Step-by-step explanation:
180 =16x-100-0.1x2
-0.1x2+16x-280=0
x2-160x+2800=0
S=160
P=2800
DELTA=160*160-4*2800
DELTA=25600-10800
DELTA=14400
x1,2=160+/-
[tex] \sqrt{14400[/tex]
divided by 2
x1,2=160+/-120 div by 2
x1=140
x2=20
Solve - 3g-2| +1 < 6.
Answer: 18=18
Step-by-step explanation:
(-5, 0) and (8, 0)
Quadratic function
We need to know about roots of a quadratic equation to solve the problem. The quadratic equation is [tex]x^{2} -3x-40=0[/tex]
Quadratic equation is an equation with the highest degree of the variable being 2. A quadratic equation has two roots. The two roots can be real and different or real and equal or imaginary. The roots of a quadratic equation can be found using factorization method. The roots of a quadratic equation can be used to find the quadratic equation itself. Here in this question we have two points (-5,0) and (8,0). These points lie on the x-axis hence we can say that they are the two roots of the equation and the quadratic equation is in terms of x since it cuts the x-axis. Hence we can say that the two roots of the equation are -5 and 8.
For a quadratic equation [tex]ax^{2} +bx+c=0[/tex] let us say that the roots are α and β
α+β=-b/a
αβ=c/a
Here α and β are -5 and 8
-5+8=-b/a ⇒b/a=-3
c/a=-5 x 8=-40
The quadratic equation is given by [tex]x^{2} +\frac{b}{a} x+\frac{c}{a} =0[/tex] which is [tex]x^{2} -3x-40=0[/tex]
Therefore we found the quadratic equation using the two points given, the equation is [tex]x^{2} -3x-40=0[/tex]
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During a marathon, Amy was in second place and was told that the leader was 100 meters ahead of her and that the closest runner behind her was 75 meters back. On a number line, let's say Amy's position is at 0, and the leader's position is on the positive side of 0. Which number sentence correctly compares the distance between Amy and the runner behind her to the distance between Amy and the leader?
A) |-75|< |-100|
B.|-75|<|100|
C.|75|=|-100|
D.|-75|>|100|
Answer:c
Step-by-step explanation:
c
COULD YALL HELP ME ?!???!
Answer:
28 degrees
Step-by-step explanation:
We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.
By combining like terms, we get 6x + 12 = 180.
Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.
Graph the following system of inequalities on the coordinate plane. You will need to explain your work. Each correct line graphed WITH the correct explanation and shading is worth TWO points.
Please tell me how you graphed each line and how you determined where to shade
Answer:
See attached graphs Graph1, Graph2 and Graph3 and detailed explanation below
Step-by-step explanation:
The process for plotting and shading are essentially the same but with different inequalities
To plot any line
We need two pointsPlug in a value for x and find the corresponding y valueRepeat for another x value and find the corresponding y valueDraw a straight line through the two pointsTo determine area to shade
Choose a point on either side of the line from the graph. See if the corresponding (x,y) values satisfy the inequality. If they do, then that's the area to shade. If not, shade the other area
1. Inequality y > -3x - 2
The line equation is y = -3x -2
Let's choose x = 0. Then y = -3(0) -2 = -2. So one point is (0, -2)
Choose another value for x, say x = 1
y = -3(1) - 2 = -3-2 = -5. So another point is (1,-5).
Draw a straight line through both points (see attached Graph1)
Determining area to shade
Choose a point on the graph on one side of the line. Let's choose (1,2). So x = 1 and y = 2. Does this satisfy the inequality y = -3x -2? Let's see
Is 2 > -3(1) - 2 ?
2 > -3-2 ?
2 > -5 ? YES since a positive number is greater than a negative number. So the area containing (1,2) should be shaded as shown in Graph 1
2. Inequality 4x + 5y ≤ 20
Line equation is 4x + 5y =20
Convert to a function of x as follows
Subtract 4x from both sides ==> 5y = 20 -4xDivide by 5 both sides ==> y = 20/5 - (4/5)x ==> y = 4- 4x/5Choose two values of x and find corresponding y values to get the coordinates of two points
Plug x = 0 into line equation ==> y = 4- 4x/5
==> y = 4 - 4(0)/5 = 4
==> (0, 4) is one point
Choose another value of x, say 5(this is a convenient value since we are dividing by 5)
==> y = 4- 4(5)/5 = 4-4 = 0
==> (5, 0) is another point
Draw straight line through (0,4) and (5,0)
To determine area to shade let's choose a point on the graph. (0,0) is a convenient point. Do the values of x=0 and y=0 satisfy the inequality
4x + 5y ≤ 20?
