Answer: (x - 1)(x + 1)(x + 7)²
Step-by-step explanation:
x⁴ + 6x² - 7
find two numbers whose product is -7 and sum is +6 --> -1 & 7
Those values go into the parenthesis: (x² - 1)(x + 7)²
Notice that (x² - 1) is the difference of squares --> (x - 1)(x + 1)
In △ABC, AB = 13.2m,
BC = 6.9m and ∠ACB = 90°. H lies on AC such that
∠BHC = 46°. Find
(i) ∠ABH
(ii) The length of AH
Answer:
(i) ∠ABH = 14.5°
(ii) The length of AH = 4.6 m
Step-by-step explanation:
To solve the problem, we will follow the steps below;
(i)Finding ∠ABH
first lets find <HBC
<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)
46° + <HBC + 90 = 180°
<HBC+ 136° = 180°
subtract 136 from both-side of the equation
<HBC+ 136° - 136° = 180° -136°
<HBC = 44°
lets find <ABC
To do that, we need to first find <BAC
Using the sine rule
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
A = ?
a=6.9
C=90
c=13.2
[tex]\frac{sin A}{6.9}[/tex] = [tex]\frac{sin 90}{13.2}[/tex]
sin A = 6.9 sin 90 /13.2
sinA = 0.522727
A = sin⁻¹ ( 0.522727)
A ≈ 31.5 °
<BAC = 31.5°
<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)
31.5° +<ABC + 90° = 180°
<ABC + 121.5° = 180°
subtract 121.5° from both-side of the equation
<ABC + 121.5° - 121.5° = 180° - 121.5°
<ABC = 58.5°
<ABH = <ABC - <HBC
=58.5° - 44°
=14.5°
∠ABH = 14.5°
(ii) Finding the length of AH
To find length AH, we need to first find ∠AHB
<AHB + <BHC = 180° ( angle on a straight line)
<AHB + 46° = 180°
subtract 46° from both-side of the equation
<AHB + 46°- 46° = 180° - 46°
<AHB = 134°
Using sine rule,
[tex]\frac{sin 134}{13.2}[/tex] = [tex]\frac{sin 14.5}{AH}[/tex]
AH = 13.2 sin 14.5 / sin 134
AH≈4.6 m
length AH = 4.6 m
Simplify: (2x2 − 9x + 3) + (−7x2 + 4x − 2)
Answer:
-5x^2-5x=+1
Step-by-step explanation:
Determine the ordered pair that satisfies the equation, 7x - 1y = 8.
Answer:
(1.142857143 , -8)
Step-by-step explanation:
Suppose f(x)=x^2 and g(x)=1/4x^2. Which statement best compares the
graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) shifted 1/4 units right.
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.
Answer:
Step-by-step explanation:
Statement A is closest to being correct. To get the graph of g(x), we compress the graph of f(x) vertically due to multiplying f(x) by (1/4).
Answer:
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
Step-by-step explanation:
a p e x
Find the radius and center of the circle given by the equation below.
(x-6)2 + (y + 4)2 = 7
Ore 17 and center at (-4.6)
or= 7 and center at (6-4)
or=7 and center at (-6.4)
or= 7 and (
6-4)
Answer:
center (6,-4)
radius = √7 unit
Step-by-step explanation:
Mathematically, the equation of a circle can be written as follows;
(x-a)^2 + (y-b)^2 = r^2
Where (a,b) represents the center of the circle with r representing the radius of the circle.
Now looking at the values in the question, we can clearly see that a = 6, while b represents -4.
The radius of the circle is √7
So the circle center is (6,-4) while √7 is the circle center
What is the standard equation of the circle on the graph?
A. (x+2)^2 + (y-3)^2 = 2
B. (x-2)^2 + (y+3)^2 = 2
C. (x-2)^2 + (y+3)^2 = 4
D. (x+2)^2 + (y-3)^2 = 4
Answer: D
Step-by-step explanation:
The equation would be (x+2)^2 + (y-3)^2 = 4 if I did it right. (Sorry if it’s wrong!)
Answer = D :)
Step-by-step explanation:
James is working at a place that ships boxes. Each box is rectangular prism that measures 2 ft long, 3 ft wide, and 2 ft tall. He is loading a small trailer that has 396 cu ft of space. What is the maximum number of boxes he can fit inside the trailer?
