Answer:
71 feet
Step-by-step explanation:
94×2=188
330-188=142
142÷2=71
Julie and Mona know that that Earth’s average distance from the Sun is approximately 93 million miles and it takes 1 year to complete an orbit of the Sun. A new asteroid has been discovered orbiting the Sun at an average distance of 1,488 million miles. How long will it take for the asteroid, in Earth years, to complete one orbit of the Sun.
Answer:
16 years
Step-by-step explanation:
Given that :
Earth's distance from sun = 93 million miles
Number of years to complete an orbit = 1 year
Average orbiting distance of new asteroid = 1488 million miles
Number of years to complete an orbit = x
93,000,000 Miles = 1
1488000000 miles = x
Cross multiply :
93000000x = 1488000000
x = 1488000000 / 93000000
x = 16 years
Period taken to orbit the sun = 16 years
Answer: 64 Earth years...
Someone please help me
Answer:
[tex]x < 4368 \frac{8}{19} [/tex]
Step-by-step explanation:
[tex]28x < 83000 + 9x[/tex]
[tex]28x - 9x < 83000[/tex]
[tex]19x < 83000[/tex]
[tex]x < 4368 \frac{8}{19} [/tex]
5x5+90
I honestly have no idea wth this answer is . Please help meeee
1. Find the Perimeter AND Area of the figure
below.
2 ft
5 ft
2 ft
5 ft
Answer:
A = 16 ft^2
P = 20 ft
Step-by-step explanation:
P = perimeter
A = area
STEP 1: divide the shape into rectangles
Rectangle 1: 2ft*3ft
Rectangle 2: 2ft*5ft
STEP 2: Find the area of each rectangle
Equation for area of a rectangle = bh
Rectangle 1: b = 2, h = 3
Rectangle 2: b = 2, h = 5
(2 * 3) + (2 * 5)
6 + 10
16 ft^2
Now, we have to find the perimeter
STEP 1: Find the unknown side lengths.
To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.
The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.
STEP 2: Add up all the side lengths
P = 2 + 5 + 5 + 2 + 3 + 3
P = 20 ft
Don't forget to label your answers!!
I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.
Will give brainliest answer
Answer:
1. log3 81 = 4
2. 4 3/2=8
Step-by-step explanation:
1. Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).
log3(81)=4
or
you can remember this
loga Y= X
so, a^x =y
2. Use the definition of a logarithm,
log
b
(
x
)
=
y
⟹
b
y
=
x
, to convert from the logarithmic form to the exponential form.
When converting 5 1/4% to decimal, Mark wrote 5.25. Explain why his answer is wrong and write the correct answer.
Answer:
Below
Step-by-step explanation:
It is 5 1/4 PERCENT not just 5 1/4.
5 1/4 % = 5.25%
= 5.25/100
= 0.0525.
The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area of the triangle?
A) A = 0.5x^2 - 15x
B) A = -0.5x^2 + 7x
C) A = -x^2 + 10x
D) A = x^2 - 10x
Answer:
B
Step-by-step explanation:
Let the base of the triangle be b and the height be h.
The sum of the base and height is 14. Thus:
[tex]b+h=14[/tex]
Recall that the area of a triangle is given by:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
From the first equation, solve for either variable:
[tex]h=14-b[/tex]
Substitute:
[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]
Distribute:
[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]
Distribute:
[tex]\displaystyle A=-0.5b^2+7b[/tex]
Let b = x. Hence:
[tex]A=-0.5x^2+7x[/tex]
Therefore, our answer is B.
Need help on the last problem
no. of right answers = 60
no. of wrong answers = 40
if sinA=√3-1/2√2,then prove that cos2A=√3/2 prove that
Answer:
[tex]\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}[/tex]
Step-by-step explanation:
Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .
Given :-
• [tex]\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}[/tex]
To Prove :-
•[tex]\sf\implies cos2A =\dfrac{\sqrt3}{2} [/tex]
Proof :-
We know that ,
[tex]\sf\implies cos2A = 1 - 2sin^2A [/tex]
Therefore , here substituting the value of sinA , we have ,
[tex]\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2 [/tex]
Simplify the whole square ,
[tex]\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8} [/tex]
Add the numbers in numerator ,
[tex]\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8} [/tex]
Multiply it by 2 ,
[tex]\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4} [/tex]
Take out 2 common from the numerator ,
[tex]\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4} [/tex]
Simplify ,
[tex]\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}[/tex]
Subtract the numbers ,
[tex]\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2} [/tex]
Simplify,
[tex]\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} } [/tex]
Hence Proved !
Find the missing term in the pattern.
