Final answer:
Writing a linear equation requires knowing the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, and the point-slope form (y - y1 = m(x - x1)), useful when a point on the line and the slope are known.
Explanation:
The ability to write a linear equation involves understanding different forms, such as standard form, point-slope form, and slope-intercept form. The slope-intercept form of a linear equation is commonly written as y = mx + b, where m represents the slope and b represents the y-intercept. The slope is the rate of change, indicating how much y increases for a one-unit increase in x. The y-intercept is the point where the line cuts the y-axis, which means when x=0.
It's important to note some variations in notation, such as y = a + bx, which is another way to express the slope-intercept form, where a is the y-intercept and b is the slope. When converting between forms, it's essential to identify these components correctly to maintain the equation's integrity.
In point-slope form, an equation of a line is written as y - y1 = m(x - x1), where (x1, y1) is a known point on the line, and m is the slope. This form is particularly useful when you have a point and a slope and need to write the equation of the line.
Wyatt is training for a race. He will run 3/4 of a mile a day for 8 days. How far will Wyatt run altogether?
Answer:
6 miles all together in them 8 days
Step-by-step explanation:
3/4 times 8
Answer:
6 miles in all
Step-by-step explanation:
3/4 *8 duh
A basketball hoop is 10 feet high. Army is 5 feet tall. How many times is the basketball hoop than army
Answer:2 times
Step-by-step explanation:
i did the assinment
The scale factor of a large oil container to a small oil container is 0.075. The large oil container can carry 144,000cm^3 of oil.
How much oil can the small container carry?
A.) 10,800cm3
B.) 810 cm3
C.) 60.75cm3
D.) 0.075 cm3
The correct Answer is option (A).10,800 [tex]cm^3[/tex] oil can the small container carry.
To determine how much oil the small container can carry, given the scale factor and the capacity of the large container, follow these steps:
1. Identify the given values:
- Capacity of the large container: [tex]\( 144,000 \, \text{cm}^3 \)[/tex]
- Scale factor from large to small container: [tex]\( 0.075 \)[/tex]
2. Calculate the capacity of the small container:
- Use the formula: [tex]\[ \text{Capacity of small container} = \text{Capacity of large container} \times \text{Scale factor} \][/tex]
- Substitute the given values: [tex]\[ \text{Capacity of small container} = 144,000 \, \text{cm}^3 \times 0.075 \][/tex]
3. Perform the multiplication:
[tex]\[ 144,000 \times 0.075 = 10,800 \, \text{cm}^3 \][/tex]
Therefore, the capacity of the small container is:
[tex]\[ \boxed{10,800 \, \text{cm}^3} \][/tex]
A car travels at an average speed of 45 miles per hour for 8 miles, reduces its speed by 15 miles per hour for the next 4 miles, and then returns to a speed of 45 miles per hour. How long does the car travel at the reduced speed?
Answer:
8 minutes
Step-by-step explanation:
time = distance/speed
A decrease of 15 mph from 45 mph means the speed on the second segment is 30 mph. Filling in the given values in the above equation, we have ...
... time = (4 mi)/(30 mi/h) = 4/30 h = 8/60 h × (60 min/h) = 8 min
Joe ate 7 pies on wednesday. If that is only 1/4 of the world record for pie eating what is the pie record
Answer:
The answer would be 24
Step-by-step explanation:
7 pies= 1/4 so 7 times four (to equal whole) = 24
Plz help me with this :)
Part A:
The range is the difference between the highest and lowest values:
Highest value = 78
Lowest value = 40
Range = 78-40 = 38
Part B:
The interquartile range is the difference between Q1 and Q3.
Q1 is the middle value of the lower half and Q3 is the middle value of the upper half.
There are 11 total numbers, 40 , 64, 66, 67,67,68,69,70, 71, 72, 78
The median would be the middle value, 68, so the lower half would be the 5 numbers below 68: 40 , 64, 66, 67,67.
The middle value of those numbers would be 66
The upper half are the 5 numbers above 68: 69,70, 71, 72, 78.
The middle value of those numbers is 71
The interquartile range would be 71 - 66 = 5
Part C:
The interquartile range is the better measure.
