Answer:
[tex]x \approx 0.13, 2.54[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
3x² = 8x - 1
Step 2: Rewrite
Put equation in Standard Form
Subtract 8x on both sides: 3x² - 8x = -1Add 1 to both sides: 3x² - 8x + 1 = 0Step 3: Identify Variables
a = 3
b = -8
c = 1
Step 4: Solve for x
Substitute [Quad Formula]: [tex]x=\frac{8\pm\sqrt{(-8)^2-4(3)(1)} }{2(3)}[/tex]Evaluate Exponents: [tex]x=\frac{8\pm\sqrt{64-4(3)(1)} }{2(3)}[/tex]Multiplication: [tex]x=\frac{8\pm\sqrt{64-12} }{6}[/tex]Subtraction: [tex]x=\frac{8\pm\sqrt{52} }{6}[/tex]Simplify Radical: [tex]x=\frac{8\pm2\sqrt{13} }{6}[/tex]Factor GCF: [tex]x=\frac{2(4\pm\sqrt{13}) }{6}[/tex]Simplify Fraction: [tex]x=\frac{4\pm\sqrt{13}}{3}[/tex]Evaluate: [tex]x=0.131483, 2.53518[/tex]Round: [tex]x \approx 0.13, 2.54[/tex]2[-3^(2)-(5)/(4-9)]+3(4-2^(3))
Answer:
-28
Step-by-step explanation:
Kyle asks his friend Jane to guess his age and his grandmother’s age. Kyle says his grandmother is not more than 80 years old. He says his grandmother’s age is, at most, 3 years less than 3 times his own age.
Jane writes this system of inequalities to represent k, Kyle’s age, and g, Kyle’s grandmother’s age.
Inequality 1: g > 80
Inequality 2: g ≤ 3k – 3
Which inequality did Jane write incorrectly, and how could it be corrected?
Inequality 1 is incorrect; it should be g ≤ 80.
Inequality 1 is incorrect; it should be g ≥ 80.
Inequality 2 is incorrect; it should be g < 3k – 3.
Inequality 2 is incorrect; it should be g ≥ 3k – 3.
Answer:
Inequality 1 is incorrect; it should be g ≤ 80.
Step-by-step explanation:
Kyle's grandmother is not more than 80. This means that she is either equal to 80 or less than 80.
This gives us the inequality: g ≤ 80
luther drew a scale drawing of an italian restaurant. he used the scale 1 millimeter : 6 meters. in the drawing, the restaurant's kitchen is 3 millimeters wide. what is the width of the actual kitchen?
The actual kitchen measures 18m in width.
• In mathematics, the unitary method is used to find the necessary value by first determining the value of a single unit and then multiplying the number by the single unit value.
• For example, if a car travels 60 kilometers on three litres of gasoline, we can calculate the number of kilometers traveled on one litre of gasoline using the unitary method.
We are given that Luther drew a scale drawing of an Italian restaurant. He used a scale on which 1 millimetre equals 6 meters. We need to find the width of the kitchen if in the drawing it is 3 mm wide.
So,
1mm = 6m
3 mm =?
3 mm = 6*3
3 mm = 18 m
The actual width of the kitchen is 18 m.
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Systems of equations with graphing
For the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.
We are given the equations:
7 x - y = 7 … (1)
x + 2 y = 6
x = 6 - 2 y … (2)
Substitute equation (2) in equation (1), we get that:
7 ( 6 - 2 y ) - y = 7
42 - 14 y - y = 7
15 y = 35
y = 35 / 15
y = 7 / 3
x = 6 - 2 ( 7 / 3)
x = 18 - 14 / 3
x = 4 / 3
Therefore, for the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.
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Joel is buying packs of baseball cards to add to his collection. He wants to have at least 65 total. He already has 15 and each pack has 5 cards, c, in it. How many packs will Joel need to buy in order to have at least 65 total cards?
