6x - 2y = 10
-2y = -6x + 10
reduce by dividing by -2
y = 3x - 5
slope = 3 and y int = -5
y = 3x + 2
slope = 3, y int = 2
These lines are parallel. Parallel lines will have the same slope, but different y integers. There is no solution to this because the lines never intersect.
Mark's answer is correct
A mountain climber explored a cliff that is 225 yards high in 5 equal trips. How many yards was one trip?
11 POINTS GUYS PLZ
Answer 12 and 14
12) 10.77 + 2.09 + 0.75 = 13.61
13.61 x 1.07 = $14.56
total amount = $14.56
14) C shows the possible combinations
2/9 divided by 5/12?
Please simplify in its simplest form
2/9 divided by 5/12 simplifies to 2/15
Here we have to divide,
2/9 divided by 5/12
To divide fractions,
We have to flip the second fraction and multiply it by the first fraction. This gives us,
⇒ (2/9) ÷ (5/12) = (2/9) x (12/5)
We can simplify this expression by canceling out any common factors between the numerators and denominators.
In this case,
2 and 12 have a common factor of 2, while 9 and 5 don't have any common factors. This gives us,
⇒ (2/9) x (12/5) = 24/45
To express this fraction in its simplest form,
we can divide both the numerator and denominator by their greatest common factor, which in this case is 3.
This gives us,
6/45 = (24 ÷ 3) / (45 ÷ 3)
= 8/15
Therefore, 2/9 divided by 5/12 simplifies to 8/15.
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The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 6in. width is 5/6 and the height is 1 2/6 the cube side is 1/6
The number of cubes should be 1.440.
The calculation is as follows:Calculate the volume of each shape is as follows:
Volume of rectangle = [tex]6 \times 5\div 6 \times 1\ 2\div 6 = 6\ 2\div 3[/tex] cubic inches.
And,
Volume of cube =[tex] 1\div6 \times 1\div6 \times 1\div6 = 1\div216[/tex] cubic inch.
Now
divide the volume of the rectangle by the volume of the cube:
So,
[tex]= (6\ 2\div 3) \div (1\div 216)[/tex]
= 1.440
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Your running speed is 8.5 miles per hour. A greyhound dog's speed is about 4.5 times faster than yours. What is the dog's speed?
Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%? $117 $680 $760 $820
Answer:
The correct option is B) $680.
Step-by-step explanation:
Consider the provided information.
Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest.
Let she invested x amount with 8% interest rate.
Total amount she invested was $1,500, thus the amount she invested with 6% interest rate was 1500-x.
Total interest she earn was $106.40
Write this information into mathematical form.
[tex]x\times \frac{8}{100}+\frac{6}{100}(1500-x)=106.40[/tex]
[tex]x\times 0.08+0.06(1500-x)=106.40[/tex]
[tex]0.08x+90-0.06x=106.40[/tex]
[tex]0.08x-0.06x=106.40-90[/tex]
[tex]0.02x=16.4[/tex]
[tex]x=820[/tex]
Hence, she invested $820 with 8% interest rate.
The amount she invested with 6% interest rate was 1500-x.
Substitute the value of x in above.
1500-820=680
Hence, she invested $680 with 6% interest rate.
The correct option is B) $680.
given (x-1)^2=50, select the values of x
A. x = -49
B. x = 51
C. x = 1+5√2
D. x = 1-5√2
Value of x is 1 + 5√2
Given that;
(x - 1)² = 50
Find:
Value of x
Computation:
(x - 1)² = 50
By taking square root both side
x - 1 = √50
x - 1 = 5√2
x = 5√2 + 1
x = 1 + 5√2
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The price of a share of stock started the day at $37. During the day it went down $3, up $1, down $7 and up $4. What was the price of a share at the end of the day
A particular car gets fuel mileage of 36 mpg in the city and 12% more on the highway.
What is the car's fuel mileage on the highway?
