The solution to the system of equations is: x = 0 and y = 3
To find the solution to the system of equations, we need to find the values of "x" and "y" that satisfy both equations simultaneously. We can do this by setting the two expressions for "y" equal to each other since they both represent the same value of "y".
Since both equations are equal to "y," we can set them equal to each other:
2x + 3 = -3x + 3
Now, let's solve for "x":
2x + 3x = 3 - 3
Combine the "x" terms:
5x = 0
Now, divide both sides by 5 to solve for "x":
x = 0
Now that we have the value of "x," we can find the corresponding value of "y" using either of the original equations. Let's use the first equation:
y = 2x + 3
y = 2(0) + 3
y = 3
So, the solution to the system of equations is:
x = 0
y = 3
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-3x + 2 = -7 what is the x
Answer: x = 3
Step-by-step explanation: To solve for x in this equation, we must first isolate the term containing x which in this problem is -3x. Since 2 is being added to -3x, we subtract 2 from both sides of the equation to isolate the -3x.
On the left, the +2 and -2 cancel out and on the right -7 - 2 is -9 so we have -3x = -9. Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and on the right, -9 divided by -3 simplifies to 3. So we have x = 3.
15. Marteen wants to paint 2/3 of her room today. She wants to paint 1/4
of that before lunch. How much of her room will she paint
today before lunch?
Answer:
1/6
Step-by-step explanation:
2/3 x 1/4 is 2/12, which simplified is 1/6.
Answer: Marteen will paint 1/6 of her room today.
Step-by-step explanation:
In order to solve this equation, all you have to do is multiply how much of her room Marteen wants to paint today (2/3) by how much of that amount she wants to paint before lunch (1/4). because she wants to paint 1/4 of 2/3 of her room before lunch, you have to multiply 2/3 and 1/4. SO...
Multiply: 1/4 x 2/3 = 2/12
Simplify: 2/12 = 1/6
Answer: 1/6
Hope this helps!
What is the remainder when x4 - 5x3 + 3x2 - 2x +7 is divided by x - 1?
Answer:The remainder can be calculated by doing the following steps;
Step-by-step explanation:
The remainder when f(x) = x⁴ - 5x³ + 3x² - 2x +7 is divided by x - 1 is 4.
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a).
Given that f(x) = x⁴ - 5x³ + 3x² - 2x +7 is divided by x - 1
x - 1 = 0
x = 1
f(1) = 1⁴ - 5(1)³ + 3(1)² - 2(1) + 7 = 4
The remainder when f(x) = x⁴ - 5x³ + 3x² - 2x +7 is divided by x - 1 is 4.
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The product of a nonzero rational number and an irrational number is always rational.
True
False
Answer:
Step-by-step explanation:True
Plz help really fast 4 mins left
Answer:
Options A, B, and D are correct.
Step-by-step explanation:
The given function is p(x) = x³ - 6x² - x + 30
Given that p(5) = 0, p(3) = 0 and p(-2) = 0
Therefore, putting x = 5, or x = 3, or x = -2, the function p(x) vanishes to zero.
Therefore, those are the roots of the given function p(x).
Hence, we can conclude that (x - 5), (x - 3) and (x + 2) are the factors of the function p(x) = x³ - 6x² - x + 30.
So, options A, B, and D are correct. (Answer)
Which of the following Platonic solids is also a cone?
O
A. Octahedron
B. Hexahedron
I C. None of these
D. Icosahedron
O
E. Tetrahedron
OF. Dodecahedron
Answer:
c
Step-by-step explanation:
got it right on app fuller l filler
a box 12 cm long, 5 cm wide and 12 cm height. A cardboard rectangle is inserted along the diagonal to divide the box vertically into two equal spaces. Determine the dimensions f the cardboard rectangle.
Answer:
The Cardboard dimensions are 13cm in length and 12cm in breadth
Step-by-step explanation:
We can use Pythagoras Theorem to find the length the Cardboard (a²+b²=c²). Let A be 5 and B be 12, we find that C is equivalent to 13. The height is 12, thus the breadth of the Cardboard is also 12. Hope this helps :)
Final answer:
The dimensions of the cardboard rectangle are 5 cm by 12√2 cm.
Explanation:
To determine the dimensions of the cardboard rectangle inserted diagonally into a box with given dimensions, we first need to calculate the diagonal of the box that lies in the length-height plane. The box is 12 cm long and 12 cm high.
By using the Pythagorean theorem, we can find the length of the diagonal 'd' using the formula √(l² + h²), where 'l' is the length of the box and 'h' is the height.
In this case, 'd' = √(12² + 12²) = √(144 + 144) = √(288) = 12√2 cm.
Thus, the dimensions of the cardboard rectangle are its width, which is 5 cm (the width of the box), and its diagonal, which is 12√2 cm.
