Answer:
x≤9
Step-by-step explanation:
x−6≤3
Add 6 to both sides.
x≤3+6
Add 3 and 6 to get 9
x≤9
Answer: x ≤ 9
Step-by-step explanation: When solving an inequality, your goal is the same as it would be if you were solving an equation – to get the variable by itself or isolated on one side of the equals sign.
Since 6 is being subtracted from x, add 6 to both sides of the inequality.
On the left, the -6 +6 cancel out and on the right, 3 + 6 is 9.
So we have x ≤ 9.
Paula invests $600 at a rate of r% per year simple interest. At the end of 10 years, the total interest earned is $90. Find the value of r.
Answer:
1.5%
Step-by-step explanation:
To find Rate in Simple Interest:
R = 100 S.I / T × P
R = 100 × 90/10 × 600
R = 9/6
R = 1.5%
1.5% is the rate.
order Operation
SIMPLIFY : −2b−5z−6+4b−3z
Answer:
2b - 8z - 6
Step-by-step explanation:
Rearrange the equation, so like terms are near each other
-2b+4b-3z-5z-6
Now we add the b's and z's to get,
2b - 8z - 6
Answer:
2b -8z -6
Step-by-step explanation:
−2b−5z−6+4b−3z
Combine like terms
−2b+4b−5z−3z−6
2b -8z -6
Solve: p+30 = 80
HELP !
Answer:
p=50
Step-by-step explanation:
Subtract 30 from both sides and you have your answer
Answer: 50
Step-by-step explanation:
p + 30 = 80
subtract 30 from both sides to isolate the value of "p". subtracting 30 from positive 30 cancels that out. 80 minus 30 is 50. you are left with p = 50, so the value of p is 50.
PLEASE HELP!! Solve the triangle
Answer:
Option D. m<A = 43, m<B = 55, a = 20
Step-by-step explanation:
1. Determination of angle B.
Angle C = 82
Opposite C (c) = 29
Opposite B (b) = 24
Angle B =?
Using Sine rule, we can obtain the value of angle B as follow:
b/Sine B= c/Sine C
24/Sine B = 29/Sine 82
Cross multiply
29 × Sine B = 24 × Sine 82
Divide both side by 29
Sine B = (24 × Sine 82) /29
Sine B = 0.8195
Take the inverse of Sine.
B = Sine¯¹ (0.8195)
B = 55
2. Determination of angle A.
Angle C = 82
Angle B = 55
Angle A =?
The value of angle A can be obtained as follow:
A + B + C = 180 (sum of angle in a triangle)
A + 55 + 82 = 180
A + 137 = 180
Collect like terms
A = 180 – 137
A = 43
3. Determination of side a (Opposite A)
Angle C = 82
Opposite C (c) = 29
Angle A = 43
Opposite A (a) =?
The value 'a' can be obtained as by using sine rule as illustrated below:
a/Sine A = c/Sine C
a/Sine 43 = 29/Sine 82
Cross multiply
a × Sine 82 = 29 × Sine 43
Divide both side by Sine 82
a = (29 × Sine 43) /Sine 82
a = 20
Therefore,
m<A = 43, m<B = 55, a = 20
I need answers ASAP! Thanks!
Step-by-step explanation:
43. P, U
44. 7
53. Airplanes can be traveling on different planes, one plane above the other. Cars on the same intersection are on the same plane.
55
a. You can choose (4 * 3 * 2)/(3 * 2) = 4 groups of 3 points in which order does not matter.
One of those combinations does not have K, so 3 combinations of the 4 have K.
p = 3/4
b. p = 1 since any three points are always coplanar.
A boat travels x miles per hour upstream on the Mississippi River. On the return trip, the boat travels 2 miles per hour faster. How far does the boat travel upstream?
Answer:
Distance = 17.5 miles
Step-by-step explanation:
Note.
