The distance between the points in radical form is [tex]\sqrt{52}[/tex]
What is distance formula ?
Formula for distances between pairs of points, an algebraic expression that expresses distances as a function of the coordinates of the points The Pythagorean theorem is the foundation for distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space.
To calculate the distance we use distance formula
[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]
where [tex](x_{1},y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are the 2 coordinates
[tex](x_{1},y_{1} )[/tex] = (-2,-4)
[tex](x_{2} , y_{2} )[/tex] = (4,0)
d = √(4 - (-2))² + (0 - (-4))²
d = √6² + 4²
d = √36 + 16
d = √52
√52 → radical form
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The midpoint of AB is M(1,-4). If the coordinates of A are (-3, -6), what are
the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -3}{2}~~~ ,~~~ \cfrac{ y -6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=1\implies x-3=2\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -6}{2}=-4\implies y-6=-8\implies \boxed{y=-2}[/tex]
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 8ft Find the area of the shaded region.
Use the value 3.14 for PI , and do not round your answer. Be sure to include the correct unit in your answer.
it wont let me paste the picture but please help
Answer: 6.88 cm sq.
1. Find the area of the rectangle
A=l *w
L=8cm
the width=the radius of the semicircle
Width=8/2=4
8*4=32
A=32cm sq
2. find area of the semicircle
area=pi times the radius squared divided by 2
r=4cm
A=(3.14)*4^2/2. The area =25.12 cm sq.
Area of the shaded region=32-25.12=6.88cm sq.
19. Number Sense A company had
9 x 106 dollars in sales last year. Explain
how to find the product 9 × 106.
Answer: 954
Step-by-step explanation:
9x106 = 954
PLS HELP DUE TODAY!!!
The graph g has a minimum value at it's vertex, (3, -1).
What is vertex?
The point where a parabola's line of symmetry intersects with the parabola itself is known as the vertex. The vertex of a parabola whose equation is given in standard form will be the lowest point on the graph and the highest point on the graph depending on certain conditions.
The given graph g is a upward parabola.
Since the upward parabola having a minimum value at it's vertex.
And the downward parabola having a maximum value at it's vertex.
Here, the vertex of the upward parabola is, (3, -1).
Therefore, the minimum value of g is, (3, -1).
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Waskahat wants to make a pair of earrings of different sized circles. The diameter of the first circle is 10 cm and that of the second is 6 cm. For his project, Waskahat determines that 35 beads will cover an area of 1 cm². How many beads in total will he need to make BOTH circles? Please answer with a whole number.
The number of beads needed to make both pair of earrings is 3090.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The diameter of first circle is 10 cm.
The diameter of second circle is 4 cm.
And, the area covered by 35 beads is 1 cm².
Now, the area of first and second circle is given by substituting the diameters in the expression for area πD²/4 as,
Area of the first circle = (π × 10²)/4
= 25π cm².
Area of the second circle = (π × 4²)/4
= 4π cm²
The total area is 25π + 4π = 29π cm².
Now, the number of beads can be determined using the unitary method as below,
Number of beads for 1 cm² area is 35.
So, the beads for 29π cm² area is 35 × 29π = 3090.
Hence, the number of beads required for both the circles is 3090.
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Complete (assume $100,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 25,000 A B Dept. B 75,000 C D
The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:
Ratio Amount
Department A 0.25 $25,000
Department B 0.75 $75,000
What is the ratio?Ratios show the relative values or proportions of the whole shared by two or more numbers.
Ratios are fractional values like proportions and are depicted in fractions, decimals, and percentages.
Total distributable overhead = $100,000
Ratios = 25,000:75,000
= 25:75
= 5: 15
= 1:3
Sum of Ratios = 4
OR
= 0.25:0.75
Sum of Ratios = 1
Overhead Allocation:Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 10,000 A = 1 B = $25,000 ($100,000 x 0.25)
Dept. B 30,000 C = 3 D = $75,000 ($100,000 x 0.75)
Thus, based on the cost driver ratios, Department A bears $25,000, while Department B will be allocated $75,000 of the allocated overhead costs.
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Question
Write the word sentence as an equation. Then solve.
A number x divided by −9 is −16.
Equation:
Solution: x=
Answer:
Equation: x/-9 = 16
Solution: x = -144
Step-by-step explanation:
The "number x divided by -9 is 16" means x/-9 = 16, then we solve for x by multiplying both sides by "-9" to solve for x
x/-9 = 16
-9x/-9 = 16(-9)
x = -144
HELPPPP ASAPP
The number of chapters read, y, after x days. The slope of the line is 5/4 and the y-intercept is 2. The slope of 5/4 means that....
