Answer:
See Below.
Step-by-step explanation:
We have the expression:
[tex]3pf^2-21p^2f+6pf-42p^2[/tex]
Part A:
Find the GCF. Notice that we have a three in every term and a p in every term. Thus, the GCF will be 3p. Factor:
[tex]3p(f^2-7pf+2f-14p)[/tex]
This is the most we can do.
Part B:
Continuing from where we left off, we can factor the entire expression by grouping:
[tex]\displaystyle \begin{aligned} &= 3p(f^2-7pf+2f-14p) \\ \\ &= 3p(f(f-7p)+2(f-7p)) \\ \\ &=3p((f+2)(f-7p))\end{aligned}[/tex]
Divide. 1 ÷ 0.0064. please my dear friend
Answer:
156.25
Step-by-step explanation:
[tex]\frac{1}{0.0064}\\\\\frac{10000}{64}\\ then divide \[/tex]
[tex]\frac{10000}{64} = \frac{2500}{16} =\frac{625}{4} = 156.25[/tex]
It is never possible to solve an inequality that has a number on each side. True or False?
Answer:
true
Step-by-step explanation:
because a number is always greater than, equal to, or less than another number
how many 4-digit numbers can be formed using only the digits 9, 8 and 7? :p
Answer: 81
Step-by-step explanation:
First digit and Second digit and Third digit and Fourth digit
3 choices x 3 choices x 3 choices x 3 choices = 81
50 Pts!!! Answer ASAP.
Answer:
0.8
Step-by-step explanation:
because the template should be axr^n-1
where r is the common ratio
r=0.8
Answer:
0.8
Step-by-step explanation:
John has 14 boxes of apples. Each box holds 12 apples. If 6 of the boxes are full, and 8 of the boxes are half full, how many apples does John have?
Answer:
120
Step-by-step explanation:
12 x 6 = 72
8x(12/2)=48
72+48 =120
Write the equation for a parabola with a focus at (-2,5) and a directrix at x=3 Answer has to be in Y=____ Format
Answer:
Step-by-step explanation:
The vertex of a parabola is directly in between the focus and the directrix. That means that the vertex of this parabola is at (1/2, 5). A parabola wraps itself around the focus and away from the directrix, so this parabola opens to the left. One other thing that we need to know is the distance between the vertex and the focus, the p value in the equation. So here's the equation we need (it's not a y= equation, though):
[tex]-(y-k)^2=4p(x-h)[/tex]
So here's what we know from the info above:
p = 5/2
h = 1/2
k = 5
and filling in:
[tex]-(y-5)^2=4(\frac{5}{2})(x-\frac{1}{2})[/tex] and simplifying:
[tex]-(y-5)^2=10(x-\frac{1}{2})[/tex] and then solving for x:
[tex]-\frac{1}{10}(y-5)^2+\frac{1}{2}=x[/tex]
Suppose an apple picker in China earns an average wage of 45 cents per hour. An apple picker can harvest about 2.0 bushels of apples each hour. One gallon of apple juice requires 40 apples. Each bushel contains about 126 apples. What is the labor cost of one gallon of apple juice in dollars?
Answer:
0.0398 dollars
Step-by-step explanation:
We are told in the question that
An apple picker in China earns an average wage of 45 cents per hour.
Mathematically
1 hour= 45 cents............ Equation 1
An apple picker can harvest about 2.0 bushels of apples each hour.
Mathematically
2.0 bushels = 1 hour ..............Equation 2
We are told that each bushel contains about 126 apples
1 bushel = 126 apples
2 bushels =
126 × 2
= 252 apples
Combining Equation 1 and 2 together,
We can say
An apple picker in 1 hour harvests 2 bushels of apples which is 252 apples and is paid 45 cents
1 hour = 2 bushels of apples
1 hour = 252 apples
1 hour = 45 cents
Hence we can say fro harvesting 252 apples, an apples picker is paid 45 cents
Mathematically,
252 apples = 45 cents
One gallon of apple juice requires 40 apples
We are to calculate the labor cost of one gallon of apple juice in dollars
If : 252 apples = 45 cents
40 apples = X cents
Cross Multiply
40 × 25 = 252 × X
X = (40× 25) ÷ 252
X = 3.984063745 cents
Hence the labor cost of 40 apples = 3.984063745 cents
Approximately = 3.98 cents
Converting 3.98 cents to dollars
100 cents = 1 dollar
3.98 cents =
= 3.98/100
= 0.0398 dollars.
Therefore, the labor cost of one gallon of apple juice in dollars is 0.0398 dollars.
Answer choice
D) A worker with 15 years of service gets 5 weeks of vacation and each year.
Answer: it seems to be D, but the equation makes practically no sense!
The value of the factor changes for the different amounts of service years and vacation weeks.
