The solution of the system of equations using substitution is, (2500, 5).
What is substitution method?
In the "by substitution" method, one of the equations is solved for one of the variables (you choose which one), which is then plugged back into the other equation where the chosen variable is "substituted" for and the second equation is then solved for. The first variable is then back-solved.
The equations are,
d = 200m + 1500 ..(1)
d = 500m ..(2)
Substitute d = 500m in equation (1),
500m = 200m + 1500
300m = 1500
m = 5
Plug m = 5 in equation (2),
d = 500(5) = 2500
Hence, the solution of the system of equations using substitution is, (2500, 5).
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As Mars revolves around the sun, it travels at a speed of approximately 15 miles per second. Convert this speed to kilometers per second. At this speed, how
many kilometers will Mars travel in 20 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers.
Mars travels at a rate of 24 km per second.
At this rate, Mars travel 480 km in 20 seconds.
What is speed?
The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.
Here, we have
Mars revolves around the sun, it travels at a rate of approximately 15 miles per second.
1 mile = 1.6 km (given)
15 miles = 15 ×1.6 = 24 km
So, Mars travels at a rate of 24 km per second.
In 20 seconds, Mars will travel 24×20 =480km
Hence, Mars travels at a rate of 24 km per second.
At this rate, Mars travel 480 km in 20 seconds.
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please help me with these question i know that some are answered but there not.
Answer:
1. A
2. A, B, D
Step-by-step explanation:
The first one is pretty straightforward, divide 7^2 to both the denominator and numerator, so you get 1/7^2. 7^2 is 49, which is not 14, so A is false. Everything else produces 1/49 in some shape or form.
The second question is also relatively easy. A is correct because 1/4 is 4^-1 and (4^-1)^-1 is 4^1. B is also right because if you add all the exponents up, you basically get -5+6+1=2, and 2^2 is 4. C is wrong because (1/2)^2 is 1/4, not 4. D is correct because 2^(5-3) is 2^2, which is 4. E is wrong because 4^(4-2) is 4^2, which is 16, not 4.
Overall, it's not hard, nor does it take time, you just need to remember the basic formulas: [tex]\frac{1}{x^a} =x^{-a[/tex], [tex]x^a * x^b=x^{a+b[/tex], and [tex]\frac{x^a}{x^b} = x^{a-b[/tex]
Write simplified expressions for the area and perimeter of the rectangle.
Area:
x+
Perimeter:
x+
Answer:
Area = 12x + 66
Perimeter = 2x + 35
Step-by-step explanation:
Area= 12(5.5 + x)
= 12x + 66
Perimeter = 2[(5.5 + x)+12]
= 2(17.5 + x)
= 2x + 35
What kind of transformation converts the graph of f(x) = 8x² - 7 into the graph of g(x) =
-8x²
+7?
The transformation g(x) = -f(x) converts the graph of
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
What is transformation of graph?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.
Given: f(x) = 8x^2 - 7.
We have to find what kind of transformation converts the graph
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
Let,
f(x) = 8x^2 - 7
Multiply both sides by -1.
⇒ -f(x) = -8x^2 - (-7)
- f(x) = -8x^2 + 7
Since g(x) = -8x^2 + 7
⇒ -f(x) = g(x)
⇒ g(x) = -f(x)
Therefore, the transformation g(x) = -f(x) converts the graph of
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
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What is the Domain & Range of A(t)=487-264t
Range of the given function A(t)=487-264t is (-∞, +∞)
Domain of the given function A(t)=487-264t is also (-∞, +∞)
What is domain?
it is the values which x can take in the function. so that it does not get indefined.
What is range?
It is all the values which comes after x is put in the equation.
The domain and range are defined for a given function and they are the sets of all the x-ordinates and all the y-ordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then.
Domain = it is the set of all x-coordinates = {1, 2, 3, 4}Range =it is the set of all y-coordinates = {2, 3}Given function
A(t)=487-264t
Hence, Range of the given function is (-∞, +∞)
and Domain of the given function is also (-∞, +∞)
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-2x - 4y = 10
-3x-2y=-1
Answer:
3/5 elimination
Step-by-step explanation:
mark me on brainliest please follow
Based on the data shown below, calculate the regression line (each value to two decimal places). Your answer should be in the form
ˆ
y
=
b
0
+
b
1
x
.
ˆ
y
=
+
x
r =
x y
5 25.6
6 26.52
7 28.14
8 30.56
9 32.18
10 35.1
11 37.32
12 39.74
13 40.96
14 44.58
15 46.2
The regression line, considering the points given in this problem, is defined as follows:
y = 2.16x + 13.61.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data, that can be given in a table or a in a scatter plot, into a linear regression calculator.
