factorise: 6x^2 – 5 x – 6
Answers
Step-by-step explanation:
I think it will help you.
Look at the example
Let's use mid-term splitation
[tex]\\ \rm\rightarrowtail 6x^2-5x-6[/tex]
[tex]\\ \rm\rightarrowtail 6x^2+4x-9x-6[/tex]
[tex]\\ \rm\rightarrowtail 2x(3x+2)-3(3x+2)[/tex]
[tex]\\ \rm\rightarrowtail (2x-3)(3x+2)[/tex]
Related Questions
Rebecca has $128 to spend. She
spends $78 on a running shoes.
Tank tops cost $12.50 each. Write and
solve an inequality to find how many
tank tops she can buy.
Answers
Answer:
12.5x =10x+10
12.50x=x10+10
subtract 10x from both sides
2.5x=10
divide by 2.5
x=4
Question 3 (1 point)
Which is the explicit rule for the geometric sequence?
10, -30, 90, -270, ...
Answers
Answer:
The rule for this question should be an=10*(-3)^(n-1)
Step-by-step explanation:
Because 10, -30, 90, and -270 divide (for example -30/10, 90/-30 and -270/90 which means the ratio equals -3) To find the ratio, you must divide by its previous term.
Then, the equation for the ratio would be a1 (first term in the sequence) multiplied by the ratio, then to the power of the number subtracted by 1. an=a1*r^(n-1) This is the formula to find the nth term of a geometric sequence.
Hope this helped!
The point I(–4, –1) is rotated 90 counter-clockwise about the origin. What is the image of I?
a. I(4, –1)
b. I(–1, –4)
c. I(1, –4)
d. I(4, 1)
Answers
Answer:
I(1, -4)
Step-by-step explanation:
(-4, -1) is in Quadrant 3 where x and y are negative
when it's rotated 90 ccw it will become in Quadrant 4 where x is positive and y is negative
and also the values of x and y switches
so the answer will be I(1, -4)
A skateboarding ramp is in the shape of a triangular prism, If the entire ramp is to be painted, and a can on spray paint covers 1,000 sq^2, how many cans will be needed?
Answers
Step-by-step explanation:
I don't have that much time to wait for all the clarifications, so I will make some assumptions based on what I saw in your comments so far.
please change the numbers in the calculation (and the recalculate) as necessary :
we are dealing with a triangular prism that acts as a ramp.
triangular means that the sides are in the shape of triangles.
but the front, the back and also the bottom areas are rectangles.
the area of a rectangle is length×width.
the area of a triangle is baseline×height/2
since it is supposed to be a ramp, I assume the triangle shape of the sides is right-angled. that means the back side of the ramp is standing straight up (90° angle with the bottom).
the height of the ramp is the height of the triangle side areas, and is simply the left leg of the triangle (again, going straight up with a 90° angle to the baseline).
I understand the height is 14 in.
I assume the front length is 50 in. and the depth of the ramp (the length of the baseline of the triangular sides) is 48 in.
now we get the length of the inclined "front" leg of the side triangles via Pythagoras
c² = a² + b²
with c being the side opposite of the 90° angle (exactly the inclined leg we are looking for) :
c² = 14² + 48² = 196 + 2304 = 2500
c = 50 in
that means our front rectangle of the ramp is actually a square of 50in × 50in.
the entire ramp is to be painted. that means really every side, including the bottom.
so, the whole surface area is the sum of the individual areas.
we have
1 (inclined) front area 50in × 50in
1 back side (straight up) 50in × 14in
1 bottom area 50in × 48in
2 side triangles 48in × 14in / 2 = 48in × 14in
so, we get as total area
50×50 = 2500 in²
50×14 = 700 in²
50×48 = 2400 in²
48×14 = 672 in²
---------------------------
6272 in²
now, one can of spray paint can cover 2000 in².
that means we need
6272 / 2000 = 3.136 cans.
and since we cannot buy fractions of cans, we need to round up.
we need 4 cans to do the painting job.
Can someone please help with this? I'll give brainliest. I don't understand this... or the explanation it gives... the page before was just teaching how to solve simple problems to put on graphs what's an asymptote?