At the city museum, child admission is $6.10 and adult admission is $9.30 . On Sunday, four times as many adult tickets as child tickets were sold, for a total sales of $909.30 . How many child tickets were sold that day?
Answer:
21 child tickets
Step-by-step explanation:
For this problem, you'd use a system of equations.
First, define your variables.
x = # of child tickets sold
y = # of adult tickets sold
There were 4 times as many adult tickets (y) as child tickets (x) sold, so:
4 x = y
4 x - y = 0
93 (4 x - y = 0)
372 x - 93 y = 0
The total revenue was $909.30, adult tickets were $9.30 each, child tickets were $6.10 each, so:
6.10 x + 9.30 y = 909.30
10 (6.10 x + 9.30 y = 909.30)
61 x + 93 y = 9093
372 x - 93 y = 0
433 x = 9093
433 x / 433 = 9093 / 433
x = 21
PLEASE HELP!!!
Write the equation of the given line in standard form.
x = 3
Step-by-step explanation:"Standard form" is the form ...
... ax + by = c
where a, b, c are mutually prime integers. The coefficients a and b cannot both be zero. The leading coefficient must be positive. If "a" is zero, then the leading coefficient is "b".
So ...
... x = 3
is in standard form already. (a=1, b=0, c=3)
_____
Further comments on Standard Form
Of course, if the line has irrational slope or intercept, the coefficients cannot all be integers.
The order of the variables may be swapped, in which case the coefficient of y is the leading coefficient and must be positive.
This is the only way a vertical line can be written, as slope-intercept form is undefined for a vertical line.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Factor x^2 + 25 in the complex numbers.
Answer: C
Step-by-step explanation:
x² + 25
= x² - (-25)
This can now be factored using the sum & difference formula:
a² - b² = (a - b)(a + b)√x² = x
√-25 = 5i
So, x² - (-25) = (x - 5i)(x + 5i)
Henry is saving money for college. He earns $210 each week working part time after school and the weekends. Henry currently has $2,240 in savings. His parents put $100 in his savings account each week and he saves one-third of his paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 2,240 + 170n B) 2,240 + 310n C) 2,240 + 210n + 100n 3 D) 2,240 + 210n + 100n 3 Eliminate
The answer is 2,240 + 170n
2,240 in savings
210n
3
Henry saves each week
100n parents put in savings each week
thus,
2,240 + 210n
3
+ 100n
2,240 + 70n + 100n
2,240 + 170n
The lengths of two sides of a triangle are 7 and 11. Which could not be the length of the third side?
5
10
12
19
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
5, 7, 11
5 + 7 = 12 > 11 CORRECT
7, 10, 11
7 + 10 = 17 > 11 CORRECT
7, 11, 12
7 + 11 = 18 > 12 CORRECT
7, 11, 19
7 + 11 = 18 < 19 INCORRECT
Answer: 19.Using the Triangle Inequality Theorem, the third side of the triangle must be less than the sum of other two sides and more than the absolute difference of the two sides. With the sides 7 and 11 given, the third side must be more than 4 but less than 18. Therefore, 19 cannot be the length of the third side.
Explanation:In mathematics, particularly in geometry, the length of the third side of a triangle when the lengths of two sides are known, can be determined by using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. In this case, the lengths of the two sides are given as 7 and 11. The sum of these two lengths is 18.
So the possible length of the third side must be less than 18 but more than the absolute difference of 7 and 11 (which is 4). Hence, the third side can be more than 4 and less than 18. Therefore out of the options provided, the value 19 could not be the length of the third side of the triangle.
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Which property explains why these two expressions are equal?
-5 + (x + 4) = (-5 + 4) + x
A) Associative Property
B) Commutative Property
C) Distributive Property
D) Multiplicative Identity Property what the answer
Answer:
Associative property.
Step-by-step explanation:
Associative property implies that, for instance; no matter how the numbers are grouped in the sum involving (-5, x and 4), the result is the same.
If f(x)=2x+7 and g(x)=11x-4, find (f+g)x.
