[tex] \sf :\implies \quad {\pmb{x = - 4}}[/tex]
Solution:Let's solve the given equation step by step ;
[tex] \sf :\implies \quad 6(x + 4) + 1 = x + 5[/tex]
The first step is to distribute the equation:
[tex] \sf :\implies \quad (6 \times x ) + (6 \times 4) + 1 = x + 5[/tex]
[tex] \sf :\implies \quad 6x + 24 + 1 = x + 5[/tex]
[tex] \sf :\implies \quad 6x + 25 = x + 5[/tex]
Second step is to combine the like terms:
[tex] \sf :\implies \quad 6x + 25 - x = 5[/tex]
[tex] \sf :\implies \quad( 6x - x) + 25 = 5[/tex]
[tex] \sf :\implies \quad 5x + 25 = 5[/tex]
Now, subtract 25 from both sides :
[tex] \sf :\implies \quad 5x + 25 - 25 = 5 - 25[/tex]
[tex] \sf :\implies \quad 5x = - 20[/tex]
Divide both sides by 5:
[tex] \sf :\implies \quad \dfrac{5x}{5} = - \dfrac{20}{5} [/tex]
[tex] \sf :\implies \quad \boxed{ \pmb{\sf x = - 4}}[/tex]
Hence, your answer is ; x = -4
Find the midpoint of the line segment with end coordinates of:
(-2,-4) and (-1,-5)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use section formula ~
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{mx_2 + nx_1}{m + n} [/tex]
[tex]\qquad \sf \dashrightarrow \:y = \dfrac{my_2 + ny_1}{m + n} [/tex]
And since mid point divides a line segment Into two equal parts, m : n = 1 : 1
so, take m = n = 1
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{(1 \times - 1)+(1 \times - 2)}{ 1+ 1} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{- 1- 2}{ 2} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - 3}{ 2} [/tex]
Now, let's find y - coordinate ~
[tex]\qquad \sf \dashrightarrow \:y = \dfrac{(1 \times - 5) + (1 \times - 4)}{1 + 1} [/tex]
[tex]\qquad \sf \dashrightarrow \:y = \dfrac{ - 5 - 4}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:y = \dfrac{ - 9}{2} [/tex]
So, coordinates of midpoint is ~
[tex]\qquad \sf \dashrightarrow \:( - \dfrac{3}{2} ,- \dfrac{9}{2} )[/tex]
If 140 people were surveyed how many preferred crab? /////Show your work!
[tex]\qquad\qquad\huge \: \sf Answer[/tex]
Number of people who prefer crabs are :
[tex] \\qquad \tt \dashrightarrow \:{30\% \:\: of \:\: 140} [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{30}{100} \times 140 [/tex]
[tex]\qquad \tt \dashrightarrow \:3 \times 14[/tex]
[tex]\qquad \tt \dashrightarrow \:42 \: \: people[/tex]
A glass jar has a height of 5 inches and a radius of 2. 5 inches. vanessa wants to fill the jar with beads that cost $0. 12 per cubic inch. how much will it cost for her to fill the jar?
One of the lamp posts at a bank has a motion detector on it, and the equation (x 15)2 (y−12)2=25 describes the boundary within which motion can be sensed. what is the greatest distance, in feet, a person could be from the lamp and be detected? 5 ft 10 ft 50 ft 125 ft
5 feet is the greatest distance that a person could be from the lamp and be detected.
What is equation of circle?A circle is defined as round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Since we have given that
The equation is :
[tex](x+15)^2+(y-12)^2=25[/tex]
It is the equation of circle in which center is (h,k) i.e. ( 15,12)
The general equation of circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here, the radius 'r' is given by
[tex]r^2=25[/tex]
[tex]r=\sqrt{25[/tex]
[tex]r=5[/tex]
Here, the greatest distance a person could be from the lamp and be detected is represented by radius i.e. r = 5 feet.
Hence, 5 feet is the greatest distance that a person could be from the lamp and be detected.
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Hey, can someone help me out with this? I don't understand how to solve it.
Answer:
261.05
Step-by-step explanation:
A=½ bh
The base is 22.7
The height is 23
22.7×23=522.1
Since the shape is a triangle we divide it by 2!!
522.1÷2=261.05
The perimeter of the figure is 261.05. Hope you understand how to solve it now :))
6 diviided by 27 and 7 divided by 50
Answer:
the first one is 0.2222222222... the second is 0.14
6 : 27
Fraction : [tex]\frac{6}{27} = \frac{2}{9}[/tex]
Decimals : 0.(2) = 0.222222222222....
