The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.
We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:
[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.
[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.
The first term is [tex]8x^2[/tex].
The second term is [tex]10x[/tex].
In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is: [tex]8x^2 + 10x[/tex]
Factoring out [tex]2x[/tex] gives us:
[tex]2x(4x + 5)[/tex]
Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].
This gives two possible solutions for x:
2 * x = 0 which leads to x = 0
4 * x + 5 = 0 which leads to x = -5/4
Write two fractions that are equivalent to 5
Answer:
5/1, 25/5
Step-by-step explanation:
Please help!! question is in the picture
Answer:
C
Step-by-step explanation:
Total number of rolls = 96
There are three even numbers: 2, 4 and 6.
Number 2 was rolled 13 times
Number 4 was rolled 17 times
Number 6 was rolled 20 times
Hence, even number was rolled [tex]13+17+20=50[/tex] times.
The experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
Therefore,
[tex]P=\dfrac{50}{96}=\dfrac{25}{48}[/tex]
one number is 6 more than another. the sum of the numbers is 30. find the numbers.
To find the numbers, we can set up a system of equations and solve for the variables.
Explanation:Let's represent the numbers as x and y. According to the problem, one number is 6 more than the other. This can be written as:
x = y + 6
The sum of the numbers is 30. This can be written as:
x + y = 30
We can solve this system of equations by substituting the value of x from the first equation into the second equation:
(y + 6) + y = 30
Combining like terms:
2y + 6 = 30
Subtracting 6 from both sides:
2y = 24
Dividing by 2:
y = 12
Now, we can substitute the value of y back into the first equation to find the value of x:
x = 12 + 6
x = 18
Therefore, the two numbers are 12 and 18.
Select and place the symbol that will make the statement true.
6 ? 8
Answer:
6<8
Step-by-step explanation:
This is actually simple since the 6 is less than 8 the thing will face away from the 6 and towards the 8.
You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot dogs must you sell before your average cost per hot dog is $1.15?
The answer should be 30,000. I just do not understand how to get to it.
Thank you in advance!
Answer:
Below is the procedure to find the answer: 30,000 hot dogs.
Explanation:
The average cost is found dividing the total cost by the number of hot dogs:
[tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]
The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:
[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]
Substitute the values:[tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]
Where x is the number of hot dogs.
Solve for x from the equation:[tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]
Which shows you how you can find that the answer is 30,000 hot dogs.
Final answer:
To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.
Explanation:
The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.
To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.
This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.
Boyle’s law states that the volume of gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of gas is raised from 1 atomsphere to 3 atmospheres. What new volume does the gas occupy?
Answer: 20m³
Step-by-step explanation:
From the statement
V <> 1/p --------------------- 1
V = k/p --------------------- 2
K. = VP ---------------------- 3
V = 60 , p = 1
To find k which is a constant, we put those values in equation 3
K = 60 x 1
= 60.
Now from the second statement
V = k/p where p is 3
Therefore,
V = 60/3
= 20m³
simpilfy -19+4k-15k+k-9
Answer:
-10k-28
Step-by-step explanation:
-19+4k-15k+k-9
-28-11k+k
-10k-28
Answer:
12k+ -10
im not truely sure if this is correct... but i went off my knowlage
Find the minimum value of the
parabola
y = x2 − 4x − 5 .
Answer:
-2x-5
Step-by-step explanation:
What is 245 and 7/50 in decimal form
Answer:
245=2.45
7/50=0.14
Step-by-step explanation:
divide by 100
USE MATHAWAY DOT COM!!
ƒ(x) = 18x + 8, find x when ƒ(x) = 14.
Answer:
Step-by-step explanation:
18x+8=14
18x=6
x=1/3
When ƒ(x) is equal to 14, the value of x is 1/3.
To find the value of x when f(x) is equal to 14, we can set up the equation:
f(x) = 18x + 8
We know that f(x) is equal to 14, so we substitute that into the equation:
14 = 18x + 8
We isolate the variable x by subtracting 8 from both sides of the equation:
14 - 8 = 18x
6 = 18x
To solve for x, we divide both sides of the equation by 18:
6/18 = x
1/3 = x
Therefore, when f(x) is equal to 14, the value of x is 1/3.
