Sonia graphs the equations y = -x^2 + 4x and y = x - 4 to solve the equation -x^2 + 4x = x - 4. Her graph is shown below.
What are the solutions of -x^2 + 4x = x - 4?
A.) -5 and 0
B.) -5 and 1
C.) -1 and 4
D.) 0 and 4
Answers
x²-3x-4=0
(x-4)(x+1)=0
x-4=0
x=4
x-1=0
x=1
C.) -1 and 4
The solutions of -x^2 + 4x = x - 4 are -1 and 4
How to determine the solutions?The equation is given as
-x^2 + 4x = x - 4
When split, it becomes
y = -x^2 + 4x
y = x - 4
The graph represents the above equations.
So, the solution is the point of intersection of both equations
The equations intersect at x = -1 and x = 4
Hence, the solutions of -x^2 + 4x = x - 4 are -1 and 4
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Related Questions
what is -3x + b = 6x . Solve for x
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B=9x den divide 9 to both sides b/9=x hope this helps have a nice nite!
Factor the expression. 50k^3 – 40k^2 + 75k – 60
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I hope this helps :)
Answer:
ur final answer will be 5 x (2k^2+3) x (5k-4). its correct i just did the test
Step-by-step explanation:
Karen wants to buy a $22.50 jacket that is marked 20% off. Select from the drop-down menu to correctly complete the sentence. The best estimate for the discount can be found using the expression
Answers
discount = price times % off
discount = 22.50 x 0.20
discount = $4.50
Answer:
[tex]\$22.50*0.20=\$4.50[/tex]
Step-by-step explanation:
Let
x-------> original price
y------> percentage of discount
z-----> discount
we know that
[tex]z=xy[/tex]
In this problem we have
[tex]x=\$22.50[/tex]
[tex]y=20\%=\frac{20}{100}=0.20[/tex]
Substitute the values
[tex]z=\$22.50*0.20=\$4.50[/tex]
What is the sum of -7/18 and -3/6
a.) -4/9
b.) - 8/9
c.) 4/9
d.) 8/9
Answers
Answer:
-b) -8/9
Step-by-step explanation:
Answer:
The correct Answer is B.) -8/9
Step-by-step explanation:
HAVE AN AMAZING DAY!!
y = -3x - 2
4y = -12x - 8
how many solutions does the system have?
Answers
Final answer:
The system of equations y = -3x - 2 and 4y = -12x - 8 is dependent with an infinite number of solutions because both equations represent the same line.
Explanation:
The system of equations given is:
y = -3x - 2
4y = -12x - 8
If we examine the second equation, we can simplify it by dividing everything by 4, yielding:
y = -3x - 2
Both equations are now identical, which implies that they are the same line graphed on a coordinate plane. The system is considered dependent, and the number of solutions is infinite because every point on the line y = -3x - 2 is a solution to the system.
If Sam invested $3,000 and he earned $300 over six months, the principal is _____.
Answers
(and the net amount of money you earn is the interest, that is $300 in this one.)
Which diagram does not result in the expression 4x+4
Answers
PLEASE HELP 20 POINTS
Calculate the Average Time and Average Speed for each vehicle.
Car 1 Car 2
Trial 1 = 4.12 seconds 8.33 seconds
Trial 2 = 4.41 seconds 8.25 seconds
Trial 3 = 3.96 seconds 8.66 seconds
Average Time = ? ?
Distance = 2 meters 2 meters
Average Speed= ? ?
Answers
The average time of Car 2 is 8.41 seconds
The average speed of Car 1 is 0.48m/s
The average speed of Car 2 is 0.24m/s
How many 3/4 cup servings are in 1/2 of a cup of milk? Write your answer in simplest form.
Answers
In this question, you are asked how many cups of milk is 3/4 serving from 1/2 cup of milk. To answer this, you need to multiply the number of serving with the serving size.
If one serving is 1/2 cups of milk, then 3/4 servings would be:
3/4 servings * (0.5 cups / serving)= 3/8 cups of milk = 0.375 cups of milk
The number of 3/4 cup servings that are in 1/2 of a cup of milk is [tex]\frac{2}{3}[/tex]
In order to determine the number of 3/4 cup servings that are in 1/2 cup of milk, divide the fraction of the cup of milk by the fraction of cup servings
Cup of milk ÷ Number of cup servings
= [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{1}{2}[/tex] x [tex]\frac{4}{3}[/tex]
= [tex]\frac{4}{6}[/tex]
In order to express the answer in its simplest form, divide the numerator by two and the denominator by 2. The numerator and the denominator are both divided by two because two is a common factor of 4 and 6
= [tex]\frac{2}{3}[/tex]
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Please help! Which of the following is an example of an open equation? 5x+7=12 12+(-8)=4 25=5(5) 8+0=8
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1/4 0f 15? What is the answer
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What is the value of expression? 57.8 x 64 HELP PLEASE ASAP
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How do you turn percents into fractions?
