Answer: y = -0.2(x - 2.25)² + 1.6125
Step-by-step explanation:
[tex]y = -0.2x^2 + 0.9x + 0.6\\\\y - 0.6 = -0.2x^2 + 0.9x\\\\y - 0.6 =-0.2(x^2-4.5x)\\\\y-0.6+\underline{(-0.2)(2.25)^2}=-0.2(x^2-4.5x+\underline{2.25^2})\\\\y-0.6-1.0125=-0.2(x-2.25)^2\\\\y-1.6125=-0.2(x-2.25)^2\\\\y=-0.2(x-2.25)^2+1.6125[/tex]
Heather has to solve this system of equations using elimination. What should be her first step? 3x+6y = 12 x+5y = 10
Final answer:
To solve the given system of equations using elimination, Heather's first step should be to manipulate the equations so that the coefficients of one of the variables (x or y) are the same in both equations. She can achieve this by multiplying the second equation by 3.
Explanation:
Heather has to solve the system of equations using elimination. The given equations are 3x+6y = 12 and x+5y = 10. The first step in solving these equations using the elimination method should be to manipulate the equations so that the coefficients of one variable are the same or additive inverses.
This allows one to eliminate that variable by adding or subtracting the equations. In this scenario, an efficient approach would be to multiply the second equation by 3, which makes the coefficients of x the same in both equations. Hence, the equations become 3x + 6y = 12 (unchanged) and 3(x + 5y) = 3(10), which simplifies to 3x + 15y = 30. This prepares the equations for the next step in the elimination process, which involves subtracting one equation from the other to eliminate the x variable.
Stuart has 23.75. He wants to buy 2 tickets
Answer:
15.75 + 15.75= 31.50
31.50- 23.75= 7.75
so 7.75
which values are solutions to the inequality below? check all that apply.
x^2 > 121
A) -12
B) 3
C) 13
D) 10
take square root of 121, which is 11
so -12, 3, 10,
The values that satisfy the inequality x² > 121 are -12 and 13, as their squares are greater than 121.
The question asks which values satisfy the inequality x² > 121. To find the solutions, we need to consider when x² is greater than the square of 11, since 121 is 11². There are two cases:
Case 1: x is greater than 11.
Case 2: x is less than -11.
Now, evaluating the provided options:
A) -12: (-12)² = 144 which is greater than 121. Hence, -12 is a solution.
B) 3: (3)² = 9 which is not greater than 121. Therefore, 3 is not a solution.
C) 13: (13)² = 169 which is greater than 121. Thus, 13 is a solution.
D) 10: (10)² = 100 which is not greater than 121. So, 10 is not a solution.
Therefore, the correct answers that satisfy the given inequality are -12 and 13.
The sum of 6 consecutive integers is 519.
One way to do this is to consider what the average of these integers is. It would be 519/6, or 86.5. This means the six integers are "centered" around 86.5: they would be 84, 85, 86, 87, 88, and 89 (there are three numbers greater than 86.5 and three less than 86.5 in this list).
Write the factors and find the GCF 4,10,12,16
Answer:
2
Step-by-step explanation:
4 = 2 * 2
10 = 2 * 5
12 = 2 * 2 * 3
16 = 2 * 2 * 2 *2
Answer:
GCF is 2.
Step-by-step explanation:
GCF is just the greatest factor of the whole number series.
Everything is divisible by 2 and not anything greater in this number series.
Therefore the GCF is 2.
Which property is illustrated by the following statement? If zxy=fde
Answer:transitive
Step-by-step explanation:a p e x
Find the radius of the circle if the center is at (1,2) and the point (-3,4) lies on the circle
Answer:
4.47 units
Step-by-step explanation:
Which of these is equal to the value of 9-(-5)
The expression 9-(-5) simplifies to 9 + 5, which equals 14 when the numbers are added together.
To solve the expression 9-(-5), you should remember that subtracting a negative number is the same as adding its positive counterpart. Therefore, we change the subtraction of a negative number to the addition of a positive number. Following these steps, we have:
9 - (-5) = 9 + 5
Now, we simply add the numbers together:
9 + 5 = 14
So, the expression 9-(-5) equals 14.
John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What is the cost pero hour of each activity?
Answer:
Skiing costs $30 per hour and Boating costs $51 per hour.
Step-by-step explanation:
Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.
"John paid $222 for four hours of skiing and two hours boating":
[tex]4x+2y=222[/tex]
"He paid $213 for two hours skiing and three hours boating":
[tex]2x+3y=213[/tex]
Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y. Work shown below.
[tex]2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51[/tex]
Hence, y = 51
Now, substituting this y value into the 1st equation and solving for x will give us the value of x.
[tex]First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30[/tex]
Hence, skiing costs $30 per hour and boating costs $51 per hour.