Step-by-step explanation: The equation means that the employee is trying to figure out the value of the "v-factor" for how vacation time is earned.
If you substitute the number of service years into the left side of the "formula" and vacation weeks on the right side, then solve for "v", v(15)=5 you get v= 1/3 or 0.33
If you substitute other numbers, like v(2)=2, so v= 1 then v(30) = 8, v = 4/15 or 0.2667. You see the factor's value decreases. The company is much more generous to to employees with one or two years of service than with the older ones.
PLEASE HELP!! A car manufacturer does performance tests on its cars. During one test, a car starts from rest, and accelerates at a constant rate for 20 seconds. another car starts from rest three seconds later, and accelerates at a faster constant rate. The equation that models the distance (d) in metres the first cars equation is d=1.16t^2, where t is time, in seconds, after the car starts. The equation for the second car is: d=1.74(t-3)^2. a) in context, what is a suitable domain for the graph of the system? b) at what time will both cars have driven the same distance? c) how far will they have driven at this time?
Answer:
0 ≤ t ≤ 2516.348 seconds310.0 metersStep-by-step explanation:
a) Since these are production vehicles, we don't expect their top speed to be more than about 70 m/s, so the distance functions probably lose their validity after t = 25. Of course, t < 0 has no meaning in this case, so the suitable domain is about ...
0 ≤ t ≤ 25
Note that the domain for the second car would be 3 ≤ t ≤ 25.
__
b) The graph of this system shows the cars will both have driven the same distance after 16.348 seconds.
__
c) At that time, the cars will have driven 310.0 meters.
_____
Non-graphical solution
If you like, you can solve the equation for t:
d1 = d2
1.16t^2 = 1.74(t -3)^2
0 = 0.58t^2 -10.44t +15.66
t = (10.44 +√(10.44^2 -4(0.58)(15.66)))/(2(0.58)) = (10.44+8.524)/1.16
t = 16.348 . . . . time in seconds the cars are at the same distance
That distance is found using either equation for distance:
1.16t^2 = 1.16(16.348^2) = 310.036 . . . meters
Please answer question now
Instructions: Find the missing side. Round your answer to the
nearest ten
Answer:
trig function is tangent
tan(63)=x/19
multiply each side by 19:
tan(63)19=x
x=37.3
A track star runs twice a day. In the morning, he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps. In the afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps. How
many total miles does he run in a day?
Answer:
12.65 miles
Step-by-step explanation:
he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps:
2 1/2 *3 1/2= 5/2 * 7/2=35/4=8.75 miles
afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps
1 3/10 *3=13/10*3=39/10= 3.9
total miles he runs in a day: 8.75+3.9= 12.65 miles
Which ordered pair is in the solution set of the system of linear inequalities?
y > Three-halvesx – 1
y < Three-halvesx – 1
On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the right of the line is shaded. The second line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the left of the line is shaded.
(–5, 2)
(2, 2)
(5, 2)
no solution
Answer: No solution
Step-by-step explanation: If you are doing the Unit Test on edge2020 then D No solution is the answer.
Answer:
the answer is no "solution"
Unit Test on Edge 2023
You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.36 with a standard deviation of 0.96 You sample 60 day students, and the sample mean GPA is 2.19 with a standard deviation of 0.66 Calculate the test statistic, rounded to 2 decimal places
Answer:
Z = 0.87
Explanation:
Given the following data;
Sample 1:
n1 = 30
Mean, X = 2.36
Standard deviation, Ox = 0.96
Sample 2:
n2 = 60
Mean, Y = 2.19
Standard deviation, Oy = 0.66
The formula for test statistics for two population is;
[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]
Substituting the values, we have;
[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]
[tex]Z = \frac{0.17}{0.19488}[/tex]
Z = 0.8723
The test statistics to 2 d.p is 0.87
Therefore, Z = 0.87
Two cars leave an intersection. One car travels north: the other east. When the car traveling north had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?
Answer:
20 miles
Step-by-step explanation:
Given that :
When the car traveling north 'N' had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east
Let the distance moved by the east bound car be e,
therefore, distance between the cars when the northbound car had traveled a distance of 15 miles = e + 5
Using Pythagoras rule:
(Hypotenus)^2 = (adjacent)^2 + (Opposite)^2
(e+5)^2 = 15^2 + e^2
(e+5)(e+5) = 225 + e^2
e^2 + 5e + 5e + 25 = 225 + e^2
e^2 + 10e + 25 = 225 + e^2
e^2 - e^2 + 10e = 225 - 25
10e = 200
e = 200 / 10
e = 20 miles
Check attached picture for solution diagram
Can someone help me with this problem?