The car's fuel mileage on the highway is 40.32 mpg, which is 12% more than the 36 mpg it gets in the city.
To determine the car's fuel mileage on the highway, given that it is 12% more than the fuel mileage in the city, we start with the given city mileage of 36 miles per gallon (mpg). We calculate the additional mileage gained on the highway by taking 12% of 36 mpg, which is 0.12 × 36 mpg = 4.32 mpg. Adding this to the city mileage gives the highway mileage:
36 mpg + 4.32 mpg = 40.32 mpg on the highway.
What is the distance from (−3, 1) to (−1, 5)? Round your answer to the nearest hundredth.
A.3.60
B. 4.12
C.4.47
D.5.66
pls
Answer:
c 4.47
Step-by-step explanation:
got it right on my test
The distance from (−3, 1) to (−1, 5) is 4.47
What is slope of line?
Slope of line is defined as the angle of line.
The distance between two points is found by
[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]
[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]
[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]
[tex]d=\sqrt{(4+16)}[/tex]
[tex]d=\sqrt{(20)}[/tex]
d = 4.472135955
Rounding to the nearest hundredth
d = 4.47
Hence, the distance from (−3, 1) to (−1, 5) is 4.47
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answer both questions if you cant see all the answers its fine all u need is the question
(sum of 50 different whole numbers, each less than 51)-(sum of 45 different whole numbers, each less than 51)is at most
A:10
B:15
C:240
D:285
A scatter plot is made with the data shown below: Number of Bakers at a Cake Shop 5 6 7 8 9 10 11 12 13 Number of Cakes Baked 7 7 8 8 9 11 13 14 14 What type of association will the scatter plot for these data represent between the number of bakers at the cake shop and the number of cakes baked? No association Positive linear association Negative linear association Positive nonlinear association
Answer:
positive linear association
hope this helps
Between what pair of numbers is the product of 289 and 7?
A triangle can be formed with side lengths 5, 7 and 10. True or False
The equation A=p(1+r)^t can be used to calculate compound interest on a savings account. A = future balance, p = current balance, r = rate of interest, and t = time in years. If you deposit $2,000 at 10% each year, how much money will be in your account in 10 years
Using the formula for compound interest, if you deposit $2,000 at 10% each year, the future balance in your account after 10 years would be approximately $5,187.12. This is due to the effect of compounding where the interest is calculated on both the principal and the accumulated interest.
Explanation:The subject of this question is compound interest which is a Mathematics topic typically covered in High School. The formula A=p(1+r)^t is used to calculate the future balance in your savings account considering compound interest. Here, 'A' represents the future balance, 'p' is the current principle or balance, 'r' is the rate of interest, and 't' is time in years.
To answer your specific question: If you deposit $2,000 at a 10% rate each year, how much money will be in your account in 10 years? Let's plug the numbers into the formula. In this case, p=$2000, r=0.10 (as 10% equals 0.10 in decimal), and t=10 years.
So, A = 2000*(1 + 0.10)^10. Solving this, the future balance in your account after 10 years would be approximately $5,187.12. This is significantly more than simple interest ($100 × 0.05 × 3 = $15 in your example) due to the effect of compounding, as the interest is calculated on the principal plus the accumulated interest.
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Is it possible to represent the number 203 as a sum of several whole numbers such that their product is also equal to 203?
How does the area of triangle RST compare to the area of triangle LMN? The area of △RST is 2 square units less than the area of △LMN. The area of △RST is equal to the area of △LMN. The area of △RST is 2 square units greater than the area of △LMN. The area of △RST is 4 square units greater than the area of △LMN.
The answer would be B
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The profit on the sale of a small bag of popcorn is $1, while the profit on the sale of a medium bag of popcorn is $2. The Glee Club expects to sell fewer than 100 total bags of popcorn, but they hope to make more than $100 in profit. The system that represents this is s+m<100 and s+2m>100. The graph of the boundary lines is shown below. Which regions should be shaded (to form the solution)?
