Answer:
m = - 8 ± 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
m² + 16m - 8 = 0 ( add 8 to both sides )
m² + 16m = 8
To complete the square
add ( half the coefficient of the m- term )² to both sides
m² + 2(8)m + 64 = 8 + 64
(m + 8)² = 72 ( take the square root of both sides )
m + 8 = ± [tex]\sqrt{72}[/tex] = ± [tex]\sqrt{36(2)}[/tex] = ± 6[tex]\sqrt{2}[/tex]
Subtract 8 from both sides
m = - 8 ± 6[tex]\sqrt{2}[/tex]
Will Award Brainliest...
The table below shows the amount g(r), in dollars, after r years
r(number in years) 1///2
g(r) (amount in dollars)9,638///18,794.10
what was the percent change from year 1 to year 2?
Answer:
48.72%
Step-by-step explanation:
(18794.10-9638)/18794.10*100 = 9156.1/18794.10*100 = 48.72%
how many solutions does 6x-6=6x+15 have
Answer:
None
Step-by-step explanation:
Note that we have 6x on both sides here. If we subtract 6x from both sides, the equation becomes -6 = +15, which is never true.
Thus, this equation has NO SOLUTION.
12x + 3y = 15 for x = -1,0,1
What is 34 to 35 reduce in its simplest form of numbers
Answer:
34/35=0.9714285
Step-by-step explanation:
consider the parabola with a focus at the point (0,-3) and directrix y=2 . which two equations can be used to correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola ?
The two equations that can be used to relate the distance from the focus and the directrix to any point on the parabola are x² = 4py and y = (x-k)² + h.
Explanation:To correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola, we can use the following two equations:
x² = 4pyy = (x-k)² + hWhere p is the distance from the focus to the directrix, (h,k) is the vertex of the parabola, and the equation x² = 4py represents a parabola with its axis parallel to the y-axis, and y = (x-k)² + h represents a parabola with its axis parallel to the x-axis.
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The quadrilateral shown is a parallelogram. If m∠ADC = 125° and m∠1 = 30°, what is m∠2? A) 15° B) 25° C) 35° D) 55°
Answer:
B) 25°
Step-by-step explanation:
Assuming the quadrilateral is the one shown in the picture attached, then a triangle ADC is form, where m∠ADC = 125° and m∠1 = 30°. The addition of the three angles of a triangle is equal to 180°, so:
m∠ADC + m∠1 + m∠2 = 180°
Replacing with the known values and isolating m∠2 we get:
125° + 30° + m∠2 = 180°
m∠2 = 180° - 125° - 30°
m∠2 = 25°
Answer:
it is 25 degrees
Step-by-step explanation:
thanks for your help
plz mark as brainlest.
solve 2x + 3 = 9 nowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
x=3
Step-by-step explanation:
2
x
+
3
=
9
We want to find the variable
x
, so we have to make it alone. To do so, first subtract
3
from both sides of the equation:
2
x
+
3
−
3
=
9
−
3
2
x
=
6
Now divide both sides by
2
:
2
x
2
=
6
2
So the final answer is:
x
=
3
Hope this helps!
Answer: x = 3
Step-by-step explanation: To solve for x in the equation you see here, our goal is to get x by itself.
Our first step will be to isolate the term containing x which in this case is 2x. To isolate 2x, we have to get rid of the 3 by subtracting 3 from both sides of the equation.
On the left, the 3's cancel each other out and we are left with 2x. On the right, 9 - 3 simplifies to 6 and we are left with 2x = 6 which is a one step equation.
To get x by itself, since it's being multiplied by 2, we just divide both sides of the equation by 2. On the left, the 2's cancel and we are left with x. On the right, 6 over 2 simplifies to 3.
Therefore, our answer is x = 3.
Find the percentage of vacationers from
question 10 who spent between $1500
and $2000.