Plugging in x = 0 and y = 0 gives us
4(0) + 5(0) = 0 and 0 is indeed ≤ 20
So the inequality is satisfied at (0,0)
Shade the region on the side of the line where (0,0) is (see Graph2)
3. Inequality y > -4
The line equation is y = -4
Since this equation does not involve x, the line plot will be a horizontal line at y = -4 for all x values
Simply draw a horizontal line which crosses the y axis at y = -4
To determine which area to shade, choose a point. Use (0,0)
Does y = 0 satisfy the inequality y > -4?
0 > -4 so indeed the point (0,0) satisfies the inequality. Just shade the area on the side of the line which contains (0,0). This will be the region above the line y = -4 See Graph3
Hope that helps :)
Find the value of a and b, so that the system of equations has a solution (2, -3)
3x + 5y + 9 = 0
ax + by = 11
Please give an explanation with the answer, thats what im most worried about. 100 points :3
please help right answer will get brainliest
Answer:
[tex]\sf y = \dfrac{x }{\boxed{26}} +\boxed{-2}[/tex]
Step-by-step solution:
[tex]\rightarrow \sf x - 26y = 52[/tex]
[tex]\rightarrow \sf - 26y = 52-x[/tex]
[tex]\rightarrow \sf - 26y = -x + 52[/tex]
[tex]\rightarrow \sf y = \dfrac{-x + 52}{-26}[/tex]
[tex]\rightarrow \sf y = \dfrac{-x }{-26} + \dfrac{ 52}{-26}[/tex]
[tex]\rightarrow \sf y = \dfrac{x }{26} -2[/tex]
At this year's State Fair, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $25. If you rolled a 7, you won $2. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent. The expectation of this game is approximately dollars. X
The probability to win 25$ and 2$ are 1/18 and 1/6
Probability is the ratio of favorable cases to total sample cases.
If two dice are rolled,
Total sample cases or combinations= 6x6=36
The favorable cases to get 2 or 12 ={1,2}{6,6}= 2 total cases
The favorable cases to get 7 ={1,6}{6,1}{2,5}{5,2}{3,4}{4,3}=6 cases
The probability to win 25$=2/36=1/18
The probability to win 2$=6/36=1/6
Thus the probability to win 25$ and 2$ are 1/18 and 1/6
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Main Answer: $1.27
Given data:
If you rolled two dice and got a sum of 2 or 12, you won $25. If you rolled a 7, you won $2. Any other roll was a loss. It cost $1 to play one game with one roll of the dice.
Solving part
Step-by-step explanation:
For 2 and 12
Number of possible outcomes = 2
Gain = 25 -1 = $24
For 7
Number of possible outcomes = 6
Gain = 5-1 = $4
For others
Number of possible outcomes = 36-(4+6) = 26
Gain = -$1
Expectation of the gain;
X= (2×$24 + 6×$4 - 26×1)/36
X = $46/36
X = $1.27
Final Answer: $1.27
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I’ll give braniest
Find the coordinates of the point
7/10 of the way from A to B.
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{10}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{7}{10}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{10}-\stackrel{x_1}{(-3)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 13 ~~,~~ 13 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{-3}~~+~~\frac{7}{10}(13)~~,~~\stackrel{y_1}{-8}~~+~~\frac{7}{10}(13) \right)\implies \left(-3+\cfrac{91}{10}~~,~~-8+\cfrac{91}{10} \right) \\\\\\ \left( \cfrac{-30+91}{10}~~,~~\cfrac{-80+91}{10} \right)\implies \left(\cfrac{61}{10}~~,~~\cfrac{11}{10} \right)\implies \left(6\frac{1}{10} ~~,~~1\frac{1}{10} \right)[/tex]
You are laying brick for a custom circular patio fire pit. The radius of the fire pit is 36 inches. In square feet, what
amount of patio space is needed for the fire pit?
O 9.42 square feet
O 28.26 square feet
O 113.04 square feet
226.08 square feet
4,069.44 square feet
Answer:
The answer is 28.26 square feet.
Step-by-step explanation:
The area of a circle is [tex]\pi r^{2}[/tex], so if the radius is 36, [tex]\pi *36^{2}[/tex] is equal to about 4071.5. The formula for converting square inches to square feet is to divide by 144, and [tex]\frac{4071.5}{144}[/tex] is around 28.26.
