Answer:
(2, 7 )
Step-by-step explanation:
y = 3x + 1 → (1)
5x = y + 3 → (2)
substitute y = 3x + 1 into (2)
5x = 3x + 1 + 3
5x = 3x + 4 ( subtract 3x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
substitute x = 2 into (1)
y = 3(2) + 1 = 6 + 1 = 7
solution is (2, 7 )
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. 1/4, 1,4,16,. . . .
The sequence 1/4, 1, 4, 16, . . . . is a geometric sequence and its 10th term is 65,536
To determine whether the sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
1/4, 1, 4, 16, . . . .
In this sequence:
a(1) = 1/4
a(2) = 1
a(3) = 4
a(4) = 16
Notice that
a(2) : a(1) = 1 : 1/4 = 4
a(3) : a(2) = 4 : 1 = 4
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 4.
To find the 10th term, use the formula:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = 4, and a(1) = 1/4
a(10) = 1/4 . 4⁹
a(10) = 4⁸ = 65,536
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How would I find the coordinate of a point Q if P is the midpoint of NQ (with line over it). P is 3, -2 and N is 5, -3
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ N(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad Q(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +5}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\underset{midpoint}{\stackrel{\textit{\LARGE P}}{(3~~,~~-2)}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x+5}{2}=3\implies x+5=6\implies \boxed{x=1} \\\\\\ \cfrac{ y -3}{2}=-2\implies y-3=-4\implies \boxed{y=-1}[/tex]
The principal p is borrowed at simple interest rate r for a period of time t. find the loan's future value, a, or the total amount due at time t. round answer to the nearest cent.
4600 is the loan's future value, a, or the total amount due at time t.
What Is Simple Interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.P=$4000
r=5%
t=3 years
Now we have to find th loans future value A.
So
Simple interest me I=prt=(4000)(.05)(3)=600
Total due is Principal + Interest =4000+600= 4600
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Use the numbers 3, 4, 6, and 8 once in each exercise to make a true
statement.
The true statements are as follows:
(6 ×3) ÷ (6 + 3) = 2
4 × 6 ÷ ( 3 × 8 ) = 1
3 × (3× 3) + 6 = 18
6 ÷ (4 - 3) + 8 = 14
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
We have the numbers 3, 4, 6, and 8 once in each exercise to make a true.
⇒ (6 ×3) ÷ (6 + 3) = 2
⇒ 4 × 6 ÷ ( 3 × 8 ) = 1
⇒ 3 × (3× 3) + 6 = 18
⇒ 6 ÷ (4 - 3) + 8 = 14
Thus, the required solution is shown above.
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to solve the equation 2x=5 for x, which value would you divide ?
you would divide both sides by 2. in this case that would be 2x/2 and 5/2.
Find the geometric mean between pair of numbers.
20 and 25
The value of the geometric mean of the numbers 20 and 25 is.
Gm ( 20, 25) = 10√5
To solve this problem we define geometric mean.
Geometric meanThe geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:
Gm (a,b,c) = √(a×b×c)
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 20b = 25We substitute and solve for the square root
Gm (20, 25) = √20×25
Gm (20, 25) = √500
Gm (20, 25) = √5×100
Gm ( 20, 25) = 10√5
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Jin borrows $3,600 and plans to pay the loan off in 18 months. How much simple interest will he owe if it takes 18 months to repay the loan? Round to the nearest cent.
He will owe a simple interest of $229.50
Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.
The simple interest on the principal is calculated by using the formula
I = P · R · T ,
Here I is the interest , P is the principal , R is the rate and T is the time.
Given in the question the amount of money loaned = $3600 , this is the principal (P) ,
Rate (R) = 4.25% = 0.0425
Time (T) is given 18 months which is equivalent to 1.5 years
Now the interest will be calculated by :
I = 3600 × 0.0425 × 1.5
I = 229.50
Therefore the interest earned is $ 229.50 .
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Question:✨Jin borrows $3,600 and plans to pay the loan off in 18 months. How much simple interest will he owe if it takes 18 months to repay the loan? Round to the nearest cent.
Answer: Ok took me a while to get the answer but
He will owe a simple interest of $229.50
Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.