Answers
Step-by-step explanation:
Hello!
I'd love to help you learn.
I see the formula attached is [tex]4*(\frac{1}{2})^{x} =-2^{x}-1\\[/tex]
This problem is explaining you to graph, since algebraically it's a little more harder to try and find the solution.
Since they're both equal to each other, we can assign a variable like y, so we can make them into two individual lines.
You can use your scientific calculator to graph lines like this, or otherwise there are online sources (Desmos helps alot!) which can graph two equations as so.
Now that we have the corresponding system of equations, we can graph both.
[tex]y=4*(\frac{1}{2})^x\\ y=-2^x-1[/tex]
Let's graph them on Desmos on the same plane. The answers are attached. Red is the first equation, blue is the second.
What determines the solutions of a system of equations?
-No solution: the two lines will never intersect/does not intersect ever, which means that there are no set point where it satisfies both equations.
-One solution: the two lines intersect once and only once, meaning that there is that one set point where the x and y values both satisfy both equations.
-Multiple solutions: the two lines will intersect each other multiple times, meaning there are multiple set points where the x and y values satisfy both equations. You usually will not have to worry about these problem sets.
-Infinite solutions: the two lines are both the same line, which means every x and y value will satisfy both equations.
Looking at the solution attached, we can see that there are no places where a system of equations intersect, therefore ruling it that they have no solution.
And to answer your last question, an asymptote is a imaginary line in which a equation can approach closely and closely, but will never touch that imaginary line. Think of a line at y=[tex]\frac{1}{x}[/tex]. When you graph it, you can see that the two lines never ever EVER intersect the y-axis, or x=0; giving that x=0 as a vertical asymptote.
If a sequence is 0,1,1,2,3,5 what is the 11th number in the sequence?
Answers
Answer:
55
Step-by-step explanation:
This is the Fibonacci sequence! Filling out the rest of the numbers, 55 is the 11th number in this sequence.
Sammy then $200 as a department store she bought three rings for $21 each and spend the rest on for equallypriced bracelets. How much did each bracelet cost?
Answers
Answer:
Step-by-step explanation:
3(21) + 4b = 200
63 + 4b = 200
4b = 200 - 63
4b = 137
b = 137/4
b = 34.25...so each bracelet (b) costs $ 34.25
Please help I will give brainliest.
Answers
2. 5
Hope this helps.
a small movie theater sells children's tickets for $4 each and adult tickets for $10 each for an animated movie. The theater sells a total of $338 in ticket sales.
(c) show that after multiplying both sides of the equation in (a) by 2, c=52 and a=18 is still a solution to this equation.
Equation: 4c+10a=388
Answers
Answer:
Proved below!
Step-by-step explanation:
Start by multiplying both sides by 2 (as said in the question):
[tex]\implies 4c + 10a = 388[/tex]
[tex]\implies 2(4c + 10a) = 2(388)[/tex]
[tex]\implies 8c + 20a = 776[/tex]
Substitute the solution(s) in the equation:
[tex]\implies 8(52) + 20(18) = 776[/tex] (c = 52; a = 18)
[tex]\implies 416 + 360 = 776[/tex]
[tex]\implies \bold{776 = 776 \ \ \ (Proved)}[/tex]
Answer:
Let c = number of children's tickets sold
Let a = number of adults tickets sold
Given:
Cost of child ticket = $4Cost of adult ticket = $10Total ticket sales = $388⇒ 4c + 10a = 388
Multiply both sides of the equation by 2:
⇒ 2(4c + 10a) = 2 × 388
⇒ 8c + 20a = 776
If c = 52 and a = 18, substitute these values into the equation and solve:
⇒ 8(52) + 20(18)
⇒ 416 + 260
⇒ 776
As 776 = 776, this proves that c = 52 and a = 18 is a solution to this equation.
Find two positive consecutive
even integers such that the
square of the smaller integer
decreased by five times the
larger integer is 536.
Answers
Answer:
[tex]26[/tex] and [tex]28[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].
The square of the smaller integer would be [tex]x^{2}[/tex].