Answers
Step 1: You want to remove the percent sign and then put the number over 100.
Step 2: If the percent is not a whole number then you want to multiply the top and bottom number by 10 but only for every number that comes after the decimal point.
Step 3: Always simplify if possible.
Examples:
43% = [tex]\frac{43}{100}[/tex]
78% = [tex]\frac{78}{100}[/tex] = [tex]\frac{39}{50}[/tex]
0.4% = [tex]\frac{0.4}{100}[/tex] = [tex]\frac{4}{1000}[/tex] = [tex]\frac{1}{250}[/tex]
Converting percents to fractions involves writing the percent as a fraction with a denominator of 100 and then simplifying. For example, 75% is equivalent to 75/100, which simplifies to 3/4. Decimals can be converted to percents by multiplying by 100 and adding the percent sign.
Converting Percents to Fractions
To convert a percent to a fraction, start by writing the percent value as a fraction with a denominator of 100. For example, 75% would be written as 75/100. The next step is to simplify the fraction if possible. To simplify, you find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number. For instance, the GCD of 75 and 100 is 25, so when we divide both the numerator and the denominator by 25, we get 3/4. Hence, 75% as a fraction in simplest terms is 3/4.
When converting to decimals, simply divide the numerator by the denominator. So, 75% becomes 0.75 when turned into a decimal. Conversely, to convert a decimal to a percent, you multiply by 100 and add the percent symbol (%). For instance, converting the decimal 0.75 to a percent, you would calculate 0.75 * 100 which equals 75%, completing the conversion.
Calculating percents is about understanding the ratio or fraction that the percent represents. The term 'percent' literally means 'per hundred', so any percent can be thought of as that number over 100. For example, 3% means 3/100 and 100% represents a whole or 1 as it's equivalent to 100/100.
Write the point-slope form of the equation of the line with a slope of - 2 and an x-intercept of - 1. Include your work in your final answer.
Answers
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold. $966 = $14t
Answers
Jodys older brother is only three years less than twice Jodys age. If the sum of their ages is 30, then which of the following is the age of jodys brother? A)7 B)11 C)19 D)23
Answers
that means that jody's older brother is 3 years less than twice jodys age.
Lets try all the answers
7*2= 14-3=11 Nope
11*2=22-3=19+11=30 YUP!
19*2=35-3=32 Nope
23*2=46-3=43 Nope
Your answer is b
Jody's older brother's age can be found using the equation x + 2x - 3 = 30 and solving for x. The answer is C) 19.
Explanation:To solve this problem, we can set up an equation using Jody's age and Jody's older brother's age. Let's let Jody's age be x. According to the problem, Jody's older brother is three years less than twice Jody's age, so his age is 2x - 3. The problem also tells us that the sum of their ages is 30, so we can write an equation: x + (2x - 3) = 30. Solving this equation will give us the age of Jody's older brother.
Combining like terms and solving the equation, we get 3x - 3 = 30. Adding 3 to both sides, we get 3x = 33. Dividing both sides by 3, we find that x = 11. Therefore, Jody's older brother's age is 2x - 3 = 2(11) - 3 = 22 - 3 = 19.
So, the correct answer is C) 19.
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Find sum or difference.
1/6 + 3/8
A. 4/6
B. 4/8
C. 4/14
D. 13/24
Answers
= 4/24 + 9/24
= 13/24
answer
D. 13/24
find common denominator:
6*4 =24, 8*3 = 24
1/6 = 4/24
3/8 = 9/24
4/24 + 9/24 = 13/24
Answer is D
Which table shows a proportional relationship? x 1 2 3 4 5 y 9 10 11 12 13 b 1 4 5 7 11 c 3 12 15 21 33 p 1 3 5 7 9 q 0 2 4 6 8 r 3 6 10 12 15 s 2 4 6 8 10
Answers
Proportional relationships are relationships between two variables where their ratios are equivalent. b and c represents Proportional relationships.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent
The first table is
x 1 2 3 4 5
y 9 10 11 12 13
The ratios are not same
1/9, 2/10=1/5, 3/11, 4/12=1/3, 5/13
So it is not a proportional relationship.
b 1 4 5 7 11
c 3 12 15 21 33
The ratios are same .
