanation: The sales value itself of the dress (that is, without tax) is $65.49.
The amount charged as sales tax in Pearland is given as 8.25% (or 0.0825).
Hence if she is shopping in Pearland, the AMOUNT OF SALES TAX she would pay can be calculated as,
Sales tax = Sales price x 0.0825
Sales tax = 65.49 x 0.0825
Sales tax = 5.402925
Approximately to two decimal places, the sales tax becomes $5.40
Select the correct answer.
What is the solution for x in the equation?
-11x − 30 + 6x = 0
A. x = 6
B. x = -30/17
C. x = 30/17
D. x = -6
Answer:
D
1.collect like terms (-11x and 6x) which equal -5
2. rewrite equation (-5x-30=0)
3. Move constant to the right hand side and change its sign.(-5x=30)
4. Divide both sides by -5 (30 divided by -5 equal s -6)
*PLEASE ANSWER SOON*
The equation of a circle is (x+4)2+(y−5)2=121.
What is the center and radius of the circle?
(a) center: (−4, 5); radius: 11
(b) center: (4, −5); radius: 11
(c) center: (−4, 5); radius: 121
(d) center: (−4, −5); radius: 121
Answer:
The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].
Step-by-step explanation:
The center-radius form for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
Compare:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x+4)^2+(y-5)^2=121[/tex]
[tex]-h=4[/tex] implies [tex]h=-4[/tex].
[tex]-k=-5[/tex] implies [tex]k=5[/tex]
[tex]r^2=121[/tex] implies [tex]r=\sqrt{121}=11[/tex].
The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].
The center is (-4.5) and the radius is 11.
How to find the center and radius of the circle?The center-radius form for a circle is:
⇒ (x-h)²+(y-k)² = r²
where (h,k) is the center and r is the radius.
Compare:
(x-h)²+(y-k)²
(x+4)+(-5)² = 121
-h = 4 implies h = -4.
-k = -5 implies k = 5
r² = 121 implies r = √121= 11,
The center is (-4.5) and the radius is 11.
The center is a fixed point in the middle of the circle; usually given the general coordinates (h, k). The fixed distance from the center to any point on the circle is called the radius.
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Which of these is NOT a Pythagorean triangle?
A) 6, 8, 10
B) 3, 4, 5
C) 33, 44, 55
D) 8, 24, 25
8, 24, 25
[tex]8^2+24^2\neq 25^2[/tex]
Answer:
D
Step-by-step explanation:
solve each inequality and graph its solution 0>3x-3-6
Answer:
3 > x
Step-by-step explanation:
0>3x-3-6
Combine like terms
0>3x-9
Add 9 to each side
0+9>3x-9+9
9 > 3x
Divide each side by 3
9/3 > 3x/3
3 > x
Using Pythagorean Theorem solve , a= x+2, b= x. and c= 10.
Answer:
x = 6, x = -8
Step-by-step explanation:
Since the Pythagorean Theorem is L^2 + L^2 = H^2, all we have to do is substitute each variable and its equation for our L's.
(x + 2)^2 + (x)^2 = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
Using quadratics, sorry, there was no other way, we get:
x = 6 or x = -8.
Check:
6 + 2 = 8^2 = 64
6^2 = 36
64 + 36 = 100 = 10.
-8 works as well.
Therefore, x = 6, x = -8 are correct.
Answer: a= -6 or 8
b=6 or -8
Step-by-step explanation:
From the result in the diagram
X=6 or -8
Remember
A=x+2
Substitute for x=6
A=6+2=8 or
A= -8+2= -6
So how answer for
A= -6 or 8
B=6 or -8
5x - 3y = -15 solve for y
Answer:
y = 5/3 x + 5
Step-by-step explanation:
5x - 3y = -15
Subtract 5x from each side
5x-5x - 3y = -15-5x
-3y = -5x-15
Divide each side by -3
-3y/-3 = -5x/-3 -15/-3
y = 5/3 x + 5
To solve 5x - 3y = -15 for y, you need to isolate y, by adding 5x to both sides and then dividing by -3, yielding the solution y = -5x/3 + 5.
Explanation:To solve the equation 5x - 3y = -15 for y, we need to isolate y on one side of the equation. Here's a step-by-step process:
Move the term with x to the other side by adding 5x to both sides of the equation. This gives us -3y = 5x - 15.Now, divide every term by -3 to solve for y. Doing this, we get y = (5x - 15) / -3.Simplify the equation which gives us y = -5x/3 + 5. This is our solution for y in terms of x.Using this method, we can solve any linear equation in two variables for one of the variables. In this case, we have expressed y as a function of x.