Given question is not complete
Given:
Speed upstream = x
Time taken in upstream = 3.5 hour
Speed in return trip = (x+2)
Time taken in return trip = 2.5 hour
Computation:
Distance = speed × time
Distance = x (3.5)
Distance = 2.5 (x+2)
Distance = 2.5x + 5
So,
2.5x + 5 = 3.5 x
1.5 x = 5
x = 5 miles/hour
Distance = x (3.5)
Distance = 5 (3.5)
Distance = 17.5 miles
Question 11 (1 point)
(01.02)
Given the function f(x) = 4(x+3) - 5, solve for the inverse function when x = 3. (1 point)
а. -21
b. -16
с. -10
d. -1
Answer:
D
Step-by-step explanation:
Insert 3 in place of x in the inverse function.
if 5 + 2root3/7 + root3 = a-root3b find a and b where a and b are rational no
Answer:
a = 29/46
b= - 9/46
Step-by-step explanation:
Given:
(5 + 2√3)/(7 + √3) = a - √3bRationalizing the left side:
(5+2√3)(7-√3)/(7+√3)(7-√3) = (35 + 14√3 - 5√3 - 2√3²)/(7² - √3²) =(35 - 6 + 9√3)/(49 - 3) =(29 + 9√3)/46 = 29/46 + √3 (9/46)Comparing the left and right sides:
a - √3b = 29/46 + √3 9/46a = 29/46b = - 9/46A plane is flying at a cruising speed of 900 km/h. How far will the plane travel from 11:15 a.m. to 1:30 p.m. on the same day?
Step-by-step explanation:
so the answer must be 2025 km.
The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be 2025 km.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A plane is flying at a cruising speed of 900 km/h.
The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be
From 11:15 a.m. to 1:30 p.m., there are 2.25 hours.
Then the distance will be
D = 900 x 2.25
D = 2025 km
More about the speed link is given below.
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Which lists all the integer solutions of the equation |x| = 7? –7 and 7 7 only 0 and 7 –7 only
Answer:
aa
Step-by-step explanation:
somebody please help me on this it’s for geometry please don’t waste my answers i’ll mark you the brainliest
What is the domain and range of the graph below? You must use either interval notation or set notation
Answer:
See below.
Step-by-step explanation:
The domain of a function is simply the span of x-values the graph will encompass.
And the range of a function is simply the span of y-values the graph will encompass.
Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
And in set notation, this is:
[tex]\{x|x\in\mathbb{R}\}[/tex]
For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.
In interval notation, this is:
[tex](-\infty,-4][/tex]
We use brackets because we include the -4 in the solution set.
Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.
And in set notation, this is:
[tex]\{y|y\in\mathbb{R},y\leq 4}\}[/tex]
Daniel buys 17 raffel ticket a total of 280 tickets were soldFind the probability that daniel does not win
Answer:
280-17=273
Step-by-step explanation:
because 80-17 equals 73 sooooooo add 200
evaluate the expression
Answer:
[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]
Step-by-step explanation:
So we have the expression:
[tex]12-[20-2(6^2\div3\times2^2)][/tex]
Recall the order of operations or PEMDAS:
P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.
E: Within the parentheses, if exponents are present, do them before all other operations.
M/D: Multiplication and division next, whichever comes first.
A/S: Addition and subtraction next, whichever comes first.
(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)
Thus, we should do the operations inside the parentheses first. Therefore:
[tex]12-[20-2(6^2\div3\times2^2)][/tex]
The parentheses is:
[tex](6^2\div3\times2^2)[/tex]
Square the 6 and the 4:
[tex](36\div3\times4)[/tex]
Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:
[tex](36\div3\times4)\\=(12\times4)\\=48[/tex]
Therefore, the original equation is now:
[tex]12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)][/tex]
Multiply with the brackets:
[tex]=12-[20-96][/tex]
Subtract with the brackets:
[tex]=12-[-76][/tex]
Two negatives make a positive. Add:
[tex]=12+76=88[/tex]
Therefore:
[tex]12-[20-2(6^2\div3\times2^2)]=88[/tex]
If you are on a ship at sea navigating to a point that is 300 miles north and 400 miles west, find the distance from tour ship to that point. Show your work.
Answer:
[tex]\huge \boxed{\mathrm{500 \ miles}}[/tex]
Step-by-step explanation:
A right triangle is formed.
300 miles and 400 miles are the legs of the triangle.
We can apply Pythagorean theorem.
[tex]c=\sqrt{300^2 +400^2 }[/tex]
[tex]c=\sqrt{90000 +160000}[/tex]
[tex]c=\sqrt{250000}[/tex]
[tex]c=500[/tex]
Which geometric figures are drawn on the diagram? Check all that apply. Line segment C A Ray A C ∠ABC Circle C Ray B E ∠BCE Line segment A E
The geometric figures are drawn on the diagram are option A,B,D, and F.