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Y = -1/3 x + 2
Y= x + 2
What is the solution to the system of equations?
A. (0, 2)
B. (2, 0)
C. (-1, 3)
D. (0, -2)
Answer:
X = 0
Y = 2
so Option A (0,2) IS CORRECT
Step-by-step explanation:
Y = -1/3 x + 2 equation 1
Y = x+ 2 equation 2
from equation 2 we have
y = x+ 2 Put in equation 1
x + 2 = -1/3 x + 2
x +1/3x = 2 -2
0.67 x = 0
X = 0
so put x =0 in equation 2 then we have
y = x +2
Y = 0+ 2
Y = 2
Show how to add 24+9 by making 10s
If you add 10 and then subtract 1, you get the same result as if you just added 9.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to add 24+9 by making 10s.
As per the given question, the required solution would be as:
24 + 10 - 1 = 33
Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.
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Final answer:
To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.
Explanation:
To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.
Add 6 to 24 to make a round number, which is 30.
Now you have made a '10' because 30 is a multiple of 10.
Next, add the remaining 3 to get 33.
So, 24 + 9 = 33.
At the beginning of the year,
Shelby could run 2 miles. Now
she can run 3.5 miles. What is
the percent increase in the
distance she can run?
Answer:
175% increase
Step-by-step explanation:
(3.5 / 2) * 100 = 175%
How would you solve 8(6-k)+2k ≥-15-(-3k) ( please show each step)
Answer:
Step-by-step explanation:
8(6-k)+2k ≥-15-(-3k)
Opening bracket
48 - 8k + 2k ≥ -15 + 3k
-8k - 3k + 2k ≥ -15 - 48
-9k ≥ -63
k ≤ -63/-9
k ≤ 7
Answer:
k ≤ 7
Step-by-step explanation:
8 (6 - k) + 2k ≥ - 15 -(-3k)
Let's simplify this by solving each side.
First side:
8 (6 - k) + 2k ≥ - 15 -(-3k)
48 - 8k + 2k ≥ - 15 -(-3k)
48 - 6k ≥ - 15 -(-3k)
Second side:
48 - 6k ≥ - 15 -(-3k)
48 - 6k ≥ -15 + 3k
DONE SIMPLIFYING!
Now solve for "k" algebraically (transitions are in bold):
48 - 6k ≥ -15 + 3k
-6k ≥ -15 - 48 + 3k
-6k ≥ -63 + 3k
-6k - 3k ≥ -63
-9k ≥ -63
-k ≥ -63 ÷ 9
-k ≥ -7
k ≤ 7
calculus 1 limits and derivatives chapter help. delta and epsilon proof
Answer:
[tex]\delta=\frac{\epsilon}{3}[/tex]
The proof is in the explanation.
Step-by-step explanation:
Compare [tex]\lim_{x\rightarrow 7}(3x-2)=19[/tex] to [tex]\lim_{x\rightarrow a}f(x)=L[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-a|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|3x-2-19|<\epsilon[/tex].
[tex]|3x-2-19|<\epsilon[/tex]
Simplify:
[tex]|3x-21|<\epsilon[/tex]
Factor on left side inside the | |:
[tex]|3(x-7)|<\epsilon[/tex]
|ab|=|a||b|:
[tex]|3||x-7|<\epsilon[/tex]
|3|=3:
[tex]3|x-7|<\epsilon[/tex]
Divide both sides by 3:
[tex]|x-7|<\frac{\epsilon}{3}[/tex]
So we will need to choose [tex]\delta=\frac{\epsilon}{3}[/tex].
We want to prove there exists a [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
Proof:
Let [tex]\epsilon>0[/tex]. We will choose [tex]\delta=\frac{\epsilon}{3}[/tex] such that [tex]0<|x-7|<\delta[/tex] will give us [tex]|f(x)-L|<\epsilon[/tex].
