Answer:
B
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.When multoplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of equation)
Answer:
B
Step-by-step explanation:
“ The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $15 per ticket to the planetarium. The second day they paid $90 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club. An expression that represents the total cost in dollars for two days for the n members of the club is given by .”
Answer:
[tex]x = \$187n[/tex]
Step-by-step explanation:
let x be the total cost in dollars for two days for the n members
Given:
The first day the members paid $70 for transportation plus $15 per ticket to the planetarium.
The second day they paid $90 for transportation plus $12 per ticket to the geology museum.
We need to write an an expression to represent the total cost in dollars for two days for the n members of the club.
Solution:
First day each member pay $70 for transportation and $15 for ticket,
[tex]Cost\ per\ member\ for\ the\ first\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = 70+15[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = \$85[/tex]
Therefore, cost for n members for the first day.
[tex]Cost\ for\ n\ member\ for\ the\ first\ day = \$85n[/tex]
Similarly for the second day each member pay $90 for transportation and $12 for ticket,
[tex]Cost\ per\ member\ for\ the\ second\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = 90+12[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = \$102[/tex]
Therefore, .
[tex]Cost\ for\ n\ member\ for\ the\ second\ day = \$102n[/tex]
Now, we write an expression to represent the total cost in dollars for two days for the n members of the club, so cost for n members for two days is equal to sum of the two days expenses for n members.
[tex]Cost\ for\ n\ member\ for\ the\ two\ day = \$85 + \$102n[/tex]
[tex]x = \$85n + \$102n[/tex]
[tex]x = \$187n[/tex]
Therefore, total cost for two days for the n members [tex]x = \$187n[/tex]
Prove using good format: log(nb)x=(log(b)x)/(1+log(b)n)
Answer:
[tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
Step-by-step explanation:
i) [tex]$\log_{nb} x[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
ii) therefore simplifying i) we get
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
iii) Hence the equation is proved.
Let f(x) = 2x + 4 and g(x) = 6x + 5. Find f.g.
Step-by-step explanation:
To find fg(x), you first open up the g.
This will make f(6x+5). How you substitute 6x + 5 for the x in the f.
This means you get 2(6x+5)+4
Which equals 12x+14
Explanation for #4-8
Answer:
Sorry I can't read it :(
(-6+7) - (-4x - 2) ?
the answer to your question is 7
Answer:
4x + 3
Step-by-step explanation:
(-6 + 7) - ( -4x - 2)
1 - ( -4x -2 )
distribute the negative sign to the parenthesis
( remember a negative plus a negative equals a positive )
1 + (4x + 2)
Answer: 4x + 3
What is 2 3/4 • 6 2/3
ILL GIVE BRAINLESS AND POINTS.I need step by step explanation
The answer for P(A∪B) is 40/45 (or) 8/9.
Step-by-step explanation:
Given,
The number of students that play only stringed instruments (A) = 35 students.
The number of students that play only brass instruments (B) = 10 students.
The number of students that play both of the instruments = 5 students.
The number of students that play none of the instruments = 5 students.
Probability = Number of required events / Total events
To find the total number of students,
TOTAL = A + B - both + neither.
TOTAL = 35 + 10 - 5 + 5 = 45 students.
P(A∪B) = P(A) + P(B) - P(A∩B)
Probability of A, P(A) = 35 students / 45 students = 35/45
Probability of B, P(B) = 10 students / 45 students = 10/45
Probability of A∩B (both), P(A∩B) = 5 students / 45 students = 5/45
P(A∪B) = (35/45) + (10/45) - (5/45)
= 40/45
P(A∪B) = 8/9
Given: F(x) = 3x^2+1, G(x) = 2x - 3, H(X) = x
Find F(x) + G(x) =
[tex]F(x)+G(x)=3x^2+2x-2.[/tex]
Solution:
Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]
To find F(x) + G(x):
Adding two functions which gives another function.
Substitute F(x) and G(x), we get
[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]
[tex]=3x^2+1+2x-3[/tex]
[tex]=3x^2+2x-3+1[/tex]
[tex]=3x^2+2x-2[/tex]
[tex]F(x)+G(x)=3x^2+2x-2[/tex]
Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]
explain how you know the numbers of the decimal places that should be in the product when you multiply two decimal numbers together
Answer:
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
Step-by-step explanation:
Let's remember that multiplying decimals is the same as multiplying whole numbers except that you have to put the decimal point in the answer. When you multiply decimals, the decimal point is placed on the product so that the number of decimal places in the product is the sum of the decimal positions of the factors.