The simple interest on the principal is calculated by using the formula
I = P · R · T ,
Here I is the interest , P is the principal , R is the rate and T is the time.
Given in the question the amount of money loaned = $3600 , this is the principal (P) ,
Rate (R) = 4.25% = 0.0425
Time (T) is given 18 months which is equivalent to 1.5 years
Now the interest will be calculated by :
I = 3600 × 0.0425 × 1.5
I = 229.50
Have an awesome night/day<3
Is the sequence geometric? If it is, what are a₁ and r ?
c. 2³, 2⁷, 2¹¹, 2¹⁵, . . . . . . . .
Answer:
a₁ = 8 and r = 16
Step-by-step explanation:
the sequence has a common ratio r between consecutive terms and is therefore geometric , that is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2^{7} }{2^3}[/tex] = [tex]2^{(7-3)}[/tex] = [tex]2^{4}[/tex] = 16
r = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2^{11} }{2^7}[/tex] = [tex]2^{(11-7)}[/tex] = [tex]2^{4}[/tex] = 16
r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{2^{15} }{2^{11} }[/tex] = [tex]2^{(15-11)}[/tex] = [tex]2^{4}[/tex] = 16
the first term a₁ = 2³ = 8
biofuel for a jet engine is made up of 50% jet A 47.5% jatropha and the rest is algae. what percent of biofuel is algae?
Answer:
Tell what each power means but don't determine its value
Which of the following is not a way to represent the solution of the inequality 2(x − 1) less than or equal to 10?
A number line with a closed circle on 6 and shading to the right
A number line with a closed circle on 6 and shading to the left
6 greater than or equal to x
x less than or equal to 6
x less than or equal to 6 is the following is not a way to represent the solution of the inequality.
What is inequality in math?
A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.2(x − 1) ≤ 10
2x - 2 ≤ 10
2x ≤ 10 + 2
2x ≤ 12
x ≤ 6
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Evaluate each finite series for the specified number of terms. 12+2+ 1/3+ . . . ; n=4
For n= 4 the term = 1/18
A geometric sequence is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Here the sequence is in a geometric sequence, as there is a common ratio between the two-term of the sequence.
Common ratio= 2/12 = [tex]\frac{1}{3}[/tex]/2=1/6
To find the nth term of the geometric sequence we have a formula
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a = first term of the sequence
r= common ratio
n = number of term
To find the term where n= 4, we have,
[tex]a_{4}[/tex]= 12[tex]\frac{1}{6}^{4-1}[/tex]
= 12[tex]\frac{1}{6}^{3} }[/tex]
= 12/216
=1/18
Therefore for n= 4 we have the term 1/18.
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considered cx-d=2x+4 if d value is 2 than what is c's value so this has
no solution
The value of c so that cx-d=2x+4 has No Solution is c=2.
In the given question ,
we have
cx-d=2x+4 ....(i)
Given that d = 2 ,
We substitute the value of d=2 in equation (i)
On substituting we get
cx-2=2x+4
Simplifying further we get
cx=2x+4+2
cx=2x+6
cx-2x=6
x(c-2)=6
x=6/(c-2)
For x to have NO SOLUTION the denominator should be 0.
because when denominator becomes 0 the value becomes not defined , hence will have no solution.
Substituting the denominator = 0
we get c-2=0
c=2.
Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.
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Luna has consumed 900 calories so far today. She has also burned 500 calories in dance class. She wants to keep her daily calorie total to 1,500 calories per day. How many calories does she have left to consume for the day? Is 1,200 a viable solution to this problem?
No; 1,200 is more than the 500 she burned dancing.
No; 1,200 will cause her to exceed 1,500.
Yes; 1,200 is less than 1,500.
Yes; 1,100 is less than 1,500.
Answer:
No; 1,200 will cause her to exceed 1,500.
Step-by-step explanation:
Luna has,
→ consumed 900 cal
→ burned 500 cal
She wants to keep her daily calorie,
→ 1,500 cal/day
Calories she have left to consume,
→ 1500 - (900 - 500)
→ 1500 - 400
→ 1100 cal
Hence, she has to consume 1100 cal more to reach 1,500 cal/day.
A 320 meter long tightrope is suspended between two poles. Assume that the line has an equal chance of breaking anywhere along its length.
b. Determine the probability that the break will occur within 20 meters of a pole.