A. Every 4 days, you read 5 chapters
B. Every 5 days you read 4 chapters
C. You started on chapter 4 out of 5 chapters
How can I solve 2/1 divided by 3/11 using the giant one method
Giant one method: It is the method in which we multiply any fraction and we get an equivalent fraction.
For example:
1/2 x 1 (giant one) can also be written as:
=> 1/2 x 8/8
=> 8/16
It is also the method in which we divide any fraction and we get an equivalent fraction.
For example:
21/30 ÷ 1 (giant one) can also be written as:
=> 21/30 ÷ 3/3
=> 7/10
Solving the question:
2/1 ÷ 3/11
Solving this we get
=> 2 x 11/3 = 22/3
Multiplying giant one (1) through the giant one method.
=> 22/3 x 1 (giant one)
Multiplying both numerator and denominator by 3.
=> 22/3 x 3/3
=> 66/9
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Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −1≤x≤4
The average rate of change of the function h(x) = - x² + x + 4 is equal to 22 / 5.
How to determine the average rate of change of a function
In this problem we find the definition of a function and its interval regarding an average rate of change. Graphically speaking, the average rate of change of the function over an interval is represented by the slope of a secant line that passes through two function points related to the interval limits.
The average rate of change is represented by the following formula:
m = [h(b) - h(a)] / (b - a), for a ≤ x ≤ b
If we know that h(x) = - x² + x + 4, a = - 1 and b = 4, then the average rate of change is:
m = [h(4) - h(- 1)] / [4 - (- 1)]
m = [h(4) - h(- 1)] / 5
m = (- 4² + 4 + 4 + (- 1)² - (- 1) - 4) / 5
m = (17 + 5) / 5
m = 22 / 5
The average rate of change is equal to 22 / 5.
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The equation m=3b represents the times in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b) A: 3 B: 6 C:1/3 D: 1
For the given equation:
m = 3b
The constant of proportionality is 3, so the correct option is A.
How to determine the constant of proportionality?
After a small search on the internet, I've found that this question asks for the constant of proportionality.
Remember that a proportional relation is of the form:
y = k*x
Where k is the constant of proportionality, and x and y are the variables.
Here the relation is:
m = 3*b
Where m and b are the variables, then the remaining coefficient is the constant of proportionality, which is 3.
In this way, we can see that the correct option is A.
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98x972-67=??????????????????????????
Answer:
95,189
Step-by-step explanation:
98x972-67
95256-67
95189
Answer:95189
Step-by-step explanation: First you ave to multiply 98 x 972 which would equal to 95256 ten subtract 67 which would give you the answer 95189
Kevin has a coin collection. He keeps 5 of the coins in his box, which is 25% of the collection. How many total coins are in his collection?
Answer:
20 coins
Step-by-step explanation:
[tex]\frac{5}{\frac{25}{100} }[/tex] = 20
Answer:
[tex]\huge\boxed{\sf Total\ collection = 20\ coins}[/tex]
Step-by-step explanation:
25% of the collection = 5 coins
Total collection = 100%So,
100% = 25% + 25% + 25% + 25%
100% = 5 + 5 + 5 + 5
100% = 20 coins
Total collection = 20 coins[tex]\rule[225]{225}{2}[/tex]
A car travels 55 miles per hour for 2 hours
How much will it travel 1/2 per hour
How much will it travel in 1 1/2 per hour?
Answer:
2 hours 110
Step-by-step explanation:
Adan is writing a comic book. His publisher has requested that he turned 50 pages draft by one day. If he's written 40 pages what percent does he still need to complete?
What is the GCF of x*y2z and x1y?
Answer:
xy
Step-by-step explanation:
if you take xy out of xy^2z it will become yz
if you take you xy out of xy it becomes 1 so this is the greatest factor
(please tell me if i got any digits wrong i assumed some were exponets)
hopes this helps please mark brainliest
Answer:
1. x² 2. x
Step-by-step explanation:
For these problems, there actually pretty easy. What you do is the numbers like x2 are x times 2. So, like if x is 3, it would be equal to 6 because 3 times 2 is 6. Easy, right?
But this time, it is asking you for GCF. It's harder, but it will be easy after you understand it.
#1
So, it organizes the equation. So x2 gets simplified to x times 2. x*2 is double the amount. x + y and x - z. Take the x's that is 2 x's. So x2. Then y and z which are unknown has the value left. And 1 more thing. Since there is no operation, it turns in to times/multiply. Please don't ask why. Ask it in a new question. So you can cross them off and multiply x2 with y times z. The equation now is basically x2 y times z). y times z. Again, the numbers are unknown. So you need to count them as zero. Add 2 zero's together is 0. Add x2 to 0. Which is x2.