[tex]|f(x)-L|=|(3x-2)-19|[/tex]
[tex]=|3x-21|[/tex]
[tex]=|3||x-7|[/tex]
[tex] =3|x-7|<3\delta=3\frac{\epsilon}{3}=\epsilon[/tex].
Therefore, we have for all [tex]\epsilon>0[/tex], [tex]\delta=\frac{\epsilon}{3}[/tex] is the number that satisfies the definition.
You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
You will need 119 cups to sell all of the lemonade.
Step-by-step explanation:
Given,
Diameter of cups = 9 cm
Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]
Height of cups = 12 cm
We will find volume of cup.
[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]
Putting all the values
[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]
Therefore;
Each cup can hold 254.34 cubed centimeter of lemonade.
Number of gallons = 8
1 gallon = 3785 cm³
8 gallons = 3785*8 = 30280 cm³
Let,
x = Number of cups
Volume of lemonade in one cup * Number of cups = Volume of 8 gallons
254.34x=30280
Dividing both sides by 254.34
[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]
Rounding off to nearest whole number
x = 119
You will need 119 cups to sell all of the lemonade.
Keywords: volume, division
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Solve the following system of equations by using the method of your choice
3x-y=-28
-5x-4y=-10
Answer:
(x, y) =(-6,4)
Step-by-step explanation:
3x-y=-28
-5x-4y=-10
y=3x+28
-5x-4(3x+28)=-10
y=3x+28
-5x-12x-112=-10
y=3x+28
-17x=-10+112
y=3x+28
-17x=102
y=3x+28
x=102/(-17)
y=3x+28
x=-6
y=3*(-6)+28
x=-6
y=-24+28
x=-6
y=4
x=-6
(x,y)=(-6,4)
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours
Answer:
d
Step-by-step explanation:
Answer:
24 hours
24 hours is the solution to 300=10(2)^t/15
QUESTION 10
The park manager wants to conduct a survey to determine how people like the park facilities. Which would give her the most representative sample for the survey?
conducting the survey at the softball diamond
conducting the survey at a shopping mall
conducting the survey as visitors leave the park
conducting the survey at the playground
conducting the survey as visitors leave the park
The park manager wants to figure out how people like the park so she will conduct the survey as people leave the park.
Final answer:
The most representative sample for a survey on park facilities satisfaction would be obtained by conducting the survey as visitors leave the park, ensuring a broad and unbiased cross-section of park users are included.
Explanation:
The question asks which method would provide the most representative sample for a survey about how people like the park facilities. The most representative sample would be achieved by conducting the survey as visitors leave the park. This method ensures a wide cross-section of park users are surveyed, capturing various interests and usage patterns of the park facilities, from those who come for leisure activities at the softball diamond or playground to those seeking quiet contemplation or exercise.
Conducting the survey in other locations like a shopping mall or specific areas within the park, such as the softball diamond or playground, would likely bias the results. Surveying at a shopping mall doesn't guarantee participants have visited or are familiar with the park, and focusing solely on one area within the park would not capture the diverse usage and opinions of all park visitors. Therefore, surveying as visitors leave the park is the most inclusive and unbiased approach to understanding how the facilities meet the needs of the community.
What is the value of the expression below?
(9-3)+4(6-7)
-7
-1
7
20
Final answer:
The expression (9-3)+4(6-7)-7 is calculated following PEMDAS, resulting in a value of -5 after simplifying the operations within the expression.
Explanation:
The value of the expression (9-3)+4(6-7)-7-1720 seems to have a typo, and it should probably read (9-3)+4(6-7)-7. To evaluate this expression, you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the parentheses: (9-3) = 6 and (6-7) = -1.
Next, perform the multiplication: 4 * (-1) = -4.
Finally, add and subtract from left to right: 6 + (-4) - 7 = 6 - 4 - 7 = 2 - 7 = -5.
The value of the expression is -5.
Does anyone know this?
