Answer:
Below.
Step-by-step explanation:
This is the correct solution:
6 - 2x + 5 + 4x
= -2x + 4x + 6 + 5
= 2x + 11.
It looks like they added unlike terms together (4x + 5) to give 9x (incorrect) then added the 4x to give 13x.
A marathon swim follows a triangular course marked with three buoys, A, B, and C. The distance from buoy A to B is 400 meters, B to C is 500 meters, and C to A is 600 meters. What is the smallest angle the swimmers must turn between the buoys
By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.
How to determine the smallest angle?In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.
Given the following data:
Side AB = c = 400 meters.Side BC = a = 500 meters.Side CA = b = 600 meters.
Form the law of cosine, we have:
[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]
C = 41.4°.
For angle B, we have:
[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]
B = 82.8°.
For angle A, we have:
[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]
A = 55.8°.
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What is the area of the painting shown ?
Area = length x width
Length = x + 6 + x + 2 = 2x + 8
Width = x + 4 + x = 2x + 4
area = 2x + 8 * 2x + 4
multiply each term by each term
Area = 4x^2 + 24x + 32
Answer: I think this is correct but i'm not sure! the answer should be 48 im not sure though
Step-by-step explanation:
6 x 2 = 12 x 4 = 48
There are six people on a bus. This is in total. At the first stop, eight more people get on. At the second, four get on and two hop off. At the third stop, the bus becomes practically full as 15 passengers get on. Four get off. At the last stop, 8 people get off. How many people are on the bus?
Just a fun problem for you :D
P.S. Answer it correctly ;)
Answer:
This was a nice way to spend my time :) how'd I do?
Step-by-step explanation:
Total: 6
1. +8
After stop 1, total is 14 people
2. +4, -2
After stop 2, total is 16 people
3. +15, -4
After stop 3, the total is 27 people
4. -8
Total # of people on the bus: 19
(A little voice in the back of my mind is telling me that I overthought this entire problem, and that the answer is just 6)
If cost of 15 eggs is Rs. 75, then find out the cost of 4 dozens eggs.
a.₹ 185
b.₹ 150
c.₹ 300
d.₹ 240
Answer:
The answer is d 240. You will first find how much 1 egg costs then times 12 times 4 equal to 48 times how much 1 egg Costs equal to 240
What theorem can be used to prove that the two triangles are similar? A) SSS Similarity Theorem B) SAS Similarity Theorem C) SSA Similarity Theorem
Answer:
C) SSA Similarity Theorem
Step-by-step explanation:
The SAS Similarity Theorem asserts that if two sides of one triangle are proportionate to two sides of another triangle, and both triangles' included angles are congruent, the two triangles are similar.
| x- ( - 18) | if x < - 18
Answer:
well x-(-18) x+18 but the if part is x<-18 will stay the same
Step-by-step explanation:
Can someone help
kaitlin buys candy that costs $8 per pound. she will spend less than $40 on candy. what are the possible numbers of pounds she will buy?
use p for the number ofpounds kaitlin will buy.
write your answer as an inequality solved for p.
Answer:
x≤5p
Step-by-step explanation:
40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds
Find the values of the numbers m and n that will make (2x + m)2 = 4x2 + nx + 9 true, given
that both m and n are positive numbers.
The values of the numbers m and n that makes the given expression true are 3 and 12 respectively
Solving an equationFrom the question, we are to determine the values of the numbers m and n that will make the given expression true
The given expression is
(2x + m)² = 4x² + nx + 9
Opening the bracket on the left hand side,
(2x + m)²
(2x + m)(2x + m)
4x² + 2mx + 2mx + m²
4x² + 4mx + m²
∴ 4x² + 4mx + m² = 4x² + nx + 9
By comparing,
4mx = nx;
Then, 4m = n
and
m² = 9
∴ m = ±√9
m = ±3
Since we are given that both m and n are positive numbers,
∴ m = 3
Substitute the value of m into the equation, 4m = n
4×3 = n
∴ n = 12
Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively
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6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is (1 point)
not drawn to scale.
11 m
12 m
6√3
01,540 m²
0770 m²
0396 m²
0749 m²
Area of hexagon
6(1/2BH)3BH3(6√3)(12)216√3m²Now
area of upper 6 triangles
3BH3(11)(12)396m²Total area
396+216√3770.112m²770m²Answer:
770 m²
Step-by-step explanation:
The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).
Apothem: The line segment from the center of the regular polygon to the midpoint of one of its sides.
Area of the base
The base of the prism is a regular polygon with 6 sides (hexagon).
[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]
where:
n = number of sidess = side lengtha = apothemGiven:
n = 6s = 12 ma = 6√3Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]
Area of one side
The sides of the regular pyramid are congruent triangles.
