Answer:
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is [tex]4.[/tex]
2 - What is the highest degree of [tex]x[/tex] that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is 1, since [tex]x[/tex] is not in every term.
3 - Multiplying the results above,
The GCF is 4.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})[/tex]
3) Simplify each term in parentheses.
[tex]4(3{x}^{3}-15{x}^{2}+x-5)[/tex]
4) Factor out common terms in the first two terms, then in the last two terms.
[tex]4(3{x}^{2}(x-5)+(x-5))[/tex]
5) Factor out the common term [tex]x-5[/tex].
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Nina and Jo both ran a 13 km race.
Nina took 2 hour 10 minutes to run the whole race.
Jo started the race 7 minutes later than Nina but caught up when they had both travelled 11 km.
If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
We will see that Jo's speed, rounded to 2 digit places, is:
S = 6.42 km/h
How to get Jo's speed?
Remember that:
speed = distance/time.
Nina takes 2 hours and 10 minutes to finish the race, first, let's write the time in hours:
1 hour = 60 min.
Then:
10 min = (10/60) hours = 0.167 hours.
So we can write the time as:
2.167 hours.
And the distance is 13km, so her speed is:
S = 13km/2.167h = 6 km/h
The time that she takes to reach a distance of 11km (where she meets with Jo) is:
T = 11km/(6 km/h) = 1.83 hours.
Now, Jo starts 7 minutes after Nina, then the time in which he travels the 11 km is:
1.83 hours - 7 minutes.
Where:
7 min = (7min/60 min) hours = 0.117h
Then the time is:
T= 1.83h - 0.117h = 1.713 hours.
So he travels 11km in 1.713 hours, then his speed is:
S = 11km/ 1.713 hours = 6.42 km/h
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Please Help I Don't Understand!
Answer:
3/4
Step-by-step explanation:
Scale factor is the ratio between two different triangles. They can be scaled if they are similar triangles, which they are (in this case). Since we know that these two triangles are similar, we want to match all the sides up in a way where they all have the same ratio.
NK=3 and AH = 4, so NK/AH = 3/4.
GK=6 and LH = 8, so GK/LH = 6/8 = 3/4.
GN = 15 and LA = 20, so GN/LA = 15/20 = 3/4.
We found the matching ratios, so the answer is 3/4.
HELP ASAPPPP 10 POINTS
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Answer: COSINE
Step-by-step explanation:
I PROMISE
Answer:
See below
Step-by-step explanation:
For a right triangle, with the information given, tangent function is most appropo
tan 41 = 4/x re-arrange to
x = 4 / tan(41) then x = 4.60
Part A
Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct? {Box}
Part B
Explain why or why not.
I NEED THE ANSWER ASAP pls
Answer:
Jan is not correct
Step-by-step explanation:
Rhombus and parallelogram both have their opposite angles to be equal and the opposite sides to be parallel but Rhombus has all its sides to be equal like the square while the parallelogram has only the opposite sides to be equal like the rectangle
Move point C so that ∠BAC and ∠CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements for this case.
The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.
What are supplementary angles?Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;
adjacent non-adjacent. Adjacent supplementary anglesAdjacent supplementary are angles with a common vertex and arm.
Non-adjacent supplementary anglesNon- adjacent supplementary angles are angles without a common vertex or arm.
∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.
They add up to 180°.
∠ BAC = 110° and ∠CAD = 70°
Hence, the angles could be 110° and 70°.
Note, this is an overview as the question is not complete.
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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.
Step-by-step explanation: Edmentum Answer
Which expression gives the distance between the points
(-3, 4) and (6, -2)?
O A. (-3-4)²+(6+2)²
O B. (-3-6) +(4+2)²
O C. (-3-6)²+(4+2)²
O D. (-3-4)²+(6+2)²
The expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
How to determine the expression?The points are given as:
(-3, 4) and (6, -2)
The distance between two points is calculated using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
This gives
[tex]d = \sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
Hence, the expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
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Function k is a transformation of the parent exponential function f. what are the domain and range of function k? k(x)= 2^x
Answer:
Domain: All real numbersRange: All real numbers greater than 0Assessment
Read, analyze, then solve each problem. Answer each question.
A. A bowl of mango jelly was poured into a 14 cm x 8 cm x 3
cm rectangular container. If the mango jelly completely filled
the container, how much mango jelly was there?
1. What is asked in the problem? __________________________
2. Show your solutions. _________________________________
3. State the final answer. ________________________________
B. Ana is cleaning a box which is 6 dm long, 4 dm wide and 15
dm tall. What is the volume of the box?