Answer:
10 cards
Step-by-step explanation:
In order to find how many packs Joel needs to buy we need Make an equation
Equation = 5c + 15 = 65
where,
c = cards5c+15=65
Step 1: Subtract 15 from both sides.
5c+15−15=65−15
5c=50
Step 2: Divide both sides by 5.
5c/5 = 50/5
c=10
Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards
An expression is shown.
4 · (−12)
Select all equivalent expressions.
• -7-6
• -12.4
• -12-(-4)
• 8-(-6)
• −3 - 16
Expression: 4*(-12)= -48
-7-6= -13
Equivalent: -12*4= -48
8-(-6)= 14
-3-16= -19
how many calories would you consume if you were to eat a large size pizza (16 inches) by yourself? give your answer to the nearest hundred.
So nearest hundred of calories of pizza is 3384.
As it is given that its an pizza of 16 inches .
A Calorie is unit of heat used to indicate the amount of energy foods produce in the human body that is equal to 1000 calories.
Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.
So as we all know pizza of 16 inches contains 3384.00 calories
And its been asked to the nearest hundred so divide it by 100And we get 3384 calorie. So a 16 inch pizza contains 3384 calories.
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which is equivalent to the following expression 4p^2+5.5m+2.5p^2-m+3m
The equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m
How to determine the equivalent expression?The expression is given as
4p^2+5.5m+2.5p^2-m+3m
Rewrite properly as
4p^2 + 5.5m + 2.5p^2 - m + 3m
Collect the like terms in the above equation
4p^2 + 5.5m + 2.5p^2 - m + 3m = 4p^2 + 2.5p^2 + 5.5m - m + 3m
Evaluate the like terms in the above equation
4p^2 + 5.5m + 2.5p^2 - m + 3m = 6.5p^2 + 7.5m
Hence, the equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m
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[tex] {x}^{2} + 70 = 17x[/tex]
solve
I really neeed this done asap
Answer: x=7 x=10
Step-by-step explanation:
[tex]x^2+70=17x\\x^2+70-17x=17x-17x\\x^2-17x+70=0\\x^2-7x-10x+70=0\\x(x-7)-10(x-7)=\\(x-7)(x-10)=0\\x-7=0\\x=7\\x-10=0\\x=10[/tex]
Answer:
x = 7, x = 10
Step-by-step explanation:
x² + 70 = 17x ( subtract 17x from both sides )
x² - 17x + 70 = 0 ← in standard form
consider the factors of the constant term (+ 70) which sum to give the coefficient of the x- term (- 17)
the factors are - 10 and - 7 , since
- 10 × - 7 = + 70 and - 10 - 7 = - 17 , then
(x - 10)(x - 7) = 0 ← in factored form
equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x - 10 = 0 ⇒ x = 10
Which of the following represents (picture)
The interval that represents the inequality 1 < x ≤ 6 is given by:
B. (1,6].
What is the standard interval notation?The standard interval notation of an interval of lower bound a and upper bound b is given by:
[a,b].
The inequality notation is:
a ≤ x ≤ b
The set builder notation is:
{x | a ≤ x ≤ b}.
In this problem, we are given the inequality 1 ≤ x ≤ 6, hence a = 1 and b = 6, and open at x = 1 and closed at x = 6, hence the interval is:
B. (1,6].
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You go to a restuarant with 4 friends. You all agree that you will pay the bill and everyone will contribute equally to pay for their part. The total bill was $62.65. Write an equation and solve it to find out how much each person will pay.
a. 5x = 62.65 Each will pay $15.66
b. 4x=62.65, Each will pay $15.66
c. 5x=62.65, Each will pay $12.53.
d. 4x=62.65 Each will pay $12.53
The required equation for sharing the bills equally is 5x = 62.65 and each will pay $12.53
How many friends went to the restaurant altogether?
