Answers
Answer:
10
---------
9 t^2
Step-by-step explanation:
10t 20t-40
----------- * ------------
6t-12 30 t^3
Factor
10t 20(t-2)
----------- * ------------
6(t-2) 30 t^3
We can cancel 10t
1 20(t-2)
----------- * ------------
6(t-2) 3 t^2
We can cancel t-2
1 20
----------- * ------------
6 3 t^2
We can cancel a 2 from the 20 and from the 6
1 10
----------- * ------------
3 3 t^2
10
-----------
9 t^2
Related Questions
Identify an equation in point-slope form for the line perpendicular to
y=-4x – 1 that passes through (-2,7).
Answers
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+\dfrac{15}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==================================[/tex]
[tex]\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=\dfrac{1}{4}x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=\dfrac{1}{4}(-2)+b\\\\7=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\7\dfrac{1}{2}=b\to b=7\dfrac{1}{2}=\dfrac{7\cdot2+1}{2}=\dfrac{15}{2}\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+\dfrac{15}{2}[/tex]
how do I solve this: 9b less than 40
Answers
Answer:
b < 4.44
Step-by-step explanation:
This is an inequality.
The sign for 'less than' is '< '
Write 9b less than 40 in inequality form.
9b < 40 (Take 9 on the other side of the inequality and divide it by 40)
b < 40/9
b < 4.44
!!
Help please and fast
Answers
Answer:
b. 7/16
Step-by-step explanation:
We can see in the figure that the total dimension parallel to C is 15/16.
The other half dimension with c is 1/2
We will get the dimension C by subtracting 1/2 from 15/16
So,
C = 15/16 - 1/2
= (15-8)/16
=7/16
So the dimension C is 7/16.
Hence option b is correct ..
m2 - 36 = 0
Several solutions please
Answers
Answer:
m = ±6
Step-by-step explanation:
m^2 -36 =0
Add 36 to each side
m^2-36 +36 = 0+36
m^2 = 36
Take the square root of each side
sqrt(m^2) = ±sqrt(36)
m = ±6
Answer:+6 or -6
Step-by-step explanation:m^2 - 6^2
it becomes difference of two squares,
(m+6) (m-6)=0
m-6=0,m=6
m+6=0,m=-6
Select the correct answer from each drop-down menu. The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Answers
Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
H - height of pyramids
Pyramid A:
[tex]B=(10)(2)=200\ m^2[/tex]
[tex]V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3[/tex]
Pyramid B:
[tex]B=10^2=100\ m^2[/tex]
[tex]V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3[/tex]
[tex]V_A>V_B\\\\V_A=2V_B[/tex]
The volume of the pyramid A is twice as large as the volume of the pyramid B.
The new height of pyramid B: 2H
The new volume:
[tex]V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3[/tex]
The volume of the pyramid A is equal to the volume of the pyramid B.
To compare the volumes of the two pyramids, we first need to calculate the volume of each pyramid using the formula for the volume of a pyramid:
\[ V = \frac{1}{3}Bh \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
First, let's calculate the volume of pyramid A:
\[ \text{Area of base of pyramid A} = \text{length} \times \text{width} = 10 \, \text{meters} \times 20 \, \text{meters} = 200 \, \text{square meters} \]
Now, let's call the height of pyramid A (and originally pyramid B) \( h \). Then, the volume of pyramid A is:
\[ V_{\text{A}} = \frac{1}{3} \times 200 \, \text{m}^2 \times h = \frac{200h}{3} \, \text{cubic meters} \]
Next, let's calculate the volume of pyramid B with its original height \( h \):
\[ \text{Area of base of pyramid B} = \text{side} \times \text{side} = 10 \, \text{meters} \times 10 \, \text{meters} = 100 \, \text{square meters} \]
So the original volume of pyramid B is:
\[ V_{\text{B}} = \frac{1}{3} \times 100 \, \text{m}^2 \times h = \frac{100h}{3} \, \text{cubic meters} \]
Now we can compare the volumes of pyramid A and the original volume of pyramid B:
\[ \frac{V_{\text{A}}}{V_{\text{B}}} = \frac{\frac{200h}{3}}{\frac{100h}{3}} = \frac{200}{100} = 2 \]
So, pyramid A has twice the volume of pyramid B.
