The common factors of the numbers 18 and 30 is 6
How to determine the common factors of the numbers?The numbers are given as
18 and 30
Express 18 and 30 as a product of its factors
So, we have
18 = 2 * 3 * 3
30 = 2 * 3 * 5
Multiply the common factors in the above expression
Common factors = 2 * 3
Evaluate the product
So, we have
Common factors = 6
Hence, the common factors of the numbers 18 and 30 is 6
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What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
Solution of exponential equation is , x = [tex]800. 7^4[/tex]
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a = the base of function
x = main expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponential :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
[tex]7^{-4} x = 800[/tex]
=> [tex]\frac{1}{7^4} x = 800[/tex]
=> [tex]x = 800 . 7^4[/tex]
Thus solution for this equation is x = [tex]800. 7^4[/tex]
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The complete question is :
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
b. 5.2³x=400
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)
Equation practice with angle addition
Question 15
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Question 15
Which point on the number line is closest to √130?
2022 Muminate Education, Inc.
Q Zoom
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5
11
6
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818
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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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Look at the diagram
Angle Diagram
3
A
B
23°
67°
(7x - 5)º
O
2
7
1 point
Which equation can be used to solve for x?
30x-5-67
30x+5-67
7x+18-67
7x+28-67
1 point
The equation that can be used to determine the value of x is 7x + 18 = 65
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the value of x?The figure that completes the question is added as an attachment
The given parameter is the angles in the figure
From the figure, we have the following angles:
Angle 1 = 23
Angle 2 = 7x - 5
Angle 3 = 67
The relationship between the above angles is
Angle 1 + Angle 2 = Angle 3
This is so because the angles 1 and 2 are adjacent angles and they add up to angle 3
Substitute the known values in the above equation
So, we have
23 + 7x - 5 = 65
Collect the like terms in the above equation
So, we have
23 - 5 + 7x = 65
Evaluate the like terms in the above equation
So, we have
18 + 7x = 65
Rewrite the above equation as
7x + 18 = 65
Hence, the equation that can be used to determine the value of x is 7x + 18 = 65
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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
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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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
HELP ME plsss show with work ! thank u !!
Answer: .8 or 4/5
Step-by-step explanation:
You can do this a couple ways.
1) what you started is right, you can change your fraction into a decimal and divide.
2/5 = .4
.32/.4 = .8
2) you can change .32 into 32/100 and divide by 2/5
32/100 divided by 2/5
When you divide fractions, you flip the divisor and multiply
32/100 x 5/2
Multiply across
160/200
Simplify
4/5
4/5a - 8 = a + 2, my math teacher doesn't teach, so i don't know this stuff works (:
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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PLEASE HURRY!! APPROXIMATE THE VALUE AND CHOOSE CORRECT STATEMENT
The correct statements among given statements are statement C and E.
What is a rational number ?
If p & q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.
A number is given which is √22.
√22 = 4.69041576
Let's check which of the statements are correct.
A.
√22 is not rational number as the number has non - terminating decimal value which is 4.69041576 and it doesn't lies between 10 and 12. So , this option is not correct.
B.
This option is also not correct as the value of √22 nearly equals 4.69 is and not greater than 4.691.
C.
The value of √22 is 4.69041576.
If we round off to the nearest hundredth , 9 is at the hundredth place , so the value will be 4.69. This is a correct option.
D.
√22 is not a rational number as the number has non - terminating decimal value which is 4.69041576 but it lies between 4 and 5. So , this option is not correct.
E.
The value of √22 is 4.69041576. We can observe that the decimal number doesn't repeat. So , this is a correct option.
F.
As we know √22 is not a rational number we can't represent it as fraction. This option is not correct.
Therefore , the correct statements among given statements are statement C and E.
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Suppose two friends are standing next to each other. One friend runs 35.7 yards in one direction. The other friend runs 18.1 yards in the opposite direction, stops, and then continues in
the same direction for 10.5 more yards. How far apart are the friends?