The fact that the person went with 4 friends and paid for every means that he made payments for the 5 of them and he is expected to get refund from 4 persons, in other words, in order to share bills equally, the 5 friends would have to contribute equally, which means we would divided total bills by the number of friends, which is 5 not 4 because the first person would also his part of the bills
Let x be the amount paid person, the total amount paid would be x paid person multiplied by the number of friends, 5
total amount paid=5*x
total amount paid =5x
the amount paid in dollars is $62.65
5x=62.65
x=62.65/5
x=$12.53
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The quotient of a number and negative six plus eight is twenty-four
Answer:
the number is ..let X
X/-6+8=24X/2=24criss cross the number and we get 48an equation that is true for all values of the variable is called an
Answer:
an identity............
Answer:
An identity
Step-by-step explanation:
An identity is an equation, which is true for all values of the variables in the equation.
-10
-8
-6
-4 -2
10
00
8
9
4
54
2
-2
-4
-6
op
-10
2
4
9
8
00
10
10/586=582824448
55359=5244+88556-89595
=8388256
HELP ASAP!!!
Solve for m in the following equation.
4m/3= 8
m= 10
m= 6
m= 2
m= 96
You buy three more than twice as many pounds of apples as bananas. If you bought seven pounds of apples, how many pounds of bananas did you buy?
What is the correct equation and solution for this problem?
3p – 2 = 7; p = 3 pounds
2p – 3 = 7; p = 5 pounds
3p + 2 = 7; p = 3 pounds
2p + 3 = 7; p = 2 pounds
Thank you!!
Answer:
1. STEPS FOR SOLVING LINEAR EQUATION
[tex] \frac{4m}{3} = 8[/tex]
Multiply both sides by 3.
4m=8×3
Multiply 8 and 3 to get 24.
4m=24
Divide both sides by 4.
[tex]m = \frac{24}{4} [/tex]
Divide 24 by 4 to get 6.
m=6
2. 2p+3=7; p=2 pounds
What is 9+9?
Easy points and brainliest if 2 ppl answer
Answer:
18
Step-by-step explanation:
Describe in words where cube root of 35 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
plss help fast
The cube root of 35 would be plotted on a number line A. Between 3 and 4, but closer to 3.
How to illustrate the information?It should be noted that cube root of a number simply means a number that you can multiply three times that will give the original number.
In this case, the cube root of 35 will be 3.2.
This means that it's closer to 3. It's also between 3 andmd 4.
Therefore, the cube root of 35 would be plotted on a number line between 3 and 4, but closer to 3.
In conclusion, the correct option is A.
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32. XY, given X(7, 2) and Y(2, 0)
Domain
Range
Based on the coordinates of XY which are X(7, 2) and Y(2, 0), the domain and range are:
Domain : (2, 7)Range: (0, 2)What are domain and range?The domain of a line refers to all the points on that line that the value of the x-axis can take.
In line XY, the only two x-axis values are 7 and 2. This means that the domain is therefore (2, 7).
The range of a line on the other hand, are all the points that the value on the y-axis can take.
The range in this case is therefore (0, 2).
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What is the scale factor from the drawing to the actual airplane
the scale factor is _
Answer: 2
Step-by-step explanation: I just did this lesson
A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
If the height of the actual airplane is 20m and the in the scale drawing the height is 10m.
The scale factor of the airplane is 200.
What is a scale factor?A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
We have
The height of the plane in scale drawing:
= 10 cm
The height of the plane in an actual airplane.
= 20 m
The scale factor of the height of the airplane:
= 20m / 10 cm
[ 1 m = 100 cm ]
= (20 x 100) cm / 10 cm
= 200
Thus,
The scale factor of the airplane is 200.
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- The circles are identical. Find the circumference of each circle. Round your
answer to the nearest tenth.
4x
6x - 6
Answer:
Circumference = 75.4
Step-by-step explanation:
Since the circles are identical, that means that the radii must be equal.