You can now do problem 2 by yourself after you read the explanation. Remember, your answer isn't always like this type of explanation. Some one's work, try this for all your problems related. See if it works.
Therefore, the GCF of x2(x + y) (x - z) is x2
ASAP 100 Points!!!!!
The table represents the amount of money in a bank account each month.
Month Balance ($)
1 3,600.00
2 3,960.00
3 4,356.00
4 4,791.60
5 5,270.76
What type of function represents the bank account as a function of time? Justify your answer.
This is an exponential function because there is a common difference in the balance between the months.
This is an exponential function because there is a common ratio in the balance between the months.
This is a linear function because there is a common difference in the balance between the months.
This is a linear function because there is a common ratio in the balance between the months.
Answer:
the second answer
Step-by-step explanation:
Answer:
This is an exponential function because there is a common ratio in the balance between the months.
Step-by-step explanation:
If we look at the first and second month of balance, we can see that the difference is 360. If we multiply that by 5, it equalls 1800. If we subtract 5270--3600, it equals 1670, meaning that there is not a linear function, nor a common difference, meaning that the second answer would be correct.
5 It is given that x2 - 5x + 6 and x3 - 6x² +11x + a have a common factor.
Find the possible value of a.
The possible value a using common factor is -6.
What is factors of the expression?
A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in a product, then the numbers we are multiplying are factors of the product because the product is divisible by them.
Here the given expression is,
=> [tex]x^2-5x+6=x^2-2x-3x+6[/tex]
=>x(x-2)-3(x-2)
=>(x-2)(x-3)
For the pair of polynomial have a common factor, 2 or 3 must be a root of the second polynomial.
If 2 is root then,
=> [tex]x^3-6x^2+11x+a[/tex] = 0 for x=2
=>8-24+22+a=0
=>6+a=0
=>a=-6.
If 3 is root then,
=> [tex]x^3-6x^2+11x+a[/tex] = 0 for x=3
=>27-54+33+a =0
=>6+a=0
=>a=-6.
Hence the possible value of a is -6.
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Help me please its the last question before I finish.
Answer:5/2
Step-by-step explanation: Slope is rise (how far up or down) over run (how far left to right. Look for points where the line crosses a perfect grid line intersection. The graph goes up to 50 and right 20 (started at 10 and ended at 30). The rise/run is 50/20 or 5/2 reduced.
first, find two places on the line that intersects the grid boxed neatly. This occurs at (10 , 0) and (30 , 50).
slope = change in rise / change in run
slope = change in y / change in x
slope = ( 0 - 50) / (10 - 30)
slope = -50/-20
slope = 50/20
slope = 5/2
Solve for m.
- 3/7 m = 12
Answer:
-28
Step-by-step explanation:
Isolate m in the equation first: m = 12 / (-3/7)
Simplify and solve: m = -84/3 = -28
Answer:
-28
Step-by-step explanation:
3/7=0.4285714285714
0.4285714285714 × 28 equals 11.99 which is estimated to 12.
Solve for the missing measure of X
Answer:
x = 4
Step-by-step explanation:
4x+8 = 6x
6x-4x = 8
2x = 8
2/2 x = 8/2
x = 4
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
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Point C is an orthocenter. Solve for X
Look at pic thanks
In the triangle Point C is the orthocenter then the value of x will be equal to 42.
What is Orthocenter?The intersection of the cutting point of the triangle's three elevations is known as the orthocenter. The height in this instance is indeed the line to be drawn from the triangle's apex that is perpendicular to the other side.
As per the given diagram and data in the question,
The orthocenter is at Point C.
C = 3x - 36
3x - 36 = 90
3x = 90 + 36
3x = 126
x = 126/3
x = 42
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The area of square $ABCD$ is 100 square centimeters, and $AE = 2$ cm. What is the area of square $EFGH$, in square centimeters?
The area of square EFGH is 68 square centimeters
What is the area of a geometric figure?The area of a geometric shape or figure is the area enclosed in its boundary.