Answer:
(f+g)(x) = 13x + 3
Step-by-step explanation:
Rewrite f(x)=2x+7 and g(x)=11x-4 in columns, as follows:
f(x)=2x+7
+g(x)=11x-4
----------------
Now add each column separately.
f(x)+g(x) = (f+g)(x) ("the sum of functions f and g")
2x + 11x = 13x, and, finally, 7-4 = 3.
Therefore,
f(x)=2x+7
+g(x)=11x-4
----------------
(f+g)(x) = 13x + 3
Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 34 and center of dilation (0, 0) .
Answer:
See attached diagram
Step-by-step explanation:
Given quadrilateral has vertices at points A(-8,4), B(4,-4), C(0,-8) and D(-4,-4).
A dilation with a scale factor of [tex]\dfrac{3}{4}[/tex] and a center of dilation (0,0) has a rule
[tex](x,y)\mapsto \left(\dfrac{3}{4}x,\dfrac{3}{4}y\right).[/tex]
Then
A(-8,4)→E(-6,3);B(4,-4)→F(3,-3);C(0,-8)→G(0,-6);D(-4,-4)→H(-3,-3).See attached diagram for details.
Remark: If a scale factor is 34, then the rule is (x,y)→(34x,34y) and image vertices have coordinates (-272,136), (136,-136), (0,-272), (-136,-136).
Someone please help!!!
A company is selling two types of treadmills. Treadmill x sells for $750 and treadmill y sells for $900. Three times the number of treadmill y sold must be less than or equal to twice the number of treadmill x sold. The company has at most 100 treadmills to sell. What is the maximum revenue that the company can make from the treadmill sales?
$75,000
$81,000
$84,000
$90,000
Answer:
Option B is correct
The maximum revenue that the company can make from the treadmill sales is, $81,000
Step-by-step explanation:
Let x represent the number of treadmill x sold and y represents the number of treadmill y sold
As per the statement: Three times the number of treadmill y sold must be less than or equal to twice the number of treadmill x sold.
⇒[tex]3y\leq 2x[/tex] ......[1]
Also, it is given that the company has at most 100 treadmills to sell.
⇒[tex]x+y\leq 100[/tex]
using a graph tool for equation [1] and [2] as shown in figure given below;
⇒ the solution is the shaded area
The maximum revenue that the company can make is for the point, (60, 40)
⇒ x = 60 treadmills
and y = 40 treadmills
Maximum Revenue = [tex]60 \times 750 + 40 \times 900 = 45000+36000 = \$81,000[/tex]
Therefore, the maximum revenue that the company can make from the treadmill sales is, $81,000
A line that intersects a circle at exactly one point is called a ______
Chord
Tangent
Secant
A line that intersects a circle at exactly one point is called a tangent.
What is a tangent to a circle?A line segment that touches a circle specified to only one point is called a tangent to that circle.
The point where it touches the circle is called the point of tangency.
We can see that point line segment PT is the tangent of our circle and point P is the point of tangency.
Therefore, A line that intersects a circle at exactly one point is called a tangent.
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Tim is measuring the weight (in ounces) of a substance for a science experiment. Tim added a mystery substance (m) to his experiment. Tim used the equation 12.93 + m = 17.0 to find out how much he added. How much of the mystery substance (m) did Tim add to his experiment?
A)4.07 ounces B)4.97 ounces C)5.03 ounces D)5.17 ounces
Answer:
A: 4.07 ounces
Step-by-step explanation:
17.0 - 12.93 = 4.07
Answer:
The weight of the mystery substance added by Tim is 4.07 ounces. Hence option A is correct.
Solution:
Given, Tim is measuring the weight (in ounces) of a substance for a science experiment.
Tim added a mystery substance (m) to his experiment.
Tim used the equation 12.93 + m = 17.0 to find out how much he added.
We have to find how much of the mystery substance (m) did Tim add to his experiment?
Now, from the given equation, 12.93 + m = 17.0 → m = 17.0 – 12.93 → m = 4.07
Hence, the weight of the mystery substance is 4.07 ounces, i.e. option A is correct.
What is the ratio of soccer balls to footballs?
A) 1 : 3
B) 2 : 4
C) 3 : 1
D) 4 : 2
A box is shaped like a cube. The box has a length of 1 foot, a width of 1 foot, and aheight of 1 foot. What is the volume of the box.
