Given:
The quadratic equation is:
[tex]x^2+x-30=0[/tex]
To find:
The solutions of the given equation.
Solution:
We have,
[tex]x^2+x-30=0[/tex]
Splitting the middle term, we get
[tex]x^2+6x-5x-30=0[/tex]
[tex]x(x+6)-5(x+6)=0[/tex]
[tex](x+6)(x-5)=0[/tex]
Using zero product property, we get
[tex]x+6=0[/tex] and [tex]x-5=0[/tex]
[tex]x=-6[/tex] and [tex]x=5[/tex]
Therefore, the solutions of the given quadratic equation are -6 and 5.
Find the inverse function.
x - 3
f(x) =
+ 2
5
f-1(x) = [ ? ]x + [ ]
Evaluate the expression and identify any domain restrictions. Use order of operation.
Answer:
Its in the picture so you can understand it better.
Step-by-step explanation:
A 2-gallon jug of juice costs $10.88. What is the price per cup?
Answer:
it's ¢.34
Step-by-step explanation:
a gallon has 16 cups
since there are two gallons that's 32
the price of the two gallons divided my 32 is how much each cup would be so 10.88/32 would be ¢.34
fill in the missing numbers to complete the pattern ___, 2.6, 3.1, 3.6,___, 4.6
2.1 and 4.1
.................
Answer:
2.1 should be the first one, and 4.1 should be the next one
vertex of the graph of x^2 + 8x + 12=0
Answer:
Step-by-step explanation:
Hope this helps u!!
PLEASE HELP!!! Which number line shows the solution 2/3x-5>3
Answer:
last option is the answer; all values greater than 12
Step-by-step explanation:
2/3x - 5 > 3
2/3x > 8
x > 24/2
x > 12
Answer:
the last one
Step-by-step explanation:
I took the test
Pls pls help me !!!!
PLEASE HELP!!!!!! In which week was the rainfall in Portland the highest and how much fell?
weekly rainfall bar graph
Week 3, 800 cm
Week 4, 1400 cm
Week 4, 1200 cm
Week 3 900 cm
Answer:
Week 4, 1400
Brainliest plz
Step-by-step explanation:
Answer:
Week 3 and 900 cm
Step-by-step explanation:
Brainliest Please!
Please help me with this i didn’t get the answer
[Easy Points] Kanna Kamui sees 3 snowmen. Then he sees 2 more. How many snowmen did Kanna see in all?
Answer:
the correct answer is 5 snowmen
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
12, 6, 3, ...
Answer:
The sequence is geometric
The common ratio is 0.5
Step-by-step explanation:
In the arithmetic sequence, there is a common difference between each two consecutive terms
In the geometric sequence, there is a common ratio between each two consecutive terms
Let us check the given sequence
∵ The first 3 terms are 12, 6, 3
∵ 6 - 12 = -6
∵ 3 - 6 = -3
∵ There is no common difference between the consecutive terms
∴ The sequence is not an arithmetic sequence
∵ 6 ÷ 12 = 0.5
∵ 3 ÷ 6 = 0.5
∴ There is a common ratio between each two consecutive terms
∴ The sequence is a geometric sequence
∴ The common ratio is 0.5
A marine biologist compared two large pools that could be used for a new dolphin training arena. Pool A held 2 x 10¹⁰ gallons, and pool B held 2 x 10⁸ gallons. How many times more gallons will the larger pool hold than the smaller pool?
O4
O 20
O 100
O 200
Answer:
20
Step-by-step explanation:
2 x 10 = 20
divided by 4 = 5
The larger pool will hold is 100 times more gallons than the smaller pool
What is capacity and measurement?From the question, we are to determine how many times more gallons the larger pool holds than the smaller pool
From the given information,
Capacity of the larger pool = 2 × 10¹⁰ gallons
Capacity of the smaller pool = 2 × 10⁸ gallons
To determine how many times more gallons the larger pool holds more than the smaller pool, we will simply divide the capacity of the larger pool by the capacity of the smaller pool
That is,
[tex]\frac{2 \times 10^{10} }{2 \times 10^{8}}[/tex]
= 10²
= 100
Hence, the larger pool will hold is 100 times more gallons than the smaller pool.
Learn more on Capacity here: https://brainly.com/question/7598008
#SPJ2
Find the values of x and y. Write your answers in simplest form.
Answer:
To find X you'll need this formula Tan 30, and this one to find y cos 30.
Step-by-step explanation:
tan 30 = 9 / x.
tan 30*x = 9
x = 9 / tan 30
x = 15.58
To find y, the value of X will be needed, which is 15.5 that we just found.
Cos= A/H
Cos 30 = 15.58/ y
Cos 30 * y = 15.58
y = 15.58/ cos 20
y = 17.99
PLEASE HELP ASAP I WILL MARK BRANLIST!!!!!!