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = 1
▹ Step-by-Step Explanation
y = mx + b
'm' represents the slope. since there is no number before the x, the coefficient will always be 1. therefore, the slope is 1.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
9/10 of the weight of a loaf of bread comes from the flour used in its baking. 2/9 of the weight is the protein what fraction of the weight is protein?
Answer:
1/5
Step-by-step explanation:
2/9 * 9/10 = 2/10 = 1/5
On a coordinate plane, a line goes through (negative 4, negative 1) and (0, 1). Square a is around (negative 5, negative 2), square b is around (negative 1, 1), square c is around (1, 2), and square d is around (4, 4). The linear equation y = one-half x + 1 is represented by the graphed line. A second linear equation is represented by the data in the table. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 7, 6, 5, 4. In which square is the solution located?
Answer: D
Step-by-step explanation:
The solution of the two equations does not exist since they are parallel.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.
Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.
Given linear equation of a line in slope intercept form as,
y = 1/2 x + 1
Here slope = 1/2 and y intercept = 1
y intercept is the y value of a point where it touches the y axis.
A second linear equation is to be found by using the values in the table.
Taking two points (2, 7) and (0, 6).
Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2
Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.
y intercept = 6
Equation of the second line is,
y = 1/2 x + 6
Since the slopes of two lines are equal, they are parallel.
There is no solution for two parallel lines.
Hence there is no solution for the linear equations given.
To learn more about Slope, click on the link :
https://brainly.com/question/19131126
#SPJ3
Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power
Answer:I think it’s 7x^3
Step-by-step explanation:
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 3/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Answer:
Cantidad que Lupe dejó en casa con inicialmente = 127.5 soles.
Amount that Lupe left home with initially = 127.5 soles.
Step-by-step explanation:
Pregunta correcta
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 1/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Solución
Deje que la cantidad de dinero que Lupe dejó en casa sea x soles.
Lupe compra comestibles con 2/5 de su dinero. Es decir, Lupe gasta (2/5) × x = (2x/5)
En este punto, Lupe se queda con
x - (2x/5) = (3x/5) soles.
Lupe luego gasta 1/3 de lo que queda en la carne
(1/3) de lo que queda = (1/3) × (3x/5) = (x/5)
Lo que significa que Lupe gasta (x/5) soles en la sección de carne.
Cantidad restante después de la sección de carne = (3x/5) - (x/5) = (2x/5)
Lupe gasta 3 soles en el viaje de ida y vuelta al mercado y se queda con 47 soles después de todo.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
¡¡¡Espero que esto ayude!!!
English Translation
Lupe goes to the market and buys groceries with 2/5 of her money; then he goes to the meat section and buys with 1/3 of what he has left; if you spend 3 soles on a round trip ticket; How much money did you leave your home with if you arrive home with 48 soles?
Solution
Let the amount of money Lupe left home with be x soles.
Lupe buys groceries with 2/5 of her money
That is, Lupe spends (2/5) × x = (2x/5)
At this point, Lupe is left with
x - (2x/5) = (3x/5) soles.
Lupe then spends 1/3 of what is left on meat
(1/3) of what is left = (1/3) × (3x/5) = (x/5)
Meaning that Lupe spends (x/5) soles at the meat section.
Amount left after the meat section = (3x/5) - (x/5) = (2x/5)
Lupe spends 3 soles on round ticket trip to market and is left with 47 soles after everything.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
Hope this Helps!!!
Which table represents a function?
Answer:
Table 4 represents a function.
Step-by-step explanation:
Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.
Solve for X and determine the measure of each angle.
X
(x - 35)
X
(2x - 75°)
it's a quadrilateral
interior angles add up to 360
x + 2x - 75 + x + x - 35 = 360
5x - 110 = 360
5x = 360 + 110
x = 470 ÷ 5
x = 95
and x - 35 = 60
2x - 75
= 190 -75
= 115
Answer:
see explanation
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Sum the given angles and equate to 360
x + x + x - 35 + 2x - 75 = 360, that is
5x - 110 = 360 ( add 110 to both sides )
5x = 470 ( divide both sides by 5 )
x = 94 , then
x - 35 = 94 - 35 = 59
2x - 75 = 2(94) - 75 = 188 - 75 = 113
Thus
The 4 angles are 59°, 94°, 94°, 113°
The sum of five consecutive numbers is 360. What is the smallest of these numbers? *
Answer:
70
Step-by-step explanation:
An easy way to do this is to simply take 360(the sum) and divide it by 5(the number of numbers) to get 72. Thus, 72 is the middle number and the numbers are:
72
72,72,73
70,71,72,73,74
The smallest of these numbers is 70
Hope it helps <3
Hello!
Answer:
70 is the smallest number.