Answer:
20
Step-by-step explanation:
Screenshot of the question
9514 1404 393
Answer:
x = 1, x = 7
Step-by-step explanation:
You can see from the graph that the x-intercepts of f(x) are ...
0 = f(-3)
0 = f(3)
To find the corresponding values of x for f(x-4), we can solve ...
0 = f(x -4)
x -4 = -3 ⇒ x = 1
x -4 = 3 ⇒ x = 7
The x-intercepts of the function after translation 4 units right are ...
x = 1, x = 7
__
Your sketch will be the same curve moved 4 units to the right. (Add 4 to every x-value shown.)
Solve the system of equations below.
x + y = 7
2x + 3y = 16
A. (5, 2)
B. (2, 5)
C. (3, 4)
D. (4, 3)
Answer:
A. (5, 2)
Step-by-step explanation:
Given
[tex]\begin{cases}x+y=7,\\2x+3y=16\end{cases}[/tex],
Multiply the first equation by 2, then subtract both equations to get rid of any terms with [tex]x[/tex]:
[tex]\begin{cases}2(x+y)=2(7),\\2x+3y=16\end{cases}\\\implies 2x+2y=14,\\2x+3y=16,\\2x-2x+2y-3y=14-16,\\-y=-2,\\y=\boxed{2}[/tex]
Substitute [tex]y=2[/tex] into any equation to solve for [tex]x[/tex]:
[tex]x+y=7,\\x+2=7,\\x=7-2=\boxed{5}[/tex]
Since coordinates are written as (x, y), the solution to this system of equations is (5, 2).
Answer:
A. ( 5 , 2 )
Step-by-step explanation:
solve by elimination methodIn order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
x + y = 7, 2x + 3y = 16To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.
2x + 2y = 2 × 7, 2x + 3y = 16Simplify.
2x + 2y = 14, 2x+3y=16Subtract 2x+3y=16 from 2x+2y=14 by subtracting like terms on each side of the equal sign.
2x - 2x + 2y - 3y = 14 - 16Add 2x to -2x. Terms 2x and -2x cancel out, leaving an equation with only one variable that can be solved.
2y - 3y = 14 - 16Add 2y to -3y.
-y = 14 - 16Add 14 to -16.
-y = -2Divide both sides by -1.
y = 2Substitute 2 for y in 2x+3y=16. Because the resulting equation contains only one variable, you can solve for x directly.
2x + 3 × 2 = 16Multiply 3 and 2
2x + 6 = 16Subtract 6 from both sides of the equation.
2x = 10Divide both sides by 2.
x = 10The system is now solved.
x = 5 and y = 2
A jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint. Each time you draw out an item, you record the outcome and put the item back in the jar before making another draw. What is the probability that you get exactly the following sequence: candy—mintmcandy, in that order?
(a) 0.0300.
(b) 0.0530.
(c) 0.1607.
(d) 1.2143.
Answer:
The correct answer is B.
Step-by-step explanation:
Since a jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint, and each time you draw out an item, you record the outcome and put the item back in the jar before making another draw, to determine what is the probability that you get exactly the sequence candy-mint-candy, in that order, the following calculation should be performed:
4 + 7 + 3 = 14
7/14 x 3/14 x 7/14 = X
0.5 x 0.2142 x 0.5 = X
0.053 = X
Therefore, the probability that the chosen sequence will be obtained is 0.0530, or 5.3%.
Mis directly proportional to r?
When r= 2, M= 14
a) Work out the value of M when r= 12.
b) Work out the value of r when M = 224.
Answer:
M = 84 , r = 32
Step-by-step explanation:
Given M is directly proportional to r then the equation relating them is
M = kr ← k is the constant of proportion
To find k use the condition when r = 2, M = 14 , then
14 = 2k ( divide both sides by 2 )
7 = k
M = 7r ← equation of proportion
(a)
When r = 12
M = 7 × 12 = 84
(b)
When M = 224 , then
224 = 7r ( divide both sides by 7 )
32 = r
The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is inches and the foci are inches from the vertices. Assume the center of the hyperbola is at the origin.
The equation of the hyperbola is,
(x/12)² - 4y²/(527) = 1
The standard equation of the hyperbola is
(x/a)² - (y/b)² = 1
Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x
Foci are (c, 0) & (-c, 0)
Then a² + b² = c²
Here we have to give that.,
2a = 24
a = 12
And 2c = 7
c = 7/2
Therefore a = 12 and c = 3.5
Substituting a and c in Pythagorean identity;
b² = 527/4
Then, the equation of the hyperbola is
(x/12)² - 4y²/(527) = 1
For further information regarding hyperbolas, kindly refer
brainly.com/question/28989785
#SPJ4
We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.
