Answer:
Step-by-step explanation:as we know that arc length is
s=r*∅
as given angle in degree so convert it in radian we get
angle=2.09 rad
r=3.5 cm
hence we get
s=3.5*2.09 =7.315 cm
perimeter of sector = s +d where d=2*r=2*3.5=7 cm
perimeter of sector=7.315+7=14.315 cm
if you like it then hit the stars and tag it a brain-list
Solve for x in the equation below(all in picture).
Answer:
x = - 5, x = 2
Step-by-step explanation:
Using the rules of logarithms
log x - log y = log ([tex]\frac{x}{y}[/tex] )
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
note that log x = [tex]log_{10}[/tex] x
Given
log (x² + 3x) - log10 = 0, then
log([tex]\frac{x^2+3x}{10}[/tex] ) = 0, thus
[tex]\frac{x^2+3x}{10}[/tex] = [tex]10^{0}[/tex] = 1 ( multiply both sides by 10 )
x² + 3x = 10 ( subtract 10 from both sides )
x² + 3x - 10 = 0 ← in standard form
(x + 5)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 2 = 0 ⇒ x = 2
Solution is x = - 5, x = 2
Answer:
The equation has the solution(s) x = - 5, and x = 2
Step-by-step explanation:
Let's start by adding log(10) to either side of the equation --- (1)
[tex]\log _{10}\left(x^2+3x\right)-\log _{10}\left(10\right)+\log _{10}\left(10\right)=0+\log _{10}\left(10\right)[/tex]
= [tex]\log _{10}\left(x^2+3x\right)=\log _{10}\left(10\right)[/tex]
If you recall, one property proves that [tex]\log _{10}\left(10\right):\qu 1[/tex]. We can substitute this value back into the simplified equation --- (2)
[tex]\log _{10}\left(x^2+3x\right)=1[/tex]
We can also apply the logarithmic definition, If logₐ(b) = c then b = aᶜ. Using this definition we receive a further simplified equation --- (3)
[tex]x^2+3x=10^1[/tex]
[tex]x^2+3x=10[/tex]
Solving for the expression we receive the solution(s) x = 2, and x = - 5, our first option.
Note : The first solution is correct, but I wanted to take a slightly different approach
Joan is filling a 2-liter soda bottle with different colors of sand to make an art project for her class. She has 1,000 milliliters of
red sand, 35 centiliters of blue sand, and 2,5 deciliters of yellow sand in the bottle, but it is not full yet. How many liters of
purple sand will she need to use to have the bottle completely full?
Answer:
0.4 l of purple sand
Step-by-step explanation:
Volume to be filled in:
2 liter = 2000 mlRed sand
1000 mlBlue sand
35 centiliters = 35*10 ml = 350 mlYellow sand
2.5 deciliters = 2.5*100 ml = 250 mlTotal volume filled:
1000 + 350 + 250 = 1600 mlPurple sand needed:
2000 - 1600 = 400 ml = 0.4 lAnswer is 0.4 l of purple sand required
|4x + 8| + 12= 4 I subtracted 12 by 4 and got -8. Would I still solve the equation or would it be no solution?
Answer:
no solution
Step-by-step explanation:
|4x + 8| + 12= 4
Subtract 12
|4x + 8| = -8
An absolute value must be non negative
Since ours is negative, there is no solution
PLEASE HELP!! Find the length of UT¯¯¯¯¯¯¯+CV¯¯¯¯¯¯¯¯. A. 53 B. 4x + 35 C. 65 D. 59
Answer:
C. 65
Step-by-step explanation:
By the property of intersecting chords inside a circle.
[tex] TW\times WU = CW\times WV[/tex]
[tex] 14\times (2x + 2)= 12\times (2x + 5)[/tex]
[tex] 28x + 28= 24x + 60[/tex]
[tex] 28x - 24x =60-28[/tex]
[tex] 4x =32[/tex]
[tex] x =\frac{32}{4}[/tex]
[tex] x =8[/tex]
UT = 14+ 2x + 2
CV = 12+2x+5
UT + CV = 14 + 2x + 2 + 12 + 2x + 5
UT + CV = 4x + 33
UT + CV = 4*8+ 33 = 32 + 33 = 65
UT + CV = 65
[10 points]
find the range of each of the following function. All the function are definied for all values of x.
f(x) = 3(x+5)² +2
Can you give the answer and explanation?
what does 'all the function are definied for all values of x'?