[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]
Given:
base = 12 mheight = 11 mSubstitute the given values into the formula:
[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]
Total Surface Area
[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]
Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution. Log(x-1)+log5x=2
Answer:
see attached
Step-by-step explanation:
We prefer to solve these by rewriting the equations to the form f(x) = 0, then having a graphing calculator show us the x-intercepts of f(x). This is illustrated in the second attachment.
__
The applicable rules of logarithms are ...
log(a) +log(b) = log(ab) . . . for logs of any baselog(a) = b ⇔ 10^b = aln(e^a) = alog(a) = log(b) ⇔ a = b . . . . for a > 0 and b > 0We can apply these rules to the given expressions to solve for x algebraically.
__
log(x-1) ...Taking antilogs, we have ...
(x -1)(5x) = 10^2 = 100
x(x -1) = 20 . . . . . . . . . . . divide by 5
x² -x -20 = 0 . . . . subtract 20, put in standard form
(x -5)(x +4) = 0 . . . . factor
x = 5 or x = -4 . . . . . . the latter is an extraneous solution
x = 5 only
__
ln(x +5) ...Taking antilogs, we have ...
x +5 = (x +1)(x -1)
x² -x -6 = 0 . . . . . . . subtract (x+5), write in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or x = -2 . . . . . . the latter is an extraneous solution
x = 3 only
__
e^x² ...Taking natural logarithms, we have ...
x² = 4x +5
x² -4x -5 = 0 . . . . . write in standard form
(x -5)(x +1) = 0 . . . . factor
x = 5 or x = -1 . . . . values that make the factors zero
__
log₄(5x² ...Taking antilogs, we have ...
5x² +2 = x +8
5x² -x -6 = 0 . . . . . write in standard form
(5x -6)(x +1) = 0 . . . . factor
x = 6/5 or x = -1 . . . . values that make the factors zero
_____
Additional comment
A solution is extraneous when it does not satisfy the original equation. Here, solutions are extraneous because they make the argument of the log function be negative in the original equation. The log function is not defined for negative arguments. (Actually, it gives complex values for negative arguments.)
We could have gone to the trouble to determine the applicable domain of each of the log equations. It is easier to (a) use a graphing calculator, or (b) test the solutions found.
What is the solution for x in the equation?
-2x+14+10x=34
A. x=5/2
B. x=2/5
C. x=1/8
D. x=6
Can someone explain how to convert a quadratic function in standard form to vertex form using the "complete the square" method? Oh, please give steps so I can write them down
The required steps are explained below to convert the quadratic function into a perfect square.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the quadratic function be y = ax² + bx + c.
The first step is to take common the coefficient of x². We have
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c[/tex]
Add and subtract the half of the square the coefficient of x,
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c[/tex]
Then we have
[tex]\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c[/tex]
These are the required step to get the perfect square of the quadratic function.
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PLEASE HELP!!!
Which of the following is the Best Buy?
1 L for $1.68
0.5 L for $1.29
2 L for $3.40
3 L for $5.07
Answer:
it's 1 L
Step-by-step explanation:
it's pretty easy just do some multiplication
Find the gradient of the line segment between the points (-5,-2) and (4,3).
Give your answer in its simplest form.
Answer:
5/9
Step-by-step explanation:
Solution
The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points
m =
[tex] \frac{y2 - y1}{x2 - x1 } [/tex]
Here two points given, (-5,-2) and (4,3)
gradient (m):
[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]
I am thinking of a number. I multiply it by 8 and subtract 56.
I get the same answer if I multiply by 5 and subtract 8
What is my number?
Answer:
16
Step-by-step explanation:
[tex]8x-56=5x-8\\\\3x-56=-8\\\\3x=48\\\\x=16[/tex]
So, the number is 16
the original price for a set of golf clubs is $500 at the beginning of the seasons the price was marked up by 20% at the end of the seasons the price at the beginning of the season is marked down by 20% how does the final price compare with the original price of $500
Answer: The final price is less than the original
Step-by-step explanation:
Let us break this down a bit.
The original price is $500
-> At the beginning, the price was marked up by 20%
-> At the end, the price at the beginning of the season is marked down by 20%
We are solving for: "How does the final price compare with the original price of $500"
First, we will find the price at the beginning.
-> Please note a percent divided by 100 becomes a decimal
20% / 100 = 0.2
$500 * 0.2 = $100
$500 + $100 = $600
Now, we will find the price at the end.
$600 * 0.2 = $120
$600 - $120 = $480
The final price is less than the original price of $500.
Answer:
Step-by-step explanation:
price marked up by 20%= 500+ [tex]\frac{20}{100}[/tex]×500
=$600
price marked down by 20%= 600- [tex]\frac{20}{100}[/tex]×600
=$480
the final price is less than the original price
in need of some help <3
If ∆ABC~∆XYZ, area (∆ABC) : the area (∆XYZ) = 4:9, then AB:XY is...