4. What is asked in the problem? __________________________
5. What are given? _____________________________________
6. State the final answer. ________________________________
C. Wenalyn baked a cassava cake which measures 18 cm x 10
cm x 4 cm. She wants to share the cake with her two
classmates so she cuts it into three parts all of the same
sizes. How much cassava cake will each of her classmates
receive?
7. Show your solutions or illustration.
8. What is the final answer? _____________________________
D. A ream of bond paper is 28 cm long, 22 cm wide and 4 cm
thick. It contains 500 sheets. If 250 sheets were removed
from the ream of bond paper, what is the volume of the
remaining sheets?
9. Write the equation. __________________________________
10.What is the final answer? ___________________________
The formula for the volume of a rectangular prism is: length x width x height
Volume of the mango jelly : 14 x 8 x 3 = 336 cm³
Volume of the cleaning box: 6 x 4 x 15 = 360 dm³
Volume of the cake each classmate would get = (18 x 10 x 4) / 3 = 240 cm³
Volume of the remaining ream of paper : (28 x 4 x 22) / 250 = 9.9 cm³
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Help me please!!!!!!!!
Answer:
the third option
Step-by-step explanation:
because the numbers down there are the coefficients of the top equations
if a= 2x-3 and b= 2x+5
determine the product of a and b by using formulae. if x=2, ab= what?
help pleasee would appreciate a lot
Answer:
a= 2x-3 b= 2x+5
ab= (2x-3)(2x+5)
= 2x*2x+ 2x*5- 3*2x- 3*5
= 4x+ 10x- 6x- 15
= 14x- 6x- 15
= 8x -15
x= 2
= 8(2)- 15
= 16-15
= 1
How to find the surface area of a hexagon?
Answer:
adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.
Step-by-step explanation:
Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B. ∠TRF and ∠NRLC. ∠LRE and ∠FRAStep-by-step explanation:
→ The lines TN and FL intersect each other
at the point R forming the opposite angles ∠TRF and ∠NRL
then
∠TRF and ∠NRL are verticals angles.
………………………………………………………………………
→ The lines LF and AE intersect each other
at the point R forming the opposite angles ∠LRE and ∠FRA
then
∠LRE and ∠FRA are verticals angles.
Which of the following statements is true concerning ABC below?
B
11
11
A
OA. ZB is the smallest angle.
B. ZA is the largest angle.
OC. ZA is the smallest angle.
D. ZB is the largest angle.
14
C
Angle B is the largest angle. , Option D is the correct answer.
What is an Isosceles Triangle ?A triangle that has two sides equal is called an Isosceles Triangle.
It is given in the question a triangle ABC
With BA =BC
therefore angle A is equal to angle C
In a triangle the angle opposite to the longest side is the biggest angle
Therefore angle B is the largest angle.
Option D is the correct answer.
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13) Greenhouse gases are contributors to climate change as they absorb outgoing solar radiation and convert it to thermal energy. The main contributors to the
warming are carbon dioxide, methane, dinitrogen monoxide, and F-gases. The sources of these gases are shown in the pie chart here. What questions are relevan
these gases and their impacts on the climate change over the past 100 years? Select ALL that apply.
A) Does an increase in fossil fuel combustion create a local weather change?
B) Can a legislation that reduces the F-gases help prevent a global climate change?
C) Can reforestation of trees reduce the amount of carbon dioxide that is present in the atmosphere?
D) Can an increase in meat production occur without increasing methane and nitrogen from fertilizers?
E) Can a reduced reliance on fossil fuels decrease the atmospheric carbon dioxide and prevent rising global temperatures?
Answer:
e)as we know in this current century many modern country is polluting air pollution that may lead to impact our health
What is the perimeter of the following shape? (use an approximate value) pie = 3.14
===========================================================
Explanation:
A full circle of radius r = 14 cm has a circumference of...
C = 2pi*r
C = 2*3.14*14
C = 87.92
This is the approximate distance around the circle, aka the perimeter.
Half of this is 87.92/2 = 43.96 which is the curved distance of this semicircle.
The straight line portion is 14+14 = 28 cm long.
The total perimeter of the semicircle shown is 43.96+28 = 71.96 cm
Factor 6x¹ − 5x² + 12x² − 10 by grouping. What is the resulting expression?
(6x + 5)(x²-2)
(6x - 5)(x²+2)
(6x² + 5)(x-2)
(6x²-5)(x+2)
Answer:
[tex](6x-5)(x^2+2)[/tex]
Step-by-step explanation:
[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]
wright the follwing in decimlal form:3/11
Answer:
3/11 in decimal form is 0.272727272727....
