Answer:
3x=14
Explanation:
Given the two equations:
[tex]\begin{gathered} 5x-y=6 \\ -2x+y=8 \end{gathered}[/tex]Adding the two equations gives:
[tex]\begin{gathered} \lbrack5x+(-2x)\rbrack+\lbrack-y+y\rbrack=6+8 \\ \lbrack5x-2x\rbrack+0=14 \\ 3x=14 \end{gathered}[/tex]fill in the blanks so the left side is a perfect square trinomial
We need to complete the perfect square. A perfect square has the following form:
[tex]a^2\cdot x^2+2\cdot a\cdot b\cdot x+b^2=(a\cdot x+b)^2[/tex]In our case we have:
[tex]x^2-8x+\cdots[/tex]We can immediately deterine the value of "a", which is the root of number multiplying x², since this number is 1, then:
[tex]a=1[/tex]This also means we can find "b", because the second term is equal to the product of 2, a, and b. So we have:
[tex]\begin{gathered} b=\frac{8}{2} \\ b=4 \end{gathered}[/tex]With this we can determine the blank, because it is b². So we have:
[tex]\begin{gathered} x^2-8x+4^2 \\ x^2-8x+16=(x-4)^2 \end{gathered}[/tex]The first missing space is 16 and the second is 4.
it cost $6 per hour to water the grass. how much will it cost to water the grass for 7/3 hours
start by writing a relation
[tex]\begin{gathered} 1hour\longrightarrow\text{ \$6} \\ \frac{7}{3}hour\longrightarrow x \end{gathered}[/tex]find x using the relationship
[tex]x=(\frac{7}{3}\text{hour)}\cdot\frac{\text{ \$6}}{1\text{hour}}[/tex][tex]x=\text{ \$14}[/tex]Determine which equation is false based on the solution set.
S:{5}
6 = 2y − 4
4(b + 5) = 40
one fifth times x plus 16 equals 17
−32 = 2(3p − 6)
PLEASE QUICKLY!
The equation that is false based on the solution set is D. −32 = 2(3p − 6)
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
6 = 2y − 4
This will be:
2y - 4
2(5) - 4
10 - 4 = 6
4(b + 5) = 40
4(5 + 5)
4(10) = 40
one fifth times x plus 16 equals 17
1/5x + 16
1/5(5) + 16
1 + 16 = 17
Therefore, the last option doesn't fit in.
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Answer:D. −32 = 2(3p − 6)
Step-by-step explanation:
please help thank you..
Use the graph of f to describe the transformation that yields the graph of g. f(x)=3^xg(x) = −3^x−2
Solution:
Given the functions:
[tex]\begin{gathered} f(x)=3^x \\ g(x)=-3^{x-2} \end{gathered}[/tex]The graph of f(x) is as shown below:
The graph of g(x) is as shown below:
Description:
In the above graph, we observe that in the transformation, the f(x) plot is reflected across the x-axis and shifted downwards by 2 units to obtain the g(x) plot.
Jake, Jonathan and Joshua each have a subscription on different movie websites. On the website Jake buys from, there is no flat fee to use the website but each time you buy a movie it is 50 cents. On Joshua’s website, there is a flat fee of $5 to use the site and each time you buy a movie you must pay 50 cents. On Jonathan’s website, there is a flat fee of $8 to use the site and each time you buy a movie it is 20 cents. Based off the data, how many movies would each person buy to pay the same amount of money from each website? Write a system of linear equations and graph the problem.
Jake
There is no flat fee = $0
To buy a movie = 50 cents = $0.50
Joshua
Flat fee = $5
To buy a movie = 50 cents = $0.50
Jonathan
Flat fee = $8
To buy a movie = 20 cents = $0.20
Then, we have the following expressions:
[tex]\begin{gathered} 0+0.50x \\ 5+0.50z \\ 8+0.20t \end{gathered}[/tex]Next, to pay the same amount of money from each website. This is:
Let y = number of movies
[tex]0.50x=5+0.50z=8+0.20t=y[/tex]So, solve the system:
[tex]\begin{gathered} y=0.50x \\ y=5+0.50z \\ y=8+0.20t \end{gathered}[/tex]He gives Ms. Danso 0.6 of the tray of brownies and tells her that it contains 330 grams of sugar. How many grams of sugar did Mr. Butcher use for the whole tray?
We can form an equation to solve this
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. An equation can be compared to a scale on which objects are weighed. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Algebra focuses on two primary families of equations: the specific case of linear equations and polynomial equations.
We form an equation as 0.6x=330
The equation can be solved as
0.6x = 330
or, x = 330/0.6 = 550 grams
Hence Mr. Butcher used = 550 - 330 = 220grams of sugar
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Find the amount of time to the nearest day it would take a deposit of $1000 to grow to $1 million at %3 compounded continuously.