Step-by-step explanation:
If the sum of 5 consecutive numbers is 360, we can solve for the smallest number algebraically:
Let 'x' represent the smallest number:
and (x + 1), (x + 2), (x + 3), and (x+4) represent the other consecutive numbers:
x + (x + 1) + (x + 2) + (x + 3) + (x+ 4) = 360
Combine like terms:
5x + 10 = 360
Subtract 10 from both sides:
5x = 350
Divide both sides by 5:
x = 70. This is the smallest of the consecutive numbers.
We can check our work:
70 + 71 + 72 + 73 + 74 = 360.
Hope this helped!
ERROR ANALYSIS Describe and correct the error
in finding the value of c that makes the expression a
perfect square trinomial.
x² + 30x + c
Х
x2 + 30x +
30
2
x2 + 30x + 15
La picture of your work or type your work.
Step-by-step explanation:
Our polynomial is x²+30x +c with a missing value c
c should make this polynomial expression a perfect square
Write the expression with a decreasing order of degreesx²+ 30x+c
write the terms as factorsx² + 2*15*x +c
notice that the in the middle we have 2*15*x so our third term will be 15²x²+2*15*x+15² ⇒ c = 15²=225
arrange your perfect square(x+15)²
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Answer:
The correct option is;
A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25
Please find attached the graphs of the table data
Step-by-step explanation:
Each of the given table data of in the tables are analysed to find direct variation;
Table 1
x, -3, -1, 2, 5, 10
y, -4.5, -3.0, -1.5, 0.0, 1.5
-4.5/-3 = 1.5 ≠ -3.0/-1 = 3
No direct variation
Table 2
x, -5.5, -4.5, -3.5, -2.5, -1.5
y, 10, 8, 6, 4, 2
10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9
However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2
Adjusted direct variation
Table 3
x, -5.5, -5.5, -5.5, -5.5, -5.5
y, -3, -1, 2, 5 , 10
-3/(-5.5) ≠ -1/-5.5
No direct variation
Table 4
x, -3, -1, 2, 5, 10
y, -7.5, -2.5, 5.0 , 12.5, 25
-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10
Direct variation exists
Answer:
so D
Step-by-step explanation:
Solve the equation. 2x + 4 = 3x – 2
Answer:
X=6
Step-by-step explanation:
2x+4=3x-2
-4 -4
2x=3x-6
-3x -3x
-1x=-6
--- ---
-1 -1
X=6
Answer:
6
Step-by-step explanation:
2x+4=3x-2
2x-3x=-2-4
-x=-6
(divide both sides by -1)
X=6
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5?
Answer: (1.5,-3) and (4.5, -3)
Step-by-step explanation:
The dilation rule to dilate a point (x,y) by a scaler factor of k is given by :0
[tex](x,y)\to (kx,ky)[/tex]
Given: A Line Segment has the points (1,-2), and (3,-2).
Scale factor = 1.5
Then, the new points after dilation will be :
[tex](1,-2)\to(1.5\times1,\ 1.5\times-2)=(1.5,\ -3)[/tex]
[tex](3,-2)\to (1.5\times3,1.5\times-2)=(4.5,\ -3)[/tex]
Hence, the new points after its dilated by a scale factor of = (1.5,-3) and (4.5, -3)
Which could be used to solve this equation? 3 and one-fifth + n = 9 Subtract 3 and one-fifth from both sides of the equation. 3 and one-fifth minus 3 and one-fifth + n = 9 + 3 and one-fifth Add 3 and one-fifth to both sides of the equation. 9 + 3 and one-fifth = 12 and one-fifth
Answer:
Subtract [tex]3\frac{1}{5}[/tex] from both sides.
Step-by-step explanation:
We want to isolate the variable [tex]n[/tex]. To do this, we have to get rid of [tex]3\frac{1}{5}[/tex], which we can do by subtracting itself, since it equals 0.
[tex]3\frac{1}{5} + n =9[/tex]
[tex]n = 5\frac{4}{5}[/tex]
Answer:
ITS A
Step-by-step explanation:
If a circle is dilated by a scale factor of
what will be the lenth of the new radius?
18m
12 m
9 m
36 m
27 m
Answer/Step-by-step explanation:
The scale factor is missing in the question. However, here's how to find the length of the new radius if given a known scale factor.
Length of new radius = length of the radius of the dilated circle × scale factor of dilation
Length of the radius of the dilated circle is given as 18m
Therefore,
Length of new radius = 18m × scale factor.
If the scale factor is a fraction, it means the new length would be smaller than 18m. But if the scale factor is a whole number, the new length of the radius would be greater than 18m.
Let's assume any of the following scale factors was what was given in the question:
*If scale factor given is ½, new radius length = 18m × ½ = 9m
*If scale factor given is 2, new radius length = 18m × 2 = 36m
0.719 to the nearest hundredth
Answer:
.72
Step-by-step explanation:
9 rounds up because 1-4 stay the same and 5-9 round up
Answer: 0.719 to the nearest hundredth is 0.72