Heldpdlsoemss
Answer:
y ≥ 2
Step-by-step explanation:
The range is all of the values that f(x) can have. In order to find the range, let's first find the vertex. That's pretty easy to do since f(x) is already written in vertex notation (vertex notation is f(x) = a(x - c)² + d where (c, d) is the vertex). Since c = -5 and d = 2, the vertex is (-5, 2). Because the value of a is positive (a = 3 in this case, which is positive) we know that the parabola opens upward, therefore the vertex is the minimum. This means that the y-coordinate of the vertex is the smallest possible y-value of the function, therefore, since the y-coordinate of the vertex is 2, the range is y ≥ 2. Note that we use ≥ and not >, this is because y can be 2, therefore, it is included in the solution set.
Answer:
Hey there!
First, we must understand what range is. Range is just another word for all the possible y values of the equation.
This equation, f(x) = 3(x+5)² +2 is in vertex form. We see that this creates a parabola with a vertex at (-5, 2) and opens up.
Thus, the range of this graph would be: [2,∞) in interval notation. Note, the [ is used for greater than or equal to, or less than or equal to, and the ")" is used for less than or greater than.
We use ) for ∞, because ∞ is just a concept, not a real number.
Finally, all functions are defined for all values of x means that this is an f(x) function, and the f(x) is equal to something that can be written in terms of x.
Let me know if this helps :)
The length of a rectangle is 6 feet more than three times the width of the
rectangle. The length of the rectangle is 24 feet. What is the width of the
rectangle?
Answer:
width = 6 feetStep-by-step explanation:
let l be the length of the rectangle
let w be the width of the rectangle
The statement
The length of a rectangle is 6 feet more than three times the width of the
rectangle is written as
l = 6 + 3w
From the question
l = 24 feet
Substitute the value into the above formula and solve for the width
That's
24 = 6 + 3w
3w = 24 - 6
3w = 18
Divide both sides by 3
w = 6
Therefore
width = 6 feetHope this helps you
Four pounds of apples cost $5. Eight pounds of apples cost $10. If the total cost of apples, y, varies directly with the number of pounds of apples purchased, x, what is the cost of 6 pounds of apples? Round your answer to the nearest hundredth.
5 / 4 =1.25PER LB
1.25 x 6 =7.5
Go to my profile and go to the question where it says “what is the simplified expression.....” and please answer I need help!!
Answer:
Noun. (plural simplified expressions) (mathematics) an expression that has been condensed and shortened, so that all the like terms have been combined.
Step-by-step explanation:
you are welcome!
Answer:
i answered all of them!
Step-by-step explanation:
If you were to plot the point (-2, -6) what would be the correct method? *
Solve the equation. Write no solution if there is none
Answer:
no solution
Step-by-step explanation:
|m|/2 -1=-3
step 1= |m|/2=-3+1
step 2=|m|/2=-2
Step 3: Solve Absolute Value.
|m|=−4
No solutions. (Absolute value cannot be less than 0.)
Greetings,
I hope you and your family are staying safe and healthy!
Answer: No Solution
Step-by-step explanation:
[tex]\frac{|m|}{2} - 1 = -3\\\\\frac{|m|-2}{2} = -3\\\\[/tex]
Alternate forms assuming m > 0
[tex]\frac{m}{2} -1 = -3\\\\\frac{m-2}{2} = -2[/tex]
[tex]\frac{\sqrt{m^2} }{2} - 1 = -3[/tex]
Therefore,
No solutions exist.
I guaranteed correct answers only. Please kindly rate my answer and press the heart. Thanks!
Use this information for problems 1 and 2. When full, one of the pools at Sapphire Island will hold 43,000 gallons of water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute.
Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level.
a
\large 130+20000\left(60h\right)=43000
b
\large 60\left(130\right)+20000h=43000
c
\large 130\left(60h\right)-20000=43000
d
\large 130\left(60h\right)+20000=43000
Answer:
The correct option is;
d. 130·(60·h)+2000 = 43000
Step-by-step explanation:
The volume of water held by a pool at Sapphire island = 43,000 gallons
The volume of water the pool currently holds = 20,000 gallons
The rate at which the pool is being filled = 130 gallons/minute
The equation to find h, the number of hours it will take to fill the pool from its current level can be written as follows;
The rate at which the pool is being filled in gallons per hour = 130 × 60 gallons/hour = 7800 gallons/hour
We have;
The volume of water pumped in h hours = (130×60) gallon/hour × h hour = 130×60×h gallons
Whereby we want the total volume of water in the pool to be 43,000 gallons, we add the volume of water obtained from pumping for hours to the volume of water already in the pool, to get 43,000 gallons as follows;
130×60×h gallons + 20,000 gallons = 43,000 gallons
Therefore, the correct option is 130·(60·h)+2000 = 43000.
Read the question and help me, please.
===============================================
Explanation:
Add the equations by adding the terms straight down.
The x terms add to x+x = 2x.
