It should be noted that the value of angle B in thee complementary angle is 60°.
How to illustrate the information?It should be noted that the total angles on a complementary angle is illustrated as 90°.
Therefore, based on the information given, it should be noted that we will add the equation and equate them to 90°.
This will be:
5x + 8 + 6x + 4 = 90°
11x + 12 = 90°
11x = 90° + 12°
11x = 102°
Divide
x = 102° / 11
x = 9.27
Therefore the value of angle B will be:
= 6x + 4
= 6(9.27) + 4
= 55.6 + 4
= 59.6°
= 60° approximately
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Simplify each number. 64³.⁵
The result of simplifying the number 64³.⁵ using the exponent rules is
1.24x10^27
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(64³)⁵
64 ⁽³*⁵⁾ =
64¹⁵ =
1.24x10^27
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Precious and Jia are members of different debate clubs. Precious's debate club costs $39.16 each year and $7.65 per visit. Jia's debate club costs $55.69 each year and $7.08 per visit. Last year they both spent the same amount of money on their debate clubs AND visited the same number of times. How many times did they visit their club?
[tex]\bf\implies[/tex]29 times they visit their club.
Step-by-step explanation:Step 1) : Based on the given conditions, formulate:
[tex] \bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}[/tex]
Step 2) : Solve the equation
[tex] \bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}[/tex]
Rearrange variables to the left side of the equation[tex] \bf \longrightarrow{7.65x - 7.08x= 55.69 - 39.16}[/tex]
Combine like terms[tex] \bf \longrightarrow{0.57x= 55.69 - 39.16}[/tex]
Calculate the sum or difference[tex] \bf \longrightarrow{0.57x= 16.53}[/tex]
Divide both sides of the equation by the coefficient of variable[tex] \bf \longrightarrow{x= \frac{16.53}{0.57} }[/tex]
Multiply both the numerator and denominator with the same integer[tex] \bf \longrightarrow{x= \frac{1653}{57} }[/tex]
Cross out the common factor[tex] \bf \longrightarrow{x= 29 }[/tex]
Therefore, 29 times they visit their club.Use f(x) = |x| , f(x)is shifted left 5 and shifted up 2 to create g(x). Write the equation g(x).
Answer:f
(
x
+
2
)
=
3
x
+
2
Step-by-step explanation:
Interpret, in a written description, what the graph is saying about the relationship between the variables. A graph has time (hours) on the x-axis, and distance (miles) on the y-axis. A line increases to 2 hours, is constant through 3 hours, and then increases through 6 hours. a. You leave home and drive for 6 hours with no stops. b. You leave home, drive for 1 hours at a constant speed, stop for 30 minutes, continue at the same speed, stop for 1 hour and then continue at the same speed as before. c. You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before. d. You leave home, drive for 3 hours at a constant speed, and then stop for 2 hours. Finally you continue at the same speed as before.
The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.
Which answer choice is the best interpretation of what the graph is saying about the relationship between the variables?According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.
Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.
Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.
Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.
Therefore, Choice C correctly represents the interpretation of the relationship between the variables.
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Use the distributive property
to remove the parentheses
(-3+3v+2v)(-9)
Hampton ate 7 slices of fruit at lunch. after dinner, he ate some more, he ate a total of 15 pieces of fruit.
Answer:
8
Step-by-step explanation:
WHYYY
the total amount of fruit slices eaten = 15
1st meal = 7
2nd mean = x
now do this
7+x=15
x=15-7
x=8
Simplify the expression 7‐²(-3)²
Answer:
The answer to that question is 58
The length of a bacterial cell is 5.4x10-6 m.express the length of the cell in stand form
Answer: The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m
Step-by-step explanation:
It is given by that the size of a bacterial is 0.000000054 m , which can be with in as 5.4x10-6 m in standard form
We need to find the value of m.
Clearly the standard form of
0.000000054 = 5/10000000
= 5 x 1/10000000
= 5 x 1/[tex]10^{6}[/tex]
0.000000054 = 5 x [tex]10^{-6}[/tex]
Therefore,
5 x [tex]10^{-m}[/tex] = 5 x [tex]10^{6m}[/tex]
and the value of m = 6
So,
The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m
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5. The picture below shows the amount of money in 3 banks. $5.20 $4.64 $2.16 Mrs. Doe emptied all three banks and put the money into two equal groups. How much was in each group?