What is 9 x 5.63 show how you got your answer.
Answer:50.63
Step-by-step explanation: line them up on top of each other and multiply 9 by all them and if its over 10 put the 2nd digit the the next number.
The number of species, N, on an island as a function of the area, A, of the island is N=kA‾‾√3.
(a) What is the exponent of this power function?
-[tex]\sqrt{3}[/tex] is the exponent of the power function.
The power function is generally just f(x) = c x^p for some constant c and some real number exponent p. (It can only be defined for positive values of x.) For example, the square root function f(x) = √x is a power function with p = 1/2.
In this case, N=kA‾‾√3 , -[tex]\sqrt{3}[/tex] is the exponent of this function.
Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b to the n".
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The exponent of the power function is 1/2.
How often we are multiplying a number by itself is indicated by its exponent. To multiply 3 four times, for instance, we get 34. It is 3333 in its enlarged form. A number's power is another name for an exponent. It may take the form of an integer, a fraction, a negative integer, or a decimal.
A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. Square root of the base is a number having a power of half.
Hence we get the exponent of the function as 1/2.
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Help!
solve for x 13,14, and 16 only!!!
Answer:
13:
x= 86°
14:
x= 30°
16:
x= 59°
tim goes on a car journey for the first 15 minutes his average speed is 40mph
Answer:
For the first 15 minutes his average speed is 40 mph. He then stops for 25 minutes. He then completed the journey at an average speed of 45 mph. The total journey time is 1 hour.
The difference of two numbers is 6. Twice the smaller is 4 more than the larger. Find the larger
number
Answer:
16
Step-by-step explanation:
Difference means subtract
Let the two numbers be x and y
x-y = 6
Let y be the smaller number
2y = x+4
Using substitution
x = 6+y
2y = 6 +y +4
2y = y+10
Subtract y from each side
2y-y = y+10-y
y = 10
Now we need to find x
x-y = 6
x-10 = 6
Add 10 fo each side
x-10+10 =6+10
x = 16
Kai is buying boxes of cookies at a bakery. Each box of cookies costs \$4$4dollar sign, 4. He wrote this equation to find how many dollars he'll spend (d)(d)left parenthesis, d, right parenthesis when he buys some number of boxes of cookies (c)(c)left parenthesis, c, right parenthesis:
d=4cd=4cd, equals, 4, c
Identify the dependent and independent variables.
The number of boxes of cookies Kai buy : independent variable
The amount of the cookies will cost in dollars : dependent variables
Based on the given conditions, formulate,
Each box of cookies costs is = \$4$4dollar (sign, 4).
Cookie represented by c
The required equation is,
d = 4cd = 4cd = 4c
The price is determined by the number of cookies purchased.
c is the independent variable
when c is changes d is changed
So, d is the dependent variable
variables of the equation.
So,
We can write,
d = 4c
where d represents the cost of cookies in dollar and c represents the number of boxes of cookies.
Then, the cost of each box of cookies is $4.
It means,
The cost of 1 box of cookies is = $4.
The cost of 2 boxes of cookies is = $(4+4) = $(2×4)
The cost of 3 boxes of cookies is = $(4+4+4) = $(3×4)
The cost of cookies = (Number of boxes × 4)
The required equation is,
d = 4c
where d represents the cost of cookies in dollar and c represents the number of boxes of cookies.
Therefore,
The boxes of cookies Kai buy : independent variable
The cookies will cost in dollars : dependent variables
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Boxes of cookies (c) is Independent.
Dollars spent (d) is Dependent.
graph each function and give its domain
f(x) = √x - 2
Domain = ∈ [2, ∞]
Range = ∈ [0, ∞]
Graph [tex]\sqrt{x - 2 [-10, 10, -5, 5]}[/tex]
Just outline the function.
The typical root operation is:
[tex]y = a * \sqrt{(x - h)} + k[/tex]
where x - h ≥ 0
The value within the root sign of a square root function CANNOT be < 0
∴ x - h ≥ 0
∴ x ≥ 2
Therefore, Domain = ∈ [2, ∞]
Regarding range, the function we were provided doesn't have a K value.
As a result, the range spans from 0 to infinity.
Therefore, Range = ∈ [0, ∞]
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Lines AB and C'D are parallel. Find the measures of the three angles in triangle ABF.