Of 10 test scores, six are less than or equal to 82 What is the percentile rank of a test score of 82?
The percentile rank of 82 is…
Answer:
60% of the test scores are less than or equal to 82
Step-by-step explanation:
I need help. I will give brainlist if right answer.
Fill in the table using this function rule.
y=2+3x
Answer:
I need to see the table bro
The three inside angles (A,B and C) of a right-angled triangle are in the ratio 7:18:11. Th smallest angle is 35. Work out angles A, B and C
Answer:
<A = 35degrees
<B =90degrees
<C = 55degrees
Step-by-step explanation:
Given the ratios of a triangle as 7:18:11
Total ratio = 7+18+11
Total ratio = 36
Since the smallest angle is 35degrees, hence <A = 35degrees
Get angle B;
<B = 18/36 * 180 (sum of angle in a triangle is 180degrees)
<B = 1/2 * 180
<B = 90degrees
Get angle C;
<C = 11/36 * 180
<C = 11 * 5
<C = 55degrees
Hence the value of A, B and C are 35, 90 and 55 degrees repectively
Find the area of a trapezoid with base 1 is 10 cm, base 2 is 12 and the height is 8
Answer:
88 sq cm
Step-by-step explanation:
A=(b1+b2) x H divided by 2
nadia will survey 50 students in her town to find out what their favorite summertime activity is which group would likeyl give the best representation for her survey
Answer:
B. 50 students in her school
Step-by-step explanation:
Every other answer is at a seperate place designed to help someone in a specific field, besides the school.
Find x and y, when AB and MN are similar
Please I need your help quickly
Answer:
x is 5 but sorry I can't Find the value of y
Answer:
y=3
x=5
Step-by-step explanation:
it's similar so CN =NB
that means y=3
so MN=AB
x=5
SHOW YOUR WORK. The volume of the cylinder is 235.6 ft cubed. Find the height.
Answer:
Answer: 3 feet
Step-by-step explanation:
Here's the complete question:
The volume of the cylinder is 235.6 cubic feet the radius is 5ft. Find the height.
Note that Volume of a cylinder = πr²h
where Volume = 235.6 feet³
Radius = 5 feet
Height = Unknown
Then, we put the values back into the question and this will be:
V = πr²h
235.6 = 3.14 × 5² × h
235.6 = 3.14 × 25 × h
235.6 = 78.5 × h
h = 235.6 / 78.5
h = 3 feet
The height is 3 feet
Step-by-step explanation:
In a box containing 20 cans, 12 of the cans contain vegetables. In the box, 5 of the cans are dented, with 2 of the dented cans containing
vegetables
What is the probability that a randomly selected can in the box is dented or contains vegetables?
OA 65%
OB. 75%
OC. 95%
OD 85%
Answer: B.) 75%
Step-by-step explanation:
12 cans contain veggies and 5 cans are dented, since two of the dented cans contain veggies don't count those two. This means you'll add 12 and 3 which equals 15. 15 out of 20 is an example of three fourths or 75%.
Luka buys 210 coat hangers.
The coat hangers are sold in boxes.
There are 35 coat hangers in each boz.
Each box of coat hangers costs £19.50
Work out the total cost of the boxes of tiles Luka buys.
Answer:
$117
Step-by-step explanation:
[tex]210 \div 35 = 6[/tex]
[tex]19.50 \times 6 = 117[/tex]
Factorise fully 12x^3-4x^2
Answer:
4x² (3x - 1)
Step-by-step explanation:
12x³ - 4x²
4x² (3x - 1)
The Movie Haven is planning to order new medium-size popcorn containers. It has a choice of four different containers. It costs the company $0.02 per cubic inch of popcorn to fill a container. The company does not want the new container to cost more than $3.00 to fill. Which container should the company use? Use 3.14 for Pi.
Container A
A cylinder with height 5 inches and diameter 7 inches.
Container B
A cylinder with height 6 inches and radius 3 inches.
Container C
A cylinder with height 12 inches and B = 11.14 inches squared.
Container D
A cylinder with height 10 inches and diameter 6 inches.
container A
container B
container C
container D
Answer:
only option less than $3 is (C)
Step-by-step explanation:
Volume(cylinder) = πr²h or Bh
I used the guess-and-check method and got the following:
A) 3.85
B) 3.39
C) 2.67
D) 5.65
I need it today please
Answer:
$207.66
Step-by-step explanation:
30% off is the same as saying there is 70% not off, and 70% is the same as 0.70
0.70*349= 244.30
15% off is the same as saying 85% is not off, and
85% is the same as 0.85
0.85*244.30=207.655
because it's money, you round to 2nd decimal place
$207.66
hope this was helpful :)
Are the dotted lines in the shape parallel, perpendicular or intersecting?