These points are composed by a value of x and a value of y, and these values are listed as follows:
Values of x: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.Values of y: 25.6, 26.52, 28.14, 30.56, 32.18, 35.1, 37.32, 39.74, 40.96, 44.58, 46.2.Inserting these points into the linear regression calculator, the equation is given as follows:
y = 2.16x + 13.61.
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Equivalent fractions for 5/6 and 4/5 using the least common denominator
The equivalent fraction using the least common denominator for 5/6 is 25/30 and for 4/5 is 24/30 .
In the question ,
it is given that ,
the fraction is 5/6 and 4/5 ,
the least common denominator of 6 and 5 is 30 .
the first fraction is 5/6 ,
since the least common denominator is 30,
we multiply the numerator and denominator by 5 ,
we get
= (5×5)/(6×5)
= 25/30
the second fraction is 4/5 ,
since the least common denominator is 30,
we multiply the numerator and denominator by 6 ,
we get
= (4×6)/(5×6)
= 24/30
Therefore , The equivalent fraction using the least common denominator for 5/6 is 25/30 and for 4/5 is 24/30 .
The given question is incomplete , the complete question is
Write Equivalent fractions for 5/6 and 4/5 using the least common denominator .
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PLEASE HELPPP
One of your friends missed the class on scientific notation. Describe how you would explain to your friend what it means for a number to be in scientific notation and how to convert a number from standard form to scientific notation.
Using the concept of scientific notation we can write 5.14*10^5 to convert from 5.14*10^5.
What is scientific notation?
Using scientific notation, one can express extremely big or extremely small values.
When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
The scientific notation consists of a coefficient multiplied by 10 and raised to an exponent.
To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 × 10 × 10 × 10 × 10 × 10 = 514000(there are only 4 zeros because you cancel one zero to remove the decimal) so we write 5.14*10^5 to convert from 5.14*10^5.
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If the domain of a one-to-one function f is [6,&), the range of its inverse, f-1 , is
If the domain of a one-to-one function f is [6,&), the range of its inverse, f-1 of the one to one function is [6, &)
What is one to one function?In mathematics, functions are said to be one-to-one functions, when one input value only give an output. No two input values give same output value in a one to one function
Usually in mathematics, functions may have two inputs which give same outputs however for one to one functions one input value gives only one output value
Relating this to domain (input values) and range (output values) and inverse.
The domain of a one to one function will be the range of inverse of the one to one function
This is among the property of one to one function
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An equivalent expression for 4(3a+7)+3(2a+5). If a=5 are the answers the same?
(18a + 43) is an equivalent expression for the given expression i.e.
4(3a + 7) + 3(2a + 5).
Yes, the answers are same from both the expressions i.e. 133.
Given, an expression i.e. 4(3a + 7) + 3(2a + 5)
Now, we are asked to find an equivalent expression for the given expression.
So, on simplifying the given expression, we get
4(3a + 7) + 3(2a + 5)
12a + 28 + 6a + 15
12a + 6a + 28 + 15
18a + 43
So, (18a + 43) is an equivalent expression for the given expression i.e.
4(3a + 7) + 3(2a + 5)
Now, On putting the value of a = 5 in both the expressions, we get
4(3(5) + 7) + 3(2(5) + 5)
= 4(15 + 7) + 3(10 + 5)
= 4(22) + 3(15)
= 88 + 45
= 133
also in (18a + 43),
= 18(5) + 43
= 90 + 43
= 133.
Hence, (18a + 43) is an equivalent expression for the given expression i.e.
4(3a + 7) + 3(2a + 5).
Yes, the answers are same from both the expressions i.e. 133.
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Which situation is best modeled by an exponential function with time as the
independent variable?
A. an investment that takes 2 years to increase in value by $50 and
10 years to increase in value by $250
B. an investment that increases by a constant factor of 1.03, or at a
rate of 3%, every year
OC. an investment that increases by $30 every year
D. an investment that increases by $1 every 2 weeks
An investment that takes 2 years to increase in value by $50 and
10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find the exponential function with time as the independent variable.
Exponential growth refers to the original value from the range increases by the same percentage over equal increments found in the domain.
an investment that takes 2 years to increase in value by $50 and
10 years to increase in value by $250
an investment that increases by a constant factor of 1.03, or at a
rate of 3%, every year
an investment that increases by $30 every year
an investment that increases by $1 every 2 weeks
Hence, an investment that takes 2 years to increase in value by $50 and
10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable
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What number can you add to √7 to get a rational number?
