[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-5)]^2 + [-7 - (-4)]^2}\implies d=\sqrt{(3+5)^2 + (-7+4)^2} \\\\\\ d=\sqrt{8^2 + (-3)^2}\implies d=\sqrt{64+9}\implies d=\sqrt{73}[/tex]
Simplify
(6√2+2√3)(√10-4√7)
Answer:
[tex]\boxed{\tt = 1 2√5−24√(14)+2√(30)−8√(21)}[/tex]
Or
[tex]\boxed{ \tt \approx88.7}[/tex]
Step-by-step explanation:
Apply FOIL method to expand:
[tex] =\tt6√2(√(10)−4√7)+2√3(√(10)−4√7)[/tex]
[tex] \tt \:=6√2√(10)+6√2(−4√7)+2√3(√(10)−4√7)[/tex]
[tex] \tt \: = 6√2√(10)+6√2(−4√7)+2√3√10+2√3(−4√7)[/tex]
Simplify:
[tex] =\tt6√(20)+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]
[tex] \tt \: = 6 \sqrt{2 {}^{2} \times 5} +6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]
[tex] \tt \: = 6(2√5)+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]
[tex] \tt = 12√5+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]
[tex] \tt = 12√5−24√(14)+2√3√(10)+2√3(−4√7)[/tex]
[tex] \tt \: = 12√5−24√14+2√(30)+2√3(−4√7)[/tex]
[tex] \tt \: = 12√5−24√(14)+2√(30)−8√(21)[/tex]
or
[tex] \tt \: \approx88.7[/tex]
[tex]\rule{230pt}{2pt}[/tex]
[tex]\left( 6 \sqrt 2 + 2 \sqrt 3 \right) \left( \sqrt{10} -4 \sqrt7 \right)\\\\=\left(6\sqrt 2 \right) \left(\sqrt{10} \right) - \left(6\sqrt 2\right)\left(4\sqrt 7 \right)+\left(2\sqrt 3 \right) \left(\sqrt{10} \right)-\left(2\sqrt 3 \right) \left(4 \sqrt 7 \right)\\\\=6\sqrt{2 \cdot 10} -24\sqrt{2 \cdot 7} + 2\sqrt{10 \cdot 3} - 8 \sqrt{3 \cdot 7}\\\\=6\sqrt{4 \cdot 5}-24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\=6\cdot 2\sqrt 5-24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\[/tex]
[tex]=12\sqrt{5} -24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\\approx -88.68[/tex]
If a ∝ b and a = 18 when b = 3, then find a when b = 5.
show how you got ur answer so I can see if it makes sense!
"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that
a = kb
We're given that a = 18 and b = 3, so that
18 = 3k ⇒ k = 6
Then when b = 5, we would have
a = 6 × 5 = 30
Need help in math ASAP
Answer:
B
Step-by-step explanation:
Find the volume of the wading pool
Use V = pi * r^2 * h
Givens
r = 6 feet
h = 1.5 feet
pi = 3.14
2 f^2 takes 2 minutes.
Solution
V = pr * r^2 + h
r = d/2
r = 6 / 2
r = 3 feet
Put the givens into the formula
V = 3.14 * 3 * 3 * 1.5
V = 42.39 cubic feet
Time
2 cubic feet takes 1 minutes
42.39 cubic feet takes x
2/42.39 = 1/x Cross multiply
2x = 42.39 Divide by 2
2x/2 = 42.39/2
x = 21 rounded to the nearest whole number.
Round your answer to the nearest hundredth.
A= ?
Answer:
ok , using Pythagoras theorem hyp²=opp²+adj² therefore /CB/ will be opp , Making A the angle
7²=opp²+5² which is 49=x²+25
x²=49-25=✓24
=4.9
using SOH CAH TOA
sin A = 4.9/7
=0.7 , A is then sin-¹ 0.7
=136
use cosine since you are given the adjacent side and the hypotenuse
Cos θ = [tex]\frac{adj}{hyp}[/tex]
Cos θ = [tex]\frac{5}{7}[/tex]
use the inverse of cosine to find the angle
θ = [tex]cos^{-1}(\frac{5}{7})[/tex]
θ = 44.4153086...
θ = 44.42°
see attachment below
Answer:
144
Step-by-step explanation:
I think.