To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.
Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).
The distance between the foci is given by the equation:
c = √(a^2 + b^2)
We know that the distance between the foci is given as 2c inches, so:
2c = 2√(a^2 + b^2)
Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:
2(a - b) = 2√(a^2 + b^2)
Squaring both sides to eliminate the square root:
4(a - b)^2 = 4(a^2 + b^2)
Expanding the equation:
4(a^2 - 2ab + b^2) = 4a^2 + 4b^2
Simplifying the equation:
4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2
Canceling out the common terms:
-8ab = 0
Dividing by -8:
ab = 0
This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.
for such more question on hyperbola
https://brainly.com/question/16454195
#SPJ8
Solve each inequality. Graph the solution on a number line.
Answer:
n>2 2/3
Draw a filled dot at a little more than 2 1/2 and continue the line to the right.
Step-by-step explanation:
Subtract 1/3 from both sides to get
2 2/3
Flip the inequality
n> 2 2/3
I hope this helps!
Select the correct answer from each drop-down menu. Julie invests $200 per month in an account that earns 6% interest per year, compounded monthly. Leah invests $250 per month in an account that earns 5% interest per year, compounded monthly. After 10 years, Julie's account balance will be After 10 years, Leah's account balance will be After 10 years, will have more money in her account.
the answer: $32,776 / $38,821 / leah
Answer:
After 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.
Step-by-step explanation:
Since Julie invests $ 200 per month in an account that earns 6% interest per year, compounded monthly, and Leah invests $ 250 per month in an account that earns 5% interest per year, compounded monthly, to determine the amount of each after 10 years, the following calculations must be performed:
200 x (1 + 0.06 / 12) ^ 10x12 = X
200 x 1.005 ^ 120 = X
200 x 1.8193 = X
363.88 = X
250 x (1 + 0.05 / 12) ^ 10x12 = X
250 x 1.00416 ^ 120 = X
250 x 1.647 = X
411.75 = X
Therefore, after 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.
Find the solution to the system
of equations.
y = 2x + 3
([?], [ ]
2
بیر
2 3 4
-4 -3 -2 -1
-1
-2
3
-4
y=-x
Enter
Answer:
The two lines meet at (-1,1)
were should i go shopping for fidgets
Answer:
Amazon
Step-by-step explanation:
Which rule describes the transformation shown?
1. (x,y) → (-y, x+7)
2. (x,y) → (x+7,-y)
3. (x,y) → (-x, y+7)
4. (x,y) → (y+7, -x)
Answer:
2. (x,y) → (x+7,-y)
Step-by-step explanation:
Point A:
The original coordinate of point A was (-6,-6).
The coordinate after the transformation is A'(1,6), which eliminates option 3.
Point B:
The original coordinate of point B was (-2,4).
After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. This means that the correct answer is:
2. (x,y) → (x+7,-y)
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Answer:
1/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that the ticket drawn has a number which is a multiple of 5 =
Number of tickets that are a multiple of 5 / total number of tickets
Multiple of 5 = 5, 10, 15, 20
there would be 4 tickets that would be a multiple of 5
= 4/20
To transform to the simplest form. divide both the numerator and the denominator by 4
= 1/5
The width of a rectangle is 2 cm less than its length. The perimeter is 52 cm. The length is:
14 cm.
12 cm.
9 cm.
None of these choices are correct.
Answer: 14 cm
Step-by-step explanation:
Rectangle:
Length = xWidth = x - 2x + x + (x - 2) + (x - 2) = 52
2x + 2(x - 2) = 52
2x + 2x - 4 = 52
4x = 52 + 4
4x = 56
x = 14
Angles PTQ and STR are vertical angles and congruent.
Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect the points on the circle and form secants P Q, Q R, R S, and S P. Angles P T Q and S T R are congruent.
Which chords are congruent?
QP and SR
QR and
PR and RS
PR and PS
9514 1404 393
Answer:
(a) QP and SR
Step-by-step explanation:
The congruent central angles intercept congruent arcs QP and SR. Chords of congruent arcs are congruent.
chords QP and SR are congruent
Answer: its A
Step-by-step explanation:
CLB is better than DONDA
Solve the rational equation x+3/3x-2-x-3/3x+2=44/9x^2-4
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
When given the following equation;
[tex]\frac{x+3}{3x-2}-\frac{x-3}{3x+2}=\frac{44}{9x^2-4}[/tex]
One has to solve for the variable (x). Remember, when working with fractions, one must have a common denominator in order to perform operations. Since the denominators on the left side of the equation are unlike, one must change them so that they are like denominators. Multiply each fraction by the other fraction's denominator on the respective side. Remember to multiply both the numerator and denominator by the value to ensure that the equation remains true.