Percentage : 22.2222...%
7 : 50
Fraction : [tex]\frac{7}{50}[/tex]
Decimals : 0.14
Percentage : 14%
Jevator has a weight limit of
7. There are 3 people inside
An elevator has a weight limit of 1 ton there are 3 people inside the elevator Each person weighs 150
pounds. How many more
Pounds can the elevator safely hold?
450 pounds
850 pounds
1,550 pounds
1,850 pounds
Answer:
i think it would be 1550?
Step-by-step explanation:
im pretty sure you add teh weight of the three people and convert it to one ton
help pls with these two about surface area
Answer:
6) 152.6
7) 348.4
Step-by-step explanation:
For question number 6, calculate the surface area of the two triangles first. And then, calculate each of the surface area for the rectangles. Finally, total up the area of the two triangles and the rectangles.
[tex](6.6 \times 9) + (4 \times 9) + (5.2 \times 9) \times (\frac{1}{2} \times 5.2 \times 4) = 152.6[/tex]
For question number 7, given that the area of a triangle is 28.4. Hence calculate the area of the three rectangles. Lastly, total up the area of two triangles and three rectangles.
[tex]28.4 + 28.4 + 3(12 \times 8.1) = 348.4[/tex]
Hope this helps =)
The perimeter of a rectangle is $98,$ and the length of one of its diagonals is $41.$ Find the area of the rectangle.
Answer:
[tex]328units^2[/tex]
Step-by-step explanation:
First off, I do want to say that you could word this more easily.
98 is the perimeter. length is 41. width is 8.
the area is length*width for rectangles.
98-41=57
57-41=16
16/2=8
8*41=328 units^2
given that ax60=b work out the value of 4b/a
Answer:
Given,
a x 60 = b
or
b = a x 60
Similarly, the value of a would be:
We need to find
Therefore, we have to put the either values of a and b in the specified equation:
Hence,
We have only put the value of one variable to evaluate or to make it variable free
or
Therefore, the value of 4b/a is 240.
please help!
complete the net worth statement by determining the total assets and total liabilities. what is the net worth?
A) $178,000
B) $180,338
C) $1,052,662
D) $1,233,000
Using it's concept, it is found that his net worth is given by:
C) $1,052,662
What is the net worth of an individual?It is given by the sum of the individual assets subtracted by the sum of it's liabilities.
In this problem:
The sum of his assets is of $178,000 + $1,055,000 = $1,233,000.The sum of his liabilities is of $145,908 + $34,430 = $180,338.Hence, his net worth is given by:
Net worth = $1,233,000 - $180,338 = $1,052,662.
Which means that option C is correct.
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n= 4/5 (m+7)
help please (solve for m)
Answer: Its not possible.
Step-by-step explanation:There aer two vairables. Whats the value of N
Hey there!
n = 4/5(m + 7)
n = 4/5(1m + 7)
n = 4/5(1m) + 4/5(7)
n = 4/5m + 28/5
n = 4/5m + 5.6
Thus, your answer is probably:
n = 4/5m + 5.6 or n = 4/5m + 28/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What’s the radius of center (-2,1) and contains the point (2,-1)
To find the radius of a circle when we're given the coordinates of its center and a point it contains, we can use the following formula for distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex](x_1,y_1)[/tex] is one point and [tex](x_2,y_2)[/tex] is anotherSolving the QuestionWe're given:
Center: (-2,1)Point: (2,-1)Plug these given points into the formula for distance:
[tex]d=\sqrt{(2-(-2))^2+(-1-1)^2}\\d=\sqrt{(2+2)^2+(-1-1)^2}\\d=\sqrt{(4)^2+(-2)^2}\\d=\sqrt{16+4}\\d=\sqrt{20}\\d\approx4.47[/tex]
AnswerTherefore, the radius of the circle is [tex]\sqrt{20}[/tex] units, or approximately 4.47 units.
567.3
What is the value of the digit 5 in this number?
Answer:
hundredth place
Step-by-step explanation:
because ummmm yeah
A sphere has a radius 4 cm. What is its volume, to the nearest cubic cm? Write your answer to the nearest 10th place and use 3.14 for π???? HELPPPPP ASAP PLEASE!!!!!!!!!!!!!!!AND THANKS
Answer:
267.95
Step-by-step explanation:
Sphere Volume = 4/3 π r³
= 4/3 × 3.14 × 4³
= 803.84/3
= 267.94666...