If 8a+7b+c=9 then what is -6c-48a-42b
Your answer would be 6
Find the distance of each data value in Exercisen1 from the mean. Then find the mean absolute deviation of the data.
Answer:
Sorry, I don't know the answer to the distance, but the MAD is 5.1666666666667, or just 5 rounded to the nearest one.
Step-by-step explanation:
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 when a = –2. Which equation represents this direct variation between a and b?
Answer:
a=-b? That might be wrong, sorry. But that's what it sounds like.
Step-by-step explanation:
The equation that represents the direct variation between the numbers a and b is b = -a.
Explanation:The equation that represents the direct variation between the numbers a and b is given by b = -a. In direct variation, when one variable increases, the other variable also increases, but in this case, they increase in opposite directions. For example, when a = -2, b = 2, and when a = 2, b = -2. Therefore, b varies directly with a, but in the opposite direction.
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A local dairy farmer collects 490 gallons of milk from his cows. He keeps 1/35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day?
Answer:
666.4 dollars per day
Step-by-step explanation:
Total milk farmer has is 490 gallons
He keeps 1/35 of 490 gallons
so he keeps = 1/35*490= 14 gallons
He sells remaining milk.
Remaining milk = 490-14 = 476 gallons
1 gallon = 4 quart (conversion formula)
so 476 gallon = 4 * 476 = 1904 quart
selling price of 1 quart = 35 cents = 0.35 dollars
so selling price of 1904 quart = 0.35*1904 = 666.4 dollars
So he makes 666.4 dollars per day.
PLEASE HELP QUICK!
AABC has vertices at (-4,4), (0,0) and (-5,-2). find the coordinates of points A, B and C after a reflection across the y- axis.
Point A’: ____
Point B’: ____
Point C’: ____
The Y axis, would be when y = 0.
Point B is located on the Y -axis, so the coordinates would be the same.
For A and C the Y coordinate would remain the same and the X coordinate would be the opposite ( from negative to positive).
A (-4,4) would become (4,4)
B (0,0) would stay the same so would be (0,0)
C (-5,-2) would become (5,-2)
The coordinates after reflection across the y-axis are:
- Point [tex]\( A' \): \((4, 4)\)[/tex]
- Point [tex]\( B' \): \((0, 0)\)[/tex]
- Point [tex]\( C' \): \((5, -2)\)[/tex]
Step 1: Identify the original coordinates of the points.
- Point [tex]\( A \)[/tex] is at [tex]\((-4, 4)\).[/tex]
- Point [tex]\( B \)[/tex] is at [tex]\((0, 0)\).[/tex]
- Point [tex]\( C \)[/tex] is at [tex]\((-5, -2)\).[/tex]
Step 2: Apply the reflection across the y-axis.
- Reflecting a point across the y-axis changes the sign of the x-coordinate, while the y-coordinate remains unchanged.
Step 3: Calculate the new coordinates.
For Point [tex]\( A \):[/tex]
- Original coordinates: [tex]\((-4, 4)\)[/tex]
- Reflected coordinates: [tex]\((4, 4)\)[/tex]
- Negate the x-coordinate: [tex]\(-(-4) = 4\)[/tex]
- Keep the y-coordinate the same: [tex]\(4\)[/tex]
For Point [tex]\( B \):[/tex]
- Original coordinates: [tex]\((0, 0)\)[/tex]
- Reflected coordinates: [tex]\((0, 0)\)[/tex]
- Negate the x-coordinate: [tex]\(-0 = 0\)[/tex]
- Keep the y-coordinate the same: [tex]\(0\)[/tex]
For Point [tex]\( C \):[/tex]
- Original coordinates: [tex]\((-5, -2)\)[/tex]
- Reflected coordinates: [tex]\((5, -2)\)[/tex]
- Negate the x-coordinate: [tex]\(-(-5) = 5\)[/tex]
- Keep the y-coordinate the same: [tex]\(-2\)[/tex]
Step 4: Write the coordinates of the reflected points.
- Point [tex]\( A' \): \((4, 4)\)[/tex]
- Point [tex]\( B' \): \((0, 0)\)[/tex]
- Point [tex]\( C' \): \((5, -2)\)[/tex]
So, the coordinates after reflection across the y-axis are:
- Point [tex]\( A' \): \((4, 4)\)[/tex]
- Point [tex]\( B' \): \((0, 0)\)[/tex]
- Point [tex]\( C' \): \((5, -2)\)[/tex]
Find the area of the figure
A)75in^2
B)70in^2
C)65in^2
D)80in^2
Answer: B, 70 inches.
Step-by-step explanation:
Let's start slow and go shape by shape.
Based on the information we have, we know that the length for the rectangle is 8 inches by 7 inches. 8*7 = 56, so we have one of the answers.