Answer:
The percentage change of vacationers is 33.3 %
Step-by-step explanation:
Given as :
The old value of the vacationers = $ 1500
The new value of the vacationers = $ 2000
Let the percentage variation = x %
Or, x % increase = [tex]\dfrac{\tyextrm new value - \textrm old value}{\textrm old value}[/tex] × 100
Or, x % increase = [tex]\dfrac{\tyextrm $ 2000 - \textrm $ 1500}{\textrm $ 1500}[/tex] × 100
Or, x % increase = [tex]\frac{500}{1500}[/tex] × 100
Or, x % increase = [tex]\frac{1}{3}[/tex] × 100
Or, x % increase = [tex]\frac{100}{3}[/tex]
∴ x = 33.3 %
So, The percentage increase change is 33.3 %
Hence The percentage change of vacationers is 33.3 % Answer
–9 = -2(x+3)+1
can you solve this to be a slope intercept
Answer:
The solution of x for the slope intercept is 2 .
Step-by-step explanation:
Given expression as :
- 9 = - 2 ( x + 3 ) + 1
Or. - 9 = - 2×( x + 3 ) + 1
or, - 9 = - 2 x - 6 + 1
or, - 9 = - 2 x - 5
or, - 9 + 5 = - 2 x
or , - 4 = - 2 x
∴ x = [tex]\frac{-4}{-2}[/tex]
I.e x = 2
Hence the solution of x for the slope intercept is 2 . Answer
pls help (kinda easy)
A function is shown: f(x) = 4x2 − 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
f(x) = (4x + 1)(4x − 1)
f(x) = (2x + 1)(2x − 1)
f(x) = 4(x2 + 1)
f(x) = 2(x2 − 1)
Answer:
[tex]f(x)=(2x+1)(2x-1)[/tex].
Step-by-step explanation:
We want to convert the function into the form that let's us easily find the x-intercept, and it would be for the form [tex](ax+b)(cx+d)[/tex] because then we can find the x-intercept in the following manner:
[tex](ax+b)(cx+d)=0[/tex]
[tex]x=-b/a[/tex]
[tex]x=-d/c[/tex]
We factor our function [tex]f(x)=4x^2-1[/tex] and get
[tex]\boxed{f(x)=(2x+1)(2x-1)}[/tex]
Now this form let's us easily find the x-intercepts:
[tex]x=-1/2[/tex]
[tex]x=1/2[/tex]
and so we pick the second choice: f(x)=(2x+1)(2x-1).
Answer:
b
Step-by-step explanation:
3. In a single growing season at the Smith Family Orchard, the average yield per apple
tree is 150 apples when the number of trees per acre is 100. For each additional tree
over 100, the average yield per tree decreases by 1.
a. What would be the average yield per tree if the number of trees per acre was
doubled? What would be the total yield in that case?
b. How many trees should be planted per acre to maximize the total yield?
Answer:
a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.
b. 25 more trees are to be planted per acre to maximize the total yield.
Step-by-step explanation:
If the no. of trees per acre is doubled then it will be equal to,
[tex]100 \times 2[/tex]
= 200
So, the no. of trees per acre is increased by (200 - 100) = 100
hence, the average yield per tree will be,
(150 - 100) = 50 in that case.
Hence, the total yield will be,
[tex]50 \times 200[/tex]
= 10,000 apples per acre
Now , if x trees are planted, the total no. of apples produced per acre will be,
[tex](150 - x) \times (100 + x)[/tex]
= [tex]15000 + 50x - x^{2}[/tex]
= f(x) [say]
So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)
= 50 - 2x---(1)
taking f'(x) = 0 , we get,
50 - 2x = 0
⇒ x = 25 --------------(2)
Again,
[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25
= -2 (<0)
So, f(x) attains it's maximum value at x = 25
Hence,
25 more trees are to be planted per acre to maximize the total yield.
1. The enrollment of a school in 2000 was 1200.
Since then, It has increased at a rate of 35
students per year. Write an equation to
represent the enrollment of the school each
year after 2000. Identify your variables. a) What is the rate of change?
b) What is the initial value
c) What is the independent variable?
d) What is the dependent variable
Answer:
equation: y=35x+1200
a) the rate of change is 35.
b) 1200.
c) The Independent Variable is amount of students per year.
d) The Dependent Variable is the year
I'm not sure about the dependent varaliable, so don't take my word.
a) The rate of change is 35 students per year.
b) The initial value is 1200 students.
c) The independent variable is "x," which represents the number of years since 2000.
d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.
Identifing The Variables.
Set up an equation to represent the enrollment of the school each year after 2000.
We can use the form of a linear equation, where "y" represents the enrollment in a given year (after 2000), and "x" represents the number of years since 2000.
a) Rate of Change (Slope):
The rate of change, which represents how much the enrollment increases each year, is 35 students per year.
b) Initial Value (y-intercept):
In the year 2000, the enrollment was 1200 students.