4x=3x+3
x=3
That means that radius = 12
The formula for the circumference = 2pi × radius
2pi × 12 = 24pi ≈ 75.4
Answer:
75.4 (nearest tenth)
Step-by-step explanation:
The diameter of a circle is the distance from one side of the circle to the other through the center. The diameter is the widest part of the circle.
The radius of a circle is the distance from the center to the circumference. The radius is half the diameter of a circle.
We have been given the radius of the circle on the left: r = 4x.
Therefore, as the diameter is twice the radius, the diameter of the circle on the left is: d = 2(4x) = 8x
We have been given the diameter of the circle on the right: d = 6x + 6
Equate the two diameters and solve for x:
⇒ 8x = 6x + 6
⇒ 8x - 6x = 6x + 6 - 6x
⇒ 2x = 6
⇒ 2x ÷ 2 = 6 ÷ 2
⇒ x = 3
Substitute the found value of x into one of the diameter expressions to find the diameter of both circles:
⇒ d = 8x
⇒ d = 8(3)
⇒ d = 24
Circumference of a circle
C = πd
(where d is the diameter)
Substitute the found diameter into the circumference formula:
⇒ C = πd
⇒ C = 24π
⇒ C = 75.39822...
⇒ C = 75.4 (nearest tenth)
Therefore, the circumference of each circle is 75.4 units (nearest tenth).
Please help and please hurry I have to submit it soon: The price of Stock A at 9 A.M. was $15.01. Since then, the price has been increasing at the rate of $0.13 each hour. At noon the price of Stock B was $15.76. It begins to decrease at the rate of $0.09 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answer: 8.3 hours
Step-by-step explanation: 15.76-15.01 is 0.75
Now just divide 0.75 from 0.09 and you get 8.3
Answer:
Step-by-step explanation:
Stock A= $15.01 increases by $0.13 an hour. $15.14
Stock B =$15.76 decreases by $0.09 an hour $15.65
15.65-15.14= 0.51
Find the surface area of the figure
Answer: 208 in^2
Step-by-step explanation:
4 2*8 rectangles
1 8*8 square
4 5*8/2 triangles
4(2*8)+8*8+4(5*8/2)=
4(16)+64+4(5*4)=
64+64+4(20)=
128+80=208 in^2
A cyclist rides at a constant speed of 15 miles per hour. At this speed about how long would it take the cyclist to ride from garden city to dodge city, Kansas
The time taken by the cyclist to ride from the garden city to dodge city, Kansas is 3.5 miles/hour.
Given that, a cyclist rides at a constant speed of 15 miles per hour.
We need to find at this speed how long would it take the cyclist to ride from the garden city to dodge city, Kansas.
What is the formula to find time with distance and speed?Calculate speed, distance or time using the formula d = st, distance equals speed times time.
Now, the distance between garden city to dodge city, Kansas 52.3 miles via US-50 E.
So, time taken=52.3/15
=3.48≈3.5 miles/hour
Therefore, the time taken by the cyclist to ride from garden city to dodge city, Kansas is 3.5 miles/hour.
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Which of the following equations has nosolution? B= -B+ 2 B + 2= b + 2 B+ b = 2 b + 2 = b-2
The equation which has no solution among the answer choices as given in the task content is; b + 2 = b-2.
Which equation has no solution?It follows from the task content that the equation which has no solution is to identified.
On this note, the equation in which case, the variable diminishes and the equality does not hold represents that which has no solution.
Hence, the required equation is; b + 2 = b-2.
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using a systematic sample guarantees that members of each group within a population will be sampled.
False
• Systematic Sampling is a probability sampling method where people or researchers select members of the population in a regular interval.
• For example, by selecting every 17th person on the list of the population. If the population is in the random order, this can imitate the benefits of random sampling.
• Systematic sampling can help in minimizing biased samples and poor survey results. If there is a low risk for manipulation of data .
• Systematic sampling introduces certain arbitrary parameters in the data. This can cause overrepresentation or underrepresentation of patterns
In systematic sampling, members from a large population are selected according to a random starting and a fixed periodic interval.