Now, if the height of pyramid B increases to twice that of pyramid A, its new height is \( 2h \). Therefore, the new volume of pyramid B is:
\[ V_{\text{B new}} = \frac{1}{3} \times 100 \, \text{m}^2 \times 2h = \frac{200h}{3} \, \text{cubic meters} \]
Comparing this new volume of pyramid B to the volume of pyramid A:
\[ \frac{V_{\text{B new}}}{V_{\text{A}}} = \frac{\frac{200h}{3}}{\frac{200h}{3}} = 1 \]
So, the new volume of pyramid B is equal to the volume of pyramid A.
In summary, the volume of pyramid A is twice the volume of pyramid B when their heights are the same. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 8 millimeters long, and each passing week it grew 2 additional millimeters.
Graph the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks).
Please help me to understand how to graph this problem.
Answers
A function that models the situation is f(x) = 2x + 8.
A graph of the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks) is shown in the picture below.
In Mathematics, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;
y = mx + b
where:
m represents the slope.x and y are the points.b represents the y-intercept or initial value.Since Rip van Winkle's beard was 8 millimeters long when he fell asleep, and each passing week it grew 2 additional millimeters, we can logically deduce the following parameters;
slope, m = 2.
initial value or y-intercept, b = 8.
In this context, an equation for the function that relates the length of his beard (in millimeters) to time (in weeks) can be written as follows;
y = mx + b
f(x) = 2x + 8
using the rate of Rs. 124.40 per using US dollar, find the US dollar for Rs. 158610.
Answers
Answer:
1275 USD
Step-by-step explanation:
124.40 Rs -----> 1 USD
158610 Rs -----> x USD
124.40x=158610
×=158610/124.40
x=1275 USD
A toy plush weighed one- sixth of a pound. A flimsy box can hold 4 pounds. How many toy plushes could the box hold?
Answers
Answer:
24 plushies
Step-by-step explanation:
1 pound = 6 toy plushies
6(4)=24
f(x) = -x^3 + 3x^2 + x - 3 Using the end behavior of f(x), determine the graph of the function
Answers
Answer:
Here, the given function,
[tex]f(x) = -x^3 + 3x^2 + x - 3[/tex]
Since, the leading coefficient is negative, and degree is odd,
Thus, the end behaviour of the function is,
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty[/tex]
Therefore, the graph rises to the left and falls to the right.
Now, when f(x) = 0
[tex]-x^3+3x^2+x-3=0[/tex]
[tex]\implies -(x-3)(x-1)(x+1)=0[/tex]
[tex]\implies x=3, 1, -1[/tex]
That is, graph intercepts the x-axis at (3, 0), (1, 0) and (-1, 0).
When x = 0,
[tex]f(x) = - 3[/tex]
That is, graph intersects the y-axis at ( 0, -3),
Also, for 0 > x > -1 , f(x) is decreasing,
For 2.55 > x > 0, f(x) is increasing,
For 3 > x > 2.55, f(x) is decreasing,
Hence, by the above explanation we can plot the graph of the function ( shown below )
Answer:w
Step-by-step explanation: it should be w i got it on plato
55. If 3x = 4y, the value of (x + y)^2 : (x - y)^2 is:
Answers
Answer:
[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]
Step-by-step explanation:
[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]
[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]
Keri and his friends are on their way to visit some family friends who lives 1050 miles away from them.based on the route they shoes they expect to complete their trip in three days. The distance and average speeds for the first two days driven are shown below:
First day : 5 hours at an average speed of 70 miles per hour
Second day: 7 hours at an average an average speed of 65 miles per hour
If the average speed on the third day is 70 miles per hour how many more hours will it take for them to reach their friends home
Answers
Answer:
3.5 hours
Step-by-step explanation:
5 x 70 = 350
7 x 65 = 455
350 + 455 = 805
1050 - 805 = 245
245/ 70 = 3.5
They will take an additional 3.5 hours on the third day to reach their destination.