What is the circle theorem?One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.
we know that
case a) ∠ABC
The geometric figure is not drawn in the diagram case is b) ∠BCE
The geometric figure is drawn in the diagram case is c) line segment CA
The geometric figure is drawn in the diagram case is d) Ray CA
The geometric figure is drawn in the diagram case is e) Circle C
The geometric figure is drawn in the diagram case is f) Ray BE
The geometric figure is not drawn in the diagram case is g) LIne segment AE
Hence, The geometric figures are drawn on the diagram are option A,B,D, and F.
Learn more about Circle here;
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Find the value of w A. 110 B. 141 C. 80 D. 100
================================================
Explanation:
The arc measures of 60 and x average to the angle 70, which is the the angle formed between the intersecting chords
70 = (60+x)/2
70*2 = 60+x
140 = x+60
x+60 = 140
x = 140-60
x = 80
The full 360 degree circle has the arc measures of 60, 79, x = 80, and w, where we don't know w yet. But we can add the four pieces of the circle to get 360
60+79+x+w = 360
60+79+80+w = 360
w+219 = 360
w = 360-219
w = 141
---------------
Or you could find angle z first
z+70 = 180
z = 180-70
z = 110
Then use the averaging technique done at the start of this problem
z = (79+w)/2
110 = (79+w)/2
2*110 = w+79
220 = w+79
w+79 = 220
w = 220-79
w = 141
Use the spider tool located on page 1 of this activity to draw a 12-pointed star for the new logo. (Hint:If the spider rotates 360 degrees -- or 720 degrees or 1080 degrees -- she will be facing in the same direction in which she started. When the spider is done drawing, you want her to be facing in the same direction in which she started. She'll be making 12 rotations, all the same size, so each rotation must be some multiple of 360/12 = 30 degrees.)
Please help urgently. Been stuck on this problem for around 45 minutes now. Thanks.
PLEASE HELPPPPP! IT SHOULD BE EASY IF YOU'RE SMART ENOUGH
Answer:
each of the 12 turns is 150°
Step-by-step explanation:
If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.
That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...
150° - dodecagon, a 12-sided figure
120° - hexagon
90° - square
60° - equilateral triangle
30° - 12-pointed star
0° - straight line
The two 12-pointed figures are shown in the attachment.
__
We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.
The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.
Answer:
Move the spide by 100 units and then turn the spider by 150 degrees. Repeat until you complete the star.
Step-by-step explanation:
people above are correct! I'm just making the steps as clear as possible for those who need it :)
Does the equation y=3x3+4x2+15x+7 represent a function? Explain. A. No, the equation is not a function because it is a polynomial and polynomials cannot be functions. B. A. No, the equation is not a function because there are multiple terms that contains the variable x. C. Yes, the equation is a function because there is only a single term that contains the variable y. D. Yes, the equation is a function because it is a polynomial and all polynomials are functions.
Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.
Step-by-step explanation: I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions ! Hope this helped
A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle
Answer:
The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
Step-by-step explanation:
We know that the area of a triangle A = 1/2bh where b = base and h = height.
Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).
So its area A = (3x + 7)(5x - 1)/2.
Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)
So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)
So the difference between the area of the original triangle and the new triangle is
A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2
= (3x + 7)(5x - 1)(3 - 1/2)
= 5(3x + 7)(5x - 1)/2
So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
-5r + 2r = -3
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Answer:
r=1
Step-by-step explanation:
-5r+2r=-3r
-3r=-3
Divide by -3 on both sides
r=1
What is the approximate area of the circle shown below?
18cm
A. 28.3 cm2
B. 1018 cm2
C. 254 cm2
D. 56.5 cm2
Answer
the answer is 254 cm 2
Step-by-step explanation:
The area of the circle will be 254 square cm. Then the correct option is C.
What is the area of a circle?Let r be the diameter of the circle. Then the area of the circle will be
A = (π / 4)d² square units
The radius of the circle is 18 cm.
Then the area of the circle will be
A = (π / 4) x (18)²
A = 254.46 ≈ 254 square cm
Then the correct option is C.