= 267.95
A. What is 0.47 expressed as a fraction in simplest form?
B. What is 0.-47 expressed as a fraction in simplest form?
C. What is 0.--47 expressed as a fraction in simplest form?
Please show your work for each part.
25 points! and Brainliest!
Answer:
See below ~
Step-by-step explanation:
Converting a decimal to a fraction :
Multiply by 100/100 and keep in the form without divisionA. (0.47)
0.47 x 100/10047/100B. (-0.47)
-0.47 x 100/100-47/100C. (0.--47)
A minus sign multiplied by another minus sign makes a positive sign0.--47 ⇒ 0.4747/100Answer:
Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100
Step-by-step explanation:
Step 1: Determine 0.47 as a fraction
0.47 can also be expressed as 47% which means that there is 47/100. We can see that there is no way that we can simplify the fraction even more so that is our final answer.
Step 2: Determine -0.47 as a fraction
0.47 can also be expressed as -47/100. We can see that there is no way that we can simplify the fraction even more so that is our final answer.
Step 3: Determine --0.47 as a fraction
Two negatives (-), means that they cancel out and cause a positive (+). For example, -1 * -1 gives us 1. Therefore it would just be like the first one which is 47/100.
Answer: Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100
2-root3/root3. Rationalize the following equation
Answer:
-1/3
Step-by-step explanation:
Multiply by root 3 on the top and bottom. Root 3 times root 3 is 3. 2-3 is -1.
There are 8 teams to play against each other in a tournament. How many ways can 1st and 2nd place be awarded at the end of the tournament?
Answer:
28
Step-by-step explanation:
Correct option is C)
Matches played between 8 teams =7+6+5+4+3+2+1=21
The number of ways that can 1st and 2nd place be awarded at the end of tournament is 56.
What is permutation?A permutation is an arrangement of objects in a definite order. The members of elements of sets are arranged here in a sequence where order matters.
According to the given question
we have to find,
Number of ways for 1st and 2nd place can be awarded
Number of ways for 1st place be awarded = 8
Number of ways for 2nd place be awarded = 7
Therefore,
The total number of ways can 1st and 2nd place be awarded = (8)×(7)
=56.
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Which of the following is true for f(x) = –2sin(x) – 3? the range of the function is the set of real numbers negative 2 less-than-or-equal-to y less-than-or-equal-to 2. the graph of the function is the graph of f(x) = –2sin(x) shifted 3 units up. the amplitude of the function is 2. the period of the function is 4 pi.
The correct option C which is true for the given form of the sine curve f(x) = –2sin(x) – 3.
What is the range of the function?The range of a function is defined as the set of all the possible output values that are valid for the given function.
The general form of the sine curve is given as
f(x) = –2sin(x) – 3
A.
Since this curve's A is -2, its amplitude is 2 and its range is from -2 to 2. but since the D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Choice A is not true.
B.
This graph is the graph of shifted 3 units down since D is negative. This choice isn't true.
C.
Because of the (minus) sign in front of the function, the function is reflected on the x-axis, but the amplitude doesn't change. Since A value is 2, the amplitude is 2. This is true.
D.
The period depends on the B value. Here, the B value is 1, so the period is normal as the parent function of a sine curve, which is, not. So this is not correct.
Therefore, C is the correct answer.
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Answer: C. The amplitude of the function is 2.
Step-by-step explanation:
If n'(x) = 2sin(2x) and n(0) = 0 what is the absolute maximum of n(x) on (0,2-}?
The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3.
How to find the absolute maximum of a differentiable function
A function is differentiable in a given interval if and only if its derivative exists for every value of the interval. To determine the absolute maximum of n(x), we need to integrate the given function, apply first derivative and second derivative test and finally evaluate n(x).
First, we integrate n'(x) in terms of x:
n(x) = 2 ∫ sin 2x dx = 2 · (- 0.5 · cos 2x) + C = - cos 2x + C
- cos 0 + C = 0
C = 1
Then, n(x) = 1 - 2 · cos 2x.