Explanation of the distance covered in the first two days and how much more time it will take on the third day to reach their destination.
The distance covered in the first two days can be calculated using the formula:
Distance = Speed x Time
First day: 5 hours x 70 mph = 350 milesSecond day: 7 hours x 65 mph = 455 milesTherefore, after the first two days, they have covered a total distance of 350 + 455 = 805 miles. They have 1050 - 805 = 245 miles left to travel.
On the third day, at an average speed of 70 mph, they will cover the remaining 245 miles. Therefore, the time it will take for them to reach their friends' home on the third day is:
Time = Distance / Speed = 245 miles / 70 mph = 3.5 hours
They will take an additional 3.5 hours on the third day to reach their destination.
Given the function f(x)=-5x^2-x+20 find f(3)
Answers
Answer:
-28
Step-by-step explanation:
-5(3)^2 - 3 + 20
-5*9 - 3 + 20
-45 -3+ 20
-48+ 20
-28
Hope it helps!
A = B/2 = C/5 a:b:c=?
Answers
Answer:
[tex]\large\boxed{A:B:C=\dfrac{1}{10A}}[/tex]
Step-by-step explanation:
[tex]A=\dfrac{B}{2}=\dfrac{C}{5}\\\\A=\dfrac{B}{2}\qquad\text{multiply both sides by 2}\\\\2A=B\to\boxed{B=2A}\\\\A=\dfrac{C}{5}\qquad\text{multiply both sides by 5}\\\\5A=C\to C=5A\\\\A:B:C=A:2A:5A=1:2:5A=\dfrac{1}{2}:5A=\dfrac{1}{2}\cdot\dfrac{1}{5A}=\dfrac{1}{10A}[/tex]
Solve the system of equations and choose the correct answer from the list of options. (4 points)
x − y = 7
y = 3x + 12
2 over 19 comma 2 over 33
negative 2 over 19 comma negative 33 over 2
negative 19 over 2 comma negative 33 over 2
19 over 2 comma 33 over 2
Answers
Answer:
x=-19/2 y=-33/2
Step-by-step explanation:
x − y = 7
y = 3x + 12
Substituting the second equation into the first
x − (3x+12) = 7
Distribute the minus sign
x-3x-12 = 7
Combine like terms
-2x-12 =7
Add 12 to each sid
-2x-12+12 =7+12
-2x=19
Divide each side by -2
-2x/-2 = 19/-2
x = -19/2
Now we need to find y
y = 3x+12
y = 3(-19/2) +12
y = -57/2 +24/2
y = -33/2
Answer:
(-19/2, -33/2)
Step-by-step explanation:
Petro was given this system of equations.
-14x-2y = 24
14x+8y = -12
Petro’s work is shown in the table. Where, if anywhere, did Petro first make a mistake?
-
A) step 1
B) step 2
C) step 3
D) no mistake
Answers
Answer:
Option C step 3
Step-by-step explanation:
we have
-14x-2y=24 ------> equation A
14x+8y=-12 -----> equation B
step 1
Solve the system by elimination
Adds equation A and equation B
-14x-2y=24
14x+8y=-12
---------------------
-2y+8y=24-12
6y=12
The step 1 is correct
step 2
Solve for y
Divide by 6 both sides
6y/6=12/6
y=2
The step 2 is correct
step 3
Find the value of x
substitute the value of y in the equation A
-14x-2(2)=24
-14x-4=24
14x=-4-24
14x=-28
x=-2
The step 3 is not correct
therefore
Petro first make a mistake in Step 3
Answer:
Step 3 in the correct answer. Thx. Just to verify with everyone it is step 3.
Step-by-step explanation:
On Edge 2020 got it correct.
helppppppppppppppppppppping
Answers
Answer:
B
Step-by-step explanation:
First we simplify the equation:
3y − 2x = k (5x − 4) + 6
3y − 2x = 5k x − 4k + 6
3y = (5k + 2) x − 4k + 6
y = (5k + 2)/3 x + (6 − 4k)/3
The line has a positive slope and negative y-intercept. So:
(5k + 2)/3 > 0
(6 − 4k)/3 < 0
Solving for k in each:
k > -2/5
k > 3/2
k must be greater than -2/5 and 3/2. Since 3/2 is already greater than -2/5, then k must be greater than 3/2.