√7
-√7
0
7
Answer: -√7 because it will cancel out to equal 0
Which best analogizes Cavalieri's Principle?
A: Two planets that have different densities and surface areas but have the same volume.
B: A tree with an equal number of branches and roots that are growing at the same rate.
C: A straight column of 10 pennies having the same volume as a leaning column of 10 pennies.
D: A short, wide glass that can hold the same volume of water as a tall, thin glass.
The best option that analogizes Cavalieri's Principle is D. A short, wide glass that can hold the same volume of water as a tall, thin glass.
What is Cavalieri's Principle?To describe the relationship between solids, Cavalier introduced parallel planes and area. If every plane parallel to these two planes intersects both regions in equal-area cross-sections, the two regions have equal volumes.
The volume of a prism is calculated by multiplying the area of the base by the height.
Cavalieri's principle, named after Bonaventura Cavalieri, is a modern implementation of the method of indivisibles in geometry. It is as follows: Case in two dimensions: Assume two plane regions are included between two parallel plane lines.
The Cavalieri's Principle describes the relationship between the volumes of two solids given their cross-sections and heights. When comparing the areas of two solids given their respective bases and heights, this principle comes in handy.
It states that the volumes of two or more solids are equal when their areas and lengths are the same.
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Answer:
C: A straight column of 10 pennies having the same volume as a leaning column of 10 pennies.
Step-by-step explanation:
someone answer these please, must have work done by tonight
A rhombus has diagonals with lengths of 24 and 20.
1. A rhombus is a parallelogram. What is a property of a parallelogram that describes the intersection of the diagonals?
2. The diagonals of a rhombus intersect in a way that does not apply other parallelograms. How do the diagonals of a rhombus intersect?
3. What is the length of a side of the rhombus? Show work to get credit.
4. What is the perimeter of the rhombus? Show work to get credit
Answer:
Step-by-step explanation:
1. The diagonals of a parallelogram are congruent.
2. The diagonals of a rhombus form congruent acute angles.
3. To get each side length of the rhombus, double each diagonal. That means 24 times 2 will be 48 and 20 times 2 will be 40.
4. The perimeter is the sum of the sides. 48+40+48+40 = 176
Assume that a three-month CD purchased for $1900 pays simple interest at an annual rate of 7%. How much total interest does it earn? What is the balance at maturity?
Answer: Total interest: $399
Balance = $2,299
Step-by-step explanation:
Total interest=
1900 * 7/100 * 3
= 133 * 3
= 399
Balance at maturity:
1900 + 399
= 2299
The hypotenuse of a right triangle measures 10 cm and one of its legs measures 8 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{8}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{10^2-8^2}=b\implies \sqrt{36}=b\implies 6=b[/tex]
Please NEEEED HELP! Whoever gets it right I will give you brainliest answer!
Answer:
solve for the supplementary angles:
140 + x = 180
x = 40
then solve for 5x
40 + 5x = 90
5x = 50
x = 10
TADA!!
Answer: x = 10
Step-by-step explanation:
J - E has to be 180. 180 - 140 is 40. DHF has to be a 90 degree angle. 90-40 is 50. 5x, 50/5 is 10 so X would be ten.
Lydia buy 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.
1. If you multiply the first equation by 2, the number to multiply the second equation by eliminating the y terms when making a linear combination is -3.
2a) The price per pound of apples is $1.25.
b) The price per pound of bananas is $0.75.
What is a system of equations?A system of equations involves two or more equations solved together.
Such equations are also known as simultaneous equations.
5x + 3y = 8.5 ... Equation 1
3x + 2y = 5.25 ... Equation 2
Multiply Equation 1 by 2:
5x + 3y = 8.5 ... (x 2)
= 10x + 6x = 17 ... Equation 3
Multiply Equation 2 by -3:
3x + 2y = 5.25 ... (x -3)
-9x -6y = -15.75 ... Equation 4
Add Equations 3 and 4:
10x + 6x = 17
+
-9x -6y = -15.75
= x = 1.25
Substitute x = 1.25 in Equation 1:
5x + 3y = 8.5
6.25 + 3y = 8.5
3y = 2.25
y = 0.75
Check variables in Equation 2:
3x + 2y = 5.25
= 3(1.25) + 2(0.75) = 5.25
= 3.75 + 1.5 = 5.25
5.25 = 5.25
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Question Completion:5x + 3y = 8.5
3x + 2y = 5.25
1. If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?
2. Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Last week, a florist sold 715 roses. Of the
roses sold, 7 out of every 11 roses were
red. How many red roses did she sell?