Therefore, initial value (the value of "y" when "x" is 0) is 1200.
c) Independent Variable: The independent variable, "x," represents the number of years since 2000.
d) Dependent Variable: The dependent variable, "y," represents the enrollment of the school each year after 2000.
We can write the equation:
y = 35x + 1200
a) The rate of change is 35 students per year.
b) The initial value is 1200 students.
c) The independent variable is "x," which represents the number of years since 2000.
d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.
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The new merry go round can hold a total weight of 500 pounds. Susie weighs 45.67 pounds, Johnny weighs 76.9 pounds, Grace weighs 66.72 pounds, and Max weighs 89.3 pounds. Can the merry go round hold all of the children? Show and explain your answer.
Answer:
Yes, it can
Step-by-step explanation:
45.67+76.9+66.72+89.3= 278.59
278.59 is less than 500
The merry-go-round can hold all the children.
To find if the merry go around can hold all children, we need to find the total weight of all the children.
[tex]\text{total weight of all children} = Susie\ +\ Johnny\ +\ Grace\ +\ Max\\\\\text{total weight of all children} = (45.67 +76.9+ 66.72+ 89.3)\ pounds = 278.59\ pounds[/tex]
The total weight of all the children is 278.59 pounds, which is less than the maximum capacity of the merry-go-round which is 500 pounds.
So, the merry-go-round can hold all the children.
plant a is 4.7 centimeters tall and growing at the rate of 3.5 centimeters a month. plant b is 5.2 centimeters tall and growing at the rate of 2.5 centimeters a month. When will plant a axceed the height of plant b? what will the hights of the plants be after 3 months
After 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
To find when to plant A will exceed the height of plant B, we need to set up an equation:
Let t be the number of months, then the height of plant A after t months is:
Height of plant A = 4.7 + 3.5t
The height of plant B after t months is:
Height of plant B = 5.2 + 2.5t
We want to find when to plant A will exceed the height of plant B, so we need to solve the equation:
4.7 + 3.5t = 5.2 + 2.5t
Simplifying, we get:
t = 1.0
Therefore, plant A will exceed the height of plant B after 1 month.
To find the heights of the plants after 3 months, we substitute t = 3 into the equations:
Height of plant A = 4.7 + 3.5(3) = 14.2 centimeters
Height of plant B = 5.2 + 2.5(3) = 12.7 centimeters
Therefore, after 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.
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Final answer:
After solving linear equations for growth over time, Plant A will exceed the height of Plant B after 1 month. After 3 months, Plant A will be 15.2 cm tall and Plant B will be 13.7 cm tall.
Explanation:
The question involves two plants with different initial heights and growth rates. To find out when Plant A will exceed the height of Plant B and their heights after 3 months, we can use linear equations.
Calculation for Exceeding Height:
Let x represent the number of months it will take for Plant A to exceed the height of Plant B. The equation for Plant A's height over time is:
Height of Plant A = 4.7 + 3.5x (in centimeters)
The equation for Plant B's height over time is:
Height of Plant B = 5.2 + 2.5x (in centimeters)
To find out when Plant A exceeds Plant B, we set the equations equal and solve for x:
4.7 + 3.5x = 5.2 + 2.5x
Solving for x, we find that x = 1. Therefore, after 1 month, Plant A will exceed the height of Plant B.
Heights After 3 Months:
Height of Plant A = 4.7 + 3.5(3) = 15.2 cm
Height of Plant B = 5.2 + 2.5(3) = 13.7 cm
Create a system of equation.
The following system of equations represents the given statement;
x = y+z
y = 2z
10x+15y+40z = 600
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Step-by-step explanation:
Let,
Small pizza = x
Medium Pizza = y
Large Pizza = z
Cost of one small pizza = $10
Cost of one medium pizza = $15
Cost of one large pizza = $40
According to given statement;
They usually sells as many small pizzas as medium and large pizzas combined.
x = y+z
The number of medium pizzas sold is usually twice as many as large ones.
y = 2z
How many of each pizza must they sell to get $600.
