What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12? (–6, 0), (2,0) (–2, –16), (0, –12) (–6, 0), (–2, –16), (2, 0) (0, –12), (–6, 0), (2, 0)
Answer:
(-6, 0) and (2, 0)
Step-by-step explanation:
To find the x-intercepts, we can factor the expression:
f(x) = x² + 4x - 12
2 factors of -12 that add up to 4 are 6 and -2
(x + 6)(x - 2)
Set each factor equal to 0 and solve for x:
x + 6 = 0
x = -6
x - 2 = 0
x = 2
So, the x intercepts are (-6, 0) and (2, 0)
Answer:
It's the first option, (-6, 0) (2, 0)
Step-by-step explanation:
100% on Edge
Solve the equation
—3x +1+ 10x = x +4
X=1/2
X=5/6
X=12
X=18
Answer:
x = 1/2
Step-by-step explanation:
-3x + 1 + 10x = x + 4
7x + 1 = x + 4
6x + 1 = 4
6x = 3
x = 3/6
x = 1/2
Answer:
It's (A) [tex]x\frac{1}{2}[/tex]
Step-by-step explanation:
Two cars leave the park at the same time. One travels north at a speed of 50 km/h for 2 hours. The second car travels west at a speed of 80 km/h for 2 hours. After the 2 hours, how far apart are the two cars? Be sure to draw a diagram illustrating this situation.
Step-by-step explanation:
This question requires the Pythagorean theorem.
Car A travels north 100km in two hours.
Car B travels west 160km in two hours.
Imagine a triangle the line going up is 100km
the line going left is 160km
the formula for the Pythagorean theorem is
a^2+b^2=c^2
100^2+160^2=c^2
10000+25600=c
35600=c
√35600=c
You can draw a diagram.
Which of the following explains why cos 60º = sin 30° using the unit circle?
5. In an A.P, the sum of three consecutive terms is 24. When 1 is subtracted to the first term, 2 to the
second, then the terms form a G.P. Find the terms of the A.P.
Answer:
Step-by-step explanation:
Let the three numbers be a-d, a, a+d being a series in AP.
The sum of the three numbers is 24 = a-d+ a+ a+d = 3a
Thus a = 8.
Now a-d-1, a-2, a+d form a GP. It means, the common ratios should be equal or the middle term should be the Geometric Mean of the first and third terms, or
(a-d-1)(a+d) = (a-2)^2 or
(8-d-1)(8+d) = (8-2)^2, or
(7-d)(8+d) = 36, or
56 -8d +7d -d^2 = 36, or
56 -8d +7d -d^2 - 36 = 0, or
d^2 +d -20 = 0
(d+5)(d-4) = 0
Thus d = -5 or 4
So the AP is 13,8,3 or 4,8,12
Check: 13,8,3 in AP becomes (13–1), (8–2), 3 = 12, 6, 3 which is a GP with r = (1/2)
4,8,12 in AP becomes (4–1), (8–2), 12 = 3, 6, 12 which is a GP with r =2
Am I right or wrong (don't answer the last one!)
Answer:
1) Distributive Property of Multiplication (The terms are distributed)
2) Addition property of equality (Adding 14 to both sides)
3) Simplifying (We simplified the expression)
4) Division property of equality (Dividing both sides by 6)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
- 14 + 6m = 10
Distributive Property of Multiplication
2 is distributed to -7 and 3m
- 14 + 14 + 6m = 10 + 14
Addition Property of Equality
Adding 14 to both sides.
6m = 24
Simplifying
Simplifying the equation.
[tex]\displaystyle \frac{6m}{6} =\frac{24}{6}[/tex]
Division Property of Equality
Dividing both sides by 6.
For any number y, ⌂y=2y3 . What is the value of ⌂2 + ⌂5 ? NEED HELP ASAP
Answer:
276
Step-by-step explanation:
∆y = 2y3
∆2 = 2(2)3 = 16
∆5 = 2(5)3 = 250
∆2 + ∆5 = 250 + 16 = 276
precalculus help! i'm having some trouble with my summer assignment. help would be very appreciated :)))
6.
[tex]y^2\sqrt[8]{8}[/tex]
Step-by-step explanation:
[tex]\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}[/tex]
Since there are eight y's in two groups we can take them out which turns into
[tex]y^2\sqrt[8]{8}[/tex]
:)
3.
Problem 3:
We are given the following complex number and I'm assuming we want to simplify it:
[tex]\dfrac{5+i}{6+i}[/tex]
Using the complex arithmetic rule (research about this if you're not familiar with it, it's very helpful):
[tex]=\dfrac{(5\times6+1)+(6-5)i}{6^2+1^2}[/tex]
[tex]=\dfrac{31+i}{37}[/tex]
Simplifying gives us:
[tex]=\dfrac{31}{37}+\dfrac{1}{37}i[/tex]
Problem 6:
You seem to have done this problem correctly
[tex]\sqrt[8]{8y^{16}}[/tex]
Expanding gives us:
[tex]=\sqrt[8]{y^{16}}\times\sqrt[8]{8}[/tex]
[tex]=y^2\sqrt[8]{8}[/tex]
This can't be simplified further as the 8th root of 8 gives us an irrational number
Let me know if you need any clarifications or extra help, thanks!
