Answer:
[tex]x=\pm2\sqrt{10}[/tex]
Step-by-step explanation:
You want to solve ...
[tex]40 -x^2=0\\\\40=x^2\qquad\text{add $x^2$}\\\\\pm\sqrt{40}=x\qquad\text{take the square root}\\\\\boxed{x=\pm2\sqrt{10}}\qquad\text{simplify}[/tex]
Work out 5/7 of 100
Give your answer correct to the nearest whole number.
Answer:
71
Step-by-step explanation:
100÷7≈14.1
14.1×5=70.5
70.5 rounded to the nearest whole number is 71
find the two smallest possible solutions to part 1a
============================
Work Shown:
12*sin(2pi/5*x)+10 = 16
12*sin(2pi/5*x) = 16-10
12*sin(2pi/5*x) = 6
sin(2pi/5*x) = 6/12
sin(2pi/5*x) = 0.5
2pi/5*x = arcsin(0.5)
2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n
2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n
x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)
x = 5/12+5n or x = 25/12+5n
these equations form the set of all solutions. The n is any integer.
--------
The two smallest positive solutions occur when n = 0, so,
x = 5/12+5n or x = 25/12+5n
x = 5/12+5*0 or x = 25/12+5*0
x = 5/12 or x = 25/12
--------
Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.
Answer:
a
Step-by-step explanation:
12sin(⅖pi x) + 10 = 16
sin(⅖pi x) = 6/12
⅖pi x = sin^-1(½)
⅖pi x = pi/6, pi - pi/6
⅖pi x = pi/6, 5pi/6
x = 5/12, 25/12
pls answer i will make u BRAINLIST >_< HELP ME PLS
Answer:
see below
Step-by-step explanation:
1/2 + 4/6
Get a common denominator of 6
1/2 * 3/3 = 3/6
3/6 + 4/6 = 7/6
We change back to a mixed number
1 1/6
Answer:
7/6 or 1 1/6
Step-by-step explanation:
In this case, you're adding 1/2 plus 4/6.
One strategy you can use to solve this problem is by getting the common denominator.
1/2 is equal to 3/6.
Then you could add 3/6 to 4/6 and you'll get 7/6.
Now depending on the teacher they might want you to have an improper fraction or mixed number.
You can get this mixed number by dividing 7/6 which equals 1 1/6.
Hope this helped :)
David drove 634 miles on 19.8 gallons of gas.
What was his gas mileage, rounded to the nearest mpg?
A) 24 mpg
B) 27 mpg
C) 32 mpg
Answer:
C) 32 mpg
This is because to get his miles per gallon,
We divide 634 miles by 19.8 miles to give us 32.0202020....... rounded to 32 mpg
Please help me in this question.Easy question.
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You can use Pythagoras theorem as it is a right angle
a^2 + b^2 = c^2
where 'c' is the hypotenuse
Rearrange this to find a side length
c^2 - a^2 = b^2
where 'b' is the missing length
10^2 - 8^2 = b^2
100 - 64 = b^2
b^2 = 36
Square root this to get the answer
b = 6cm
Have A Nice Day ❤
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All of the following are radii except
Answer:
all of the following are radi except ij or ji the other two are right
Step-by-step explanation:
Solve for X
x - 8= -10
a. x=2
b. x = -2
c. x = 18
d. x= -18
Answer:
b. x = -2
Step-by-step explanation:
x - 8 = -10
x = -10 + 8
x = -2
You have been tracking how much you spend on gas every month for several months and found that on average you spend about $60 per month. If you had to guess, what would you expect the IQR (Interquartile Range) of your gas spending to be? Would $1, $5 or $100 be most logical? Give statistical reasoning to back up your answer.
Answer: $5
Step-by-step explanation: The interquartile range (IQR) refers to the difference between the upper(75%) quartile and lower(25%) quartile of a distribution. Hence, ensuring that the middle 50% is being captured. With the average given as $60, having a interquartile range capturing the middle 50% as $1 seems so small from a statistical stand point. Similarly, an interquartile range of $100 capturing the middle 50% is also too large and nearly impossible if the average price is $60. However, a price of $5 sit well in between considering the average price of $60
Which statements are true ?
Answer:
The true statements
Step-by-step explanation:
lol
Can you please help
#6 GRADE
Answer:
the interger would be 15 because you earn 15 so therfore it would be 15.