10x+15y+40z = 600
The following system of equations represents the given statement;
x = y+z Eqn 1
y = 2z Eqn 2
10x+15y+40z = 600 Eqn 3
Putting value of x and y from Eqn 1 and 2 in Eqn 3;
[tex]10(y+z)+15(2z)+40z=600\\[/tex]
We know that y=2z from Eqn 2,
[tex]10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600[/tex]
Dividing both sides by 100;
[tex]\frac{100z}{100}=\frac{600}{100}\\z=6[/tex]
Putting z=6 in Eqn 2;
[tex]y=2(6)\\y=12[/tex]
Putting value of y and z in Eqn 1;
[tex]x=12+6\\x=18[/tex]
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Keywords: linear equations, substitution method
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There are 450 students, 20 teachers and 5 teacher's aides at Canyon Hills Middle School. What is the ratio of students to teachers and their aides?
A
9:2
B
90:1
C
1:18
D
18:1
Answer:
D. 18 : 1
Step-by-step explanation:
Students : teachers and aides
450 : 25
Treat it like a fraction. 450 over 25 simplifies to 18 over 1 because 450/25=18 and 25/25=1.
Therefore, the ratio is 18 : 1
Answer: 18:1
Step-by-step explanation:
450 students : 25 teachers
18 students : 1 teachers
450/25= 18
Please help :DDDDDD
question is in the pic!
Equivalent expressions to given expression are:
A : -8+19-3x
C : -11x+19
Step-by-step explanation:
Given
[tex]-5+4(-2x+6)-3x[/tex]
We will simplify the given expression to find the equivalent expressions
[tex]-5+4(-2x+6)-3x\\= -5-8x+24-3x\\= -8x+19-3x\\=-11x+19[/tex]
by observing the simplification we can see that the equivalent expressions are:
A : -8+19-3x
C : -11x+19
Keywords: Polynomials, Expressions
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all
Answer:
The number of large boxes is 55 and the number of small boxes is 70
Step-by-step explanation:
The complete question is
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4150 pounds in boxes, how many of each type of box is it carrying?
Let
x ------> the number of large boxes
y -----> the number of small boxes
we know that
[tex]x+y=125[/tex] -----> equation A
[tex]50x+20y=4,150[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is (55,70)
therefore
The number of large boxes is 55 and the number of small boxes is 70
What is the value of x?
3
4
6
8
Answer:
4
Step-by-step explanation:
Gave a picture to explain
Answer: I can confirm x=4
Step-by-step explanation:
Jim went to a carnival with $25.00. He bought some food for $3.75. Jim wants to spend the rest of his money on tickets for rides, r, which cost $1.25 each. Which represents, r, the number of tickets Jim can purchase?
(A) r less than equal 17
(B) r greater than equal 17
(C) r less than equal 20
(D) r greater than equal 20
Answer:
A
Step-by-step explanation:
25.00-3.75 is 21.25. divide that by 1.25 to get exactly 17.
Answer:A
Step-by-step explanation:
A rectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?
Answer:
x = 1 mStep-by-step explanation:
Area of pool:
6*4= 24 m²Area of walkway:
(6+2x)(4 +2x) - 24 =24 + 12x + 8x + 4x² - 24 =4x² + 20xIf the areas are equal, then:
4x² + 20x = 24x² + 5x - 6 = 0x = (-5 ±√25+24)/2x = (-5 ± 7)/2x = 1 and x = -6 (excluded as negative)Final answer:
To find the value of x when the area of the walkway equals the area of the pool, set up an equation and solve for x. The value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
Explanation:
To find the value of x when the area of the walkway equals the area of the pool, we need to set up an equation. The area of the pool is the length multiplied by the width, which is 6 meters multiplied by 4 meters, or 24 square meters. The area of the walkway is the total area of the larger rectangle minus the area of the pool.
The total area of the larger rectangle is the length plus twice the width, all multiplied by the width. So, the area of the walkway is x(6 + 2x - 4). Setting the area of the walkway equal to the area of the pool gives us the equation: x(6 + 2x - 4) = 24.
To solve this equation, we can first simplify it by distributing the x through the parentheses: 6x + 2x^2 - 4x = 24. Combining like terms, we have 2x^2 + 2x - 24 = 0. To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us 2(x + 6)(x - 2) = 0. So either (x + 6) = 0 or (x - 2) = 0. Solving for x, we find that x = -6 or x = 2.