Only stratified sampling, where the population is divided into several data, guarantees the member of each group within a population will be sampled.
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Which of these choices are square roots of 100? Check all that apply.
A -100^1/2
B -50
C 10
D -10
E 50
F 100^1/2
Answer:
C. 10
Step-by-step explanation:
It is very easy to find the square root of a number that is a perfect square. For example, 100 is a perfect square, 100 = 10 × 10. So, 10 is the square root of 100 and this can be expressed as √100 = 10. The square root of any number, in general, can be found by using any of the four methods given below:
Repeated Subtraction MethodPrime Factorization MethodEstimation and Approximation MethodLong Division Method(b) Find the equation of the straight line which passes through 81 +88 (i) the point (3, 2) and makes an intercept on the x-axis is twice as long as that on the y-axis. (ii) the point (-1, 3) whose intercept on the y-axis is thrice that on x-axis.
3x+y=0 and x+2y=7
i)
a= intercept on x axis
b= intercept on y axis
from the question
a=2b
x/2b+ y/b=1
x+2y=2b
since it passes through the point (3,2)
then 3+4=2b
7/2=b
x+2y=7 putting the value of b
ii) given b =3a
then x/a+ y/ 3a =1
3x+y=3a
it passes through ( -1,3) then
-3+3=3a
a=0
3x+y=0
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San Diego's family took a road trip to Mount Rushmore San Diego fell asleep 44% of the way through the trip if the total length of the trip was 400 miles how many miles have they traveled when he fell asleep
The number of miles that they traveled when San Diego fell asleep will be 176 miles.
How to illustrate the information?It should be noted that from the information, San Diego's family took a road trip to Mount Rushmore and San Diego fell asleep 44% of the way through the trip.
In this case, the total length of the trip was 400 miles.
Therefore, the number of miles that they traveled when he fell asleep will be:
= Percentage × Total miles
= 44% × 400
= 0.44 × 400
= 176 mile
Therefore, the number of miles that they traveled when San Diego fell asleep will be 176 miles.
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4x = 0.5(2x- 12) solve for x
Answer: x = -2
Step-by-step explanation:
4x=0.5(2x−12)
Use the distributive property to multiply 0.5 by 2x−12.
4x=x−6
Subtract x from both sides.
4x−x=−6
Combine 4x and −x to get 3x.
3x=−6
Divide both sides by 3.
x= 3−6
Divide −6 by 3 to get -2.
struggling to figure out problem D on this, please help!
Answer:
See answers below
Step-by-step explanation:
This type o problem is known as a Diamond problem
From the diamonds on the top row, it is clear that the top cell of the diamond is the product of the two side numbers and the bottom is the sum of these numbers.
I will use top for the top cell and bottom for the bottom cell, left for and right respectively for left and right cells
a. Top = 2 x 5 = 10; Bottom = 2 + 5 = 7
b. Top = -2 x -1 = 2; Bottom = -2 - 1 = -3
c. Top = Left x Right = 8
Bottom = Left + Right = 6. The only two numbers that satisfy this equation are Left = 4 and Right = 2 since 4 x 2 = 8 and
4 +2 = 6
Answer to c: Left = 4, Right = 2
d We have Let unknown left be L and unknown bottom be B
We have L x (1/2) = 4 for the product
[tex]\rm{\frac{L}{2} = 4}\\\\L = 2 x 4 = 8[/tex]
We have Bottom = Left + Right = 8 + 1/2 = [tex]8\frac{1}{2}[/tex] = 17/2
Answer to d. : Left = 8, Bottom = 17/2
e. Similar to c.
Top = Left x Right = 12;
Bottom = Left + Right = -7
12 can be 2 x 6 or 3 x 4 (same as 4 x 3) or 12 x 1. 4 and 3 are the obvious choices and since they add up to - 7 they both have to be negative
So Left = -3, Right = -4
Note: (-3) x (-4) results in +12