The line 3x – 2y = 12 has
A a slope of
and a y-intercept of -6
B a slope of -
and a y-intercept of 6
© a slope of 3 and a y-intercept of -2
O a slope of —3 and a y-intercept of -6
The line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.
What is the slope intercept form of a line ?
The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
The equation of a line is given which is 3x – 2y = 12.
This can be also written as :
3x - 2y - 12 = 0
We know that general equation of a line is given by ax + b + c = 0.
So , the given equation is :
3x – 2y = 12
dividing by 12 on both sides we get "
[tex]\frac{3x}{12}[/tex] - [tex]\frac{2y}{12}[/tex] = [tex]\frac{12}{12}[/tex]
[tex]\frac{x}{4}[/tex] - [tex]\frac{y}{6}[/tex] = 1
or
[tex]\frac{x}{4}[/tex] + (- [tex]\frac{y}{6}[/tex]) = 1
This is the slope intercept form of the given equation.
So , using the slope intercept form of line ,
y = mx + c
y = [tex]\frac{3}{2}[/tex] x - 6
If we compare : we get
c = y intercept = -6
and
Slope (m) = [tex]\frac{3}{2}[/tex]
Therefore , the line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.
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Final answer:
The line 3x – 2y = 12 has a slope of 3/2 and a y-intercept of -6, corresponding to choice A.
Explanation:
The equation of the line is given as 3x – 2y = 12. To find the slope and the y-intercept, we should rewrite this equation in slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. To do this, solve the given equation for y:
Add 2y to both sides: 3x = 2y + 12Subtract 12 from both sides: 2y = 3x - 12Divide everything by 2: y = (3/2)x - 6So, we have the slope (m) as 3/2 and the y-intercept (b) as -6, which corresponds to choice A.
Solving a Real-World Problem A kite has a width of 16 inches and a height of 18 inches. Jasmine made three kites like the one shown. How much total material did she use? The area of one kite is in2. The amount of material Jasmine needs for three kites is in2.
The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.
Step-by-step explanation:
Diagonals of the kite = 16 inches and 18 inches
Area of the kite = (16 x 18) /2
= 144 square inches
Area of 3 kites = 3 x 144
= 432 square inches.
The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.
Answer:
the first one is 144 and the second one is 432
Step-by-step explanation:
Mary bakes a chocolate cake, a vanilla cake, and a strawberry cake. Each cake is the same size. Angela eats four-eighths of the chocolate cake, two-eighths of the vanilla cake, and two-fourths of the strawberry cake. David eats one-fourth of the chocolate cake, three-eighths of the vanilla cake, and one-half of the strawberry cake. Who eats more cake, Angela or David? How much more cake? How much of each cake is left? Show all your mathematical thinking.
Answer:
Angela eats more cake
Angela ate 1/8 more cake
1/4 of the chocolate
3/8 of the Vanilla
no more Strawberry
Step-by-step explanation:
Angela: 4/8 + 2/8 + 4/8 = 10/8 = 1 1/4
David: 2/8 + 3/8 +4/8 = 9/8 = 1 1/8
Chocolate: 4/8 + 2/8 = 6/8, 8/8 - 6/8 = 2/8 or 1/4
Vanilla: 2/8 + 3/8 = 5/8, 8/8 - 5/8 = 3/8
Strawberry: 4/8 + 4/8 = 8/8, 8/8 - 8/8 = 0
Final answer:
Angela ate more cake than David by 0.125 of a cake after calculating fractions consumed by each. The remaining amounts of cake are 1/4 of chocolate, 3/8 of vanilla, and none of the strawberry cake is left.
Explanation:
To find out who eats more cake, Angela or David, we need to calculate the fractions of each cake they consumed. Firstly, we can simplify the fractions of the cake Angela and David ate by converting them to have the same denominator or to represent them as decimals. The total amount of each cake consumed needs to be added up individually for Angela and David.
Angela's Cake Consumption:
Chocolate Cake: 4/8 (simplified to 1/2 or 0.5)
Vanilla Cake: 2/8 (simplified to 1/4 or 0.25)
Strawberry Cake: 2/4 (simplified to 1/2 or 0.5)
Total cake eaten by Angela = 0.5 (chocolate) + 0.25 (vanilla) + 0.5 (strawberry) = 1.25
David's Cake Consumption:
Chocolate Cake: 1/4 (or 0.25)
Vanilla Cake: 3/8 (simplified to 0.375)
Strawberry Cake: 1/2 (or 0.5)
Total cake eaten by David = 0.25 (chocolate) + 0.375 (vanilla) + 0.5 (strawberry) = 1.125
Angela ate more cake than David by 0.125 of a cake.