Step-by-step explanation:
Brian has 5 marbles, Sarah has 9 marbles, Jimi has 4 marbles, and Juan has 6 marbles. They want to redistribute the marbles so that each person has the same number of marbles. If the marbles are redistributed, then how many should each person get?
Answer:
6
Each Person should get 6 marbles
Step-by-step explanation:
edg2020
Which is equivalent to log Subscript 2 Baseline n = 4?
log n = StartFraction log 2 Over 4 EndFraction
n = StartFraction log 2 Over log 4 EndFraction
n = log 4 times log 2
log n = 4 log 2
Answer: log n = 4log2
Step-by-step explanation:
The 4th option is correct. The expression [tex]\log n=4(\log 2)[/tex] is equivalent to the given expression.
Important information:
The given expression is [tex]\log_2 n=4[/tex].We need to find the equivalent equation.
Logarithms:Using the property of logarithm, the given expression can be written as:
[tex]\dfrac{\log n}{\log 2}=4[/tex] [tex]\left[\because \log_ab=\dfrac{\log b}{\log a}\right][/tex]
[tex]\log n=4(\log 2)[/tex]
Thus, the 4th option is correct.
Find out more about 'logarithms' here:
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how many times smaller is the surface area of a cube if the side length is multiplied 1/2
Answer:
1/4, or 4 times smaller
Step-by-step explanation:
Since the surface area of a cube is just the combination of the area of all of the square sides, and the formula for those is s^2, if the side length was decreased by 1/2 then the surface area would decrease by (1/2)^2=1/4. Hope this helps!
Determine if line AB is tangent to the circle.
Answer:
Is a tangent
Step-by-step explanation:
~ By definition, a tangent to circle is a straight line, presently perpendicular to a radius if one. In this case tangent AB should be perpendicular to the radius. If we were to call the center O, we would say AB should be perpendicular to OA. ~
1. Now let us say at the moment that AB is a tangent. If that is so, it should be that m∠A = 90 degrees ( ° ), provided AB is ⊥ to OA by definition.
2. Now the triangle ABO is a right triangle, and with that is should be that Pythagorean Theorem is applied. This can help us prove if AB is a tangent or not. If Pythagorean Theorem is not applicable it would mean ABO is not a right angle triangle, that AB is not ⊥ to OA, and thus can't be a tangent.
3. Let us say x ⇒ side OA, and that side BO = 9 + 8 + 17:
AB^2 + OA^2 = BO^2,
15^2 + x^2 = 17^2,
x = 8
4. Now there are two radii present, OA is only one of them. As radii are ≅, OA = other radii, 8 = 8
5. This proves that Pythagorean Theorem is applicable, that ABO is a right triangle, that m∠A = 90°, and that by definition AB is a tangent
* I have already answered this question before *
como calcular el área de un cono?
Answer:
La fórmula para el área total de superficie de un cono recto es T. S. A. = π rl + π r 2 . Ejemplo 2: Encuentre el área lateral de superficie de un cono recto si el radio es de 6 pulgadas y la altura de inclinación es de 10 pulgadas.
Answer:
La fórmula para el área total de superficie de un cono recto es TSA = π rl + π r
2. Ejemplo
2: encuentre el área lateral de superficie de un cono recto si el radio es de 6 pulgadas y la altura de inclinación es de 10 pulgadas.
Step-by-step explanation:
Use the spinner to find the theoretical probability of the event. Type your answer in box below in simplified fraction form.
a. Spinning red ___________
b. Spinning a 1 __________
c. Spinning an odd number ___________
d.Spinning a 9 _____________
Answer:
A.) 1/3
B.) 1/6
C.) 1/2
D.) 0
Step-by-step explanation:
Total number of faces on spinner = 6
Probability = (required outcome / Total possible outcomes)
A)
P(spinning Red):
n(Red) / n(total)
n(red) = 2, n(total) = 6
P(spinning red) = 2/6 = 1/3
B.)Spinning a 1 :
n(1) = 1
Therefore, P(spinning 1) = 1/6
C.) spinning an odd number :
Odd numbers = 1,3,5
P(spinning an odd number) = 3/6 = 1/2
D.) spinning a 9:
9 isn't a number on the wheel
P(spinning a 9) = 0/6 = 0
Someone please help me
Answer:
1 infinity
2 one
3 no
4 one
5 infinity
Step-by-step explanation:
Audrina brought $35.25 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Audrina had $1.50 leftover after buying these items. What was the cost of each item?