Next, we do the triangle. Based on the information we have, we know that the triangle is 4 inches by 7 inches divided by 2. 4*7 = 28 [tex]\frac {28}{2} = 14[/tex]
Adding 14 and 56, we got the answer to be B, 70 inches.
What values of c and d make the equation true? Assume x>0 and y >=0.
square root of 50x^6y^3/9x^8 = 5y^c square root of 2y/dx.
A.c = 1, d = 3
B.c = 1, d = 32
C.c = 2, d = 8
D.c = 2, d = 32
Answer:
A. c=1, d=3
Step-by-step explanation:
If x>0 and y>0, then
[tex]\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.[/tex]
If
[tex]\dfrac{5y\sqrt{2y}}{3x}[/tex]
is equal to
[tex]\dfrac{5y^c\sqrt{2y}}{dx},[/tex]
then
[tex]y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.[/tex]
Select the three expressions that give the area of the figure in square units
Answer:
the top middle and two at the bottom
Which dose not appear in an algebraic expression
An equal sign.
If there was an equal sign kt would turn into an algebraic equation imstead of an expression.
Happy to help! Marking my answer as the Brainliest would really be aprreciated.
Brainliest ASAP.
Divide 30 by 1/2. Then add 10. What do you get?
A.70
B.200
Answer:
A
Step-by-step explanation:
30/.5 = 60
60 + 10 = 70
Answer:
hi there your answer is: A) 70
Step-by-step explanation:
STEP 1 : 30 ÷ 1/2 = 60
Step 2: 60 + 10 = 70
i hope this you out
Have a great evening
FaithRawlins14
the 8th grade student council sold 180 tickets to its pancake breakfast fundraiser.
6 ounces of pancake mix makes enough pancake for 5 people.
How many ounces of pancake mix are needed to make pancakes for 180 people?
What is the fifth term of the geometric sequence 5,15,45,...
Answer:
405
Step-by-step explanation:
This is a geometric sequence, so we need the common ratio and the first term
To find the common ratio, we take the second term and divide by the first term
15/5 =3
The common ratio is 3
We are multiplying by 3 each time
The first term is 5
The formula is
an = a1 * (r) ^ (n-1) where n is the term number
We want the 5th term
a5 = 5 * (3) ^ (5-1)
a5 = 5 *3^4
= 5 *81
= 405
The fifth term is 405.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex]* [tex]r^{n-1}[/tex]
In this formula,[tex]a_{1}[/tex] is the first term,
r is the common ratio, and
n is the term number.
From the given sequence 5, 15, 45,..., we can identify the following:
[tex]a_{1}[/tex] = 5
r = 15 / 5 = 3 (common ratio)
Now, we need to find the fifth term (n = 5):
[tex]a_{5}[/tex] = 5 * [tex]3^{5-1}[/tex]
= 5 * [tex]3^{4}[/tex]
= 5 * 81
= 405
So, the fifth term of the geometric sequence is 405.
59 =7r+3 what is the answer
Answer:
r=8
Step-by-step explanation:
59 =7r+3
Subtract 3 from each side
59 -3 = 7r+3-3
56 = 7r
Divide each side by 7
56/7 = 7r/7
8 =r
Answer:
[tex]\boxed{\bold{r=8}}[/tex]
Step-by-step explanation:
Switch sides
[tex]\bold{7r+3=59}[/tex]
Subtract 3 from both sides
[tex]\bold{7r+3-3=59-3}[/tex]
Simplify
[tex]\bold{7r=56}[/tex]
Divide both sides by 7
[tex]\bold{\frac{7r}{7}=\frac{56}{7}}[/tex]
Simplify
[tex]\bold{r=8}[/tex]
I need help. PLEASE HELP ME!!!!!!!
Answer:C.
Its C because 2/5+3/10=7/10.
Answer:
C
Step-by-step explanation:
CCCC!!
Which shows the list of numbers in order from least to greatest?
Answer:
[tex]\textsf{A)}\;\;\; -2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|[/tex]
[tex]\newline[/tex]
Step-by-step explanation:
[tex]\newline[/tex]
Given numbers:
[tex]\newline[/tex]
[tex]|-4.2|, \;\left|-\dfrac{4}{5}\right|, \; |-1|, \;-2, \; |3.5|[/tex]
[tex]\newline[/tex]
The absolute value of a number represents the distance of a number from zero on the number line, regardless of direction. This means that the absolute value of a number is always non-negative. For example, |-4.2| = 4.2, because the distance from -4.2 to 0 is 4.2 units.