If k > 3/2, then it's also true that k > 0. So the answer is B.
simplify the following fraction (9/16/1/4)-1/5
Answers
Answer: [tex]\frac{41}{20}[/tex]
Step-by-step explanation:
The first step is to make the division of the fractions [tex]\frac{9}{16}[/tex] and
[tex]\frac{1}{4}[/tex]. To do this, you can flip the fraction [tex]\frac{1}{4}[/tex] over and multiply the numerators and the denominators of the fractions. Then:
[tex](\frac{\frac{9}{16}}{\frac{1}{4}})-\frac{1}{5}=(\frac{9}{16}*4)-\frac{1}{5}=\frac{36}{16}-\frac{1}{5}[/tex]
Reduce the fraction [tex]\frac{36}{16}[/tex]:
[tex]=\frac{9}{4}-\frac{1}{5}[/tex]
Now you can make the subtraction: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators. Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then subtract the products. Therefore you get:
[tex]=\frac{45-4}{20}=\frac{41}{20}[/tex]
1.
1400
Simplify: -
Show your work.
Answers
Answer:
1400
Step-by-step explanation:
Nothing can be done further. If I saw the rest of the question, I would be capable of assisting you.
I am joyous to assist you.
HELP!!!! PLEASE need help now its an emergency.
Answers
Answer:
121,6
Step-by-step explanation:
Since the only difference between the triangles are the letters and a few missing numbers, just replace the letters to get your answer. A and D are the same B and E are the same and C and F are the same. So the measurement of angle A is 121 degrees and the length of AB is 6
Two lines and a transversal form corresponding angles that are congruent. Describe the two lines
Answers
Answer:
parallel
Step-by-step explanation:
If you have two lines and a transversal that form corresponding angles that are congruent. Then the alternate interior angles are congruent and the same-side interior (some people call these consecutive angles) are supplementary.
This has to deal with Parallel Lines Theorem or the Converse of Parallel Lines Theorem.
The lines would be parallel.
Two lines will be parallel.
What is corresponding angle?When two lines are cut by a transversal then the angles formed relatively same position in their respective line at the intersection transversal and two lines are called corresponding angles.
What is converse of corresponding angles theorem?
Converse of corresponding angles theorem states that When two lines are cut by a transversal and the formed corresponding angles are congruent then the two lines will be parallel.
Here given that two lines and transversal are forming corresponding angles which are congruent. So by converse of corresponding angles theorem, the two lines will be parallel to each other.
Therefore two lines will be parallel.
Learn more about corresponding angle
here: https://brainly.com/question/2496440
#SPJ2
Which expression is equivalent to -3 - 3x – 1 + x?
A. 2x - 4
B. -2x+4
C. -2x-4?
D. 4-2x
Answers
Answer:
C. -2x-4
Step-by-step explanation:
-3 - 3x – 1 + x
Combine like terms
-3 -1 -3x +x
-4 -2x
Rearrange the order to put the x term first
-2x-4
c
just got it right on edge
Is 24/40= 4/8 true proportion?
Answers
Answer:
No, that is not the true proportion.
Step-by-step explanation:
40 divided by 8 is 5. 5 multiplied by 4 is 20. Therefore, the true proportion would be 20/40 = 4/8.
Alex and his father took a taxi cab that charges $2.60 per mile plus $1.50 for each passenger, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3 for this situation and found b=6. Which statement is true about the solution b=6?
Answers
Answer:
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi
Step-by-step explanation:
Given
18.60=2.60b+3
Here 18.60 is the total amount paid, 2.60 is the rate per mile and 3 is the charges for two passengers.
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi i.e. b represents miles ..
the answer is: the solution b = 6 gives the number of miles the taxi traveled.
i just did the workbook :)
The apother is 4 m and a side is 5.8 m. What is the area
of the pentagon? Round to the nearest whole number.