The probability that the break will occur within 20 meters of a pole is 12.5%.
Probability:
The term probability refers the possible occurrence of the required event.
Given,
A 320 meter long tightrope is suspended between two poles.
Here we assume that the line has an equal chance of breaking anywhere along its length.
Now, we need to determine the probability that the break will occur within 20 meters of a pole.
From the given question,
The line has an equal chance of breaking anywhere along its length.
The first and last 20meters form,
=> [ (20 + 20) / 320 ] x 100
=> [ 40 / 320 ] x 100
=> [ 1 / 8 ] x 100
=> 12.5 %.
Therefore, the probability that a break will occur within 20 meters of a pole is about 12.5%.
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Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 7,13,19,25,31, . . . .
Arithmetic Progression is a recursive mathematical sequence in which the next term is generated by adding the previous term with a fixed number that is called the Common difference represented by 'd'. This is calculated by the difference between any two terms in the given sequence.
The formula to calculate the 12th term of an Arithmetic Progression is :
=> [tex]a_{12} = a_{(12-1)} + d[/tex]
Here, a = first term, n = nth term, and d = common difference
In the given question, First term a = 7, n = 12, and calculating d,
=> [tex]d = a_{2} - a_{1}[/tex] => d = 6
But for a12 we need to find out a11, a10, a9, a8, a7, a6 using the same formula we get :
[tex]a_{6} = 37, a_{7} = 43, a_{8} = 49, a_{9} = 55, a_{10} = 61, a_{11} = 67[/tex]
Now for a12 we have a11 = 67, by using formula :
[tex]a_{12} = a_{11} +d[/tex]
[tex]a_{12} = 73[/tex]
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what is the value of digit 4 in the decimal 5.04
The value of the 4 is in the hundredth value.
the answer is 100+ 30= 130
Answer:
Step-by-step explanation:
yes the answer is correct 100 + 30 = 130
mark me brainliest
Answer:
it is correct
Step-by-step explanation:
100
+ 30
___
=130
___
$60/year is equivalent to $_____/month.
Answer:
5 dollars a month
Step-by-step explanation:
There are 12 months in a year, so we divide the yearly amount by 12
60/12 = 5
5 dollars a month
The radius r og a sphere is increasing at a rate of 6 inches per minute. find the rate of change of the volume when r=11 inches
The rate of change of the volume is 9123 . 185 inches³/min.
What is volume of the sphere?
V = 4/3 r3 is the formula for a sphere's volume. See how the formula is applied in an example where the sphere's diameter is provided.Volume of sphere is
V = 4/3 π r³
differentiating with respect to time
[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]
now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex] when r = 11
[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]
= 2904 π cubic inches per minute
≅ 9123 . 185 inches³/min
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21=7e-4f
solve for f
step by step
Thanks
The solution for f in expression 21 = 7e - 4f is (7e - 21) / 4
Given,
The expression: 21 = 7e - 4f
We have to solve this expression for f:
Then,
21 = 7e - 4f
Add 4f to both sides
21 + 4f = 7e - 4f + 4f
Then we will get,
21 + 4f = 7e
Add -21 to both sides
21 + 4f - 21 = 7e - 21
Then we will get,
4f = 7e - 21
Take 4 from left hand side to right hand side.
That is,
f = (7e - 21) / 4
Therefore, the solution for f in expression 21 = 7e - 4f is (7e - 21) / 4
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X=2y-2 z=5x+3y-4 3y=9
The values of the variable x, y and z are x = 4; y = 3 and z = 25.
What is the method of substitution?There are two approaches to resolving simultaneous linear equations: graphical methods and algebraic methods. The algebraic method comprises the substitution method as one of its categories.The algebraic method for solving simultaneous linear equations is the substitution method. The amount of one variable through one equation is interchanged in the other equation, as the name implies. In this manner, a pair of linear equations is transformed into a single linear equation only with one variable, that can then be solved easily.Now, as per the given question, the three equations are given below;
x = 2y - 2 .......eq 1
z = 5x + 3y - 4 .........eq 2
3y = 9 ...............eq 3
From equation , calculate y.
3y = 9
y = 9/3 = 3.