Answer:
$6 in each group
Step-by-step explanation:
$5.20+$4.64+$2.16=12
12/2=6
Write your own word problem and share it with the group. then translate your problem into its resulting math equation. what steps would you then follow to solve for the variable?
write your own word problem that involves a multistep linear equation. then translate your problem into its resulting math equation. what steps would you then follow to solve for the variable? be sure to list your steps in the correct order.
think of a situation when someone would need to make a measurement with extreme precision. describe the setting, why the measurement must be so precise, and some of the consequences that might occur if it were not precise.
The translation of word problems into mathematics equations enables the determination and prediction of precise values in real life situations.
First part:
The work rate of one person if 3 people takes two days to do a job is given by the equation;
[tex] \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} = \frac{1}{2} [/tex]
Which indicates that one person takes 6 days to get the same work done
Second part;
Where the costs of a combination of cakes and orange drinks can be expressed using the equations;
2•c + o = 0.4
3•c + 3•o = 0.9
It indicates that a cake costs $0.1, and an orange drink costs $0.2
Third part;
Precision is required to conduct a scientific experiment remotely
What is a word problem?A word problem in science is the expression of sufficient or significant background information of a problem is given using every day language, rather than using mathematical notations.
First part;
An example word problem is as follows;
It takes 3 people 2 days to get a particular work done. How long will it take one person to do the same work.The translation of the above question is as follows;
Let C represent the work rate or the number of days one person takes to do the same work, we have;
[tex] \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} = \frac{1}{2} [/tex]
Which gives;
[tex]C = \frac{3}{ \frac{1}{2} } = 6[/tex]
The number of days it takes one person to do the work, C = 6 days
Second part;
A word problem that involves multi step linear equations is as follows;
Two cakes and one orange drink costs $0.4. Three cakes and three orange drinks costs $0.9How much does a cake cost
How much does an orange drink cost
Solution;
Let c represent the cost of a cake and let o represent the cost of an orange drink, we have;
2•c + o = 0.4...(1)
3•c + 3•o = 0.9...(2)
Multiplying equation (1) by 3 and subtracting equation (2) from the result, gives;
3×(2•c + o) - (3•c + 3•o) = 3×0.4 - 0.9
Which gives;
3•c = 0.3
c = 0.3/3 = 0.1
c = 0.1
The cost of one cake, c = $0.1
From equation (1), we have;
2•c + o = 0.4
Which gives;
2×0.1 + o = 0.4
o = 0.4 - 2×0.1 = 0.2
The cost of one orange drink, o = $0.2
Third part;
A setting where someone will need to make a measurement with extreme precision is in determining the amount of fuel required to take an science experiment submarine vehicle to reach a predetermined depth in the ocean.The consequence that might occur if the measurement were not precise is that the vehicle and equipment may not be able to make it back to the surface.
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4/5a - 8 = a + 2, my math teacher doesn't teach, so i don't know this stuff works (:
what is - 9/14 + 2/7
Answer:
-5/14
Step-by-step explanation:
common denomatior is 14
-9/14 + 4/14 (since 2/7 and 4/14 are the same thing)
numerator: -9+4=-5
denominator stays the same.
-5/14 is your answer
- - - - - - - - - - - - - - - - - - - - - - - -
These fractions have denominators in common, so let's find them!
7 x 2 = 14, so 2/7 also equals 4/14.
9/14 + 4/14 = 13/14
- - - - - - - - - - - - - - - - - - - - - - - -
Have a wonderful day/night! :)
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~pinetreee
What is the least common multiple of 4 and 10? Enter the answer in the box.
Answer:
20
Step-by-step explanation:
multiples of 4 (4,8,12,16,20....)
multiples of 10 (10,20....)
Lloyd bought two pumpkins. On a coordinate grid, he plotted each pumpkin’s weight (x), in ounces, and price (y), in dollars. He then drew a straight line that passed through both points and the origin. The line he drew also passed through the point (1, n) for some number n. What does the number n represent?
Since the line Lloyd drew also passed through the point (1, n) for some number n, the number n represents: (A) the price, in dollars, per ounce of pumpkin.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the points on a cartesian coordinate are generally written as an ordered pair (x, y) which represents the horizontal line and vertical line respectively.
Since the line Lloyd drew also passed through the point (1, n) for some number n, we can reasonably infer and logically deduce that the number n represents the price, in dollars, per ounce of pumpkin.
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Complete Question:
Lloyd bought two pumpkins. On a coordinate grid, he plotted each pumpkin’s weight (x), in ounces, and price (y), in dollars. He then drew a straight line that passed through both points and the origin. The line he drew also passed through the point (1, n) for some number n. What does the number n represent?
(A) the price, in dollars, per ounce of pumpkin
(B) the price, in dollars, of one of the pumpkins
(C) the weight, in ounces, of one of the pumpkins
(D) the weight, in ounces, of a pumpkin with a price of $1.00
A sign at a store reads, 4 shirts for &52.50. What’s the unit rate?