(1,5) and (2,3) write a linear function in the form y=Mx+b for the line
Answer:
y= -2x + 7
Step-by-step explanation:
A sporting goods stores sells footballs, basketballs, and volleyballs. A football costs $35, a basketball costs
s , and a volleyball costs $15. On a given day, the store sold 5 times as many footballs as volleyballs. They
brought in a total of $3750 that day, and the money made from basketballs alone was 4 times the money
made from volleyballs alone. How many footballs, basketballs, and volleyballs were sold? Just set up the
problem
Answer:
The number of footballs, basketballs and volleyballs were sold are 75, 36 and 15 respectively.
Step-by-step explanation:
Consider the provided information.
A football costs $35, a basketball costs $25 and a volleyball costs $15.
Let F represents the football, B represents the basketball and V represents the volleyball.
On a given day, the store sold 5 times as many footballs as volleyballs.
[tex]F=5V[/tex]......(1)
They brought in a total of $3750 that day,
[tex]35F+25B+15V=3750[/tex]......(2)
The money made from basketballs alone was 4 times the money.
[tex]25B=4(15V)[/tex]......(3)
By equation 1, 2 and 3.
[tex]35(5V)+4(15V)+15V=3750[/tex]
[tex]250V=3750[/tex]
[tex]V=15[/tex]
Substitute the value of V in equation 1 and 3.
[tex]F=5(15)=75[/tex]
[tex]25B=4(15\times 15)\\B=36[/tex]
Hence, the number of footballs, basketballs and volleyballs were sold are 75, 36 and 15 respectively.
The system of equations is as follows:
35F + 25B + 15V = 3750
1 F = 5V
25B = 60V
Let's define the variables first:
F: Number of footballs soldB: Number of basketballs soldV: Number of volleyballs soldWe are given the following information:
A football sells for $35, then the money made from footballs is 35F.A basketball sells for $25, then the money made from basketballs is 25B.A volleyball sells for $15, then the money made from volleyballs is 15V.The store sold 5 times as many footballs as volleyballs: F = 5VThe total sales amounted to $3750: 35F + 25B + 15V = 3750The money made from basketballs was four times the money made from volleyballs: 25B = 4 × 15VWe can write the system of equations as:
35F + 25B + 15V = 3750
F = 5V
25B = 60V
Complete question:
A sporting goods store sells footballs (F), basketballs (B), and volleyballs (V). A football sells for $35 a basketball sells for $25, and a volleyball sells for $15. On a given day, the store sold 5 times as many footballs as volleyballs. The sales brought in a total of $3750 that day, and the money made from basketballs alone was four times the money made from volleyballs. Write the system of equations to determine how many of each type of ball were sold by entering relevant numbers in the boxes provided below to complete each equation. Do not solve the system.
___ F + ___ B + ___ V = 3750
___ F = ___ V
____ B = ____ V
84.19 take away 49.79 equal
Answer:
34.4
Step-by-step explanation:
Answer:
34.4
Step-by-step explanation:
USE A CALCULATOR!!!!
Complete the statement to describe the expression (a+b+c)(d+e+f)
The expression consists of _ factors, and each factor contains _ terms.
fill in the blanks.
Answer:
The expression consists of two factors, and each factor contains three terms.
Step-by-step explanation:
Factors are numbers that multiply. The two brackets are written stuck to each other without any symbol between them, which means they are multiplying.
(a+b+c) is the first factor.
(d+e+f) is the second factor
Terms are numbers that separated by addition or subtraction.
Inside the first bracket, the terms are "a", "b", and "c".
Inside the second bracket, the terms are "d"", "e", and "f".
Write the ratio as a fraction in simplest form.
6 out of 9
Answer: 2/3
Step-by-step explanation: We can rewrite the ratio 6 out of 9 as the fraction 6/9 by putting 6 in the position of the numerator and 9 in the position of the denominator.
Notice however, 6/9 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 6 and 9 which is 3 to get the equivalent fraction 2/3.
Therefore, the ratio 6 out of 9 can be rewritten as the fraction 2/3.
HELP PLESE!!!!!! Subtract. State the difference in simplest form.
Evaluate: (4 + 6 ⋅
3) + 3
16
66
33
25
Answer:
25
Step-by-step explanation:
(4 + 6*3) + 3
(4+18) +3
25
Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can travel 1 block in 20 sec on his bicycle. if it takes youssef 10 min longer to walk to work than to ride his bike, how many blocks away from work does he live ?