Which represents the solution(s) of the graphed system of equations, y = x2 x – 2 and y = 2x – 2? (–2, 0) and (0, 1) (0, –2) and (1, 0) (–2, 0) and (1, 0) (0, –2) and (0, 1)
The solution to the system of equation are (0, -2) and (1, 0)
Solution to system of equationsSystem of equations are equations that has unknown and more than 1 equations.
Given the system of equations
y = x^2 + x – 2
y = 2x – 2
Equate both expressions
x^2 + x -2 = 2x - 2
x^2 - x = 0
x(x-1) = 0
x = 0 and x - 1 = 0
x = 0 and 1
If x = 0
y = 0 - 2 = -2
If x = 1
y = 2 - 2 = 0
Hence the solution to the system of equation are (0, -2) and (1, 0)
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WILL MARK BRAINLIEST!!
The times taken to assemble a clock at a factory are approximately normally distributed with a given mean l = 3 hr and standard deviation o = 0.5 hr. What percentage of the times are between 2 hr and 4 hr?
PLEASE SHOW WORK! :)
•95%
Answer:
95%
Step-by-step explanation:
Find the value of x.
135⁰
(7x+2)
x = [?]°
A parabola opening up or down has vertex (0,-4) and passes through (-12,14). Write its equation in vertex form
The value of a will be 0.125. Then the value of a is positive then the parabola will be upward.
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.
A parabola opening up or down has vertex (0,-4) and passes through (-12,14).
The equation of the parabola is given as
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
(h, k) = (0, -4)
Then the equation of the parabola will be
y = a(x)² - 4
The parabola is passing through (-12, 14). Then the value of a will be
14 = a(-12)² - 4
14 = 144a - 4
144a = 18
a = 1/8
a = 0.125
Then the equation of the parabola will be
y = 0.125x² - 4
If the value of a is positive then the parabola will be upward.
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manny spent $36 on 30 bottles of soda. how much would he spend on 12 bottles
Answer:
He would spend $14.40 on 12 bottles.
For fundraiser a student is selling pizza for $5 and subs for $3. the students sold 11 more subs than pizza. he sold a total of $233. many many pizza and subs did he sells
Answer:
25 pizzas and 36 subs
Step-by-step explanation:
5x+3x=233 --> but there are 11 more subs that pizza, so 11x3 is 33
(5x+3x) +33 = 233
5x+3x= 200
8x=200
x=25
so then 5 dollars by 25 pizzas, and 36 (25+11) subs at 3 dollars = 233$
Mary needs a board 4 feet and 8 inches long she cut a board 56 inches long is the board mary cut the right length? give a clear and appropriate answer, and tysm for whoever will help me
Answer:
4 ft 8 inches = 56 inches
Step-by-step explanation:
We know that there are 12 inches in a foot so first convert 4 ft to inches
4 ft = 4*12 = 48 inches
Add the 8 inches left over
48 inches + 8 inches
56 inches
4 ft 8 inches = 56 inches
At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the school should issue standardized grades (or 2-scores), in addition to the regular grades. How might this work? Harry was in four classes, each with 20 students. Harry's score, the class mean, and the class standard deviation are given below. Compute his standardized grade in each class. If we judged by standardized grades, where did he do best? Where did he do worst?
Answers:
The z scores are approximately:
Care of Magical Creatures: z = 0.333Defense Against the Dark Arts: z = 0.583Transfiguration: z = -0.263Potions: z = -0.533From those scores, we can say:
Best grade = Defense Against the Dark ArtsWorst grade = Potions=====================================================
Further Explanation:
We'll need to convert each given score to a corresponding standardized z score.
The formula to use is
z = (x - mu)/sigma
where,
x = given grade for each class mu = meansigma = standard deviationLet's find the z score for the Care of Magical Creatures class
z = (x - mu)/sigma
z = (3.80 - 3.75)/(0.15)
z = 0.333 approximately
Repeat this process for the Defense Against the Dark Arts score.
z = (x - mu)/sigma
z = (3.60 - 3.25)/(0.60)
z = 0.583 approximately
And for the Transfiguration class as well
z = (x - mu)/sigma
z = (3.10 - 3.20)/(0.38)
z = -0.263 approximately
The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.