Answer:
The brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.Step-by-step explanation:
Givens
Audrian has $35.25The brush was 1/6 as much as the sketchbook.The sketchbook cost 3/4 the cost of the paint set.Audrina had $1.50 leftover.She bough a brush, a sketchbook and a paint set.Based on the given information, we can form the following equations.
[tex]b=\frac{1}{2}s[/tex]
Where [tex]b[/tex] is the brush and [tex]s[/tex] is the sketchbook.
[tex]s=\frac{3}{4}p[/tex]
Where [tex]p[/tex] is paint set.
Now, the sum of all three items would give $1.50 of leftover.
[tex]p+b+s=35.25-1.50[/tex]
Replacing expressions, we have
[tex]p+\frac{1}{2}s+\frac{3}{4}p=30.75\\ \frac{7}{4}p +\frac{1}{2}(\frac{3}{4} p)=30.75\\\frac{7}{4}p+\frac{3}{8}p=30.75\\ \frac{56p+12p}{32}=30.75\\ 68p=984\\p=\frac{984}{68}=14.50[/tex]
Then, we use this value to find the other variables
[tex]s=\frac{3}{4}(14.50)=10.88[/tex]
[tex]b=\frac{1}{2}(10.88)=5.44[/tex]
Therefore, the brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.
Answer: paint set costs $18
sketchbook costs $13.5
Brush costs $2.25
Step-by-step explanation:
Let x represent the cost of the paint set.
The sketchbook cost 3/4 the cost of the paint set. It means that the cost of the sketchbook is
3/4 × x = 3x/4
The brush was 1/6 as much as the sketchbook. It means that the cost of the brush is
1/6 × 3x/4 = 3x/24 = x/8
Audrina brought $35.25 to the art supply store. If Audrina had $1.50 leftover after buying these items, it means that the amount spent on the items is
35.25 - 1.5 = 33.75
Therefore,
x + 3x/4 + x/8 = 33.75
Multiplying through by 8, it becomes
8x + 6x + x = 270
15x = 270
x = 270/15
x = 18
The cost of the sketchbook is
(3 × 18)/4 = 13.5
The cost of the brush is
1/8 × 18 = 2.25
I WILL GIVE BRAINLIEST!!!! - YEAR 9 MATHS!!
ABCD is a square with sides of length 9cm. How many points (inside or outside the square) are equidistant from B and from C, and are exactly 6cm from A?
Answer: one point only.
Step-by-step explanation:
Since the length of the sides of the square is 9 cm, taking a point outside the square which is equidistant from point B and C will never give exact 6 cm from A.
The only way to achieve this is by taking a equidistant point inside.
You can achieve exactly 6 cm from point A from point between B and C
But can only achieve a single point if it has to be equidistant from point B and C.
Giving 15 points need answer ASAP
Answer:
[tex] 2 \frac{2}{3} [/tex]
Step-by-step explanation:
[tex] - 2 \frac{1}{3} - ( - 5) = - \frac{(6 + 1)}{3} + 5 \\ \\ = - \frac{7}{3} + 5 \\ \\ = - \frac{7}{3} + \frac{15}{3} \\ \\ = \frac{ - 7 + 15}{3} \\ \\ = \frac{8}{3} \\ \\ = 2 \frac{2}{3} [/tex]
whats the answer to 4(6p+9y)
Answer: The answer is 60p.
Step-by-step explanation:
1) You first simplify what is in parenthesis.
(6p+9p) = (15p)
2) Next, you multiply (15p) by 4.
4(15p) = 60p
3) You simplified the expression of
4(6p+9p) to 60p.
Use the graphing calculator to graph each function
and find the matching graph.
Cube Root
f(x) = x
DONE
Exponential
fx)= 2²
DONE
Logarithmic
f(x) = logx
Cute Root: C
Exponential: D
Logarithmic: A
A function assigns the value of each element of one set to the other specific element of another set. The options can be matched with the function as C, D, and A, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function of different functions is mentioned below.
f(x) =∛x → Option C → Red Linef(x) = 2ˣ → Option D → Green Linef(x) = log(x) → Option A → Blue LineHence, the options can be matched with the function as C, D, and A, respectively.