The time required to the nearest day to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days.
In the question ,
it is given that
the deposit ( principle amount P) = $1000
the final amount (A) = 1 million = $1000000
the rate of interest (r) = 3% = 0.03
let the time taken to make $1000 to 1 million be " t ".
The continuous compounding interest is given by the formula
[tex]A = P\times e^{r t}[/tex]
where A is the final amount
P is the principle amount
r is the rate of interest
t is the time taken
Substituting the values of A , P , r and t from above , we get
1000000 = 1000×[tex]e^{0.03*t}[/tex]
10000000/1000 = [tex]e^{0.03t}[/tex]
1000 = [tex]e^{0.03t}[/tex]
taking ln on both the sides
㏑(1000) = ㏑([tex]e^{0.03t}[/tex])
㏑(1000) = (0.03t)*㏑(e)
6.9077 = (0.03t)*1 .... as ln(e) = 1 and ln(1000)=6.9077
6.9077 = 0.03*t
t = 6.907755/0.03
t = 230.2585
So , time required is 230.2585 years .
to convert into days , we multiply by 365.
time ( in days) = 230.2585×365
= 84044.3525
≈ 84044 days
Therefore , the time required to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days .
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The table below shows the cost of downloading songs from a website.
\text{Number of Songs}Number of Songs \text{Total Cost}Total Cost
1515 \$7.20$7.20
1717 \$8.16$8.16
2020 \$9.60$9.60
What is the constant of proportionality between the total cost and the number of songs?
I hate my math teacher
F = cost of the songs.
C = number of songs
F ∝ C
F = KC
K = constant of proportionality.
The constant of proportionality is 0.0048.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x = 6 is an equation.
We have,
Number of songs Total cost
1515 $7.20
1717 $8.16
2020 $9.60
Let F = cost of the songs.
C = number of songs
F ∝ C
F = KC
K = constant of proportionality.
We see that,
The total cost of the songs = 0.0048 x the Number of songs.
7.20 = 0.0048 x 1515
8.16 = 0.0048 x 1717
9.60 = 0.0048 x 2020
Thus,
F ∝ C
F = KC
F = cost of the songs.
C = number of songs
K = constant of proportionality.
The constant of proportionality is 0.0048.
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Devon bought a new suit that was discounted 40% off the original price. If the original price of the suit was $280, what was the discounted price?a) $140b) $392c) $112d) $168
40% of $280
40/100 x280
[tex]=\frac{40}{100}\times280[/tex][tex]=\frac{11200}{100}[/tex]= 112
The discounted price = 280 -112
= $168
Evaluate o = √npq, where q=1 - p, for n = 80 and p = 0.4.
The formula for the variance of the binomial distribution is o = √npq
Equating the value is the equation
o = √npq,
[tex]o = \sqrt{80\times1\times\0.4}[/tex]
o = 5.6568
What is binomial distribution?
The binomial distribution is defined as the number of trials or observations when each trial has the same probability of reaching a certain value. The binomial distribution determines the probability of observing a certain number of successful outcomes for a given number of trials.
The binomial distribution model allows us to calculate the probability of observing a certain number of "successes" if a process is repeated a certain number of times (eg, in a patient population) and the result for a given patient is either successful. or failure.
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NOV 16, 7:18.A What is the image of the point (-3,-5) after a rotation of 180° counterclockwise about the origin?
when we rotate a point 180°, we have to change the sign in every coordinate. Therefore we get that the new point is (3,5)
Find the mode for the amounts: $17,371; $14,950, $13,592, $14,589, $18,508; $14,950.Select the correct choice below and fill in any answer boxes within your choice.(Use a comma to separate answers as needed.)O A. The mode(s) is/are $OB. There is no mode.
The mode of a data set is the number that repeats the most.
In this case, we can see that teh value $14,950 is twice.
Then the correct answer is option A. The mode is $14,950
Help me out here please
To find the scale factor, we have to divide two corresponding sides
[tex]\frac{DE}{AB}[/tex]Using the given information, we have
[tex]\frac{20}{10}=2[/tex]Hence, the scale factor is 2.mikes's fittness center charges $30 per month for a membership. all day fitness club charges $22 per month plus an $80 initiation fee for a membership. after how many months will the total amount paid to the two fitness clubs be the same
Answer: 7 months
Step-by-step explanation: by 7 months you would have paid both memberships $300
What is the point-slope from of the equation of the line that passes through the point( -1, -4) and has a slope of 3?
The equation of the line in point-slope form passing through ( - 1, - 4 ) and slope 3 is y + 4 = 1( x + 1 ).