Example:
214 * 32 = 6,848
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
7 * 11 = 77
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
what is the value of the expression 2 -12
Answer:
-10
Step-by-step explanation:
2-12 =
-12+2 = -10
Which of these equivalent
ratios is the unit rate?
90 miles
3 hours
60 miles
2 hours
30 miles
1 hour
Answer:
30 miles/1 hour is the unit rate.
Step-by-step explanation:
This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.
The total temperature change over 3 days in Gritty City was −6 degrees Celsius.
What was the average temperature change each day?
Answer:
-2 degrees celcius
Step-by-step explanation:
-6/3
Answer:
Each day, the temperature rises plus -6 Celsius
help, please! Thankyou!!!!
Answer: C
Step-by-step explanation: simply apply the distributive property to each half of the expression to be left with terms that can be combined.
(8x + 16y)/2 = 4x + 8y
4(x - y) = 4x - 4y
(4x + 8y) + (4x - 4y) = 4x + 4x + 8y - 4y
= 8x + 4y => C
Answer:
[tex]\frac{8x+16y}{2}+4(x-y)=\frac{2*4x+2*8y}{2}+4*x-4*y\\\\=\frac{2*(4x+8y)}{2}+4x-4y\\\\=4x+8y+4x-4y=8x+4y[/tex]
Step-by-step explanation:
What part of an hour elapses from 4:56 P.M. to 5:32 P.M.?
Answer:
[tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]
Step-by-step explanation:
Given hours is from 4:56 P.M. to 5:32 P.M.
Now, finding the part of an hour elapases.
We know the starting time is 4 minutes to 5:00 P.M and end time is 32 minutes past 5 P.M.
∴ Total times elapses= [tex]4\ minutes + 32\ minutes= 36\ minutes[/tex]
Hence, 36 minutes elapses out of an hour.
Remember; 1 hours= 60 minutes
Next, finding the fraction of an hour elapses.
[tex]Part\ of\ an\ hour\ elapses= \frac{36}{60}[/tex]
∴ [tex]Part\ of\ an\ hour\ elapses= \frac{3}{5} \ hour[/tex]
Hence, [tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex] from 4:56 P.M. to 5:32 P.M.
The table below shows selected points from a function.
Fist section box answer choice: Constant, not Constant
second section box answer choice: linear, non-linear
The rate change of interval for the given table is Constant , so the function a linear function.
Step-by-step explanation:
A linear function is defined as a function which yields a line in a graph and the rate of change(constant) is called as slope.
Since the rate is constant, then function will result in a straight line.
From the given table the slope m=1 and it changes constantly.
The linear equation formula is y=mx+c.
where m is the slope and c is the y-intercept.
The linear equation for the given table is y=x+1.
∴ The rate change of interval for the given table is Constant , so the function a linear function.
If the graph for a function has any shapes other than a straight line then it doesn't have a constant slope and it will be a non-linear function.
Which of the following describes the graph of y = x² - 7x + 12?
1) The graph has zeroes at x = -4 and x = -3 and it opens downward.
2) The graph has zeroes at x = 4 and x = 3 and it opens downward.
3) The graph has zeros at x = -4 and x = -3 and it opens upward.
4) The graph has zeroes at x = 4 and x = 3 and it opens upward.
Answer:
4
Step-by-step explanation:
its a parabola that opens upward, the zeros are x=4 and x=3
PLEASEEEE help with #7
Answer:
The answer is B ⅚ because there's only one out of 6 chance that the spinner will land on 6.
suppose the hot dogs come in packs of 9 and the buns come in packs of 12.it was the least number of each for which this is possible.
Answer:
Step-by-step explanation:
Least common number for 9 and 12 is 36
36/9=4
36/12=3
4 packs of hot dogs and 3 packs of buns
Fine the value of x in the triangle.
A.) 84
B,) 87
C.) 93
D.) 115
Answer:
The correct answer is B. 87°
Step-by-step explanation:
Let's recall that the interior angles of a triangle add up to 180°,
therefore, we have:
∠x + 28 + 65 = 180
∠x = 180 - 65 -28
∠x = 180 - 93
∠x = 87°
The correct answer is B. 87°
Carmen often orders party trays from her favorite Mexican food restaurant For company events. For a recent company party, she spent $58 on one burrito platter and one taco platter. For a company meeting, she spent $90 on to burrito platters and one taco platter. How much does each type of platter cost?