Answer:
Exactly $13.125 (approx $13.13)
Step-by-step explanation:
52.50 divided by 4 is 13.125. 1 shirt costs exactly $13.125. Round the half cent up to a whole cent.
Find the value of cos W rounded to the nearest hundredth, if necessary.
U
24
7
W
Answer:
CosW =0.28
explaination:
first find value of the Hypotenuse side,
then find value of Cos W as recalled from
Cos W =Adjacent side/Hypotenus side
f(x)=x
3
−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x
Over which interval does fff have a positive average rate of change?
The interval in which the function has positive average rate of change is x > √3
How to determine the interval which the function has positive average rate of change?The function is given as
f(x) = x^3 - 9x
Differentiate the above function to determine the average rate of change
So, we have
f'(x) = 3x^2 - 9
Set the function to greater than 0
So, we have
3x^2 - 9 > 0
Add 9 to both sides
3x^2 > 9
Divide by 3
x^2 > 3
Take the square root of both sides
x > √3
Hence, the interval in which the function has positive average rate of change is x > √3
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find side x, giving your anwser to 1 decimal place
Answer: 10.8 cm
Following are the calculation to find the x:
Given:
Assuming the triangle is ABC:
then
∠A = 81∘
∠B = 40∘
A = 7cm
To find:
x=?
Solution:
To find the x value we use the Law of sine:
Putting the given value:
eighteen thousand four humdred divided by nine
Answer: 2044.444444444 repeating
Step-by-step explanation:
divide 18400/9 and that's what you get in long division
Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total of $1215 . $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Answer: 11 hours :)
Step-by-step explanation: 1215-445=770, 770 divided by 70=11 so 11 days
please help me with just the one in the middle
Answer: i cheated last year so i dont remember any of this
Step-by-step explanation:
(-4,6) and (4,6) slope-intercept
The equation of the line in slope-intercept form is: y = 6.
How to Write the Equation of the Line in Slope-intercept Form?Given that the points, (-4,6) and (4,6) lie on a line, the steps below shows how to write the equation of the line in slope-intercept form.
Step 1: Find the slope of the line:
Slope (m) = change in y / change in x = (6 - 6)/(-4 - 4)
Slope (m) = 0/-8
Slope (m) = 0
Step 2: Substitute m = 0 and (x, y) = (4, 6) into y = mx + b to find the value of b
6 = 0(4) + b
6 = 0 + b
6 = b
b = 6
Step 3: Substitute m = 0 and b = 6 into y = mx + b
y = 0(x) + 6
y = 0 + 6
y = 6
In conclusion, the equation of the line in slope-intercept form is: y = 6.
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17+4h+2=1−5h solve for h
Answer:
h=-2
Step-by-step explanation:
17+4h+2=1−5h
19+4h=1-5h
4h=-18-5h
9h=-18
h=-2
7) through: (2,-5), slope ---
5/7
9) through: (1, 2), slope -
1
2
8) through: (-4, 3), slope --
15) through: (4,2), perp. to y=-3x-4
Write the slope-intercept form of the equation of the line described.
11) through: (-1,4], parallel to y = -6x + 2
13) through: (-3, 5), perp. to y = 3x-3
72
10) through: (3,-1), slope --
12) through: (2, 2), parallel to y=-4
5
14) through: (5,0), perp. to y=-
--
Write the slope-intercept form of the equation of the line through the given points.
16) through: (0, 2) and (4, -3)
17) through: (0, 5) and (2, -1)
4y +5x = 8
y= -3x+5
The slope-intercept form of the equation of the line through the given points = 1) through: (0, 2) and (4, -3)
2 ) through: (0, 5) and (2, -1)
The general formula for slope-intercept form is y = mx + b, where m represents the slope of the line, and b represents the y-value of the line's y-intercept. The slope-intercept form of a linear equation makes it easier for us to identify how steep a line is and where it crosses the y-axis.
1) through: (0, 2) and (4, -3)
m = y2-y1 /x2-x1
m= -3-2/4-0
m=-5/4
y = mx
y-y1 = m(x-x1)
y- 2 = -5/4(x-0)
y-2= -5x/4
4(y-2) = -5x
4y -8 = -5x
4y +5x = 8
2 ) through: (0, 5) and (2, -1)
m = y2-y1 /x2-x1
m= -1-5/2-0
m= -6/2
m= -3
y = mx
y-5 = m(x-0)
y-5 = -3(x)
y-5 = -3x
y= -3x+5
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question is in the picture!