Answer:
AB : XY = 2 : 3
Step-by-step explanation:
We know that :
area ∝ length²So, if the areas ΔABC and ΔXYZ are in the ratio 4 : 9, then :
ΔABC : ΔXYZ ∝ AB² : XY²4 : 9 ∝ √4 : √94 : 9 ∝ 2 : 33
Find the surface area of the figure shown below.
1 mm
1 mm
1 mm
Figure not drawn to scale
Surface area is?
Answer:
6
Step-by-step explanation:
Since this is a cube, and the lengths that are given are 1 mm, then you just add all the sides of a cube. There are 6 sides in a cube, 1+1+1+1+1+1=6
Find the length of the segment that joins the points (-5,2) and (4,-3).
Answer:
10.2956
Step-by-step explanation:
formula:
d = √((x2-x1)2 + (y2-y1)2)
(x1, y2) and (x2, y2)
(-5,2) and (4,-3).
Find the difference between coordinates:
(x2-x1) = (4 - -5) = 9
(y2-y1) = (-3 - 2) = -5
Square the results and sum them up:
(9)2 + (-5)2 = 81 + 25 = 106
Now Find the square root and that's your result:
Exact solution: √106 = √106
Approximate solution: 10.2956
PLS HELP ILL MARK U BRAINLIST
Answer:
∠ FLW = 112°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ FLW is an exterior angle of the triangle , then
∠ FLW = x + 32 , that is
2x - 48 = x + 32 ( subtract x from both sides )
x - 48 = 32 ( add 32 to both sides )
x = 80
Then
∠ FLW = 2x - 48 = 2(80) - 48 = 160 - 48 = 112°
write down all the prime numbers
Answer:
The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Step-by-step explanation:
also it goes on and on so i dont think you meant but i hope this helps if it dosnt m very sorry
Can someone help me with this please
HELP ASAP PLEASE, this is the last question i promise T^T
WILL MARK BRAINLIEST AND GIVE POINTS
find the perimeter of a circular sector if the diameter of its circle equals 10cm and its arc length = 10cm. equals = ......... cm.
a) 10
b) 20
c) 30
d) 40
an explanation for future reference would be greatly appreciated, thank youuu <33
Answer:
A= 10
Step-by-step explanation:
[10 + 2/360˚(10)]
Please help!!! thank you!
Answer:
30 again if I’m wrong then it’s 40
Step-by-step explanation:
most of the pizzas that are sold are in the 30’s or below
Guys, Please Help me Fast
I will help u so fast, first
you help me
can u answer this
some fanicial and environmental damages that have been made by cars.
please help me
this is exam
teacher giving us 10 minutes to discuss about and I am in washroom of school writing this
In general, 60 beats per minute (bpm) is a heart rate that is considered too slow for an adult when at rest and 100 bpm is considered too high. As one way of measuring the stress of Canadian air traffic controllers, heart rates of 173 randomly selected air traffic controllers were measured across Canada. Of this sample of air traffic controllers, 47 had a resting heart rate over 100 bpm. What is the true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm
The true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm is; 0.2717 or 27.17%
How to calculate true proportion?We are given;
Sample size; n = 173
Number of people who had a resting heart rate over 100 bpm = 47
Now, formula for true proportion is;
p' = x/n
where;
x represents the number of successes
n represents the sample size.
p′ is the sample proportion which is the point estimate for the true population proportion.
Thus;
p' = 47/173
p' = 0.2717
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The graph of the function above is shown below. Which of the following statements about f(x) is true? A. The function f(x) does not have an inverse because it never crosses the x-axis. B. The function f(x) has an inverse because it passes the horizontal line test. C. The function f(x) does not have an inverse because it does not pass the horizontal line test. D. The function f(x) has an inverse because it passes the vertical line test.
Answer:
The correct answer is b)
Step-by-step explanation:
Which set of real numbers contains 23 and .45?
rational numbers
integers
natural numbers
whole numbers
Answer:
Option A, rational numbers
Step-by-step explanation:
Step 1: Determine which option is correct
Option B and D are automatically ruled out because only one of them is a whole number and the other one is a decimal. Option C doesn't work also because natural numbers are all the whole numbers that are greater than 1. The only option that makes sense is option A which includes whole numbers and decimals.
Answer: Option A, rational numbers
kyle is pulled back on a swing so that the rope forms an angle of 30 degress with the vertical the distance from the top of the swing set directly to the ground is 12 feet find kyles height off the ground
Answer:
12 ft - 2 ft = 10 ft
The rope is 10 feet long.
10 · cos 30° = 10 · √3 / 2 = 8.66 ft
x = 12 - 8.66 = 3.34 ft
Answer:
A ) 3.34 feet
(2y + 5) (5y + 7)
Simplify your answer.
Answer:
10y^2 + 39y + 35
Step-by-step explanation:
Simplify using FOIL