Part 1
∠FBA = 42° (alternate interior angles)
Part 2
∠FDC = 23° (linear pair)
∠BAD = 23° (alternate interior angles)
Part 3
∠AFBA = 115° (sum of angles in a triangle)
Joshua Kelly estimates that taking some classes would result in earning $11,100 more a year for the next 20 years. Based on an annual
interest rate of 8 percent, calculate the future value of these classes. Use Exhibit 1-B. (Round time value factor to 3 decimal places
and final answer to 2 decimal places.)
Answer:
$507 958.20
Step-by-step explanation:
11 100 x table value for 20 years , 8%
11,100 x 45.762 = $ 507,958.20
distance between (4,9) (9,2)
The distance between the two points is 8.6 units
How to determine the distance between the two points?The points are given as
(4, 9) and (9, 2)
The distance between the two points is then calculated as
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(4 - 9)^2 + (9 - 2)^2
Evaluate the sum of exponents
So, we have
d = √74
Evaluate the exponents
So, we have
d = 8.6
Hence, the distance between the two points is 8.6 units
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f(x)=5x-12what is f(-4)
0.695 into fraction in the simplest form
Answer:
139/200
Step-by-step explanation:
.695 can be represented as 695/1000. Divide the numerator and denominator by 5, you get 139/200.
Answer: 139/200
Step-by-step explanation:
I am guessing
If Alpha and Beta are the roots of 2x² - 5x - 6=0, find the equation whose toots are ( Alpha -1) and (Beta+1).
pls help with this and lots of explanations.Tnx
Answer:
[tex]x = 28[/tex]
[tex]2x { } ^{2} - 5x - 6 = 0[/tex]
Question 6
WORLD RECORD The world's largest ice cream cake was created on May 10, 2011, in Toronto, Canada. The cake
was 4.45 meters long, 4.06 meters wide, and 1 meter tall. All surfaces of the cake except the bottom were covered
with a cookie crumble topping. Use an appropriate two-dimensional model to approximate the area covered by the
cookie crumble topping. Round your answer to the nearest tenth of a square meter.
m²
The surface area covered by the rectangular cookie crumble topping is of 35.1 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
For this problem, the bottom is not covered, hence the surface area will be of:
S = 2(hw + lh) + lw.
The dimensions are given as follows:
l = 4.45, w = 4.06, h = 1.
Hence the surface area is:
S = 2(4.06 x 1 + 4.45 x 1) + 4.45 x 4.06 = 35.1 m².
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A food and nutrition organization reported that 58 out of every 100 people want to lose weight. If 499 students were surveyed at random in the student union,
how many would want to lose weight? Round to the nearest whole number.
About
of the students would want to lose weight.
Answer:
500
Step-by-step explanation:
A company's sales in Seattle were $330,000 in 2012, while their sales in Portland were $245,000 for
the same year. Complete the following statements:
a. Seattle's sales were
% larger than Portland's.
b. Portland sales were
% smaller than Seattle's.
c. Portland sales were
% of Seattle's.
One day total attendance at the state fair was 126,945. Round 126,945 to the nearest ten thousand, nearest ten thousand and the nearest thousand. Which of these rounded amounts is closest to the actual attendance?
Answer: To the nearest thousand.
Step-by-step explanation:
First, we will round 126,945 to the requested place values;
(it says ten thousand once, so I'm going to include hundred thousand)
hundred thousand ➜ 126,945 ➜ 100,000
ten thousand ➜ 126,945 ➜ 130,000
thousand ➜ 126,945 ➜ 127,000
Next, we will subtract these values from 126,945, and see which absolute value is the smallest.
hundred thousand ➜ 126,945 - | 100,000 | = 26,945
ten thousand ➜ 126,945 - | 130,000 | = 3,050
thousand ➜ 126,945 - | 127,000 | = 55
The rounded amount that is closest to the actual attendance is thousand.
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find the inverse of this grapg
Answer:
Can you please send the picture of the graph
Step-by-step explanation:
4Y-4(-2z+6y)-2z simplify
The simplified expression of 4y - 4(-2z + 6y) - 2z is -20y + 6z
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
4y - 4(-2z + 6y) - 2z
Open the bracket
4y - 4(-2z + 6y) - 2z = 4y + 8z - 24y - 2z
Collect the like terms
4y - 4(-2z + 6y) - 2z = 4y - 24y + 8z - 2z
Evaluate the like terms
4y - 4(-2z + 6y) - 2z = -20y + 6z
Hence, the simplified expression of 4y - 4(-2z + 6y) - 2z is -20y + 6z
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!