A catering service offers 8 appetizers, 11 main courses, and 4 desserts. A banquet chairperson is to select 5 appetizers, 9 main courses, and 2 desserts for a banquet. In how many ways can this be done?
PLEASE HELP I'M BEING TIMED!!!!
if the diameter of a youth softball is 3.5 inches and the diameter of an adult softball is 3.8 inches, what is the approximate difference in their volumes? Use 3.14 for pi . Round to the nearest tenth of a cubic inch.
A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Final answer:
The slope for a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). By substituting the given points into the formula, the slope for the line passing through (1, 0.1) and (7, 26.8) is found to be 4.5.
Explanation:
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
To find the slope for the given points (1, 0.1) and (7, 26.8), we can substitute the values into the formula:
m = (26.8 - 0.1) / (7 - 1) = 4.5
Therefore, the slope for the line passing through the given points is 4.5.
a. The equation for the line in point-slope form is [tex]\( y + 1 = \frac{5}{6}(x - 2) \).[/tex]
b. The equation in standard form is ( 5x - 6y = 16 ).
Explanation:a. To find the equation of the line in point-slope form, we use the formula [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line. Given the points (2, -1) and (8, 4), we can calculate the slope (m) as [tex]\(\frac{{y_2 - y_1}}{{x_2 - x_1}}\)[/tex]. Substituting the values, we get:
[tex]\[ m = \frac{{4 - (-1)}}{{8 - 2}} = \frac{5}{6} \][/tex]
Now, using the point-slope form, we substitute the values for (m) and [tex]\((x_1, y_1)\)[/tex]:
[tex]\[ y + 1 = \frac{5}{6}(x - 2) \][/tex]
b. To convert the equation to standard form, we want to eliminate fractions and express it as (Ax + By = C), where (A), (B), and (C) are integers. Multiply both sides of the equation by 6 to clear the fraction:
6(y + 1) = 5(x - 2)
Distribute the terms:
(6y + 6 = 5x - 10)
Bring all terms to one side:
[ 5x - 6y = 16 ]
So, the equation in standard form is (5x - 6y = 16). This form is preferred for certain applications, making it easier to identify coefficients and intercepts.
What is the next value 1I2L3F4
The profit function for a new product is given by p(x) = -4x^2+28x-40, where x is the number sold in thousands. How many items must be sold for the company to break even?
Final answer:
The company must sell either 2,000 or 5,000 items to break even, as determined by setting the profit function to zero and factoring the resulting quadratic equation.
Explanation:
To determine how many items must be sold for the company to break even, we need to set the profit function p(x) equal to zero and solve for x. In this case, the profit function is given by p(x) = -4x^2 + 28x - 40. Setting this to zero, we have:
-4x^2 + 28x - 40 = 0
Now, we need to solve this quadratic equation for x. To do this, we can factor the equation, use the quadratic formula, or complete the square. Since the coefficients are manageable, we'll try to factor first:
-4(x^2 - 7x + 10) = 0
Let's look for two numbers that multiply to 10 and add up to 7, which are 5 and 2. We can now factor further:
-4(x - 5)(x - 2) = 0
From the factored form, we get two potential solutions for x when the profit is zero:
x = 5
x = 2
Since x represents the number of items sold in thousands, the company must sell either 2,000 or 5,000 items to break even.
Which of the following represents the zeros of f(x) = 4x3 − 13x2 − 37x + 10? 5, −2, −1 over 4 5, −2, 1 over 4 5, 2, −1 over 4 5, 2, 1 over 4
Answer:
The three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.
Step-by-step explanation:
The given polynomial is,
[tex]f(x)=4x^3-13x^2-37x+10[/tex]
Use hit and trial method, Put x=-2
[tex]f(x)=4(-2)^3-13(-2)^2-37(-2)+10=0[/tex]
Since the value of function is 0 at x=-2 therefore (x+2) is a factor of the given polynomial.