Substitute the value of y in eq 1.
x = 2y - 2
x = 2×3 - 2
x = 6 - 2
x = 4
Now, put the value of x and y in equation 2.
z = 5x + 3y - 4
z = 5×4 + 3×3 - 4
z = 20 + 9 - 4
z = 25
Thus, the values of the three variables are;
x = 4; y = 3 and z = 25.
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There are 5 yellow cards, 3 blue cards, and 7 red cards in a bag. A card is chosen at
random. What is the probability of choosing a yellow card and without replacing it,
choose blue card?
Answer:
0.714
Step-by-step explanation:
Argument
The total number of cards = 5 yellow. 3 blue and 7 red = 15 cards in all.
The probability of choosing a yellow card first is 5/15 = 1/3.
We are now down to 14 cards
There are 3 blue cards.
P(yellow then blue) = 1/3 * 3/14
P(yellow then blue) = 1/14 = 0.0714
Given F= {(2, 6), (3, 1), (4, 5), and (5,3)} find F-¹(3)
The value of the reverse permutation is F-¹(3) = 5.
What is defined as the inverse permutation?An inverse permutation is one in which each number as well as the number of the place it occupies are swapped.
(1) (2), for example, are inverse permutations because the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in are and the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in are also.It is important to note it never says that "f" is a function; rather, it asserts that the inverse of "f" is a function is if domain of f is restricted.For, the given values in the question;
So, if you remove the last point, (5,3), the inverse is a function because it contains only the points.
F= {(2, 6), (3, 1), (4, 5), and (5,3)}.
Thus, it can be written as;
F: 2 → 3 → 4 → 5
F: 6 → 1 → 5 → 3.
Thus, F-¹(3); 3 → 5.
F-¹(3) = 5.
Therefore, the value of the reverse permutation is F-¹(3) = 5.
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The solution to the original system is the pair and Explain why it makes sense that this pair of values is also the solution to the equation
Sum of the two separate equations.
The values satisfies the equation is 2430.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Given that,
Equations for the two separate days :
125a +65 s = 1,200 - - - Friday
140a +50s = 1,230 - - - Saturday
Because, Inputting the solution, satisfied the equation:
a = 7 ; s = 5
265a+115s=2430
265(7) + 115(5) = 2430
1855 + 575 = 2430.
Therefore, The values satisfies the equation is 2430.
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Gas prices averaged $4.33 per gallon in january and $3.89 per gallon in february. what was the percent decrease of the average gas price from january to february? 8.98% 10.16% 11.31% 44%
The percent decrease is 10.16%
How to calculate the percent decrease ?Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100
The first step is to calculate the decrease
= 4.33 - 3.89
= 0.44
The percent decrease can be calculated as follows
= 0.44/4.33 × 100
= 0.1016 × 100
= 10.16
Hence the percent decrease is 10.16 %
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Answer:
(B) 10.16%
Step-by-step explanation:
Correct on my quiz.
Write a recursive definition for each sequence. 1,4,7,10, . . . .
We get the following order:
1, 4, 7, 10, ....
Given that each term has a common difference, this is an arithmetic
sequence. In this instance, the next item in the series is obtained by multiplying the preceding term by 3.
The formula for arithmetic series is as follows:
an = a + (n - 1)d
Our first term is now a1 = 1.
Common variation d=3
Therefore, by entering these numbers into the given formula,
an = 1 + (n-1)3
an = 3n - 2
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Which inequality is true?
Write the function rule for each function reflected in the given axis.
f(x)=2 x-6 ; y -axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The function's reflection should be similar in size and shape to the original function.
f(x)=2x-6; y -axis
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Find the value of x .
2=x . 4/√3
The value of variable x for the given expression 2=x . 4/√3 is (√3 /2).
As given in the question,
Given expression :
2=x . 4/√3
To get the value of variable x
Multiply both the side of the expression by √3
2 × √3 = ( x × 4 × √3 ) / √3
Divide both the side of the expression by 4
( 2 × √3 ) /4 = (x × 4 ) / 4
⇒ x = √3 / 2
Therefore, the value of variable x for the given expression 2=x . 4/√3 is
(√3 /2).
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State the property that justifies the following statement.
If 7(x-3)=35, then 35=7(x-3).
The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.
Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab
Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.
The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.
So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.
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