By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Explanation:To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.
We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.
Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.
Step 1: Establish the Equations
The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.
Step 2: Solve the Equations
From the first equation, we can express T in terms of B: T = 58 - B.
Substitute the expression for T in the second equation: 2B + (58 - B) = 90.Simplify and solve for B: B = 32.Substitute the value of B back into any of the original equations to find T: T = 26.Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.
What is the x intercept and y intercept of this equation.
Answer:
x intercept is 15 and y intercept is -3.75
Step-by-step explanation:
The first thing is to form equation with the given tow point using the formula
y-y1/x - x1 = y2 - y1/ x2 - x1
y + 5/x + 5 = -2 + 5/7 + 5
y + 5/x + 5 = 3/ 12
3x + 15 = 12y + 60
12y - 3x = -45
On x intercept y = 0
x = 15
On y intercept x = 0
y = -3.75
13. Marisa walked her dog mile on Saturday and 55 mile on Sunday. How far did she walk her dog in all?
Marissa walked her dog 1/10 mile on saturday and 55/100 mile on sunday. how far did she walk her dog in all?
Answer:Marissa walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday
Solution:Given that, Marissa walked her dog
From given information,
[tex]\text{Miles walked on saturday } = \frac{1}{10} \text{ mile }\\\\\text{Miles walked on sunday } = \frac{55}{100} \text{ mile }[/tex]
We have to find the distance walked in all
[tex]\text{Total distance } = \text{Miles walked on saturday + Miles walked on sunday }[/tex]
Substituting the values we get,
[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]
Make the denominators same for easier calculations by taking L.C.M of 10 and 100
Prime factors of 10 = 2 x 2 x 5
Prime factors of 100 = 2 x 2 x 5 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 5, 5
Multiply these factors together to find the LCM
LCM = 2 x 2 x 5 x 5 = 100
[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]
[tex]\text{Total distance } = \frac{1 \times 10}{10 \times 10} + \frac{55}{100}\\\\\text{Total distance } = \frac{10}{100} + \frac{55}{100}\\\\\text{Total distance } = \frac{10+55}{100} = \frac{65}{100}[/tex]
Thus she walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday
What is the balance after Anna writes check #1620? A) $1536.24 B) $1606.42 Eliminate C) $1734.81 D) $1760.61
The correct answer is B) [tex]$1606.42[/tex]. The balance after Anna writes check is
[tex]$1606.42[/tex].
To solve this problem, we need to follow the transactions in Anna's checking account to determine the balance after check #1620 is written. Let's assume that the initial balance before any transactions is $0.00.
Let's check each option:
A) [tex]$1536.24[/tex][tex]- $1452.77 = $83.47[/tex] (This cannot be the correct balance after check #1620 because it does not match the balance after check #1612.
B)[tex]$1606.42 - $1452.77 = $153.65[/tex] (This is the amount spent on groceries, indicating that the balance after check #1612 is correct and no additional funds were withdrawn by check #1620.)
C)[tex]$1734.81[/tex][tex]- $1452.77 = $282.04[/tex] (This would mean an additional $282.04 was withdrawn after the groceries purchase, which is not possible since we are looking for the balance after one check, #1620.)
D) [tex]$1760.61[/tex][tex]- $1452.77 = $307.84[/tex] (This would also mean an additional amount was withdrawn, which is not possible for the same reason as option C.) Therefore, the only logical balance that matches our calculations after check #1620 is option B) $1606.42, which implies that check #1620 did not change the balance from what it was after check #1612. This means that check #1620 was for the same amount as the groceries purchase ($153.65), which brought the balance back to $1606.42 after the groceries were bought
Choose the correct simplification of (3p)(5q).
pq
2pq
8pq
15pq
Answer:15pq
Step-by-step explanation:
The correct expression is 15pq.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
Expression Definition in MathAn expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given:
(3p)(5q).
=3p * 5q
=15 pq
Hence, the simplified expression is 15 pq.
Learn more about expression here:
https://brainly.com/question/14083225
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You have just bought a new Sony 55” 3D television set for $2300. The TV’s value decreases at a rate of $250 per year. Construct a linear function to represent this situation. Clearly indicate what your variables represent.
Answer:
2300-x(250) is the best i could think of hope it helps
Step-by-step explanation:
We need to represent the value of a TV whose value decreases yearly.