Divide the given polynomial by using synthetic division or long division.
[tex]f(x)=(x+2)(4x^2-21x+5)[/tex]
Use grouping method to find the factors,
[tex]f(x)=(x+2)(4x^2-20x-1x+5)[/tex]
[tex]f(x)=(x+2)(4x(x-5)-(x-5))[/tex]
[tex]f(x)=(x+2)(x-5)(4x-1)[/tex]
Equate each factor equal to 0.
[tex]x=-2,5,\frac{1}{4}[/tex]
Therefore, the three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.
Which conversions from scientific notation to standard notation are true? Check all that apply.
The correct conversion from scientific notation to standard notation are:
b) [tex]8.05\times 10^5[/tex]
e) [tex]7.09\times 10^{-6}[/tex]
Step-by-step explanation:We know that when we have a power of 10 as positive then the decimal is shifted to the right and if the power of 10 is negative then we shift the decimal to the left.
a)
[tex]1.71\times 10^3[/tex]
As the power of 10 is positive hence we shift the decimal to the right 3 places.
Hence, the conversion is:
[tex]1.71\times 10^3=1710[/tex]
b)
[tex]8.05\times 10^5[/tex]
Again the power of 10 is positive and hence we will shift the decimal 5 places to the right and the conversion is done as follows:
[tex]8.05\times 10^5=805000[/tex]
c)
[tex]2.4\times 10^4[/tex]
Since, the power of 10 is positive and hence we will shift the decimal 4 places to the right and we convert the number to standard notation as:
[tex]2.4\times 10^4=24000[/tex]
d)
[tex]8.25\times 10^{-3}[/tex]
Since, the power of 10 is negative and hence we will shift the decimal 3 places to the left and we convert the number to standard notation as:
[tex]8.25\times 10^{-3}=0.00825[/tex]
e)
[tex]7.09\times 10^{-6}[/tex]
Since, the power of 10 is negative and hence we will shift the decimal 8 places to the left.
Hence, we convert our number to standard notation:
[tex]7.09\times 10^{-8}=0.00000709[/tex]
It is accurate to convert scientific notation to standard notation in the following ways:
B [tex]8.05x10^5=805,000[/tex]
C [tex]2.4x10^4= -24,000[/tex]
E [tex]7.09x10^-^6=0.0000070[/tex]
To solve this problemFirstly, Let's evaluate each conversion one by one:
[tex]1.71x 10^3=0.00171[/tex]
This conversion is not true. The correct value of[tex]1.71x 10^3[/tex] is 1710.
[tex]8.05x10^5=805,000[/tex]
This conversion is true.
[tex]2.4x10^4= -24,000[/tex]
This conversion is true.
[tex]8.25x10^-^3=-8,250[/tex]
This conversion is not true. The correct value of [tex]8.25x 10^-^3[/tex] is 0.00825.
[tex]7.09x10^-^6=0.0000070[/tex]
This conversion is true.
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The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams =
pounds
700 grams =
pounds
The weight of each tire in pounds is approximately:
Full steel bead tire: 1.76 pounds.
Lighter wheel: 1.54 pounds.
Given that the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams.
We need to convert the weights into pound.
To convert the weight of each tire from grams to pounds, we'll use the conversion factor that there are 453.592 grams in one pound.
Weight of a full steel bead tire in pounds:
800 grams x (1 pound / 453.592 grams) ≈ 1.76 pounds
Weight of a lighter wheel in pounds:
700 grams x (1 pound / 453.592 grams) ≈ 1.54 pounds
Rounded to 2 decimal places:
Weight of a full steel bead tire = 1.76 pounds
Weight of a lighter wheel = 1.54 pounds
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Find the midpoint of the segment between the points (15,3) and (2,-14)
Question: Rationalize the denominator