Learn more about Function:
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What is the answer to this question? Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a to the third power and 4a to the third power.
Answer:
Step-by-step explanation:
Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as
Hypotenuse² = one leg² + other leg²
Therefore,
h² = (3a)³ + (4a)³
h² = 27a³ + 64a³
h² = 91a³
Taking square root of both sides,
h = √91a³
The formula for determining the perimeter of a triangle is expressed as
Perimeter = a + b + c
a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is
√91a³ + (3a)³ + (4a)³
= √91a³ + 91a³
HELP!!! THIS IS URGENT!!!
Explain how you could use less than or equal to and greater than or equal to in a real life scenario.
Please come up with an original scenario! I really need help! Giving 35 points!
Answer:
Step-by-step explanation:
Consider a utlity bill which shows a minimum initial cost plus variable costs dependent upon how many units are sold.
Then: total cost ≥ (fixed cost) + (unit cost)(number of units sold)
This involves the "equal to or greater than" concept.
A bag has 11 red marbles and 4 yellow marbles. Half of the yellow marbles are made of plastic. A marble is selected at random from the bag. What is the probability that it is a yellow, plastic marble? Write your answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
total marbles=11+4=15
plastic yellow marbles=4/2=2
P=(plastic marbles)/(total marbles)=2/15
Answer:
2/15
Step-by-step explanation:
11+4 = 15 marbles
Half of the yellow marbles are made of plastic = 2 plastic yellow marbles
P(yellow plastic marbles) = number of yellow plastic marbles / total
=2/15
Pleaseeeeee helpppppppp i will mark brainlest
Answer:
B
Step-by-step explanation:
Answer:
B=40°
Step-by-step explanation:
Sum of angles in a triangle =180°
90°+50°+x°=180°
140°+×°=180°
Collect like terms
x°=180°-140°
x°=40°
A school wants to have a metal gate placed around it. However they only want to cover three sides of the school and they only have 2000 feet of gate. What are the dimensions of the school if the area is 240,000 square feet?
Answer:
Width = 139.445 ft and Length = 1721.11 ft or
Width = 860.555 ft and Length = 278.89 ft
Step-by-step explanation:
If the school has a rectangular shape, we have that its perimeter and area are:
Perimeter = 2*Length + 2*Width
Area = Length * Width
If we just want to cover 3 sides of the school, we can affirm that:
2000 = Length + 2*Width (eq1)
And the area is 240,000 ft2, so:
240000 = Length * Width (eq2)
From (eq1), we have that:
Length = 2000 - 2*Width
Using this value in (eq2), we have:
240000 = (2000 - 2*Width) * Width
240000 = 2000*Width - 2*Width^2
Width^2 - 1000*Width + 120000 = 0
Using Bhaskara's formula, we have:
Delta = 1000^2 - 120000*4 = 520000
sqrt(Delta) = 721.11
Width1 = (1000 + 721.11)/2 = 860.555 ft
Width2 = (1000 - 721.11)/2 = 139.445 ft
If we use Width = 139.445 ft, we will find Length = 1721.11 ft
If we use Width = 860.555 ft, we will find Length = 278.89 ft
Both pairs of dimensions are valid answers, as they would use 2000 feet of gate and the area of the school would be 240,000 ft2
What is a
1/3 + a = 5/4
Simplify by combining like terms: 9x - 14y + 9 + 13y
Answer:
9x-y+9
Step-by-step explanation:
so what you do first is combine -14y and 13 y and you get -y
what is the y-intercept of the quadratic function f(x) = (x-6)(x-2)
Answer:
Its letter B.
Step-by-step explanation:
on edge 2021
The y-intercept of the quadratic function f(x) = (x-6)(x-2) is (0,12).
Given,
f(x) = (x-6)(x-2)
We need to find the y-intercept of this given function f(x).
What is the y-intercept?The point at the y-axis where the function passes through is called the y-intercept.
We take x = 0 for finding y-intercept.
We have,
f(x) = (x-6)(x-2)
Let f(x) = y.
y = (x-6)(x-2)
Put x = 0 in y.
y = (0-6)(0-2)
y = -6 x -2 = 12.
The y-intercept is at 12 on the y-axis and we represent it as (0, 12).
Thus the y-intercept is (0,12).
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