Use this formula to get the total angle measurement of the figure:
T=180(n-2)
Since there are 7 sides, the total measurement must be:
180(7-2)
180(5)
900 degrees
Set up an equation and solve for x:
123+121+127+128+139+125+x=900
763+x=900
x=137
So the missing angle is 137 degrees.
Hope this helped!
Of the 40 students in Ms. Carr's class, 87.5% live less than 10 miles from school. How many of the students in Ms. Carr's class live less than 10 miles from school.
Answer:
35
Step-by-step explanation:
Total number of students in class is 40
87.5% of the class = 87.5/100 *40 =35
The students in Ms. Carr's class that live less than 10 miles from school are 35 students.
To find out how many students in Ms. Carr's class live less than 10 miles from school, we can use the percentage provided in the question.
1. Identify the total number of students in the class:
Ms. Carr has a total of 40 students in her class.
2. Determine the percentage of students living less than 10 miles from school:
We know that 87.5% of these students live less than 10 miles from school.
3. Convert the percentage to a decimal for calculation:
To convert 87.5% to a decimal, we divide by 100:
[tex]\[ 87.5\% = \frac{87.5}{100} = 0.875 \][/tex]
4. Calculate the number of students:
Now, multiply the total number of students by the decimal:
Number of students = 0.875 × 40 = 35
5. Conclusion:
Therefore, 35 students in Ms. Carr's class live less than 10 miles from school.
how do you solve 17- ||-16|-9|
Evaluate the inside absolute values first:
17-|16*9|
17-|144|
17-144
-127
Hope this helped!
Need help ASAP please
-8|4k-10|=-48 okay y'all can you help me out with this?
Answer:
k = 4
Step-by-step explanation:
-8|4k-10|=-48
|4k-10|=-48/-8
|4k-10|= 6
4k = 6+10
4k = 16
k = 4
What number represents an elevation of 80 feet below sea level
Answer:
-80
Step-by-step explanation:
The answer is -80 because 80 feet below sea level would be a negative number. So you just add a negative sign to 80 and voila! You get the answer. Your welcome, by the way!
Elevation 80 feet below sea level can be represented by the negative number -80 in mathematics. This is because negative numbers are used to represent depths or locations below sea level.
Explanation:In mathematics, when we talk about locations below sea level, we represent them with negative numbers. So, an elevation of 80 feet below sea level will be represented as -80. This numerical representation helps us have an accurate and easy understanding of above and below sea level elevations. Such as, 0 represents sea level, positive numbers represent elevations above sea level, and negative numbers represent depths below sea level.
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Find the circumference of this figure. Show your calculations.
Answer:
Circumference of circle= 37.68 units
Circumference of sector= 6.28 units
Step-by-step explanation:
The given figure is a circle with given radius OB= 6 units.
The circumference of a circle is the total length of its boundary.
For the complete circle its circumference can be calculated by;
Circumference= [tex]2\pi r[/tex]
[tex]=2*3.14*6\\=37.68[/tex] units
For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:
[tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units
So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.
Which choice is equivalent to the expression below ?
The answer is B, 7i.
sqrt(-49)
Pull out an i.
i*sqrt(49)
Take the square root to get 7i.
⭐ Answered by Hyperrspace (Ace) ⭐
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The diagonals of a rhombus are 14 and 48 cm Find the length of a side of the rhombus
A blue rope is three times as long as the red rope. A green rope is five times as long as the blue rope. If the total length is 508.25 meters, what is the length of the blue rope?
Answer:
The length of the blue rope is 80.25 meters.
Step-by-step explanation:
B = Blue Rope
G = Green Rope
R = Red Rope
B=3R (Blue is 3 x as long as Red)
G=5B (Green is 5 x as long as Blue)
B+G+R = 508.25 (The three ropes together are 508.25 meters)
Since B=3R, I will rewrite the equation above
3R + G + R = 508.25
Now, I will write G in terms of R:
G=5B
B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.
Rewrite the equation again in terms of R:
3R + 15R + R = 508.25
19R = 508.25 (combine like terms)
R = 26.75 (divide both sides by 19 to solve for R)
Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):
B=3R
B=3(26.75)
B=80.25 meters