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.
The point-slope form of an equation of the line is given as:
y - y₁ = m( x - x₁ ) where m is the slope and ( x₁, y₁ ) is the point on the line.
Now, the equation of line passes through ( - 1, - 4 ) and m = 1
Then,
y - y₁ = m( x - x₁ )
y - ( - 4 ) = 1( x - ( - 1 ) )
y + 4 = x + 1
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Evaluate. − [−1 4/5÷0.3(1.2)]−5/6 What is the value of the expression? Enter your answer as a simplified mixed number in the box.
The value fo the expression - [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 as a mixed number is 4 1/6.
Consider the expression,
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6
By using the BODMAS rule, we will first solve the inner parenthesis.
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 9/5 ÷ 0.36 ] - 5/6
Now dividing the terms in the inner parenthesis {}.
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 1.8 ÷ 0.36 ] - 5/6
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 5 ] - 5/6
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 5 - 5/6
By the BODMAS rule subtracting the remaining terms.
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 5/1 - 5/6
The LCM of 1 and 6 is 6.
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = ( 30 - 5 )/6
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 25/6
- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 4 1/6
The value of the expression - [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 is 4 1/6.
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You deposit $5000 in a savings account that earns 1.5% interest compounded daily. After 1 yeat, you deposit an additional $5000 into the same savings account, but the interest is now 1.75% compounded daily. What is the value of the account after the second year?
The value of the amount after the second year is $10163.817.
In order to compute compound interest, we multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. Then we are left with the principal amount of the loan plus compound interest.
Amount after Compound Interest [tex]A = P(1+\frac{r}{nt} )^{nt}[/tex] where A is the amount, P is the Principle value, r is the rate of interest, n is the number of times it is compounded daily, and t is the time.
Given Information :
For 1st year, Principal Amount (P) = $5000
Interest (r) = 1.5 %
Time = 1 year
The amount is calculated compounded daily,
So, Calculating the amount after 1 year,
[tex]A = P( 1+\frac{r}{nt}) ^{nt} \\A = 5000(1+\frac{1.5}{365*100}) ^{365*1} \\A = 5000(1+0.00004109)^{365} \\A = 5000*1.015\\A =5075.55[/tex]
For 2nd Year, Principal Amount= (P) $5000
Rate of Interest (r) = 1.75%
Time (t) = 1 year
The amount is calculated compounded daily,
So, Calculating the amount after 1 year,
[tex]A =P(1+\frac{r}{nt}) ^{nt\\}\\A= 5000(1+\frac{1.75}{365*100}) ^{365*1} \\ A = 5000(1.00004795)^{365} \\A =5000*1.077\\A =5088.26[/tex]
Now, the value of the amount after the second year = $5075.55 +$5088.26 =$10163.817.
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write the given interval notaion (-12,8] into set-builder notation
If we plot the values of x representing the given interval on the number line, the least value would be - 12. It would be on the left and also non inclusive. The greatest value of x would be 8 on the right and inclusive. By writing it in set builder notation, it is expressed as shown in the attached photo
The stereo that Dontay bought wasoriginally priced at $199. Dontay boughtthe stereo on sale for 20% off. How muchmoney did Dontay save?
We are told that Dontax bought the stereo on a sale of 20% off, meaning he will only have to pay 100% -20% = 80% of the price.
Now, 80% of $199 is
[tex]199\times\frac{80}{100}[/tex][tex]=\$159.2[/tex]Hence the amount of money Dontay saved is
[tex]199-159.2=\$39.8[/tex]Which is our answer!
What is multiplied to get -50 but also adds to get 5
Explanation:
To determine the numbers, we need to find factors of -50:
We only have one of the numbers with negative because we are finding factor of a negative number.
Multiplication of opposite signs give negative number.
[tex]\begin{gathered} -1\text{ }\times\text{ 50} \\ -2\text{ }\times\text{ 25} \\ -5\text{ }\times\text{ 10} \\ -10\text{ }\times\text{ 5} \\ -25\text{ }\times\text{ 2} \\ -50\text{ }\times1 \end{gathered}[/tex]From the factors listed above, we find the two numbers sum up to give -50:
[tex]\begin{gathered} -1\text{ + 50 = 49} \\ -2\text{ + 25 = 23} \\ -5\text{ + 10 = 5} \\ -10\text{ + 5 = - 5} \\ -25\text{ + 2 = -23} \\ -50\text{ + 1 = -49} \end{gathered}[/tex]What is the value of x in the figure below? In this diagram ABD ~ CAD
Answer:
√39
Step-by-step explanation:
x/13 = 3/x
x^2 = 39
x = √39
The product of the polynomials (3x + 2) and (-x^3-3) is ______.When this product is multiplied by (3 + x), the coefficient of x^4 in the result is______.