The required equation is [tex]y=2300-250x[/tex]
The cost of the TV set is $2300.
The decrease in value is $250 per year.
Let [tex]x[/tex] be the number of years that has passed after buying the TV
and [tex]y[/tex] be the cost of TV after [tex]x[/tex] years have passed.
The linear equation that represents the situation is [tex]y=2300-250x[/tex]
Learn more:
https://brainly.com/question/11897796
https://brainly.com/question/2263981
An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a building is 38°. The engineer knows the building is 300 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot? ✓ 384 ft 487 ft X 234 ft 185 ft
Answer:
My best guess is 384 ft
Step-by-step explanation:
Tangent 38° = opposite side / adjacent side
Tangent 38° = 300 ft / x ft
The value of x from the equation is 383.98 ft. Thus, the engineer is 383.98 ft.
Rounding it up gives us 384 ft.
Answer:
384 ft.
Step-by-step explanation:
We know the opposite side of the triangle and we need the adjacent side.
So tan 38 = opposite / adjacent
= 300 / x
x = 300 tan 38
x = 383.98 feet.
A spinner has equally sized sections, of which are gray and of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue ?
Answer:
25%
Step-by-step explanation:
50% chance for spin one to be gray and 50% chance for spin two to be blue. Put them together for that order and you get 25%.
Answer:
Let's Take 8 sections and in which 6 are grey and 2 are blue.
The probability that the first spin lands on blue = 2/8 = ¼
The probability that the second spin lands on gray = 6/8 = ¾
The probability that the first spin lands on blue and the second spin lands on gray is
(¼)(¾) = 3/16
These events are independent, so you can just multiply the probabilities
Solve 3/5y=6 ''''''''''''''''''''''''''
Answer:
y = 10
Step-by-step explanation:
The question is a simple equation and ought to be 3y/5 = 6 ( in stead of 3/5y=6)
Multiply through by the lowest common multiple (LCM) of denominator (which equals 5)
5 × 3y/5 = 6 × 5
3y = 30
Divide through by 3
3y/3 = 30/ 3
y = 10
Therefore, y = 10
Check
3y/5 = 6
y = 10
3(10)/5 = 6
30/5 = 6
6 = 6
Given Angle 1 = Angle 2,
find x.
Answer:
x = 6
Step-by-step explanation:
Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is
[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross- multiply )
x(x - 4) = 12 ← distribute left side
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
However, x > 0 , thus x = 6
I need to solve by completing the square but I just can’t seem to get the correct answer, the quadratic is 2x^2- .5x-28=0
Answer:
x - 5.19 or x = -2.67 is the correct answer.
Step-by-step explanation:
Here, the given quadratic equation is: [tex]2x^2- 5x-28=0[/tex]
To solve it by : Completing The Square
Step : 1 Make the coefficient of leading variable x² as 1.
Divide whole equation by 2,we get:
[tex]x^2- \frac{5}{2} x-14=0\\\implies x^2- \frac{5}{2} x = 14[/tex]
Step 2: Find the coefficient of x in the equation and DIVIDE it by 2 to HALF THE VALUE
Here, the coefficient of x = (-5/2)
Dividing ot by 2, we get the value = (-5/4)
Step 3: ADD THE SQUARE of the found value on BOTH sides.
And USE: [tex](a - b)^2 = a^2 + b^2 - 2ab[/tex]
[tex]x^2- \frac{5}{2} x = 14 \implies x^2- \frac{5}{2} x + (\frac{5}{4} )^2= 14 + (\frac{5}{4} )^2\\\implies (x -\frac{5}{4})^2 = 14 + \frac{25}{16} = \frac{224 + 25}{16} = \frac{249}{16} \\\implies (x -\frac{5}{4})^2 = \frac{249}{16} = (\frac{15.7}{4})^2\\ \implies (x -\frac{5}{4})^2 = (\frac{15.7}{4})^2[/tex]
Step 4: TAKE ROOT ON BOTH SIDES, we get:
[tex](x -\frac{5}{4})^2 = (\frac{15.7}{4})^2\\\implies (x -\frac{5}{4}) = \pm (\frac{15.7}{4})\\\implies x = (\frac{15.7}{4}) +(\frac{5}{4}) = 5.19\\or, x = - (\frac{15.7}{4}) +(\frac{5}{4}) = -2.67\\[/tex]
So, either x - 5.19 or x = -2.67