¿Cuál es el número resultante de sumarle 3 al triple de
su mitad es igual a 33?
Answer:
15
Step-by-step explanation:
1. 2x + 3 = 33
2. 2x = 33 - 3
3. 2x = 30
4. x = 15
Find the product, list the units. 5Ib times $6.00/Ib
9. Given B is between A and C and AB = 16,
BC = 12. Find AC. (Draw it).
Answer:
28
Step-by-step explanation:
Draw a line segment. Put A on one end and C on the other. Put B between these two points. Mark the distance between A and B as 16 and the distance between B and C 12. Add these two numbers together to get the distance of 28.
What is an algebraic expression for 15 more than the product of 52 and a number?
52y(15)
52y + 15
52y − 15
15 − 52y
Answer:
(b) 52y +15
Step-by-step explanation:
You want an algebraic expression for 15 more than the product of 52 and a number.
ProductIf y represents "a number", then "the product of 52 and a number" can be written as ...
52 × y = 52y
MoreThe wording "15 more than ..." means the value 15 is added to the product. That makes the expression ...
(b) 52y +15
<95141404393>
I need help with this!!!!!
3^4x + 2 = 9^x +2
12. The Height of the CN Tower is about 550 m. What is the height of the CN Tower in a scale drawing if the scale is 1:11 000?
The height of the CN Tower on scale drawing is 0.05.
What is scale?A scale is a group of levels or numbers that are applied to a certain system of measurement or comparison.
Given that,
The height of CN Tower = 550 m,
Also, the scale is 1/11000
Let the height of the CN Tower in the scale is x,
Then,
x/550 = 1/11000
⇒x= =550/11000
⇒x = 0.05
The height of the CN Tower on scale drawing is 0.05.
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The shallow end of a swimming pool is 3.75 feet below the pool's surface. The
deep end of the pool is 5.75 feet deeper. Write and evaluate a subtraction
expression to find the depth of the deep end of the swimming pool.
The depth of the deep end of the swimming pool is 9.50 feet.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Since the shallow end of a swimming pool is 3.75 feet below the pool's surface and the deep end of the pool is 5.75 feet deeper, the depth will be:
= -3.75 - 5.75
= - 9.50
It is 9.50 feet deep.
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"I'm thinking of a number. If you multiply it
by 5 and then take away 7, you will got 53.
What is my number?"
Equation:
Answer:
Answer: 12
Equation: 12 times 5 - 7.
Step-by-step explanation: 12 times 5 is 60 and take away 7 would be 53.
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The number of laps Amelie swam daily for the past 3 weeks is shown in the dot plot. A number line going from 2 to 10. 3 dots are above 2. 2 dots are above 3. 3 dots are above 4. 5 dots are above 5. 4 dots are above 6. 2 dots are above 7. 1 dot is above 10. Use the dot plot to complete the statements. The dot plot shows that Amelie swam 3 laps times. Amelie most frequently swam laps. The data distribution is .
Regarding the data-set, we have that:
The dot plot shows that Amelie swam 3 laps two times.Amelie most frequently swam 5 laps.The data distribution is left skewed.What is shown by the dot plot?The dot plot shows the absolute frequencies of each observation, hence we have that:
Amelie swam two laps three times.Amelie swam three laps two times.Amelie swam four laps three times.Amelie swam five laps five times. -> most frequent due to the highest number of dots.Amelie swam six laps four times.Amelie swam seven laps two times.Amelie swam ten laps one time.The distribution is analyzed considering the mean and the median.
The mean is given by the sum of all observations divided by the number of observations, hence:
Mean = (2 x 3 + 3 x 2 + 4 x 3 + 5 x 5 + 6 x 4 + 7 x 2 + 10 x 1)/(3 + 2 + 3 + 5 + 4 + 2 + 1) = 4.85.
There are 20 observations, hence the median is composed by the mean of the 10th and of the 11 observation, which are both of five, hence the median is of five.
Since the median is greater than the median, the data distribution is left skewed.
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Answer:
5, skewed right
foster needs to divide a plot of land covering 5 3/8
The whole plots he can make are 43/6=7.1666
What is a ratio?A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, while that of lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can include any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers must be positive in the majority of situations.
Given, the covering land is 5(3/8) acres
That is 43/8 acres
By dividing the plots as 3/4 each, we get
(43/8)*(4/3)=43/6=7.1666
The whole plots he can make are 43/6=7.1666
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