The product of the polynomials (3x+2) and (-x^3-3) is:
(3x+2)*(-x^3-3) = (3x)*(-x^3) + (3x)*(-3) + 2*(-x^3) + 2*(-3) = -3x^4 - 2x^3 -9x - 6
Multiplying it by (3 + x), we got:
(3 + x)*(-3x^4 - 2x^3 -9x - 6) = 3*(-3x^4) + 3(-2x^3) + 3*(-9x) +3*(-6) + x*(-3x^4) + x*(-2x^3) + x*(-9x) + x*(-6) = -3x^5 -11x^4 -6x^3 -9x^2 - 33x - 18
Therefore, the coefficient of x^4 is -11.
help help help pleaseeeee!!!!!!
The domain of the relation is [1,6]. The domain can be written in the roster form method like {x I x ∈ {1,....,6}} The range of the function is [1,2].
As we can see that the range of values in x-axis is from [1,6]. Hence, it is the domain of the relation.
Also, he range of values in y-axis is from [1,2]. Hence, it is the range of the relation.
Domain of a relation
The domain or set of departure of a function is the set into which all of the input of the function is constrained to fall.
Range of a relation
The set of the second elements of all the ordered pairs of a relation is the range of a relation.
Set roster form
The elements (or members) of a set are listed in a row inside the curly brackets.
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simplifying like terms and distributive property;2(m + 1) + 5m
2(m + 1) + 5m
step 1
Apply distributive property
2*(m)+2*(1)+5m
2m+2+5m
Combine like terms
7m+2Pentagon ZEBRA is similar to pentagon
LIONS. What is the length of RA in feet?
E
22 ft
13 ft
Z
18 ft
R
20 ft
A
10.4 ft
I
14.4 ft
17.6 ft
N 12 ft S
L
16 ft
After performing some mathematical operations, the length of RA is 15 feet.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. The four mathematical operations are functions that take numerical inputs (i.e., inputs) and turn them into numerical outputs (i.e., another number). These are multiplication, division, subtraction, and addition.So, the length of RA is:
As both the pentagons are similar, then:
EB/IO = 13/10.4 = 1.25BR/ON = 18/14.4 = 1.25ZA/LS = 20.16 = 1.25EZ/IL = 22/17.6 = 1.25Similarly,
RA/NS = RA/12 = 1.25RA = 12 × 1.25 = 15 ftTherefore, after performing some mathematical operations, the length of RA is 15 feet.
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Whcih graph shows a function and its inverse A. B. C. D.
Graph A shows a function and its inverse A. B. C. D.
What is a function and its inverse?An output is produced by a function after it accepts inputs, applies specific operations to the values, and produces an output. The inverse function works, agrees with the resultant, and returns to the original function An inverse relationship is created when an independent variable is switched out for a variable that depends on a given equation; an inverse relationship may or may not be a function.
Inverse functions, indicated by f-1(x).on, are those in which the inverse of a function is that function itself.
It is common practice to swap the coordinates x and y when calculating an inverse. This new inverse is not necessarily a function, but it is a relation.
To guarantee that the inverse function is also a function, the initial function must be a one-to-one function.
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Select all of the angle pairs that are supplementary when two parallel lines are intersected by a transversal.
Linear pair
Vertical angles
Corresponding angles
Alternate interior angles
Alternate exterior angles
Consecutive interior angles
Consecutive exterior angles
Write an inequality for the following statement A is less than 9
The inequality that corresponds to the following expression, "A is less than 9" is:
[tex]A<9[/tex]Josh works as a tutor for $15 an hour and as a waiter for $13 an hour. This month, he worked a combined total of 95 hours at his two jobs.
Lett be the number of hours Josh worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
total earned (in dollars)
An expression for the combined total dollar Josh earned this month is X = 15t + 13(95 - t).
What is a mathematical expression?A mathematical expression is a statement using a combination of numbers, variables, and mathematical operands.
Mathematical expressions may also use the equal symbol (=) to show that the two expressions are equal. Sometimes, the inequality signs are used when two expressions are not equivalent.
The pay rate per hour as a tutor = $15
The pay rate per hour as a waiter = $13
The combined total hours worked for the month = 95 hours
Let t = the number of hours worked as a tutor
Let X = Josh's total dollars earned for the month.
Josh's total earnings as a tutor for the month, A = 15t
Josh's total earnings as a waiter for the month, B = 13(95 - t)
The combined total dollar Josh earned this month, X = A + B
X = 15t+ 13(95 - t).
Thus, the total earnings by Josh for this month can be expressed as X = 15t+ 13(95 - t).
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