Youssef lives 15 blocks away from his work
Solution:
Given that Youssef can either way from his home to his workplace or ride his bicycle
Let "x" be number of blocks away from work Youssef works
Case 1: walking
He walks at a pace of 1 block per min
Therefore,
1 block = 1 minute
Thus to cross "x" blocks he takes "x" minutes
Case 2: Bicycle
He can travel 1 block in 20 sec on his bicycle
We know that,
To convert seconds to minute, divide the time value by 60
[tex]\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes[/tex]
Thus he takes 1/3 minutes for 1 block
So to cross "x" blocks he will take [tex]\frac{x}{3}[/tex] minutes
Given that it takes youssef 10 min longer to walk to work than to ride his bike
This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes
[tex]\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15[/tex]
Thus he lives 15 blocks away from his work
Final answer:
Youssef lives 15 blocks away from his workplace, which is determined by solving the equation x = x/3 + 10 after converting his biking speed to 3 blocks per minute.
Explanation:
To solve for how many blocks away Youssef lives from his workplace, we'll set up an equation using the information given. First, let's convert Youssef's bicycling speed to blocks per minute. Since he can travel 1 block in 20 seconds, and there are 3 sets of 20 seconds in a minute, he travels at a speed of 3 blocks per minute on his bicycle.
Let's denote the number of blocks to Youssef's workplace as 'x'. According to the question, walking there takes Youssef 10 minutes longer than biking. If he walks at the pace of 1 block per minute, walking to work takes 'x' minutes. Biking, at 3 blocks per minute, would take 'x/3' minutes. The relationship between the walking time and biking time is therefore 'x = x/3 + 10'.
We can solve the equation by multiplying each term by 3 to get rid of the fraction: '3x = x + 30'. Solving for 'x' gives us '2x = 30', and thus 'x = 15'. Youssef lives 15 blocks away from his workplace.
i need help figuring out how to factor
[tex]3 {x}^{2} - 11x - 4[/tex]
Answer:
Step-by-step explanation:
What is the answer to -x = 12
the value of x is x=1/12'
HOPE IT HELPS U.
The graph of the function y = x2 + 2 is shown. Which equation will shift the graph of the function down 4 units?
A) y = x2 + 6
B) y = x2 - 2
C) y = (x + 4)2 + 2
D) y = (x - 4)2 + 2
Answer: OPTION B.
Step-by-step explanation:
Below are shown some transformations for a function f(x):
1) If [tex]f(x)+k[/tex], the function is shifted up "k" units.
2) If [tex]f(x)-k[/tex], the function is shifted down "k" units.
In this case you have the following function, which you can call f(x):
[tex]y =f(x)= x^2 + 2[/tex]
Based on the transformations explained before, if this function is shifted down 4 units, you know that function obtained g(x) is:
[tex]g(x)= x^2 + 2-4\\\\g(x)= x^2 -2[/tex]
Therefore, the equation that will shift the graph of the function down 4 units, is:
[tex]y= x^2 -2[/tex]
Explain how you would simplify the
following:
Answer:
Step-by-step explanation:
185,000[tex]\\\sqrt{x}[/tex]
Answer:
Step-by-step explanation:
∛108c¹⁷ = ∛2*2*3*3*3*3*c¹⁵ *c²
= 3c⁵∛4c²
Hint: c¹⁵ = (c⁵)³ = c⁵ * c⁵ *c⁵
87.5% of 64 =
38
48
58
56
87.5% of 64 is 0.875 • 64 = 56
Hope this helps.
Final answer:
To find 87.5% of 64, convert 87.5% to a decimal (0.875) and multiply by 64 to get 56.
Explanation:
To calculate 87.5% of 64, convert the percentage to a decimal and multiply by the number. Here's how you do it:
Convert the percentage to a decimal: 87.5% = 0.875.Multiply this decimal by the number: 0.875 × 64.Calculate the product to get the answer.Calculating this, we get:
0.875 × 64 = 56
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter. to the nearest inch, how many inches are in 7 meters
There are approximately 275.59 inches in 7 meters.
To find out how many inches are in 7 meters, we will first convert meters to centimeters, and then centimeters to inches.
Since there are 100 centimeters in one meter, we can calculate:
7 meters × 100 centimeters/meter = 700 centimeters
Now, we know there are 2.54 centimeters in one inch, we can convert the 700 centimeters to inches:
700 centimeters × 1 inch/2.54 centimeters ≈ 275.59 inches
To the nearest inch, there are approximately 275.59 inches in 7 meters.
solve 4x-3y=-1 and 2x+3y=13 using the elimination method
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x-3y=-1 ...(1)
2x+3y=13..(2)
add (1) and (2) : 4x-3y + 2x+3y = -1 +13
6x =12
x = 12/6 = 2
put x = 6 in (2) : 2(2)+3y = 13
4+3y =13
3y =9
y=3
What is the value of a? Enter your answer in the box. a = A right triangle with base labeled as 20. The hypotenuse is labeled as 25. The perpendicular is labeled as a. The angle made between the base and the perpendicular is marked as a right angle.
Answer:
x= 33.49
Step-by-step explanation:
Answer:
15 according to the test
Step-by-step explanation:
Point G is the incenter of the triangle.
