3/5b-8=4, step by step plz
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.
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.
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?
The width of a vegetable garden is 3 times it's length.If the length of the garden is 4 1/2 feet,what is the width in simplest form?
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
the legs of a right triangle are 75 and 100. what is the length of the hypotenuse?
A: 5 square root 5
B: 250
C:125
D: 625
right triangle us pythagorean theorem
a^2 + b^2 = c^2
75^2 + 100^2 = C^2
5625 +10000 = c^2
15625 =c^2
c=Sqrt(15625) = 125
hypotenuse = 125
answer is C
Subtract the fractions and simplify the answer 13/15 -2 2/3
2 2/3 = 8/3
8/3= 40/15
13/15 - 40/15 = -27/15 = -1 12/15
Between what pair of numbers is the product of 289 and 7?
I NEED THIS DONE, PLEASE HELP...
Fill in the blank:
To prove that the medians of an isosceles triangle meet at a point, show that the ____ of a side lies on the line containing the opposite _____ and the point where the other two ____ intersect
If three lines meet at a single point, we say that the lines are concurrent.
Note that median is a line joining one vertex of a triangle with the midpoint of its opposite side.
Draw two medians for the given isosceles triangle.
Now, join the point of intersection of these medians and the third vertex.
If we prove the midpoint of the opposite side lies on this line, then it will be proved that the medians of the given isosceles triangle meet at a point.
Hence, here is the correct statement with blanks filled.
The midpoint of a side lies on the line containing the opposite vertex and the point where the other two medians intersect.
find k if the lines 3x-5y=9 and 2x+ky=11 are a) parallel and b) perpendicular
a) To find k for parallel lines, equate slopes to get k = -10/3. b) For perpendicular lines, use negative reciprocal slopes to find k = 3/10.
To determine the conditions for parallelism and perpendicularity, we need the slope of each line. The slope-intercept form of a line is y = mx + b where m is the slope.
To find the slope of the first line, we rearrange 3x-5y=9 to the form of y = mx + b, resulting in y = (3/5)x - (9/5). Therefore, the slope is 3/5. For the second line, rearranging 2x+ky=11 gives us y = (-2/k)x + (11/k). The slope of the second line is -2/k.
For the lines to be parallel, their slopes must be equal, so 3/5 = -2/k. Solving for k, we get k = -10/3. For the lines to be perpendicular, the product of their slopes must be -1 (since perpendicular lines have negative reciprocal slopes). This gives us (3/5)(-2/k) = -1, and solving for k yields k = 3/10.
Is it possible to represent the number 203 as a sum of several whole numbers such that their product is also equal to 203?
A mountain climber explored a cliff that is 225 yards high in 5 equal trips. How many yards was one trip?
At Mei's Printing Company LLC there are two kinds of printing presses: Model A which can print 80 books per day and Model B which can print 30 books per day. The company owns 10 total printing presses and this allows them to print 400 books per day. How many of each type of press do they have?
answer both questions if you cant see all the answers its fine all u need is the question
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.
To learn more about the fraction visit:
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(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 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.
A factory used 396.25 pounds of tomatoes to make 6.25 batches of salsa. How many pounds of tomatoes were used in each batch?
Answer:
63.4 pounds of tomatoes were used in each batch
Step-by-step explanation:
A factory used 396.25 pounds of tomatoes to make 6.25 batches of salsa.
Or, In 6.25 batches of salsa 396.25 pounds of tomatoes were used.
In 1 batch of salsa , [tex]\dfrac{396.25}{6.25}[/tex] pounds of tomatoes will be used.
i.e. In 1 batch of salsa , 63.4 pounds of tomatoes will be used.
Hence, 63.4 pounds of tomatoes were used in each batch
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)?
How to write 15,409 in word form
A triangle can be formed with side lengths 5, 7 and 10. True or False
In your own words explain the place value relationship when the same two digits are next to each other in a multi digit number
In a place value relationships. The relationship between 2
the same digit place next to each other is the value of the number to left is
10 times bigger than to the value to the left and from the decimal point to the
right is 10 times smaller of value than the digit in their right.
Let say for example:
1111
1 thousands, 1 hundreds, 1 tens, and 1 ones.
Let’s start from 1 = 1 x 10 = 10
That would be 10 X 10 = 100
then 100 X 10 = 1000
Notice that their value increase base on its place value if
we multiply the given number by 10.
Another one is
912.98 in where 9 is hundreds, 1 is tens, 2 is ones and after
the decimal points, in where 9 is tenths and 8 is hundredths.
Notice each place value next to each other. Each value is ten
times in difference.
Which of the following equations has a graph that crosses the y-axis at a point lower than y=2x^2-1
A.y=-3x^2+1
B.y=3x^2-3
C.y=-3^2-1
D.y=-3^2+3
One minute after it is released, a gas-filled balloon has risen 100 feet. In each succeeding minute, the balloon rises only 50% as far as it rose in the previous minute. How far will the balloon rise in 5 minutes?
What is the next value 1I2L3F4
3x (2•5) + 45= n
What is n???
You want to buy an item that costs $100. Which is the most cost-effective choice for buying the item?
Compare prices, consider discounts, and watch for additional costs like shipping. Choose the option with the lowest total expense for buying the $100 item.
To determine the most cost-effective choice for buying the $100 item, you should consider any available discounts, promotions, or deals offered by different sellers or platforms. Here are a few strategies you could consider:
1. **Comparison Shopping**: Check multiple retailers or online platforms to see if the item is available at a lower price elsewhere. Websites and apps dedicated to comparison shopping can help streamline this process.
2. **Discounts and Coupons**: Look for any available discounts or coupons that you can apply to your purchase. Many retailers offer promotional codes or special deals that can help reduce the cost of the item.
3. **Cashback and Rewards**: Some credit cards or loyalty programs offer cashback or rewards points for purchases. If you have a card or program like this, see if you can earn rewards or cashback by buying the item through a specific retailer.
4. **Timing**: Consider timing your purchase to coincide with sales events or promotions, such as Black Friday, Cyber Monday, or seasonal sales. Buying during these periods can often result in significant savings.
5. **Shipping and Handling Costs**: Be mindful of any additional costs associated with shipping and handling. Sometimes, even if the base price of the item seems lower from one seller, the shipping costs may make the overall purchase more expensive.
By comparing prices, looking for discounts, and considering additional costs, you can find the most cost-effective option for purchasing the $100 item.
Complete Question:
Which of these is the most cost effective choice for buying the item using a paid membership card to buy it at a 10 percent discount buying it on line at a 10 percent discount without sales tax?
(sint+cost)^2=
A.) 1
B.) 1+2sint
C.) 1+sin2t
D.) sin(t^2)+cos(t^2)
E.) sin(t^2)+2sintcost+cos(t^2)
Ten times the sum of half a number and 6 is 8