A solid shape is made from centimetre cubes.
Here are the plan, side elevation and
Centimetre cubes are added to
front elevation of the shape.
make this cuboid.
Plan Side elevation Front elevation
40
4 cm
3 cm
How many cubes are added?
Write your final answer as,... cubes are added.
Answer:
30 cubes are added
Step-by-step explanation:
The image of the solid shape is attached.
From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.
The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.
30 cubes are added
The number of cubes that are added is 30.
What is Cube?
A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.
From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.
The number of blocks needed to make the cuboid
= 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added
= 48 cubes - 18 cubes
= 30 cubes.
30 cubes are added.
Hence, The number of cubes that are added is 30.
To learn more about, cubes, visit;
https://brainly.com/question/107100
#SPJ13
Mabel is comparing the prices of two car rental companies. Company A charges $35 per day and an additional $15 as service charges. Company B charges $42 per day and an additional $10 as service charges. Part A: Write an equation to represent each company's total charges for renting a car for a certain number of days. For both equations (one for Company A and one for Company B), define the variable used. (4 points) Part B: Which company would charge less for renting a car for 6 days? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company A instead of Company B to rent a car for 10 days?
Answer:
Part A:
Equation for Company A:
x = Number of days renting a car
35x + 15
Equation for Company B:
x = Number of days renting a car
42x + 10
Part B:
Company A will charge $ 37 less than Company B
Part C:
Company A will charge $ 65 less than Company B
Step-by-step explanation:
Part A:
Equation for Company A:
x = Number of days renting a car
35x + 15
Equation for Company B:
x = Number of days renting a car
42x + 10
Part B:
Renting a car for 6 days
Company A:
35 * 6 + 15 = 210 + 15 = $ 225
Company B:
42 * 6 + 10 = 252 + 10 = $ 262
Company A will charge $ 37 less than Company B
Part C:
Renting a car for 10 days
Company A:
35 * 10 + 15 = 350 + 15 = $ 365
Company B:
42 * 10 + 10 = 420 + 10 = $ 430
Company A will charge $ 65 less than Company B
simplify (2) - (x2-x3+2x-1)
Answer:
-x + 3
Step-by-step explains:
Um... You can do it on a computer...
Hurry I WILL MARK YOU AS BRAINLIEST
Answer:
Third choice is correct
Step-by-step explanation:
-2x-y=-2
-y=2x-2
y=-2x+2
3x-y=-2
-y=-3x-2
y=3x+2
These two lines intersect at (0, 2)
Which function represents the following graph?
Answer:
y = ∛(x+3) + 3
Step-by-step explanation:
I plugged each equation into a graphing calculator.
express x^2-8x+20 in the form (x-a)^2+a where a is an integer
Answer:
(x-4)²+4
Step-by-step explanation:
Answer:
[tex](x-4)^2+4[/tex]
Step-by-step explanation:
[tex]x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4[/tex]
Rewrite the expression in the form k x z^n .
Answer:
(squareroot2^2) times 27 (1/2)
Step-by-step explanation:
Answer:3z^2/9
Step-by-step explanation:
Cape Beale Lighthouse, BC, is
on a cliff that is 51 m above sea
level. The lighthouse is there
to warn boats of the danger of
shallow waters and the
possibility of rocks close to the
shore. The safe distance for
boats from this cliff is 75 m. If
the lighthouse keeper is 10 m
above ground and observes a
boat at an angle of depression
of 50°, is the boat a safe
distance from the cliff? Justify
your conclusion.
Answer:
tan 50 = (51+10)/x where x is the distance of the boat
x = 51.2 m
Boat is in an unsafe area
Step-by-step explanation:
<3
In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has? x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16. 0.05 x + 0.25 y = 2.95. x + y = 2.95. 0.10 x + 0.25 y = 16. x + y = 16. 0.01 x + 0.25 y = 2.95.
Answer: x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16.
Step-by-step explanation:
You know that there are 16 coins in all, so x + y has to equal 16 (x being dimes and y being quarters) but you also know that whatever compilation of dimes and quarters is equal to $2.95.
Hope this helped you! Feel free to ask any further questions!
The system of equations which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to form equation?Suppose the number of dimes be x and the number of quarters be y.
According to question there are 16 coins, so
x+y=16-----1
1 dime=$0.10
1 quarter=$0.25
According to question Hamid has $2,95 ,so
0.10x+0.25y=2.95.
Hence the system which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.
Learn more about equation at https://brainly.com/question/2972832
#SPJ2
.Nisha bought a backpack that was on sale at 35% off for $63. How much was the original price of the backpack?