The y terms add to y+(-y) = y-y = 0y = 0, so the y terms go away
The constants add to 5+7 = 12
The z terms add to -z+z = 0z = 0 and those go away as well
After all that adding, we have 2x = 12 which solves to x = 6 after dividing both sides by 2.
the lines on a 2 cup liquid measuring cup divide each cup into eighths. if you measure 1 3/4 cups of water, between which 2 quantities can you be certain that your exact measurement will be?
Answer:
13 th and 14 th
Step-by-step explanation:
Since the line divides the cup into one - eighth
Thus a measurement of 1 3/4
The number of 1/8th's obtainable from 1 3/4 :
1 3/4 = 7/4
7/4 divided by 1/8th
7/4 ÷ 1/8
7/4 × 8/1
= 56/4 = 14
14 gives the upper limit of the line starting from the bottom, Therefore, a measurement of 1 3/4 should be between the 13 th and 14 th line. Since the bottom of the cup will have no line.
HELP ME PLEASE ITS DUE TODAY AND EXPLAIN HOW U GOT IT AND ILL MARK U THE BRAINLIEST!!!!
Answer: p= 1/7
Step-by-step explanation:
5/7=p+4/7
-p=4/7-5/7
-p=-1/7
P=1/7
PLEASE HELP!!!!!!! Figure B is a scaled copy of Figure A. What is the scale factor from Figure A to Figure B?
Answer:
1:4
Step-by-step explanation:
Find the ratio of corresponding sides
[tex]\frac{10}{40}=\frac{1}{4}\\\\\\\frac{11}{44}=\frac{1}{4}\\\\\\\frac{18}{72}=\frac{1}{4}\\\\\[/tex]
Scale factor:
1:4
Answer:
4
To find the scale factor, we need to know what number we multiply each side length in Figure AAA by to get the corresponding side length in Figure BBB.
Let's see how the corresponding sides relate:
10×4
11×4
18×4
=40
=44
=72
(a+3) (a-3)find the products
Answer:
a^2-9
Step-by-step explanation:
if 3x-9 =12then the value of x is:
Answer:
Hey there!
3x-9=12
3x=21
x=7
Let me know if this helps :)
Answer:
x= 7Step-by-step explanation:
[tex]3x - 9 = 12 \\ collect \: like \: terms \\ 3x = 12 + 9 \\ 3x = 21 \\ divide \: both \: sides \: by \: 3[/tex]
[tex] \frac{3x}{3} = \frac{21}{7} \\ x = 7[/tex]
A scuba diver started her dive at 2{:}42 \text { p.M.}2:42 p.M.2, colon, 42, start text, space, p, point, m, point, end text and finished diving at 3{:}17 \text { p.M.}3:17 p.M.3, colon, 17, start text, space, p, point, m, point, end text How long did the dive last?
Answer:
35 minutes
Step-by-step explanation:
From 2:42 to 3:00, there are 18 minutes and from 3:00 to 3:17, there are 17 minutes so the answer is 18 + 17 = 35 minutes.
Four consecutive even integers are such that the sum of the second and fourth is 76. What is the sum of the first and third integers?
Answer:
72
Step-by-step explanation:
Consecutive even integers have a difference of 2 between them
let n be the first integer, then
n + 2, n + 4, n + 6 are the second, third and fourth, then
n + 2 + n + 6 = 76 ( sum of second and fourth )
2n + 8 = 76 ( subtract 8 from both sides )
2n = 68 ( divide both sides by 2 )
n = 34
Thus the 4 even integers are
34, 36, 38, 40
sum of first and third = 34 + 38 = 72
11. Income: $500
Expenses: $120
find the profit
lesson 3.6 practice
Which term best describes the
quadrilateral formed by A(2, 3),
B(4, 6), C(8, 9), and D(5,5)?
Answer:
A kite
Step-by-step explanation:
The coordinates of the vertices of the quadrilateral are;
A(2, 3), B(4, 6), C(8, 9), and D(5, 5), therefore, the length of the sides of the quadrilateral can be found using the following formula;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
(x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints on the side
For side AB, we have;
[tex]l_{AB} = \sqrt{\left (6 - 3 \right )^{2}+\left (4-2 \right )^{2}} = \sqrt{13}[/tex]
The slope = 1.5
For side BC, we have;
[tex]l_{BC} = \sqrt{\left (9 - 6 \right )^{2}+\left (8-4 \right )^{2}} = 5[/tex]
The slope = 3/4
For side CD, we have;
[tex]l_{CD} = \sqrt{\left (5 - 9 \right )^{2}+\left (5-8 \right )^{2}} = 5[/tex]
The slope = 4/3
For side DA, we have;
[tex]l_{DA} = \sqrt{\left (3 - 5 \right )^{2}+\left (2-5 \right )^{2}} = \sqrt{13}[/tex]
The slope = 2/3
Angle ADC = Actan (2/3 - 4/3)/(1 + 2/3*4/3) = -19.44 = 180-19.44 = 160.55°
Angle ABC = Actan (0.75 - 1.5)/(1 + 0.75*1.5) = -19.44 = 180-19.44 = 160.55°
Therefore, given that the quadrilateral has two pairs of equal adjacent sides and the angles are equal at the meeting point of the two squares, it is best described as a kite.