[tex]=\frac{x+3}{3x-2}*(\frac{3x+2}{3x+2})-\frac{x-3}{3x+2}*(\frac{3x-2}{3x-2})=\frac{44}{9x^2-4}[/tex]
Simplify,
[tex]=\frac{(x+3)(3x+2)}{(3x-2)(3x+2)}-\frac{(x-3)(3x-2)}{(3x+2)(3x-2)}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}[/tex]
Distribute the negative sign to simplify the left side of the equation;
[tex]=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-(3x^2-11x+6)}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-3x^2+11x-6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{22x}{9x^2-4}{=\frac{44}{9x^2-4}[/tex]
Since the denominators on opposite sides of the equation are like, one can now ignore the denominators,
[tex]=22x=44[/tex]
Inverse operations,
[tex]=22x=44[/tex]
÷[tex]2[/tex] ÷[tex]2[/tex]
[tex]x=2[/tex]
work out the area of this shape
Answer:
75.5
Step-by-step explanation:
First, the picture is not to scale.
The Area of the bottom (2) rectangle is 33
base x height = A
11 x 3 = 33 (where did I get 3? Total height of shape is 8. Trapezoid is 5)
(8-5 = 3)
Area of the trapezoid:
A = [tex]\frac{h (B_{1} + B_{2}) }{2}[/tex]
= [tex]\frac{(5)(6 + 11)}{2}[/tex]
= [tex]\frac{5(17)}{2}[/tex]
= [tex]\frac{85}{2}[/tex]
= 42.5
42.5 + 33 = 75.5
the expression when b=3 and y= -3
5b-y
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
b = 3
y = -3
5b - y
Step 2: Evaluate
Substitute in variables: 5(3) - -3Multiply: 15 - - 3Subtract: 18Find the length of the arc to 2 decimals places
Answer:
Step-by-step explanation:
The formula for arc length is
[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:
[tex]AL=\frac{30}{360}*2(3.14) (4)[/tex] and simplifying a bit:
[tex]AL=\frac{1}{12}(8)(3.14)[/tex] and a bit more:
[tex]AL=\frac{25.12}{12}[/tex] and finally, to
AL = 2.09 m
How can one estimate a car annual fuel expense
Answer:
determine the number of miles the car drives in a year.
divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.
Step-by-step explanation:
A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
Answer:
(a) 3178
(b) 14231
(c) 33152
Step-by-step explanation:
Given
[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]
Solving (a): Year = 1998
1998 means t = 8 i.e. 1998 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]
[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]
[tex]y = \frac{269573}{1+985*0.08509}[/tex]
[tex]y = \frac{269573}{84.81365}[/tex]
[tex]y = 3178[/tex] --- approximated
Solving (b): Year = 2003
2003 means t = 13 i.e. 2003 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]
[tex]y = \frac{269573}{1+985*0.01824}[/tex]
[tex]y = \frac{269573}{18.9664}[/tex]
[tex]y = 14213[/tex] --- approximated
Solving (c): Year = 2006
2006 means t = 16 i.e. 2006 - 1990
So:
[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]
[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]
[tex]y = \frac{269573}{1+985*0.00724}[/tex]
[tex]y = \frac{269573}{8.1314}[/tex]
[tex]y = 33152[/tex] --- approximated
Three more than twice a number is 35.
Answer:
x = 16, or if you didn't want the value for x,
2x + 3 = 35
Step-by-step explanation:
Three more: +3
Twice a number: 2x
Combined:
2x + 3 = 35.
Get rid of the 3 by subtracting it from both sides:
2x = 32
Get rid of the 2 by dividing it from both sides:
x = 16
Answer:
The number is 16.
Step-by-step explanation:
Let the unknown number be x.
Now we translate the sentence into an equation piece by piece.
Three more than twice a number is 35.
2x
Three more than twice a number is 35.
2x + 3
Three more than twice a number is 35.
2x + 3 = 35
Now we solve the equation.
Subtract 3 from both sides.
2x = 32
Divide both sides by 2.
x = 16
Answer: The number is 16.
P.S. Notice that x was a variable that was introduced solely to solve the problem. The original problem is a word problem, not an equation, and has no x in it. The correct answer makes no reference to x since x was used to solve the equation but is not part of the given problem. The person asking the question has no idea what x is. He just wants a number as an answer.