Please find attached a possible drawing of the information in the question
The area of square ABCD = 100 square centimeters
Length of segment AE = 2 cm
Therefore;'
The side length of the square ABCD, s = √(100) = 10
The length of segment AB = 10 cm
AB = AE + EB (segment addition postulate)
10 = 2 + EB (substitution property of equality)
EB = 10 - 2 = 8
EB = 8 cm
∠CFG ≅ ∠AHE (alternate interior angles)
ΔCFG ≅ ΔAHE (ASA congruency postulate)
Similarly; ΔEBF ≅ ΔHAE (ASA congruency postulate)
BF = AE (CPCTC) = 2
[tex]\overline{EF}=\sqrt{\overline{EB}^2 +\overline{BF}^2}[/tex](Pythagorean theorem)
Therefore;
EF = √(8² + 2²) = √(68)
EF = √(68)
Area of a square = (Length of one side)²
Therefore, area of square EFGH = [tex]\overline{EF}^2[/tex]
Which gives; Area of square EFGH = (√(68))² = 68
The area of square EFGH is 68 square meters
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Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
The amount Stefan spent originally to buy the bike is; $100.91.
The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.
How much did the bicycle cost originally?According to the task content;
Stefan sold the bicycle and helmet for a total of;
104 + 17 = $111.
Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have
110% × x = 111
x = (111 × 100) / 110
x = $100.91.
Therefore, Stefan spent $100.91 originally to buy the bike and helmet.
Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.
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3. Solve for x: 2x+4=x-6.
a. x=-12
b. x = 10
C. X=-16
d. x=-10
Answer:
D. x = -10
Step-by-step explanation:
2x + 4 = x - 6
combine like terms
1x = -10
-10
5 candy bars with 12 sections split between 3 friends equally. Must be in Fraction Form
Answer:
Well 5 candy bars with 12 sections would make 60 sections to divide among the 3 friends. (5 multiplied by 12)
60 sections divided by 3 friends is 20 sections each.
20/1
1/5X+8=1/10X+9
What’s the answer to this question?
1/5x+8=1/10x+9.
We move all terms to the left:
1/5x+8-(1/10x+9.)=0
The domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x+9.)!=0
x∈R
We add all the numbers together, and all the variables
1/5x-(1/10x+9)+8=0
We get rid of parentheses
1/5x-1/10x-9+8=0
We calculate fractions
10x/50x^2+(-5x)/50x^2-9+8=0
We add all the numbers together, and all the variables
10x/50x^2+(-5x)/50x^2-1=0
We multiply all the terms by the denominator
10x+(-5x)-1*50x^2=0
Wy multiply elements
-50x^2+10x+(-5x)=0
We get rid of parentheses
-50x^2+10x-5x=0
We add all the numbers together, and all the variables
-50x^2+5x=0
a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use the following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=25−−√=5
x1=−b−Δ√2a=−(5)−52∗−50=−10−100=1/10
x2=−b+Δ√2a=−(5)+52∗−50=0−100=0
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Please help, 50 points & brainiest if you answer all 3!!!
9. The plane's speed would be of 340 and 350 miles per hour.
10. She runs the downhill portion of the course at a rate of 10 miles per hour.
11. The total time would be of 24 minutes.
How to obtain the velocity?
Velocity is distance divided by time, hence the equations is:
v = d/t.
For the first plane, the velocity and the distances are given by:
v = v + 10, d = 495.
Hence:
v + 10 = 495/t
t = 495/v + 10
For the second plane, the velocity and the distance are:
v = v, d = 510.
Hence:
v = 510/t
t = 510/v
The time is equal, hence the velocity of the slower plane is obtained as follows:
495/v + 10 = 510/v
Applying cross multiplication:
510v + 5100 = 495v
15v = 5100
v = 5100/15
v = 340 mph
For the runner, we have two parts, as follows:
First part: distance of 3 miles, velocity of v - 5, time of t.Second part: distance of 4 miles, velocity of v, time of 1 - t.Hence the equations are given as follows:
v - 5 = 3/t.v = 4/(1 - t).From the first equation, we have that:
v = 5 + 3/t.
Replacing in the second, we have that:
5 + 3/t = 4/(1 - t)
(5t + 3)/t = 4/(1 - t)
Applying cross multiplication, we have that:
(5t + 3)(1 - t) = 4t
-5t² + 2t + 3 = 4t
5t² + 2t - 3 = 0.
The positive solution, as time is a positive measure, of the quadratic equation is given by:
t = 0.6.
Hence the velocity of the downhill part is given by:
v = 4/(1 - t) = 4/0.4 = 10 miles per hour.
What is the together rate?The together rate is the sum of each separate rates.
The rates in this problem are given as follows:
Jason: 1/30.Kevin: 1/120.Together: 1/x.Hence:
1/x = 1/30 + 1/120
1/x = 5/120
x = 120/5
x = 24 minutes.
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f(x) = 2x2 − 7x − 72