Since we are dealing with width, the negative solution x = -6 is not applicable. Therefore, the value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
what fraction is equal to .13
Answer: 13/100
Step-by-step explanation:
any number with 100 as it denominator and that is less than 100 is it's self but move the decimal back for how many place values it have.
for example:
1/100= .1
99/100= .99
The decimal 0.13 is equivalent to the fraction 13/100, as the number has two decimal places, and the fraction's denominator is set to 100.
The decimal 0.13 can be expressed as a fraction where the denominator is a power of 10 equivalent to the number of decimal places. To convert 0.13 to a fraction, you consider that there are two decimal places, so you use 100 as the denominator. Therefore, 0.13 as a fraction is 13 over 100, which can be written as 13/100.
This is because to convert a decimal to a fraction, you write down the numbers to the right of the decimal point as the numerator and a power of 10 that corresponds to the number of decimal places as the denominator. In the case of 0.13, since there are two decimal places, the power of 10 used is 102, which is 100.
What are all the factors of 2x^2-6x
Answer:
2x (x-3)
Step-by-step explanation:
Answer:
2x(x - 3).
Step-by-step explanation:
2x is common so if we divide 2x^2 - 6x by 2x we get x - 3 and the factors are:
2x(x - 3).
Which of the following is true of vertex-edge graphs?
(1)They can model real-world problems.
(2)They can all be solved.
(3)Euler paths are the same as Hamilton paths.
(4)All vertices must be used once in Hamilton circuits.
What is the value of the product (3-2)(3 + 2)?
O 5
O 9+ 41
O 9-4
O 13
Please help
Answer:
5
Step-by-step explanation:
3 - 2 = 1
3 + 2 =5
5 x 1 =5
3 3/5 divided by 2 1/4 in simplest form
Answer:
Exact form: 8/5
Complete the square to determine the maximum or minimum value of the function defined by the expression. −x2 − 10x + 14 A) minimum value at 25 B) maximum value at 39 C) maximum value at −5 D) minimum value at −39
Answer:
B) maximum value at 39.
Step-by-step explanation:
maximum value at 39
First, set the expression equal to 0.
−x2 − 10x + 14 = 0
Complete the square.
−x2 − 10x = −14
−(x2 + 10x) = −14
−(x2 + 10x + 25) = −39
−(x + 5)2 + 39= 0.
Therefore, the maximum value is 39.
In the xy coordinate plane the slope of line p is 1 2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept. A) y = -2x - 3 B) y = -2x + 3 C) y = -2x - 6 D) y = -2x + 6
Answer:
Option C) y = -2x - 6
Step-by-step explanation:
The correct question is
In the xy coordinate plane the slope of line p is 1/2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept.
step 1
Find the slope of a line that is perpendicular to p
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=\frac{1}{2}[/tex] ----> slope of line p
substitute
[tex](\frac{1}{2})*m_2=-1[/tex]
[tex]m_2=-2[/tex] ----> slope of the line perpendicular to p
step 2
Find the equation of the line that is perpendicular to p and intersects p at is x-intercept
we have
[tex]m=-2[/tex]
[tex]point\ (-3,0)[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-0=-2(x+3)[/tex]
[tex]y=-2x-6[/tex]
Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue. What fraction of Megan’s star sticker are blue?
Answer:
The fraction of Megan's blue stickers are 1/6.
Step-by-step explanation:
Given:
Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue.
Now, to find the fraction of stickers which are blue.
Total number of stickers = 12.
Number of red stickers are = [tex]12\times \frac{1}{2}[/tex]
= [tex]6 stickers[/tex]
Number of green stickers are = [tex]12\times \frac{1}{3}[/tex]
= [tex]4 stickers[/tex]
Number of blue stickers are = [tex]12-(6+4)[/tex]
= [tex]12-10=2 stickers[/tex]
Now, to get the fraction of stickers we divide the number of blue stickers by the total number of stickers:
Fraction of blue stickers = [tex]2\div 12[/tex]
= [tex]\frac{1}{6}[/tex]
Therefore, the fraction of Megan's blue stickers are 1/6.
can someone explain to me and give me the answer cause i don’t get it
Answer:
ONP and JKI
Step-by-step explanation:
exterior angles are the angles on the outside and if your looking for the alternate exterior angle you would go and find the equivalent angle on the opposite side of the bisector or the ray cutting the parallel lines in half