Step-by-step explanation:
Yw ! :)
1. What is the slope of a line that is parallel to the line represented by the equation y=-2/5x + 4/5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that is parallel to the line [tex]\star~\mathrm{y=-\cfrac{2}{5}x+\cfrac{4}{5}}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Parallel lines have the same slope.So let's first determine the slope of the first line, and then let's find the slope of the line that's parallel to it.
[tex]\circ\!\!\!\star\mathcal{HINT:}[/tex]
The slope is the coefficient of x.So the slope is
[tex]\star~\mathrm{-\cfrac{2}{5}}[/tex].
Can you guess the slope of the line that is parallel to the first line?
That's right! The slope is...
[tex]\star~\mathrm{-\cfrac{2}{5}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
can someone please hepl me on tis
Answer:
Answer is in pictures
Step-by-step explanation:
36=6x6 90=9x10
256+7=263 104=98+6-2
678=678 81+9=90
Question 5
The price of an apple is $1.25. If you get 20% discount, how much do you have to
pay?
Answer:
you will only pay one dollar I did this question before, and it was easy Please mark me brainiest please
Step-by-step explanation:
If ln=12x+16 what is the length is ln units
In the past week, Joe has recorded the number of tickets that a movie theater has sold during each day from Monday to Saturday. This information was shown through the following Bar Graph.
How does the Bar Graph misrepresent the data?
A. The scale along the vertical axis is divided into unequal intervals.
B. The categories along the horizontal axis are missing one of the days.
C. The widths of the bars are not equal.
D. The heights of the bars representing Monday and Thursday are not same.
Based on the information shown through the bar graph, a misrepresentation of the data is that: B. the categories along the horizontal axis are missing one of the days.
What is a bar graph?A bar graph can be defined as a type of chart that is used for the graphical represent of data (information), especially through rectangular bars or vertical columns.
Based on the information shown through the bar graph in the image attached below, we can logically deduce that a misrepresentation of the data is that the categories along the horizontal axis are missing one of the days (Friday).
In conclusion, this bar graph misrepresented the data because Friday is missing from the categories along the horizontal axis.
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Find the term that must be added to the equation x² + 6x = 1 to make it into a
perfect square.
Express the trig ratios as fractions in simplest terms.
(Image above)
Help please
The value of the angle P and Q are equal which is equal to 36.86°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From Δ it is obtained that;
[tex]\rm cos P = \frac{B}H} \\\\ \rm cos P = \frac{16}{20} \\\\ P=cos^{-1}\frac{16}{20} \\\\ P= 36.86 ^0[/tex]
[tex]\rm sin \ Q = \frac{12}{20} \\\\ Q= sin^{-1}(0.6) \\\\ Q= 36.86^0[/tex]
sin P= sin Q
Hence, the value of the angle P and Q are equal which is equal to 36.86°.
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Please help!! So confused
Answer:
A.2x^2 + 12x
Step-by-step explanation:
Here,
f(x) = 1/2 x^2 + 3x
Now,
4.f(x) = 4(1/2 x^2 + 3x) = 4/2 x^2 + 12x = 2x^2 + 12x
i need help with this question can someone answer fast please
Answer:
Below in bold.
Step-by-step explanation:
Petra uses the expression distance = time * speed
which is (4 + h)55 where 4 + h = total time for the 2 days.
Sierra uses the same expression but for each individual day and adds them:
4*55 + 55h
= 220 + 55h.
First two two terms of the given number sequence 3n + 1 are...
Answer:
the sequence begins as {4, 7, ... }
Step-by-step explanation:
a(n) = 3n + 1
The first term is a(1) = 3(1) + 1 = 4, and
the second term is a(s) = 3(2) + 1 = 7
So the sequence begins as {4, 7, ... }
Cual es la regla de la sucesion de 1,4,7,10,13,16,19,
Given, a = 1
common difference = 3
Eighth term = a+(n-1)d = 1+(8-1)3
= 1 + 21 = 22
Hope this helps :)
A whole year level of 164 students is to be divided into 18 groups. By rounding
both numbers to the nearest 10, approximate the number of students in each
group.
Answer:
10
Step-by-step explanation:
no. of students in each group=164/18=9.111111...=10 (nearest 10)
Answer:
8
Step-by-step explanation:
When rounding to the nearest 10:
If the units are 0, 1, 2, 3 or 4 → round downIf the units are 5, 6, 7, 8 or 9 → round upTherefore:
164 rounded to the nearest 10 = 160
18 rounded to the nearest 10 = 20
To approximate the number of students in each year group, divide the rounded number of students by the rounded number of groups:
⇒ 160 ÷ 20 = 8