Answer:
33
Step-by-step explanation:
2x3x2=12 396/12=33
HELPPP PLEASEE l
The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline.
The graph shows the distance, y, that car P traveled using x gallons of gasoline
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
what is the interquartile range(IQR) of the data set represented by this box plot?
A.37
B.17
C.5
D.22
Answer:
Answer:22
Step-by-step explanation:
Which data set is least Likely to resemble a normal distribution?
Look at picture
Answer: B) The heights of girls who live on a certain street in the city of Buffalo
Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.
A water balloon is thrown from the top of a house. The path of the balloon is modelled by the relation, h = -4.9t2 – 14.7t + 19.6,
where h is the balloon's height, in meters, above ground, and wheret is the time, in seconds.
a.
How tall is the house? (1 mark)
b. How long does it take for the balloon to hit the ground? (3 marks)
What is the maximum height that the balloon reaches? marks)
C.
Answer:
(a)19.6 meters
(b) 1 seconds
(c)30.625 meters
Step-by-step explanation:
The height of the balloon is modeled by the equation:
[tex]h = -4.9t^2- 14.7t + 19.6[/tex]
(a)Since the balloon is thrown from the top of the house, the height of the house is at t=0
When t=0
[tex]h(0) = -4.9(0)^2- 14.7(0) + 19.6\\h=19.6$ meters[/tex]
The height of the house is 19.6 meters.
(b)When the balloon hits the ground
Its height, h(t)=0
Therefore, we solve h(t)=0 for values of t.
[tex]h = -4.9t^2- 14.7t + 19.6=0[/tex]
[tex]-49t^2-147t+196=0\\-49(t^2+3t-4)=0\\t^2+4t-t-4=0\\t(t+4)-1(t+4)=0\\(t+4)(t-1)=0\\t+4=0$ or $t-1=0\\t=-4$ or t=1[/tex]
Therefore, the ball hits the ground after 1 seconds.
(c)To determine the maximum height, we take the derivative of the function and solve it for its critical point.
[tex]If$ h = -4.9t^2- 14.7t + 19.6\\h'(t)=-9.8t-14.7\\$Setting the derivative equal to zero$\\-9.8t-14.7=0\\-9.8t=14.7\\t=-1.5\\$Therefore, the maximum height, h(t) is:\\h(1.5) = -4.9(-1.5)^2- 14.7(-1.5) + 19.6\\=30.625$ meters[/tex]
Which circle C shows a chord that is not a diameter?
Circle C is shown. A line is drawn from one side of the circle to the other side and goes through point C.
Circle C is shown. A line is drawn on the outside of the circle and intersects the circle at one point.
Circle C is shown. A line is drawn from point C to a point on one side of the circle.
Circle C is shown. A line goes from one point on the circle to another point on the circle.
Answer:
The answer is option D
Step-by-step explanation:
Just got it right on edge :)
Answer:
d
Step-by-step explanation:
Container X contained 1200g of sand.Container Y contained 7.2kg of sand.After an equal amount if sand was removed from each container,Container Y had 7 times as much sand as container X.how much sand was removed from each container?
An arithmetic sequence has this recursive formula. a1=9 and 1-3 .
The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.
Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example, 1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term) and common differene d = 2- 1 = 1.
Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.
Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
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Arnold always sits in the second row of seats in his classroom. If there are 5 rows of seats behind Arnold and each row has 6 seats, how many seats are in the classroom?
Answer:
42 Seats.
Step-by-step explanation:
If Arnold is in the second row and there are 5 rows behind him, there are 7 rows because 2 + 5 equals 7.
So then, you multiply 6 times 7 since there are 7 rows and 6 seats in each row. And that equals 42.
Answer:
b:42
Step-by-step explanation:
A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive
Step-by-step explanation:
3*85 <= 83+91+x <= 3*90
255 <= 174+x <= 270
81 <= x <= 96
Answer:
81 ≤ x ≤ 96
Step-by-step explanation:
85 ≤ (x + 83 + 91)/3 ≤ 90
85 ≤ (174 + x)/3, (174 + x)/3 ≤ 90
81 ≤ x ≤ 96
Evaluate -31-8+31 what’s the answer
Answer:
i believe that would be -8...
Step-by-step explanation:
Answer:
the correct answer is -8
plz mark as brainliest
Step-by-step explanation:
Approximate the value of positive square root 5 to the nearest hundredth
Answer:
2.2
Step-by-step explanation:
Please help, I need this answer
Answer:
6.4
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]
Hope this helps!