Five times the larger integer would be [tex]5\, (x + 2)[/tex].
Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].
The value of this expression should be equal to [tex]536[/tex]. In other words:
[tex]x^{2} - 5\, (x + 2) = 536[/tex].
Rewrite and simplify this quadratic equation:
[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].
[tex]a = 1[/tex].[tex]b = (-5)[/tex].[tex]c = (-546)[/tex]Apply the quadratic formula to find possible values of [tex]x[/tex]:
[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].
[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].
Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.
Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].
Solve for x please and round
Answers
Answer:
[tex]\displaystyle 74,4[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{67} = cot\:42 \hookrightarrow 67cot\:42 = x \hookrightarrow 74,411038494... = x \\ \\ 74,4 ≈ x[/tex]
OR
[tex]\displaystyle \frac{67}{x} = tan\:42 \hookrightarrow xtan\:42 = 67 \hookrightarrow \frac{67}{tan\:47} = x \hookrightarrow 74,411038494... = x \\ \\ 74,4 ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
What is the median of this data set? {12, 8, 9, 12, 10, 13, 8} Enter your answer in the box.
Answers
Answer:
the median is 10
Step-by-step explanation:
8, 8, 9, 10, 12, 12, 13
8, 9, 10, 12, 12
9, 10, 12
10
Answer:
10
Step-by-step explanation:
If claire does not make any payments, how much will she owe after ten years? $12,136.67 $3,481.24 $6,090.90 $3,232.74
Answers
The interest formulas will be used to find the amount Claire owes. If the amount has a single compounding per year, simple interest is used, otherwise, compound interest is used.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.More can be learned about interest at https://brainly.com/question/25781328
Answer:
a. $12,136.67
Step-by-step explanation:
Twenty-six cards with the letters from A to Z are face down. What is the probability that a vowel will be chosen?
Answers
Answer:
5/26
Step-by-step explanation:
There are 26 letters in the english alphabet then out of that 26 there are 5 vowels so the probability is 5/26
The diameter of a circle is 6 millimeters. What is the circle's circumference?
Use 3.14 for .
Answers
Answer:
18.84
Step-by-step explanation:
Answer:
18.8495559215
Step-by-step explanation:
In order to find circuference we use the formula
C= 2π(r)
c= circumference
r= radius
since they gave you the diameter, you first have to find the radius so you would divide the diameter by two since radius is half of a circle so 6 divided by 2 is 3. From here we would plug in 3 for "r" in the formula I wrote above. So C= 2π(3). then type this into a calculator to get the answer I wrote above. Then round as directed
A bottle of perfume is spherical with a diameter of 36 mm.
Calculate the capacity of the bottle, in mL.
Answers
24.4 mL
By converting mm to cm, we get
1 mm = 1/10 cm
18 mm = 18/10 cm
radius (r) = 1.8 cm
To find the volume,
Volume of sphere = 4/3πr3
= 4/3π(1.8)3
Volume = 24.4 cm3
To find the capacity,
1 cm3 = 1 mL
Capacity = 24.4 mL
Can some please explain and solve how to do these unit rate equations?
Answers
heyyo does anyone knows how to solve this equation and the answer as well??
Answers
Answer:
A
Step-by-step explanation:
tanΘ = [tex]\frac{\sqrt{3} }{3}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{3}[/tex] ) = [tex]\frac{\pi }{6}[/tex]
since tanΘ > 0 then Θ is in first / third quadrants
Θ = π + [tex]\frac{\pi }{6}[/tex] = [tex]\frac{7\pi }{6}[/tex]
solution is { [tex]\frac{\pi }{6}[/tex] , [tex]\frac{7\pi }{6}[/tex] } in the interval 0 < Θ < 2π
8. Estimate the product. Then find the
exact product.
(25+4) (52-5)
Х
Estimate:
Exact product:
Answers
Hey there!
ORIGINAL EQUATION:
(25 + 4)(52 - 5)
= (29)(47)
= 1,363
Original answer: 1,363
____________________
SOLVING FOR THE ESTIMATION EQUATION:
25 = 30
4 = 0
~~~~~~~~
52 = 50
5 = 10
(30 + 0)(50 - 10)
= 30(40)
= 1,200
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
You are painting the outside wall of a large building. The wall has a width of 60.11 meters, and a height of 79.88 meters. You need to estimate the total area of the wall, so you know how much paint to buy. Which number below is the best estimate?