Amount of Each Cake Left:
Chocolate Cake: 1 - (0.5 + 0.25) = 1/4 or 0.25 left
Vanilla Cake: 1 - (0.25 + 0.375) = 3/8 or 0.375 left
Strawberry Cake: 1 - (0.5 + 0.5) = 0 left
Do 9 m 15 m and 9 m make a triangle ?
Answer:
56232.
Step-by-step explanation:
Answer:
Step-by-step explanation:
A rectangle has side lengths of 6 units and 3 units. Could you make a quadrilateral that is not identical using the same four side lengths? If so, describe it.
Answer:
Yes
A parallelogram with opposite sides equal to 6 units and 3 units and each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex]
Step-by-step explanation:
Given: A rectangle has side lengths of 6 units and 3 units
To check: If a quadrilateral can be made that is not identical to the given rectangle using the same four side lengths
Solution:
A parallelogram with opposite sides equal to 6 units and 3 units can be made.
Take each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex]
This parallelogram is not identical to rectangle as each of the angle of the rectangle is equal to [tex]90^{\circ}[/tex] but here each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex].
Yes, one can construct another quadrilateral, such as a parallelogram, using the same side lengths of 3 units and 6 units. While both a rectangle and parallelogram are quadrilaterals, a parallelogram is not identical to a rectangle as not all angles in a parallelogram are right angles.
Explanation:Yes, it is possible to make another quadrilateral with the same side lengths that are not identical to the rectangle.
One of the ways is to make a parallelogram using side lengths of 3 units and 6 units. While a rectangle is a type of parallelogram, the noticeable difference is that not all angles in a parallelogram are right angles. In a rectangle, all angles are right angles, making it a special case of a parallelogram.
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NEED RN, WORTH 20!
What is the value of x?
Answer:
[tex]x = 5.625[/tex]
Step-by-step explanation:
Step 1: Make an expression
[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]
Step 2: Cross Multiply
[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]
[tex]4 * x = 7.5 * 3[/tex]
[tex]4x = 22.5[/tex]
Step 3: Divide both sides by 4
[tex]4x / 4 = 22.5 / 4[/tex]
[tex]x = 5.625[/tex]
Answer: [tex]x = 5.625[/tex]
Which is a true statement about the dot plot?
Number of Rolls of a Six-Sided Number Cube to Get an Even Number
1-••••
2-••••••••
3-••••
4-••
5-•
A The Data is Skewed left.
B There is a cluster at 1,2, and 3.
C It never took more than 4 rolls to get an even number.
D Most often it took 3 rolls to get an even number.
Who ever says it's C is wrong!
Answer:
The answer is B
Step-by-step explanation:
I just took the test got a 100 on it and that is the right answer
Answer: it is b
Step-by-step explanation:
i just took the test on this and i 100 on it
please, someone, help I need the answers asap!!
Answer:
#7 : 6
#8 : 12
#9 : ?
#10 : 110
#12 : ?
Which dot plot is most strongly skewed right?
Number of Movies Seen at the Theater This Year
A dot plot going from 0 to 5. 0 has 3 dots, 1 has 1 dot, 2 has 0 dots, 3 has 4 dots, 4 has 7 dots, 5 has 6 dots.
Number of Movies Seen at the Theater This Year
A dot plot going from 0 to 5. 0 has 6 dots, 1 has 8 dots, 2 has 5 dots, 3 has 2 dots, 4 has 0 dots, and 5 has 3 dots.
Number of Movies Seen at the Theater This Year
A dot plot going from 0 to 5. 0 has 3 dots, 1 has 2 dots, 2 has 2 dots, 3 has 4 dots, 4 has 2 dots, 5 has 1 dot.
Number of Movies Seen at the Theater This Year
A dot plot going from 0 to 5. 0 has 2 dots, 1 has 5 dots, 2 has 5 dots, 3 has 6 dots, 4 has 4 dots, and 5 has 3 dots.
Answer:
The dot plot that is most strongly skewed right is the first example
This is because the numbers 4 and 5 are to the right of the graph, and the numbers 4 and 5 in this example are the highest compared to the others.
For example, in this first example, 4 has 7 dots and 5 has 6 dots.
In the rest of the examples, the highest numbers for 4 and 5 are 4 dots and 3 dots
I hope this helps :)
Which shapes have 2 obtuse angles? Choose all that are correct?