What is the value of x?
4
8
24
32
Answer:
b.) 8 on ed2020
COO
1. ABCD is a parallelogram. The diagram is not drawn to scale. If mZCDA = 125°, then mZDCB
(1 point)
m
mm
125°
65°
55°
120°
Answer:
Therefore
m∠ DCB is 55°
Step-by-step explanation:
Given:
ABCD is a parallelogram. The diagram is not drawn to scale.
m∠CDA = 125°,
To FInd
m∠DCB = ?
Solution:
ABCD is a parallelogram.
AD || BC .......{opposite sides of a parallelogram are parallel}
∴∠CDA+∠DCB = 180°{SUM of the interior angles between parallel are supplementary}
substituting the values we get
[tex]125+m\angle DCB=180\\\\m\angle DCB =180-125=55\\\\m\angle DCB =55\°[/tex]
Therefore
m∠ DCB is 55°
robert makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 2:3.
yellow paint is sold in 5 litre tins. each tin costs £26.
blue paint is sold in 10 litre tins. each tin costs £48.
robert sells all the green paint he makes in 10 litre tins. the sells each tin of green paint for £66.96.
work out Roberts percentage profit of each tin of green paint he sells.
Answer:
35%Explanation:
1. Cost of each liter of yellow paint:
Yellow paint is sold in 5 litre tins and ach tin costs £26, thus the cost of one liter is £26 / 5 liters = £5.2 per liter.
2. Cost of each liter of blue paint:
Blue paint is sold in 10 litre tins and each tin costs £48, thus the cost of one liter of blue paint is £48 / 10 liters = £4.8 per liter
3. Cost of each liter of green paint.
Green paint is made by mixing yellow paint and blue paint in the ratio 2:3
Thus, 5 liters of green paint will cost:
2 liters yellow paint: 2 liter × £5.2 / liter = £10.4
3 liters blue paint: 3 liter × £4.8 / liter = £14.4
========== ========
5 liters green paint: 5 liter £24.8
Cost of one liter of gree paint: £24.8 / 5 liter = £4.96 / liter
4. Profit
Price of each liter of green paint: £66.96 / 10 liters = £6.696 / liter = £6.70 / liter
Profit per liter = price per liter - cost per liter = £6.70/liter - £4.96 / liter = £1.74 / liter
Percentage profit = profit per liter / cost per liter × 100
Percentage profit = (£1.74 / liter) / (£4.96/liter) × 100 = 35.08% = 35%
Simplify x0y-3/x2y-1 A.1/x2y2 B. Y/x6 C. 4y3/x3 D.y3/2
Answer:
Option A) [tex]\frac{1}{x^2y^2}[/tex] is correct.
Therefore the simplified given expression [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{x^0y^{-3}}{x^2y^{-1}}[/tex]
To simplify the given expression:
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}[/tex]
Above expression can be written as
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{(1)y^{-3}}{x^2y^{-1}}[/tex]
(since [tex]x^0=1[/tex] ,anything variable to the power "0' is 1)
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{y^{-3}}{x^2y^{-1}}[/tex]
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^{-1}y^3}[/tex] (since [tex]a^{-m}=\frac{1}{a^m}[/tex] )
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^{-1+3}}[/tex] (using the property [tex]a^m+a^n=a^{m+n}[/tex])
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Therefore [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Therefore Option A) [tex]\frac{1}{x^2y^2}[/tex] is correct.
Therefore the simplified given expression [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Please help me with polynomials. What is the zeros of x^2 + 2x + 4
Answer:
-1 ± i√3
Step-by-step explanation:
You can rearrange the expression to vertex form:
x^2 +2x +1 +3
(x +1)^2 +3
You want to find the values of x that make this zero:
(x +1)^2 +3 = 0 . . . . . . . set the expression equal to zero
(x +1)^2 = -3 . . . . . . . . . subtract 3 to get the square alone
x +1 = ±√(-3) = ±i√3 . . .take the square root
x = -1 ±i√3 . . . . . . . . . . subtract 1
The zeros are the complex numbers -1+i√3 and -1-i√3.
86,700,000-3.45•10^7
Answer:8.65
Step-by-step explanation:
santa has nine reindeer that pull his sleigh on christmas eve what is the ratio of legs ears as it relates to santad reindeer?
Final answer:
The ratio of legs to ears for Santa's reindeer is 2 legs/ear.
Explanation:
The question is asking for the ratio of legs to ears as it relates to Santa's reindeer. We know that Santa has 9 reindeer and reindeer typically have 4 legs and 2 ears. So the total number of legs would be 9 reindeer * 4 legs/reindeer = 36 legs. And the total number of ears would be 9 reindeer * 2 ears/reindeer = 18 ears. To find the ratio of legs to ears, we divide the number of legs by the number of ears: 36 legs / 18 ears = 2 legs/ear.