Answer:
Parallel
Step-by-step explanation:
The dotted lines are parallel because they have the same gradient to each other, this means the two dotted lines will never touch each other.
Have a great day <3
Please help!
A rectangular tabletop has an area of.......
[tex]t^2+2t-99[/tex]
What are the possible dimensions of the tabletop? Use factoring.
The order doesn't matter, so you could say "t+11 and t-9" to mean the same thing.
=======================================================
Explanation:
Think of two numbers that multiply to -99, but also add to 2. In other words, find two factors of -99 which add to 2. We'll use trial and error.
Here are all the ways to multiply to -99 using integers only:
1 and -993 and -339 and -1111 and -933 and -399 and -1Add up each factor pair to see which sum is equal to 2.
1 + (-99) = -983 + (-33) = -309 + (-11) = -211 + (-9) = 2 is what we want33 + (-3) = 3099 + (-1) = 98We can see that 11 and -9 are the two numbers we're after, so therefore, t^2+2t-99 factors to (t-9)(t+11). The order doesn't matter with the factor multiplication.
As a more efficient alternative method, you can use the quadratic formula to solve t^2+2t-99 = 0 to end up with t = 9 and t = -11. That would lead to the two equations t-9 = 0 and t+11 = 0. Applying the zero product property then gets us (t-9)(t+11) = 0.
To help show that (t-9)(t+11) becomes t^2+2t-99, you can use the FOIL rule to expand that factorization out. This is one way to verify the answer.
What is the surface area of the prism?
1.
5 in.
4 in.
5 in
Answer:
140
Step-by-step explanation:
HIYAAAAAAA I 'OPE YOUR ALL WELL THE PROBLEM IS THAT I STUGGLE WITH MATHS...
Trust me, you're not the only one who's bad at math. '-'
I need help with geometry
Statement 1 and statement 3 contradict
======================================================
Explanation:
We'll start with statement 1 and try to build to statement 3, and you'll find that a contradiction happens.
If angle 1 and angle 2 are supplementary, then that must mean [tex]m \angle 1 + m \angle 2 = 180[/tex] because the angles can be combined to form a straight angle.
Add the measure of angle 3 to both sides
[tex]m \angle 1 + m \angle 2 = 180\\\\m \angle 1 + m \angle 2+m\angle 3 = 180+m\angle 3[/tex]
The left side matches with the left side in statement 3, but the right side is a bit off. That [tex]m\angle 3[/tex] term needs to be zero, so that the right side boils down to simply 180. However, statement 3 specifically mentions that angle 3 is nonzero. So angle 3 is some positive value.
That's why choice C is the answer.
------------------
Here's an example:
Let's say angles 1 and 2 are 50 and 130 degrees. The order doesn't really matter, but I'll make angle 1 to be the smaller angle.
This means,
[tex]m \angle 1 + m \angle 2 = 180\\\\50 + 130 = 180\\\\[/tex]
So we've made statement 1 to be true. The angles 50 and 130 are indeed supplementary.
Now let's add some nonzero value to both sides. This will represent the measure of angle 3. If we add say 10 degrees to both sides, then,
[tex]50 + 130 = 180\\\\50 + 130+10 = 180+10\\\\50 + 130+10 = 190\\\\m\angle 1 + m\angle 2 + m\angle 3 = 190\\\\[/tex]
we don't get 180 like we want in the equation of statement 3. This is where the contradiction happens, more or less. One right side is 180, the other right side is 190. The 190 will change if you use some other value for angle 3, but hopefully you can see that it's impossible to add up angles 1 through 3 to get 180. It's only possible if angle 3 were zero degrees.
We can think of it like angles 1 and 2 hog up all the oxygen, and use up 180 points of it, leaving no air for angle 3 to breathe so that's why angle 3 must be 0. Furthermore, it means that a triangle is not possible if exactly two angles are supplementary.
----------------------
Extra info:
Statements 1 and 2 can coexist just fine without any contradictions happening. If angle 1 is 110 degrees, then that makes angle 2 to be 70 degrees (110+70 = 180). That rules out choice A.Statements 2 and 3 are just fine as well, for similar reasoning as above. We can plug in 110 for angle 1, then subtract that from 180 to get 180-110 = 70. Then from here, just ensure that angles 2 and 3 add to 70. So there are infinitely many ways to do this. Choice B can be ruled out.Choice D is ruled out because we found choice C to be the answer, ie the contradicting two statements.Answer:
C) l and lll
Step-by-step explanation:
m∠1+∠2=180
m∠1+m∠2+m∠3=180
180+m∠3=180
m∠3=0 but m∠3=∦0
-----------------------------------
hope it helps...
have a great day!!