Answer:
To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4
Answer: is approx. 6.4If point P is 4 over 7 of the distance from M to N white ratio does the point P partioned the directed line segments from M to N into
Answer:
4 : 3
Step-by-step explanation:
The first segment is 4/7 of the whole, so the second segment is 1 - 4/7 = 3/7 of the whole. Then the ratio of the two segments is ...
(4/7) : (3/7) = 4 : 3
Please help……………………………………!!!!!!!!!
Answer:
4 k^4
Step-by-step explanation:
(64 k^12) ^ 1/3
We know (ab)^c = a^c * b^c
64 ^ 1/3 k^12^1/3
4 * k^12^1/3
We know a^b^c = a^(b*c)
4 k^(12*1/3)
4 k^4
Billy’s Boat Rentals charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa’s Boat Rentals does not charge a yearly fee but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for Billy’s and Lisa’s to cost the same amount?
Answer:
It will take 20 times for both cost to be same
Step-by-step explanation:
What we want to do here is to calculate the number of times it will take someone who’s wants to rent a boat by Billyboat will be able to rent Lisa boat.
The first thing to do here is calculate how much that is charged to rent Billyboats
That would be;
Let the number of times be n
so the amount will be
105 + 9.50n
Now, renting at 14.75 at n times would be 14.75n
Mathematically, we equate both
14.75n = 105 + 9.5n
14.75n - 9.5n = 105
5.25n = 105
n = 105/5.25
n = 20 times
which of these statements us true for f(x)=3•(9)^x
Answer:
C
Step-by-step explanation:
The y-intercept is at x=0, y=3.
chromesway you're smart please help me
Answer:
A
Step-by-step explanation:
If since y = 0 is a line of symmetry for the rectangle, reflection over y = 0 will just map the rectangle onto itself.
A student does an experiment and wants to make a graph comparing various amounts of materials. Which type of graph should the student choose?
Answer:
The plotting the points 1 and then you will be able to compare the materials and how they work in comparison to the other material
Answer:
Bar graph
Step-by-step explanation:
Cuz he will make bars in order to show the materi
Find the surface area of this triangular prism shown below
Answer:
Step-by-step explanation:
area of side triangles=2(1/2×6×4)=24 units²
area of 3 rectangles=6×7+2(5×7)==42+70=112 units²
or=(6+5+5)×7=16×7=112 units²
Total surface area=24+112=136 units²
What is the approximate area of the shaded sector in the circle shown below
Answer: B
Step-by-step explanation:
The area of a circle is pi*radius^2. But only a diameter is given, so in order to find the radius, you must divide the diameter by 2:
3.6/2 = 1.8
Now, you can plug the radius, 1.8, into the equation pi*radius^2 ([tex]\pi r^{2}[/tex]):
[tex]\pi (1.8)^2 = \pi(3.24)[/tex] = about 10.18
Lastly, you must divide the area 10.18 by 2 because you are looking for only half the area.
10.18/2 = 5.09
The area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
The diameter of the circle = 3.6 cm
The radius of the circle = 3.6/2 = 1.8 cm
Area of shaded region = (180/360)π(1.8)²
Area of the shaded region = 5.089 ≈ 5.09 square cm
Thus, the area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.
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A rectangular field measures 616m by 456m. Fencing posts are placed along it's sides at equal distances. What will be the distance between the posts if they are place as far apart as possible?
Answer: 766.41m
Step-by-step explanation:
Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem for one triangle.
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the diagonal distance between corners of the field, which is the distance between the posts if they are placed as far apart as possible ) and a and b are the other sides.
Replacing with the values given:
c^2 = 616^2 + 456^2
c^2 = 379,456+207,936
c^2 =587,392
c = √587,392
c = 766.41m
So, she is within the area serviced by the tower (20 miles)
Feel free to ask for more if needed or if you did not understand something.
Anybody know the answer?
Yes!
This does represent a function because all numbers in this table are real numbers.
Integers and whole numbers are apart of real numbers.
Therefore you do not have to state why this is not a function because it certainly is!
Which of the following expressions are equivalent to this expression: –1(0) = ? im lazy and dont wanna do it
Answer:
0
Step-by-step explanation:
Okay...um. Any number times 0 is 0 so the expression you choose should equal 0.