A. 4,800 m2
B. 4,400 m2
C. 5,200 m2
D. 5,300 m2
Answers
Answer: A) 4,800 m2
60.11m x 79.88= 4801.5868
Answer:
A. 4,800 m²
Step-by-step explanation:
Given :
=> width of wall is 60.11 meters.
=> height of wall is 79.88 meters.
The area of the wall is = length × breadth
=> 60.11×79.88
=> 4,801.5868m²
Approx. 4,800
AB - CD + 2D x A x (AC - BD
also i know it says im old but im in middle school
b=4 a=3 c=6 d=2
Answers
12-12+4x3x(18-8)
12-12+4x3x10
12-12+120
12-132
=-120
If I have 30 blue balls and 10 red balls and 50 green balls How many balls to I have in all? 30 points.
Answers
Answer:
90 balls
Step-by-step explanation:
simply add them
Answer: 90 balls
Step-by-step explanation:
30 + 10 = 40
40 + 50 = 90.
In the diagram below,EF is parallel to BC. IF BC is the twice length of ED,BD=36 and EF=14, find the length of ED. Figure are not necessary drawn to scale. State your answer in simplest ratio form if necessary.
Answers
Answer: sqrt(182)
Step-by-step explanation:
Kevin has a deck of cards. There are 10diamonds, 5 spades, 12 clubs and 3 hearts.A card was chosen at random. What is the
probability of not choosing a diamond card?
Answers
Answer: 2/3.
Step-by-step explanation: When you add all the spades, hearts, clubs, and diamonds cards together, you get 30 in total. 1/3 of the 30 cards in total are diamonds, so the other 2/3 can be drawn as well. The probability of not choosing a diamond card is 2/3, since the remaining 1/3 is all diamonds.
Have a great day! :)
how does the number if possible outcomes of a single event help you determine the total number of possible outcomes of a compound event?
Answers
The possible outcomes of an event is the sample space
The product of the sample spaces of the single events determines the total number of possible outcomes of a compound event
How to determine the possible outcomes?Assume that the number of outcomes of n single events are:
[tex]n_1[/tex], [tex]n_2[/tex], [tex]n_3[/tex],........ [tex]n_n[/tex]
When these single events are combined, they form a compound event.
The number of outcomes of the compound event is the product of the number of outcomes of the single events.
i.e.
[tex]Outcomes = n_1 * n_2 * ......... n_n[/tex]
Hence, the product of the sample spaces of the single events determines the total number of possible outcomes of a compound event
Read more about outcomes at:
https://brainly.com/question/24756209
The leg lengths of a right triangle are 14 in and 26 in. What is the length of the missing side?
Answers
Answer:
29.5
Step-by-step explanation:
14sq + 26sq = 872
sq root of 872 is 29.5
The area of a rectangle is given by the expression, A = 4x2 + 9x + 2 where the width is x +2. Find an expression for the length of the rectangle. Show all steps.
Answers
Answer:
4x+1
Step-by-step explanation:
1) to find the required expression for the length:
length=area/width;
2) according to the formula above:
[tex]L=\frac{4x^2+9x+2}{x+2}=\frac{(x+2)(4x+1)}{x+2}=4x+1.[/tex]
find the value of x round to the nearest 10th
I will give brainliest
Answers
10.9
Step-by-step explanation:[tex]According\ to\ the\ question,\ we\ con\ spe\ that[/tex]
[tex]\sin{40}[/tex]° [tex]=\frac{7}{x}[/tex]
[tex]x=\frac{7}{\sin{40degrees}}\\ x\approx 10.9[/tex]
I hope this helps you
:)
The 40 and 50 degree angles are?
Answers
Answer:
40 degrees is acute, 50 is also acute and they both make up a right angle (90 degrees)
Step-by-step explanation:
how many square yards of carpet should stella order if her bedroom measures nine by twelve feet