Answer:
1 cubic foot
Step-by-step explanation:
Volume = length * width * height
= 1*1*1 = 1 ft^3
The volume of the given box shaped like a cube is 1 cubic foot.
We have given that,
The box has a length of 1 foot, a width of 1 foot, and a height of 1 foot.
What is the formula of the volume?Volume = length * width * height
Volume= 1*1*1
Volume= 1 ft^3
Therefore the volume of the given box shaped like a cube is 1 cubic foot.
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Find the inverse.
f(x)= 2x-5/3x+4
Answer:
F.MBFFBLKFDKGBKK FGLK doingTDKDT
Step-by-step explanation:
What is your real rate of return is your savings account pays 2.5% interest and inflation is at 1%
Answer:
1.5
Step-by-step explanation:
The real rate of return is calculated as the difference between rate of interest and the inflation.
so,Interest=2.5%
Inflation=1%
=2.5-1
=1.5%
Answer:
1.485 % ( approx )
Step-by-step explanation:
We know that,
[tex]\text{Real rate of return}=\frac{1+\text{Nominal rate}}{1+\text{Inflation rate}}-1[/tex]
Given,
Nominal rate = 2.5 % = 0.025
Inflation rate = 1 % = 0.01,
[tex]\implies \text{Real rate of return}=\frac{1+0.025}{1+0.01}-1[/tex]
[tex]=\frac{1.025}{1.01}-1[/tex]
[tex]=1.01485149-1=0.01485149\approx 0.01485[/tex]
Thus, the real rate of return is 0.01485 or 1.485 %.
In a circle with a radius of 36.9 m, an arc is intercepted by a central angle of 8π5 radians.
Use 3.14 for π and round your final answer
Answer:
185.39 m
Step-by-step explanation:
Central angle = 8π/5 radians
Let's convert radians to degrees.
Answer:
The length of arc is 185.39 m
Step-by-step explanation:
Given that in a circle with a radius of 36.9 m, an arc is intercepted by a central angle of [tex]\frac{8\pi}{5}[/tex] radians.
we have to find the arc length.
[tex]Radius=36.9 m[/tex]
[tex]\text{Central angle=}\frac{8\pi}{5}[/tex]
The arc length can be calculated by the formula
[tex]L=r\theta[/tex]
[tex]\text{where r is radius and }\theta \text{ is central angle in radians. }[/tex]
[tex]L=36.9 \times \frac{8\pi}{5}[/tex]
[tex]L=36.9 \times \frac{8\times 3.14}{5}[/tex]
[tex]L=\frac{926.928}{5}=185.3856\sim 185.39 m[/tex]
hence, the length of arc is 185.39 m
the sum of 7 2/9 and 2 7/9 in simpliest form
Answer:
10
Step-by-step explanation:
7 2/9 + 2 7/9 common denominators already the same so add
7+2=9 first start with the whole number
2/9 + 7/9= 9/9 = 1 then add the fractions
9+1=10 then add the whole number and fraction
Answer:
10
Step-by-step explanation:
the price of a pair of shoes increases from $52 10 $64. What i the percent increase?
Answer:
Step-by-step explanation:
Step 1: Calculate the change by subtracting old cost ($52) from the new cost ($64)
Step 2: Divide that change by the old cost ($52). You will get a decimal number
Step 3: Convert the decimal number to a percentage by multiplying by 100%
Which shape best describes the object generated when the rectangle is rotated about the axis?
hollow rectangular prism
hollow cylinder
solid cylinder
solid rectangular prism
If the shape shown is rotated about the axis, a solid cylinder would be formed.
What is a cylinder?A cylinder is a three dimensional shape (has length, width and height) which has two parallel bases joined by a curved surface, at a fixed distance.
If the shape shown is rotated about the axis, a solid cylinder would be formed.
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When a rectangle is rotated about an axis, it forms a solid cylinder.
Explanation:The shape that best describes the object generated when a rectangle is rotated about an axis is a solid cylinder. When a rectangle is rotated around an axis, it forms a three-dimensional shape that is similar to a cylinder. The base of the shape is a rectangle, and the height is equal to the length of the original rectangle. The shape has a curved surface and two circular faces at the top and bottom, just like a cylinder.