Answers
Answer:
58 m^2.
Step-by-step explanation:
The area of one of the 5 triangles is:
1/2 * 5.8 * 4 = 11.6 m^2
So the area of the pentagon
= 5 + 11.6
= 58 m^2
Answer:
The area is 58 meters squared.
Step-by-step explanation:
Since the pentagon is conveniently split into 5 separate but equal triangles, we only need to find the area of 1 triangle to find the rest. The area of triangles, as I'm sure you know, is 1/2bh. Using this equation, we get (1/2)x4x5.8. This equals 11.6. This is the area of one of the triangles. There are 5 triangles, so we multiply the area of 1 triangle by 5. 11.6x5= 58 meters squared. Hope this helped. :)
$1334 is deposited into a savings account at 8% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?
Answers
Answer:
84 years
Step-by-step explanation:
The future value of an investment is given by ...
FV = P(1 +r/n)^(nt)
where P is the principal amount, r is the annual rate, and n is the number of times per year interest is compounded. Filling in the given values and solving for t, we get ...
1000000 = 1334(1 +.08/4)^(4t)
749.6252 ≈ 1.02^(4t) . . . . divide by 1334 and simplify
log(749.6252) ≈ 4t·log(1.02) . . . . take logarithms
t ≈ log(749.6252)/(4·log(1.02)) ≈ 83.57
It will take about 84 years for the account balance to reach $1,000,000.
What is the ratio of 102 steps walked in 1 minute?
Answers
Answer:
102 steps/1minute
In seconds it would be 102/60 which can be reduced to 17/10, or 1.7
PLEASE, I NEED HELP NOW!!!!!!
Find the approximate area of a circle that has a radius of 14 feet. Round your answer to the nearest hundredth.
A = ___ ft2
Don't forget to round!
Answers
Answer:
1934.2
Step-by-step explanation:
3.14*14=43.98 squared=1934.2
Answer:
615.75
Step-by-step explanation:
Use A = πr², letting r = 14, so that:
A = π(14)²
≈ 615.75 ft²
Rounding to the nearest hundredth would make the answer 618
Find the value of y .
(Either leave your answer as a fraction, or round to the nearest hundredth.)
Answers
Answer:
y=5/3 or y=1.67
Step-by-step explanation:
In this problem we have that
(5x+8)=21x ----> given problem
21x-5x=8
16x=8
x=0.5
In the same way
Remember that the slope of a line is a constant
so
20y-2=17y+3
Solve for y
20y-17y=3+2
3y=5
y=5/3 or y=1.67
If ELF is congruent to GJH, EF=12 and LF=7.8 find IJ. Round answer to the hundredths place. A. 4.78 B 5.62 C 4.98 D 5.07
Answers
EF = 12
KF = 6
LF = 7.8
LK = sqrt(7.8^2-6^2) = 4.98
IJ = LK
Answer with explanation:
→ΔELF ≅ Δ GHJ-------[Given]
→EF=GH----------[CPCT]
→GJ=FL-------[CPCT]
Let , O be the center of the circle.
→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]
→GI=IH------[Reason same as Above]
→→EK=GI, KF=HI
→→OJ=OL
→OK=KI
→OJ-OK=OL-KI
→LK=IJ
⇒→Δ LKF ≅ Δ JIG-------[SAS]
Now, In Δ LKF, By Pythagorean Theorem
→(LF)²=(LK)²+(KF)²
→(7.8)²=(LK)²+(6)²
→60.84-36=(LK)²
→24.84=(LK)²
LK=4.98
→→LK=IJ=4.98
Option C:→4.98
PLZ HELP, WILL GIVE BRAINLIEST
What is the value of x?
A.
73°
B.
45°
C.
35°
D.
25°
Answers
Answer:
x = 35
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 base angles from 180 for angle at vertex
vertex = 180° - (73 + 51)° = 180° - 124° = 56°
The vertex angle is composed of x and 21, so
x + 21 = 56 ( subtract 21 from both sides )
x = 35