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Based on the areas of the squares, determine whether the triangle shown is a right triangle. side A : 7 square inches side B : 18 square inches side C : 27 square inches It is for. khan acadmey
Answer:
The triangle ABC is not a right triangle
Step-by-step explanation:
For a right angle triangle, we have;
The square of the longest side or leg of the triangle is equal to the sum of the squares of the other two legs
The parameters given from the question, are;
The square of of the length of side A = 7 inch²
The square of of the length of side B = 18 inch²
The square of of the length of side C = 27 inch²
Therefore, the the longest side is side C and the inch² sum of the squares of the other two sides are 7 + 18 = 25 inch² which is less than the square of the length of side C = 27 inch², therefore, the triangle ABC is not a right triangle.
Answer:
Not a right angle
Step-by-step explanation:
Khan academy is never wrong :3
Eight plus the quotient of a number and 3 is −2
Answer:
The number is -30.
Step-by-step explanation:
Given that,
Eight plus the quotient of a number and 3 is −2 . We need to find the number.
So, putting given condition into mathematical expression. Let the number is x. So,
[tex]8+\dfrac{x}{3}=-2[/tex]
Subtracting on both sides,
[tex]8+\dfrac{x}{3}-8=-2-8\\\\\dfrac{x}{3}=-10[/tex]
Now cross multiplying, we get
x = -30
So, the number is -30.
From point A and B on level ground, the angles of
elevation of the top of a building
Are 25 degree and 37degrees respectively
1f AB= 57m calculate to the nearest metre the distance of the top building from A and B if they are both on the same side of
the building
Answer:
Step-by-step explanation:
Call T the top
call G the bottom
T G B is a right triangle
37 at B, 90 at G, thus 53 at BTG
TGA is a right triangle
25 at A, 90 at G, thus 65 at ATG
thus 122 at ABT
law of sines:
sin 25 / BT = sin 12/ 57
so BT = 156 meters (first answer)
now angle ABT = 180 - 12 - 25
= 143
so
sin 143 /AT = sin12/57
AT = 164 meters, second answer
1-22. Find the perimeter and area of each figure below.
Answer:
a) Area=9 units²
Perimeter=18 units
b) Area=28ft²
Perimeter=24ft
c) Area=120cm²
Perimeter=46cm
Step-by-step explanation:
a) Area=9 units²
Perimeter=18 units
b) Area=28ft² (7x4)
Perimeter=24ft (7+5+7+5)
c) Area=120cm² (15x8)
Perimeter=46cm (15+8+15+8)
what does 79 = 61 + v equal
Answer:
v = 18
Step-by-step explanation:
Given
79 = 61 + v ( subtract 61 from both sides )
18 = v
Two functions are shown in the table below:
Function
1
2 3 4 5 6
f(x) = -x2 + 4x + 12
g(x) = x + 2
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).
O x = 2
Ox= 3
O x = 5
O x = 6
Answer:
The correct option is x = 5
Please find the attached graph of the function
Step-by-step explanation:
The given functions are;
1) f(x) = -x² + 4·x + 12
2) g(x) = x + 2
The table of values are therefore;
x, f(x), g(x)
-7, -65, -5
-6, -48, -4
-5, -33, -3
-4, -20, -2
-3, -9, -1
-2, 0, 0
-1, 7, 1
0, 12, 2
1, 15, 3
2, 16, 4
3, 15, 5
4, 12, 6
5, 7, 7
6, 0, 8
Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where f(x) = g(x) = 0 and 7 respectively
To verify, we have;
Equating the two functions gives;
f(x) = g(x)
-x² + 4·x + 12 = x + 2
-x² + 4·x + 12 - (x + 2) = 0
-x² + 3·x + 10 = 0
(x + 2)(x - 5) = 0
x = 5 or -2
The correct option is x = 5.
Answer:
C. x=5
Step-by-step explanation:
Please see attachments. You'll see that at the x=5 y will equal 7.
Hope this helps!
please help second question
Answer:
I have not J.H.S 3 , because the questions look like some J.H.S 3 ,so please I am very sorry that I can't help u in this questions . Thanks
somebody please help me on this i’ll mark u the brainliest please don’t waste my answers
Answer:
5 < x < 27 {x - lenght of unknown side}Step-by-step explanation:
If we have triangle of sides: a, b, c, and a < b < c (or b<a<c) then:
for triangle to exist:
a + b > c
So:
if a=11, b=16 then 11 + 16 > c ⇒ c < 27
if a=11, c = 16 then 11 + b > 16 ⇒ b > 5
We don't know if the unknown side (x) is the longest or not, so it has to be greater than 5 and less than 27
5 < x < 27