Answer:
(-6, 2)
Step-by-step explanation:
Given system:
4x - 9y = - 42x + 5y = 4Multiply the second equation by - 4 (the opposite of the coefficient of x in the first equation) then add up the two equations, this will eliminate x and we'll solve it for y.
4x - 9y = - 42-4x - 20y = - 16 Multiplied by -4-9y - 20y = - 42 - 16-29y = - 58y = -58 / - 29y = 2Find x:
x + 5*2 = 4x + 10 = 4x = 4 - 10x = - 6Solution is: (-6, 2)
4x - 9y = -42 -------------(1)
-4x - 20y = -16 -----------(2)
-9y -20y = -42 -16
-29y = -58
y = 2
x + 5*2 = 4
x + 10 = 4
x = 4 - 10
x = -6
Answer:
(-6,2)
If you triple me and then subtract 12 the result is -87. What number am I?
Answer:
-25
Step-by-step explanation:
First, write an equation to represent the situation. To get -87, a number (lets say x) is first tripled, and then 12 is subtracted from the result.
So: -87 = 3x - 12
Then, solve for x by first adding 12 to both sides:
-87 = 3x - 12 ----> -75 = 3x
Finally, divide both sides by 3 to get x by itself:
-75 = 3x ----> -25 = x
Archaeologists use carbon-14, which has a half-life of 5730 years, to determine the age of artifacts in carbon dating. Write the exponentlal decay function for a 24 -mg sample. How much carbon- 14 remains after 30 millennia? (Hint: 1 millennium =1000 years)
The exponential decay function for 24 mg sample is given as
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex]) and 0.64mg carbon - 14 will remain after 30 millennia.
Exponential function that represent the decay is given as :
[tex]F(t) = a (0.5)^{\frac{t}{h} }[/tex] (1)
where, F(t) = amount remaining after time t
a = amount of sample is decayed
t = time in years
h = half life years
The values that we have been given are :
a = 24 mg sample
h = 5730 years
Putting the required values in equation (1) we get
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex] (2)
Now we need to find how much carbon-14 remains after 30 millennia.
That is we have to find F(t) for t = 30 millennia = 30000 years
[As 1 millennium = 1000 years]
Putting the required values in equation (2) we get
[tex]F(t) = 24 (0.5)^{\frac{30000}{5730} }[/tex]
[tex]F(t) = 24 (0.5)^{5.236}[/tex]
F(t) = 24*0.027
F(t) = 0.64 mg
Thus 0.64mg carbon - 14 will remain after 30 millennia.
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Which set of points does not represent a one-to-one function?
{(9,5), (4,9), (1,7), (8,8), (1,4)}
{(5,9), (8,3), (0, 0), (1,5), (6, 2)}
{(7,4), (1,7), (4,0), (9,5), (3, 3)}
{(9,7), (2,8), (3, 3), (8, 1), (5, 6)}
Answer:
firstg one
Step-by-step explanation:
two x's
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=4-2 √x
If the function f(x) = 4 - 2√x then the inverse function be [tex]x^{2}[/tex] −8x+18 = f(x)
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.
Assume that the function is [tex]f(x) = 4 + \sqrt{x-2}[/tex] and f(x) = 4+x−2
where the x − 2 is under the radical sign.
The first step is to swap the f(x) and x.
The new function would be
[tex]$x = 4 + \sqrt{f(x) -2}x=4+ f(x)-2[/tex]
To solve the value of f(x) in the new function
x = 4 + [tex]\sqrt[2]{f(x)-2}[/tex]
x - 4 = [tex]\sqrt{f(x)-2}[/tex]
simplifying the above equation, we get
[tex](x -4^{} )^{2}[/tex] = f(x) − 2
[tex]x^{2}[/tex] − 8x +16 = f(x) − 2
[tex]x^{2}[/tex] − 8x + 18 = f(x)
The inverse of the function f(x) = 4 - 2√x is [tex]x^{2}[/tex] −8x+18 = f(x)
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Question 15
Tools -
>>>
R
II Pause
Question 15
Which point on the number line is closest to √130?
2022 Muminate Education, Inc.
Q Zoom
H
5
11
6
7
818
9
PQ
10 11
RS
12
The point on the number line which is closest to √130 is 11
According to the question we need to find the number closest to the √130
We know that the √130 = 11.4
And 11.4 number lies between 11 and 12 . That is
11< 11.4 <12
But as we see on the number line 11 is much closest than the number 12 on the number line.
Also the
distance between 11 and 11.4 is 0.4
and distance between 11.4 and 12 is 0.6 .
Thus distance between 11 and 11.4 is small.
Hence 11 is closest point to √130 on the number line.
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