Now do the final class (Potions) to get this z score
z = (x - mu)/sigma
z = (2.50 - 2.90)/(0.75)
z = -0.533 approximately
This grade is below average as well.
----------------------------
To summarize, we have these z scores
Care of Magical Creatures: z = 0.333Defense Against the Dark Arts: z = 0.583Transfiguration: z = -0.263Potions: z = -0.533Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.
8. Dennis made an extra $500 for selling furniture. The extra $500 was 5% of the toial value of the furniture he sold. What was the total value of the furniture Dennis sold?
A parabola y= ax^2 + k
passes through the points (-1, -3) and (3, 13). Find the values of a and k
Answer:
use vertex form of parabola:
y=a%28x-h%29%5E2%2Bk....if vertex (0,7), we have
y=a%28x-0%29%5E2%2B7
y=ax%5E2%2B7......use point (3,2) to find a
2=a%2A3%5E2%2B7
2=9a%2B7
2-7=9a
-5=9a
a=-5%2F9
so, your equation is: y=-%285%2F9%29x%5E2%2B7
Step-by-step explanation:
I NEED HELP !!!
What multiples to make 63 and Adds to make 19?
Answer:
4.27985 and 14.72015
Step-by-step explanation:
4.27985 x 14.72015 = 63
4.27985 + 14.72015 = 19
how do you do elimination and substitution in math??? I am literally so confused AND I have my math final tomorrow!!!
The algebraic method for solving simultaneous linear equations is the substitution method
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The algebraic method for solving simultaneous linear equations is the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
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Help QUICKKKKK please
Answer:
Step-by-step explanation:
Remark
The exposed perimeter of the triangle is just the two smaller legs of the right triangle (6 + 8) + 10 units at the bottom of the rectangle + two 1/2 circles.
The area of the figure is the area of the triangle at the top + the area of the two 1/2 circles + the rectangle in the middle.
Givens
Shortest Triangle Leg = 6Middle Triangle Leg = 8Diameter of the 2 half circlespi = 3.14width of the rectangle in the middle = 8Length of the rectangle = 10d = 8r = d/2 = 8/2 = 4Formula
A
Perimeter = 2 legs of the triangle + 2 half circles + bottom line
B
Area = (1/2) Leg1*leg2 + pi * r^2 + L * w
Solution
A Perimeter
Perimeter = 6 + 8 + 2*pi *r + 10
Perimeter = 24 + 2*3.14*4
Perimeter = 25.12
B Area
Area = 1/2 * 8 * 6 + 3.14*4^2 + 10* 8
Area = 24 + 50.24+ 80
Area = 150.24
Answer
P = 25.12
Area = 150.24
Divide: 91,035 ÷ 51 Enter the answer in the box.
Percent of Change
Percent of increase from 43 to 78, (Round to the nearest tenth of the
percent)
Before we continue, note that "percent increase from 43 to 78" is the same as "the percentage increase from 43 to 78". Furthermore, we will refer to 43 as the initial value and 78 as the final value.
So what exactly are we calculating? The initial value is 43, and then a percent is used to increase the initial value to the final value of 78. We want to calculate what that percent is!
Here are step-by-step instructions showing you how to calculate the percent increase from 43 to 78.
First, we calculate the amount of increase from 43 to 78 by subtracting the initial value from the final value, like this:
78 - 43
= 35
To calculate the percent of any number, you multiply the value (n) by the percent (p) and then divide the product by 100 to get the answer, like this:
(n × p) / 100 = Answer
In our case, we know that the initial value (n) is 43 and that the answer (amount of increase) is 35 to get the final value of 78. Therefore, we fill in what we know in the equation above to get the following equation:
(43 × p) / 100 = 35
Next, we solve the equation above for percent (p) by first multiplying each side by 100 and then dividing both sides by 43 to get percent (p):
(43 × p) / 100 = 35
((43 × p) / 100) × 100 = 35 × 100
43p = 3500
43p / 43 = 3500 / 43
p = 81.3953488372093
Percent Increase ≈ 81.3953
That's all there is to it! The percentage increase from 43 to 78 is 81.3953%. In other words, if you take 81.3953% of 43 and add it to 43, then the sum will be 78.
The step-by-step instructions above were made so we could clearly explain exactly what a percent increase from 43 to 78 means. For future reference, you can use the following percent increase formula to calculate percent increases:
((f - n)/n) × 100 = p
f = Final Value
n = Initial Value
p = Percent Increase
Once again, here is the math and the answer to calculate the percent increase from 43 to 78 using the percent increase formula above:
((f - n)/n) × 100
= ((78 - 43)/43) × 100
= (35/43) × 100
= 0.813953488372093 × 100
≈ 81.3953
would be great if someone can help with this.
Answer:
144
Step-by-step explanation:
In a regular decagon like the one shown in the picture each angle is 144 degrees and it all adds up to 1,440. If you want proof search up "angle of a decagon"
McGrawHill
Tye has a square piece of yellow felt that has an area of 81 square inches. She wants to cut the largest circle possible from the material to
create a sun for her art project. What is the area of the felt circle? Use 3.14 for 1. Round to the nearest hundredth if necessary.
Answer:
Just Try to watch math anticsStep-by-step explanation:
Thank uy = x+3
y= -2+12
solve by substitution or elimination
NEED ASAP PLS
Answer:
Step-by-step explanation:
A rectangular garden has vertices at (4, 3), (6, 3), (6, 9), and (4, 9). Plot each vertex of the garden.
Answer:
Step-by-step explanation:
A rectangular garden has vertices at
(x = 4, y = 3), (x = 6, y = 3), (x = 6, y = 9), and (x = 4, y = 9).
To plot each vertex of the garden find on the graph the x and y coordinate of the point and mark the point.
Select ALL the sets that are the three side lengths of right triangles.
Answer: It would be C and D
Step-by-step explanation:
By the phythagorean theorem, the 2 legs would equal to the hypothesize.
Choice A would not form a triangle.
Choice B does not follow the pythagorean theorem. 84 plus 16 does not equal 100.
Choice C does. 8 + 121 = 129.
Choice D does. 1 + 3 = 4.
From a barrel of colored marbles, you randomly select 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not yellow. PLEASE ANSWER
The experimental probability is 4/5 if they randomly selected 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Total number of marbles = 6+4+2+3+5 = 20
Total number of marbles except yellow = 20 - 4 = 16
The experimental probability = 16/20
or
= 4/5
Thus, the experimental probability is 4/5 if they randomly selected 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles.
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Find m/EGD. (measurement in degrees)
Answer:
[tex]\huge\boxed{\bf\:30^{\circ}}[/tex]
Step-by-step explanation:
We need to find m ∠EGD.
From the given figure, we can see that, ∠BGA & ∠EGD are vertically opposite angles (opposite angles that share the same vertex ⟶ G).
Also, vertically opposite angles are equal to each other.
Given, ∠BGA = 30°
So, ∠EGD = ∠BGA = 30°.
[tex]\rule{150pt}{2pt}[/tex]
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
from the given figure , we can easily see that ∠AGB = ∠EGD
this is because these angles are vertically opposite , i.e. , the angles that share the same vertex ! also , it's known that two angles that are vertically opposite are equal to each other !
[tex]\therefore \: \bold{\angle \: EGD= 30\degree}[/tex]
hope helpful ~
A rectangular tank is \frac{3}{4} full of water. If you add another 320 cubic centimeters of water, the tank will be \frac{7}{8} full. what is the capacity of the tank?
A: 1,280 cm³
B: 1,920 cm³
C: 2,240 cm³
D: 2,560 cm³
Answer:
D. 2,560 cm³Step-by-step explanation:
Let :
water (when 3/4 full) = 3/4xwater (when 7/8 full) = 7/8xx is the capacity of the tankFinding the change in level
3/4x + 320 = 7/8xx/8 = 320x = 320 * 8x = 2,560 cm³How are angles formed by intersecting lines related?
Answer:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.
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please help me im failing math
Answer:
C
Step-by-step explanation:
-Since dot or where the line originates is at 4 we know the answer will have the number 4.
-The dot is hollow, meaning it does not include the number it is on. So it cannot be "blank and equal to."
-Since the arrow points towards the right, we know it wants all values greater than 4, so we do: x>4.
-Back to my second point, we know it is not D because the dot is open and it does not include 4, so it cannot be equal to it.