Answer:
Trapezoid
Step-by-step explanation:
Trapezoid is a type of parallelogram that consist of two obtuse angles and two acute angles
What do the two x's equal please help
Each angle is 40 degrees because a straight line is 180 and there is a 100 so just subtract 100 from 180 then divide 80 by 2 and you're left with 40
Which functions represent exponential growth?
y = f(x)
y = h(x)
y = g(x)
y = k(x)
Answer:
Y=h(x)
Y=k(h)
Because they are on positive
The functions y = h(x) and y = k(x) depict exponential growth.
What are exponential growth and decay?A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.
The standard form of an exponential equation is y = a(b)ˣ
where a is the initial value
b is the rate
Exponential decay is where the final value (y) is less than the initial value (a). An example would be the decrease of bacteria in a person
Exponential growth is where the final value (y) is greater than the initial value (a). An example would be the spreading of a rumor.
A graph that is flat in the beginning and instantaneously grows in the vertical direction over a period of time
therefore, y = h(x) and y = k(x) are the functions represent exponential growth.
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work out the area of a circle with radius 6mm. give your answer in terms of pi and state its units
The area of the circle is 36π mm²
A circle can be described as a round figure whose circumference (the distance round the circle) is equidistant from the centre. An image of a circle is attached.
The area of a circle = πr²
π= pi = 22/7
r = radius = 6mm
The radius of a circle is the distance from the centre of the circle to any point on the circle's circumference.
Area of the circle = π x 6² = 36π mm²
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The area of the circle with a radius of 6mm is 36π mm².
The area (\(A\)) of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(r\)[/tex] is the radius.
Given a radius of [tex]\(6 \, \text{mm}\),[/tex] substitute this value into the formula:
[tex]\[ A = \pi \times (6 \, \text{mm})^2 \][/tex]
[tex]\[ A = \pi \times 36 \, \text{mm}^2 \][/tex]
So, the area of the circle is[tex]\(36\pi \, \text{mm}^2\)[/tex] , and the units are square millimeters[tex](\(\text{mm}^2\)).[/tex]
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What is the volume of the pyramid?
A. 210 ft^3
B. 189 ft^3
C. 630 ft^3
D. 233.3.7 ft^3
Answer:
A. 210 ft
Step-by-step explanation:
What is the probability that the spinner will land on black?
Givin AB CD and AD BC prove ABCD is a parallelogram
The results of a pole indicate that between 61% and 64% of us cities residence are in favor of water rationing during the drought. What is the point estimate for the percent of residents in favor of water rationing?
62.5%...? Taking division into account, the number between 61 and 64 is 62.5 (dont trust me)
Jeans are reduced from 28.00 to 18.20 during a sale at a department store. What percentage was the original price reduced?
Answer:
The original price was reduced 35%
Step-by-step explanation:
we know that
Jeans are reduced from $28.00 to $18.20
In this problem
The original price of 28.00 represent 100%
so
using proportion
Find out what percentage represent the difference between the original price and the new price
[tex]\frac{28}{100}=\frac{28-18.20}{x}\\\\x=100(9.8)/28\\\\x=35\%[/tex]
therefore
The original price was reduced 35%
The graph of the function f(x) = (x + 2)(x − 4) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0).
Which describes all of the values for which the graph is negative and increasing?
all real values of x where x < −2
all real values of x where −2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0
Answer:
C
Step-by-step explanation:
all real values of x where 1 < x < 4
All real values of x where 1 < x < 4.
What is the Graph function?The graph of a function f is the set of all points inside the aircraft of the shape (x, f(x)). We can also define the graph of f to be the graph of the equation y = f(x). So, the graph of a character is a unique case of the graph of an equation.
How does Graph function?For graphing functions, we need to plot its asymptotes, its x and y-intercepts, holes, and some factors on it by means of building a desk of values. Then simply join the factor by not touching the asymptotes and maintaining a observation of the area and range of the characteristic.
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Solve for x in the expression for 36x + 12 = 120
Answer:
x=3
Step-by-step explanation:
First, subtract 12 on both sides
36x + 12 = 120
36x=108
Divide by 36 on both sides
x=3
Hope this helps! :)
Shay and Nadine solve this problem in two different ways.
You have $25 in your bank account. You make $7 per hour babysitting. How many hours must you babysit to have a total of $165 in your account?
Use the drop-down menus to complete the sentences below.
Answer:
20hrs
Step-by-step explanation:
165-25 = 140
140/7 = 20
= 20hrs.
This is because 20 x $7 = $140 +$25 in account = $165