1/3, 4/12=1/3, 5/15=1/3, 7/21=1/3, 11/33 =1/3.
Hence b and c table shows proportional relationship.
p 1 3 5 7 9
q 0 2 4 6 8
The ratios are not same it does not show proportional relationship.
r 3 6 10 12 15
s 2 4 6 8 10
The ratios are not same it does not show proportional relationship.
Hence the table b and C shows proportional relationship.
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What is the distance between -7.5 and -15.3 on a number line
Answers
The distance between points -7.5 and -15.3 on a number line is 7.8.
What is Number system?
A system of writing to express the number is called number system.
Given that;
The numbers on number line are -7.5 and -15.3.
Now, Distance between -7.5 and -15.3 can be calculated as;
= - 7.5 - (-15.3)
= - 7.5 + 15.3
= 7.8
Thus, The distance between points -7.5 and -15.3 on a number line is 7.8.
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Beth read 10 pages in a book stopping at the top of page a on what pages did she begin
Answers
That’s the answer
from 91 books to 145 books
find the percent increase. round to the nearest percent.
Answers
145 - 91/91 × 100 = 59.34
This has already been rounded, as the original number is repeating, but we can round it even more to 59.
ANSWER:
So, the percent increase was about 59%.
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected?
Answers
Answer: Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
what is the simplified value of 40+2⋅3−2 and 40+2⋅3−2 and 9+32−1⋅4
Answers
9+32-1*4= 37
Solve the equation 1/8x=5
Answers
Get rid of the denominator, eight, by multiplying it to both sides of the equation
1/8(8)x = 5(8)
x = 40
The value of x in the equation is 40.
How to solve equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
In other words, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's solve for the variable x in the equation as follows;
1 / 8 x = 5
cross multiply
x = 8 × 5
x = 40
The value of x is 40.
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Plz Helppppp and can u explain why ?
Answers
[tex]2\times2\times2[/tex]
which, in this case, equals 8. On the other hand, when we're asked to take the cube root of a number, we're being asked to find out which number, when multiplied by itself 3 times, gives us the number under the root sign. In our last example, finding the cube root of 8 (∛8) gets us:
[tex] \sqrt[3]{8} =2[/tex]
since 2 x 2 x 2 = 8.
In your problem, we're being asked: "What number multiplied by itself gives us 64?" Or: ? x ? x ? = 64. Finding that answer takes some knowledge of the factors of 64. 64's prime factorization is [tex]2^6[/tex], or 2 x 2 x 2 x 2 x 2 x 2. If we pair up all of the twos, we can rewrite this product as
[tex](2\times2)\times(2\times2)\times(2\times2)[/tex]
or
[tex]4\times4\times4=4^3[/tex]
since 4, when multiplied by itself 3 times, gives us 64, we know it must be our answer.
Haruka hiked several kilometers in the morning in the morning. She only hiked 6 kilometers in the afternoon, which was 25% less she had hiked in the morning. How many kilometers did haruka hike in all?
Answers
0.75x = 6
The value of x from the equation is 8. Adding together the 6 and 8 will give us an answer of 14.
Answer: 14 kilometers
The complete distance Haruka hiked can be calculated by converting the percent to decimal.
The total distance is 14 km Haruka hike in all.
Given:
She hiked in afternoon is [tex]6\: \rm km[/tex].
Let the distance hiked in morning is [tex]x[/tex].
As per the question, 6 kilometers 25% less she had hiked in morning.[tex]\begin{aligned}\left(\dfrac{100\%-25\%}{100}\right)x&=6\\0.75x&=6\\x&=\dfrac{6}{0.75}\\x&=8\\\end[/tex]
Therefore, Haruka hiked [tex]8\:\rm km[/tex] in morning.
Calculate the total distance hiked.
[tex]\rm Total\: distance=8+6=14 \:\rm km[/tex]
Thus, the total distance is 14 Km Haruka hike in all.
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Simplify and express the answer as a decimal. (−3+6) 2 ÷4.5
Answers
3^2 + 4.53
9 + 4.53
13.53 is your answer
hope this helps
If a 25 foot tall tree cast a 15 foot shadow, what is the height of a tree if it’s shadow is 6 feet long
Answers
set this up as a ratio
25 ft tree / 15 foot shadow = X ft tree / 6 foot shadow
25/15 = X/6
cross multiply:
150 / 15x
x = 150/15 = 10
the tree is 10 feet tall
Multiply: 2 4/5 x -5 2/3
Answers
Which expression equals -(9x + 8) - 2(x -5)
Answers
= -9x - 8 - 2x + 10
= -11x + 2