Now we proceed to apply first and second derivative tests:
First derivative test2 · sin 2x = 0
sin 2x = 0
2 · x = sin⁻¹ 0
2 · x = π ∨ 2π
x = 0.5π ∨ π
Second derivative testn''(x) = 4 · cos 2x
n''(π) = 4 · cos 2π
n''(π) = 4
There is an absolute minimum for x = π. [tex]\blacksquare[/tex]
n''(0.5π) = 4 · cos π
n''(0.5π) = - 4
There is an absolute maximum for x = 0.5π. [tex]\blacksquare[/tex]
Finally, we evaluate n(x) for x = 0.5π to determine the absolute maximum:
n(0.5π) = 1 - 2 · cos π
n(0.5π) = 3
The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3. [tex]\blacksquare[/tex]
RemarkThe statement of the question is poorly formatted and reports several mistakes, correct form is introduced below:
If n'(x) = 2 · sin 2x and n(0) = 0. What is the absolute maximum of n(x) on (0, 2π]?
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Which of the following is not true about the mean of a set of data?
A. The mean can be one of the data values.
B. The mean can be different from all of the data values.
C. The mean can be less than the minimum data value.
D. The mean can be the same value as the median.
Answer:B
Step-by-step explanation: it is the average of all the data and can be different from the collection
Answer:
C
Step-by-step explanation:
A. The mean can be one of the other data values but is usually not
B. The Mean can be different than the other values
C. The mean can not be bigger than the biggest number or less than the smallest number.
D. The mean can be the same value as the median.
hopefully you get the correct answer (:
4) Calculate the exact circumference of OP
5 cm
P
12 cm
12 + 5 = P + 360° - (90° x 2)
17 = 360°P - 180°
17 = 180° => P = 180° - 90° = 90° => P - 5 = P + (5 + 12) => P = 14 in <90 5 CM Angle, P = 14 - 1 = 13 without offset
13
Answer:
40.84
Step-by-step explanation:
5cm^2 +25cm^2=169
sqaure root of 169 =13
13= diameter
6.5= radius
2 pie r = circumference
6.5x2 pie = 40.84
Find X and y in the triangle.
Answer:
Step-by-step explanation:
[tex]\frac{\frac{1}{x}+ \frac{2}{x^{2} } }{x+\frac{8}{x^{2} } }[/tex]
Answer:
[tex] \frac{x + 2}{x {}^{3} + 8} [/tex]
Step-by-step explanation:
[tex] \frac{ \frac{1}{x} + \frac{2}{x {}^{2} } }{x + \frac{8}{x {}^{2} } } [/tex]
[tex] \frac{ \frac{x + 2}{x {}^{2} } }{ \frac{x {}^{3} + 8 }{x {}^{2} } } [/tex]
[tex] \frac{x + 2}{x {}^{3} + 8 } [/tex]
Please help me with my math homework
n this world, no one can survive alone. Team up with friends to fend off countless waves of zombies, fight bosses, earn coins, level up, and buy new towers! If you're feeling up for a challenge, try taking on harder bosses on harder difficulties!
b) The cheerleaders and the football team
sold 480 raffle tickets to raise money for
the cheerleader uniforms. The football
team members sold twice as many tickets
as the cheerleaders. How many tickets
were sold by the football team members?
Answer:
320
Step-by-step explanation:
cheerleaders =1
football team members=2
2+1=3
football team members= 480 ×2/3
=320
An angle measures 62.4° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
Step-by-step explanation:
If an angle measures x degrees, the measure of its supplement is (180-x) degrees.
This means that x-62.4 = 180-x, meaning that x=121.2.
So, the angles are 121.2 and 58.8 degrees.
E 18 - 3x D F 150° B с 3.1.1 Show that: BE = AB cos 0 sin (a - 6) - 3.x2 3.1.2 Show that the area of A BCE = x 2 4
Answer:
find the ratio of 15 min and 1hiyr
Can someone help me with this I have a few hours before I have to turn this in anything is appreciated
Demarcus has to wrap a gift for his friend's birthday party. the gift is in a rectangular box with the dimensions shown below. he's trying to figure out how much gift wrap he needs to cover the entire box. should he calculate the total surface area or the lateral surface area? pick the right measurement and then calculate it for him.
Amount of gift wrap to cover the entire box = total surface area of rectangular box = 1,048 in.².
What is the Total Surface Area of a Rectangular Box?The total surface area of a rectangular box is the area of all the faces of the box = 2(wl + hl + hw).
Therefore, to find the material that will cover the whole rectangular box, Demarcus should find its total surface area, given the following dimensions:
l = 20 in.w = 8 in.h = 13 in.Plug in the values into TSA = 2(wl + hl + hw):
Total surface area of rectangular box = 2(8×20 + 13×20 + 13×8) = 1,048 in.²
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