[tex]\newline[/tex]
Evaluate each term:
[tex]\newline[/tex]
[tex]|-4.2|=4.2[/tex]
[tex]\left|-\dfrac{4}{5}\right|=\dfrac{4}{5}=0.8[/tex]
[tex]|-1|=1[/tex]
[tex]-2=-2[/tex]
[tex]|3.5|=3.5[/tex]
[tex]\newline[/tex]
Now, arrange them from least to greatest:
[tex]\newline[/tex]
[tex]-2, \;0.8, \;1, \;3.5, \;4.2[/tex]
[tex]\newline[/tex]
Therefore, the list of numbers in the correct order from least to greatest is:
[tex]\newline[/tex]
[tex]\large\boxed{-2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|}[/tex]
An architect is using software to design the interior of a rectangular room. On the floor plan, the coordinates of two consecutive corners of the room are (3, 15) and (18, 2). The architect wants to place a window in the center of the wall containing these two points. What will be the coordinates of the center of the window on the floor plan?
A.) (17, 21)
B.) (10.5, 8.5)
C.) (21, 17)
D.) (8.5, 10.5)
Answer:
The answer is B.
Step-by-step explanation:
The architect wants to place a window in the center of the wall containing these two points: (3, 15) and (18, 2).
The coordinates of the center of the window are those of the mid-point betwween the two points: ( (3+18)/2, (15+2)/2 ) = (10.5, 8.5)
The answer is B.
Answer:
Step-by-step explanation:
ignore the text n focus on the coordinates (3, 15) and (18, 2) and that "the architect wants to place a window in the center of the wall containing these two points."
so the window will be right in the middle of (3, 15) and (18, 2).
take the average of the coordinates: (3+18)/2=10.5 n (15+2)/2=8.5
ans is B. (10.5,8.5)
The vertices of a triangle are A(7,5) B(4,2) and C(9,2) what is mABC
Answer:
A(7,5)
Step-by-step explanation:
This is correct because the area of a triangle is b × h = a.
Answer:
The measure of ∠ABC is 45°.
Step-by-step explanation:
Given : The vertices of a triangle are A(7,5) B(4,2) and C(9,2).
To find : What is ∠ABC ?
Solution :
First we side the length of the sides,
Using Distance formula,
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Length of side AB, A(7,5) and B(4,2)
[tex]c= \sqrt{(7-4)^2 + (5-2)^2} \\c= \sqrt{(3)^2 + (3)^2} \\c= \sqrt{9+9} \\c= \sqrt{18}[/tex]
Length of side BC, B(4,2) and C(9,2)
[tex]a= \sqrt{(4-9)^2 +(2-2)^2} \\a= \sqrt{(-5)^2 + 0} \\a= \sqrt{25} \\a= 5[/tex]
Length of the side AC, A(7,5) and C(9,2)
[tex]b = \sqrt{(7-9)^2 +(5-2)^2}\\ b= \sqrt{(-2)^2 + (3)^2} \\b= \sqrt{4+ 9}\\b=\sqrt{13}[/tex]
By the Law of Cosines,
[tex]\cos B=\frac{a^2 + c^2 -b^2}{2ac}[/tex]
Substitute the values,
[tex]\cos B=\frac{(5)^2 + (\sqrt{18})^2 - (\sqrt{13})^2}{2\times 5\times \sqrt{18}}[/tex]
[tex]\cos B =\frac{25+18-13}{10\sqrt{18}}[/tex]
[tex]\cos B=\frac{30}{10\sqrt{18}}[/tex]
[tex]\cos B =\frac{3}{\sqrt{18}}[/tex]
[tex]\cos B= \frac{3}{3\sqrt{2}}[/tex]
[tex]\cos B= \frac{1}{\sqrt{2}}[/tex]
Taking Inverse Cosine function,
[tex]B= \cos^{-1}( \frac{1}{\sqrt{2}})[/tex]
[tex]B=45^\circ[/tex]
Therefore, The measure of ∠ABC is 45°.
The lines graphed below are parallel the slope of the red line is 3 what is the slope of the green line
Answer:
[tex]\large\boxed{m=3}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\--------------------------\\\\\text{We have the slope of the red line}\ m_1=3.\\\\\text{Then the slope of the green line}\ m_2=3[/tex]
Graph the solution to y< = 1/5x+2
Answer:
FDFDD
Step-by-step explanation:
28+87 divided by 3•2 to the third power
Answer: =86
Step-by-step explanation:
* Hopefully the picture helps:) Mark me the brainliest:)
∞ 234483279c20∞
After solving the expression, the value get will be equal to 38.33.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the given data,
28+87 = 115
Then it is divided by 3
115/3 = 38.33
The value obtained is equal to 38.33.
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write 6 over 10 in simplest form
Answer:
[tex]\frac{6}{10} = \frac{3}{5}[/tex]
Step-by-step explanation:
You have to divide this by "2"
Answer: 3/5
Step-by-step explanation: 6/10 can be divided by 2 because they are both even numbers then when you can no longer divided them it is simplified