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There are 750 spectators in the stadium of which 420 of them are woman and the rest are man what percent are men
There are 750 spectators in the stadium. 420 of these spectators are women and the rest are men. What percent of the spectators are men.
The fraction [tex]\frac{420}{750}[/tex] represents the number of women in the stadium out of all the 750 people in the stadium. We can subtract 420 from 750 and we will get a difference of 330. Now we know that there are 330 men in the stadium.
The fraction [tex]\frac{330}{750}[/tex] represents the number of men at the stadium out of everyone. To find the percent of men at the stadium, we need to turn [tex]\frac{330}{750}[/tex] into a percent. [tex]\frac{330}{750}[/tex] reduced is [tex]\frac{11}{25}[/tex] because we are dividing both the numerator and denominator by the Greatest Common Factor of 330 and 750 using 30.
11 ÷ 25 = 0.44
0.44 × 100 = 44%
Therefore, 44% of the spectators in the stadium are men.
A cyclist rode at an average speed of 15 mph for 30 miles. How long was the ride? Question 6 options: 0.5 hours 1 hour 2 hours 3 hours
Answer:
2 hours
Step-by-step explanation:
using the relationship
distance = speed × time, then
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{30}{15}[/tex] = 2 hours
It will take 2 hours to cover 30 miles so option (C) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
A cyclist rode at an average speed of 15 mph for 30 miles.
So,
15 miles ⇒ hour
Multiply by 2
2 hours ⇒ 30 miles.
Hence "It will take 2 hours to cover 30 miles".
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___ can be found by making x=0
Answer:
y intercept
Step-by-step explanation:
At first I didn't think there was enough information, but there is. In general terms, for any polynomial which is also a function, making x = 0 gives the point where (0,b) = the y intercept.
For example
using f(x) = x^2 + 4x + 6 when x = 0 the result left is f(0) = 6 so the y intercept is (0,6)
If you have x^2 + 6x the y intercept is (0,0)
Mrs.Padre drives 2 hours at a n average speed of 35 miles per hour then she drives 3 hours at a speed of 48 miles per hour what is her average speed for the whole trip
She drove 2 hours at 35 miles per hour for a total of 35 * 2 = 70 miles.
She drove 3 hours at 48 miles per hour for a total of 48 * 3 = 144 miles.
Her total miles were: 70 + 144 = 214.
Her total driving time was 3 + 2 = 5 hours.
Divide her total miles by total time for her average speed:
214 / 5 = 42.8 miles per hour average speed.
Not sure if you need to round the answer or not.
Mrs. Padre's average speed for the entire trip is 42.8 miles per hour, which is calculated by dividing the total distance (214 miles) by the total time (5 hours).
To determine Mrs. Padre's average speed for the whole trip, we need to use the formula for average speed:
Average speed = Total distance / Total time
First, we calculate the distance traveled during each part of the trip:
For the first part: 2 hours * 35 miles/hour = 70 milesFor the second part: 3 hours * 48 miles/hour = 144 milesNext, we sum up the total distance and total time:
Total distance = 70 miles + 144 miles = 214 milesTotal time = 2 hours + 3 hours = 5 hoursNow we can calculate the average speed:
Average speed = 214 miles / 5 hours = 42.8 miles per hour
Clark buys 2 gallons of paint for $ 16.39. What is the cost per pint of paint? Round your answer to the nearest cent if necessary .
Answer:
$1.02
Step-by-step explanation:
We are told that Clark buys 2 gallons of paint for $ 16.39.
To find the cost per pint of paint let us convert amount of paint in gallons.
1 gallon = 8 pints.
2 gallons= 8*2 pints= 16 pints.
Now let us find cost per pint of paint by dividing the total cost of paint by number of pints in 2 gallons.
[tex]\text{The cost per pint of paint}=\frac{16.39}{16}[/tex]
[tex]\text{The cost per pint of paint}=1.024375[/tex]
Upon rounding our answer to nearest cent we will get,
[tex]\text{The cost per pint of paint}=1.02[/tex]
Therefore, the cost per pint of paint is $1.02.