Answer:
$180
Step-by-step explanation:
100%=x
35%=$63
63 x 100=6300/35=$180
Answer:
96.92
Step-by-step explanation:
If the backpack was 35% off you will still pay 100 -35 or 65%
Let x be the original price
x * 65% = 63
Change to decimal form
x * .65 = 63
Divide each side by .64
x*.65/.65 = 63/.65
x =96.92
URGENT!! HELP! 25 POINTS FOR THESE QUESTIONS!
Answer:
The correct options are;
A. 120
B. 34
Step-by-step explanation:
The given parameters are;
Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order
Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows
When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other digits is 24
Arrangement, Number of ways
1, 2, 3, 4, 5, 6, 24
1, 4, 2, 18
1, 4, 5, 2, 12
1, 4, 5, 6, 2, 6
4, 1, 2, 18
4, 1, 5, 2, 12
4, 1, 5, 6, 6
4, 5, 1, 2, 12
4, 5, 1, 4, 2 6
4, 6, 5, 6
Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways
The correct option is A. 120
2. The dimensions of the original rectangle = L by W
The dimensions of the lager rectangle = 1.5·L by 2·W
1.5·L × 2·W = 30
Given that L > W
∴ L×W = 30/(1.5 × 2) = 30/3 = 10
The possible integers that have a product of 10 are;
1 × 10 and 5 × 2
Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4
Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23
Therefore, the largest possible rectangle is 34
The correct option is B. 34.
Answer:
The correct options are;
A. 120
B. 34
Step-by-step explanation:
The given parameters are;
Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order
Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows
When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other digits is 24
Arrangement, Number of ways
1, 2, 3, 4, 5, 6, 24
1, 4, 2, 18
1, 4, 5, 2, 12
1, 4, 5, 6, 2, 6
4, 1, 2, 18
4, 1, 5, 2, 12
4, 1, 5, 6, 6
4, 5, 1, 2, 12
4, 5, 1, 4, 2 6
4, 6, 5, 6
Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways
The correct option is A. 120
2. The dimensions of the original rectangle = L by W
The dimensions of the lager rectangle = 1.5·L by 2·W
1.5·L × 2·W = 30
Given that L > W
∴ L×W = 30/(1.5 × 2) = 30/3 = 10
The possible integers that have a product of 10 are;
1 × 10 and 5 × 2
Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4
Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23
Therefore, the largest possible rectangle is 34
The correct option is B. 34.
The average (arithmetic mean) of a - 5 and a is x, and the average of a and a + 9 is y. What is the average of x and y?
a + 1
B) a +2
C) 2a + 1
D) 2a + 2
Answer:
The answer is "Option A"
Step-by-step explanation:
Given:
[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]
solve the above equation:
[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]
add both value (x and y):
[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]
average of x and y:
[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]
...................
Answer:
x = a(c + b)
Step-by-step explanation:
Step 1: Add b to both sides
x/a = c + b
Step 2: Multiply both sides by a
x = a(c + b)
A linear function includes the ordered pairs (0, 3), (3, 9), and (9, n). What is the value of n?
Answer:
the value of n will be the range
Step-by-step explanation:
lets just give an example of (9,n) and you had to find the value its actually simple
9 is the domain
n is the range
a part of ordered pair function
got it?
Which expression is equivalent to (–3y – x) – (5y – 8x)?
Answer:
-8y +7x
Step-by-step explanation:
(–3y – x) – (5y – 8x)Distribute
-3y -x -5y +8x
Combine like terms
-3y-5y -x+8x
-8y +7x
Type the correct answer in each box, If necessary, use / for the fraction bar(s).
1
-1
The point on the number line shows the opposite of
or the opposite of the opposite of
Reset
Next
Answer: -1/1
Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.
Help help help please I need help fast
The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five
Please Mark brainliest
Answer:
The answer is x=7/5
Step-by-step explanation:
because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5
Example A
Find the area of the blue sector. Leave your answer in terms of TT.
Answer: [tex]10\frac{2}{3}\pi[/tex]
Step-by-step explanation:
Do you really need it? If so, reply, if not, mark brainliest.
Simplify 2(x - 3) + 7(x + 2)
Answer:
9x + 8.
Step-by-step explanation:
2(x - 3) + 7(x + 2)
= 2x - 6 + 7x + 14
= 2x + 7x - 6 + 14
= 9x + 8.
Hope this helps!
What is X^2-9=0 I really need the answers
Answer:
X^2-9=0 is x2 = 9
Step-by-step explanation:
13. Gayle is getting ready for her first day of school. She has 7 new dresses to choose from and 4
new pairs of shoes. How many different outcomes are possible for Gayle to wear one dress and
one pair of shoes?
Answer:
49
Step-by-step explanation:
7 times 4 equals 49.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?
m∠5 + m∠6 = m∠1
m∠3 + m∠4 + m∠5 = 180°
m∠1 + m∠2 = 180°
m∠2 + m∠3 = m∠5
Answer:
m∠1 + m∠2 = 180°
Step-by-step explanation:
An interior angle and its exterior angle are supplementary (they add up to 180°).
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
c
Step-by-step explanation: