[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}~\hfill \textit{we also know that} \begin{cases} x= 35\\ y = 7 \end{cases} \\\\\\ 7=k(35)\implies \cfrac{7}{35}=k\implies \cfrac{1}{5}=k~\hfill \boxed{y=\cfrac{1}{5}x}[/tex]
y = x+3
y= -2+12
solve by substitution or elimination
NEED ASAP PLS
Answer:
Step-by-step explanation:
Solve the following equation for x.
x2−47=17
List your answers separated by a comma, not using a ± sign and do not include x= in your answer.
Question 2 options:
3, 5
-9, 9
-8, 8
-30, 0
Answer:
-8, 8
Step-by-step explanation:
[tex] {x}^{2} - 47 = 17 \\ \\ {x}^{2} = 17 + 47 \\ \\ {x}^{2} = 64 \\ \\ x = \pm\sqrt{64} \\ \\ x = \pm \: 8 \\ \\ x = - 8, \: \: 8[/tex]
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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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.
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.
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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Divide: 91,035 ÷ 51 Enter the answer in the box.
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 ~
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
Janelys needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5.75 hours and charged her $168 for parts. The total was $426.75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
Answer: x = 45
Step-by-step explanation:
The equation is 5.75 x + 168 = 426.75 and cost of the labor per hour is 45.
It is required to find the value of x.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
The expression is
5.75 x + 168 = 426.75,
where 5.75x represents the cost of labor per hour, 168 is the cost of the parts, and 426.75 is the total.
According to given question we have,
5.75 x + 168 = 426.75,
Substract 168 from both sides we get,
5.75 x + 168-168 = 426.75-168
5.75x = 258.75
x = 45
Therefore, the equation is 5.75 x + 168 = 426.75 and cost of the labor per hour is 45.
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see attachment below
Answer:
144
Step-by-step explanation:
I think.
Divide. Give the quotient and the remainder.
437/7
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.
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°
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
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:
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
How 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.
Please Vote Me Brainliest. Thank You.
Nhich net force is larger? 1M/S,20 KG or 10 M/S, 1 KG
Answer:
39
Step-by-step explanation:
not right just need points
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"
Find the value of x.
135⁰
(7x+2)
x = [?]°
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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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.
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 uA 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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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:
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]
13. The University of Oregon's football team has many different
uniforms. The coach can choose from four colors of jerseys and
pants: green, yellow, white, and black. There are three helmet
options: green, white, and yellow. Also, there are the same four
colors of socks and two colors of shoes, black and yellow.
a. How many jersey/pant combinations are there?
b. If the coach picks a jersey/pant combination at random, what is
the probability he will pick a yellow jersey with green pants?
c. Use a tree diagram to find all of the possible shoe and sock
combinations.
The dataset of the University of Oregon's football team is an illustration of combination and probability
The number of jersey/pant combinationThe given parameters are:
Jersey = 4
Pants = 4
So, the number of jersey/pant combination is:
Combination = 4 * 4
Combination = 16
Hence, there are 16 combinations of jersey/pant
The probability of picking a yellow jersey and green pantThere is only one combination of yellow jersey and green pant from the total of 16 combinations.
So, the probability is:
P = 1/16
Hence, the probability of picking a yellow jersey and green pant is 1/16
The tree diagramSee attachment
From the attachment, we have a total of 8 possible combination of shoe and sock
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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 $233. many many pizza and subs did he sells
Answer:
25 pizzas and 36 subs
Step-by-step explanation:
5x+3x=233 --> but there are 11 more subs that pizza, so 11x3 is 33
(5x+3x) +33 = 233
5x+3x= 200
8x=200
x=25
so then 5 dollars by 25 pizzas, and 36 (25+11) subs at 3 dollars = 233$
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.