Johnathan makes $27 per hour and works 25 hours per week. Every week, he has to sell 20 items. If he sells more than 20 items in a week, he receives a commission of 14% on each set of additional 5 items he sells. This week he worked for 25 hours, he sold 25 items, and he made $1,000 in sales beyond the required 20 items. Which equation will help Johnathan to compute this weeks income?
Answer:
Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815
Step-by-step explanation:
Number of hours for which Johnathan worked = 25
Salary for each hour = $27
So, income for 25 hours = 25 [tex]\times[/tex] 27 = $675
Now, it is given that he has sold 25 items.
Sales made beyond the 20 items = $1000
Additional income for additional sales = 14% on each set of 5 items
He has sold exactly 5 additional items that means 1 set of 5 additional items.
So, Additional income for additional sales = 14% [tex]\times[/tex] 1000 = $140
Therefore, total income of this week = Income for 25 hours + Income due to additional sales of 5 items
Therefore Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815
How many times greater is the value of 4 in 4735 than the value of the 4 in 6412
Answer:
10 times
Step-by-step explanation:
Since the leftmost value is called ones place.
the second leftmost value is called tens place.
the third leftmost value is called a hundred place.
the fourth leftmost value is called a thousand place and so on.
So, The value of 4 in 4,735 is 4 thousand = 4,000
and the value of 4 in 6,412 is 4 hundred = 400.
Hence, the value of the 4 in 4,735 is 10 times the value of the 4 in 6,412.
Answer:
10 times greater.
Step-by-step explanation:
4 in 4735 has a values of 4000.
In 6412 it has a values of 400.
Evaluate. 58−(14)2= ________
Answer:
the answer for 58-(14)2=
its = 30
Step-by-step explanation:
58-(14)2. It can also be written as 58-2(14)
58-28
= 30
find the distance between points P(3, 4) and Q(4, -6) If necessary round to the nearest hundredth.
Answer:
10.05 units
Step-by-step explanation:
We can find the distance between these points using the distance formula. The distance formula is:
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We know that x1 is 3, x2 is 4, y1 is 4, and y2 is -6, so we can substitute inside the equation.
[tex]\sqrt{(4 - 3)^2 + (-6 - 4)^2} \\\\\sqrt{1^2 + -10^2} \\\\\sqrt{1 + 100} \\\\\sqrt{101} \\\\\approx10.05[/tex]
Hope this helped!
Simplify the expression: (5 - 4i) (6 - 2i).
Answer:
22 - 34i
Step-by-step explanation:
note that i² = - 1
Given
(5 - 4i)(6 - 2i) ← expand factors using FOIL
= 30 - 10i - 24i + 8i²
= 30 - 10i - 24i - 8 ← collect like terms
22 - 34i
Answer:
22 - 34i
Step-by-step explanation:
How do I solve this? Please explain step by step,thankyou!
Answer:
Hey there!
Angle x would be 62 degrees because angles in a triangle add to 180 degrees.
Let me know if this helps :)
Answer:
x = 62 degrees
Step-by-step explanation:
Total degrees of a triangle = 180
=> 68.5 + 49.5 + x = 180
=> 118 + x = 180
=> 118 - 118 + x = 180 - 118
=> x = 62
HELP!!!
Which of the following data sets is illustrated by this stem and leaf plot?
Answer:
it will be A. good buddy
Step-by-step explanation:
The data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123. The correct option is B.
What is a stemplot?A stem-and-leaf display, also known as a stem-and-leaf plot, is a technique used to visualize the shape of distribution by displaying data in a graphical fashion, similar to a histogram.
The data represented by the different rows of stem-and-leaf display is,
First row → 25, 26, 27
Second row → 53, 58
Third row → 62, 67, 69
Fourth Row → 96, 96
Fifth Row → 123
Hence, the data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123.
Learn more about Stemplot here:
https://brainly.com/question/9125085
#SPJ2
What is the equation of the circle with center (–2, 5) that passes through the point (–3, 8)?
Given that g(x) = 3x - 5, evaluate g(4 + h)
————
h
Answer:
3h+7/h
Step-by-step explanation:
the parenthesis in g(4+h) is saying that is x. plug in 4+h in the x and evaluate.
so you would get 3(4+h)-5. distribute the 3 and get 12+3h-5. combine like terms to get 3h+7!
then it's just over h because you can't simplify anymore. so the real answer is 3h+7/h!!