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:
Solve each equation. Check for extraneous solutions. √5 x+1 -2√x=1
The solution of the equation √5 x + 1 - 2√x = 1 is [tex]\frac{4}{5}[/tex].
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
Consider the equation,
√5 x + 1 - 2√x = 1
Subtracting 1 from each side of the equation.
√5 x + 1 - 2√x - 1 = 1 - 1
√5 x - 2√x = 0
√5 x = 2√x
Dividing each side of the equation by √x.
( √5 x/√x ) = ( 2√x / √x )
√(5x) = 2
Squaring each side of the equation.
[ √(5x) ]² = (2)²
5x = 4
Dividing by 5 from each side of the equation.
( 5x/5 ) = ( 4/5)
x = 4/5
Now checking the extraneous solution:
[tex]\sqrt{5}x + 1 -2\sqrt{x} =1\\\sqrt{5}(\frac{4}{5} ) + 1 - 2(\sqrt{\frac{4}{5} } ) = 1\\ \frac{4}{\sqrt{5} } + 1 - \frac{4}{\sqrt{5} } = 1\\ 1 = 1[/tex]
The solution for the equation is 4/5.
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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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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.
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....)
What is the answer to this question?
Answer:
222
Step-by-step explanation:
"Evalúa 2x²+5 cuando x = 3"
Answer:
23
Step-by-step explanation:
x=3 PEMDAS says that exponents go first so 3x3=9 then 2x9=18+5=23
The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?
Answer:
Hey! the breadth is 12 m and the length is 12+6=18 m
Mark me as brain?
Step-by-step explanation:
let the breadth be X metre
so the length will be 6+ x metre
perimeter is equal to 60 m
2(6+x+x)=60
2 (6+2x)=60
12+4x=60
4x=60-12=48
x=48/4=12
so
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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The school paper says that no less than a third of the juniors went to prom. If 37 juniors went, then what is the minimum amount of juniors at the school?
Based on the fact that no less than a third of the juniors went to prom and there were 37 juniors, the minimum amount of juniors at the school was 111 juniors
How to find the juniors who went to prom?The school paper reported that out of the total juniors in school, no less than a third juniors went to prom.
We also know that 37 juniors went to prom. Assuming that 37 juniors represents a third of the juniors, the minimum amount of juniors at the school can be found as:
= Number of juniors who went to prom / Proportion of juniors who went to prom
Solving for the minimum amount of juniors at the school gives:
= 37 / 1/3
= 37 x 3/1
= 111 juniors
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Fill in the Blank
The point-slope form of the equation for a line with slope m and passing through point (x₁, y₁) is ____
Answer:
(y - y1) = m(x - x1)
Step-by-step explanation:
(y - y1) = m(x - x1)
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.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
Suppose x and y vary inversely, and x=8 when y=-7 .
a. What is the function that models the inverse variation?
The function that models the inverse variation is y = -56/x.
What exactly is the inverse variation?Inverse variation refers to a relationship between two variables in which the value of one increases while the value of the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
In an inverse function: x · y = C where C is the constant.Then,
-7 · 8 = -56 = CSince x · y = C then we obtain:
x · y = -56 ⇒ y = -56/xTherefore, the function that models the inverse variation is y = -56/x.
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1) g(a)=a³+5a²
f(a)=2a +4
Find g(3) + f(3)
Answer:
82
Step-by-step explanation:
if g(3)= substitute a as 3 = (3)^3 +5(3)^2= 27+45= 72
if f(3)= substitute a as 3= 2(3) +4=10
join them up since it said there to add g(3) +f(3)
72 +10= 82
- What is the density of an object whose mass is 180 grams and whose volume is 45 cm
B. 0.25 g/cm³
A. 4 cm³/g
C. 4 g/cm³
D. 0.25 cm³/g
The density of an object with a mass of 180 grams and a volume of 45 cm is 0.4 kg/m.
What is density?
How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.So the formula will be d = m / v
The mass of the object is 180 g
The volume of the object is 45 cm
Putting the value in the formula
d = 180 g / 45 cm = 0.4 kg/m
Thus, the density of an object will be 0.4 kg/m.
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(-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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