The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
y = (2/7)(x - 2)^2 - 6(x - 1)^2 + (y - 2)^2 = 5^2What are equations?The equation is described as the state of being equal and is commonly represented as a math expression with equal values on either side, or it refers to an issue in which many factors must be considered. 2+2 = 3+1 is an example of an equation.To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:
The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola, a is constant.
For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.
f(x) = a(x - 2)^2 - 6We will find a using f(-7) = 8:
f(-7) = a(-7-2)^2 - 6f(-7) = 49a - 649a - 6 = 849a = 14a = 14/49a = 2/7The quadratic function for the sailboat is given by:
f(x) = (2/7)(x - 2)^2 - 6 or y = (2/7)(x - 2)^2 - 6The equation for a circle with a radius of 5 and center (1, 2) is:
(x - 1)^2 + (y - 2)^2 = 5^2Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
y = (2/7)(x - 2)^2 - 6(x - 1)^2 + (y - 2)^2 = 5^2Know more about equations here:
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The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?
G.CO.5 △ABC undergoes a series of transformations to create △A'B'C'. Which of the following series of transformations will carry △ABC onto △A'B'C'?
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
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If you are choosing a single card from a standard deck of playing cards, what is
the probability that you draw a face card or a heart?
Your answer should be in the form of a fraction. Type it like this: 15/52.
Just to review:
• There are 52 cards in a deck.
• There are 4 suits with 13 cards each.
o 2 red suits - hearts and diamonds
o 2 black suites - clubs (look like clovers) and spades
• Each suit has an Ace, numbered cards 2-10, and 3 "face" cards--a Jack, Queen, and King.
Step-by-step explanation:
there are 4 suit with 13 cards each
The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $8.50, and bags of cookies cost $4.50, and sales equaled $79.00 in total. There were 6 more bags of cookies than candy sold.
Find the number of bags of candy and cookies sold by the drama club. Show your work.
The bags of candy that was sold is 6
The bags of cookies that was sold is 10.
What are the linear equations that represent the question?$8.50c + $4.50o = 79 equation 1
o - c = 6
o = 6 + c equation 2
Where:
o = bags of cookies soldc = bags of candies sold How many bags of candy and cookies were sold?Substitute for o in equation 1 using equation 2
$8.50c + $4.50(6 + c) = 79
$8.50c + 27 + 4.50c = 79
$8.50c + 4.50c = 79 - 27
$13c = 52
c = 52 / 13
c = 4
Substitute for c in equation 2
0 = 6 + 4 = 10
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Use 3.14 for pi. ROUND YOUR FINAL ANSWER TO THE NEAREST TENTHS PLACE!
Answer:
379.94
Step-by-step explanation:
3.14 x 11^2 = 379.94
The area of the given circle is 95 square ft.
Calculation for the Area of the Circle:
It is given in the diagram that,
The diameter of the circle, d = 11 ft.
Now, we know that the radius of a circle is equal to half of the diameter.
Therefore, radius of the given circle, r = 11/2 ft.
The formula for the area of the circle is given as follows,
A = π × r²
Substituting the values, π = 3.1, and r = 11/2, we get,
A = (3.14) × (11/2)²
A = (3.14) × 30.25
A = 94.985
A ≈ 95
Hence, the area of the given circle with diameter 11 ft. comes out to be 95 ft².
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A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. event a is defined as drawing a black tile from the bag on the first draw, and event b is defined as drawing a white tile on the second draw. if two tiles are drawn from the bag, one after the other without replacement, what is p(a and b) expressed in simplest form?
P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To express P(A and B) in the simplest form:
P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Will’s collection?
Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of stamps that are in Will’s collectionIn this case, a system of linear equations must be proposed taking into account that:
W: Number of stamps that are in Will’s collectionC: Number of stamps that are in Carlton’s collectionA: Number of stamps that are in Ashley’s collectionOn the other hand, you know that:
Ashley has 30 stamps and she has a third as many as Carlton has → A= [tex]\frac{1}{3}[/tex]C → 30= [tex]\frac{1}{3}[/tex]CWill has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. → W= 2(C + A)So, the system of equations to be solved is
[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the first equation:
30= [tex]\frac{1}{3}[/tex]C
30÷[tex]\frac{1}{3}[/tex]= C
90= C
Substituting the value in the second equation:
W= 2(90 + 30)
W= 2×120
W=240
Finally, 240 stamps are in Will’s collection.
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The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to:
The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
How to determine the degrees of freedom applied to a cross-tabulation ?The given parameters are:
Rows = 5
Column = 2
The degrees of freedom is then calculated as:
df = Rows + Column - 1
Substitute the known values in the above equation
df = 5 + 2 - 1
Evaluate the expression
df = 6
Hence, the degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
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DIVINE TOK A MATH TEST AND GOT 36 CORRCET AND 9 INCORRECT WHAT WAS THE PERCANTHGE OF CORRECT ANSWERS
Answer: 80% correct
Step-by-step explanation:
If Divine got 36 correct and 9 incorrect, then we can find the total number of questions.
36 + 9 = 45 questions
Now, we will divide the number of questions answered correctly by the total number of questions.
[tex]\displaystyle \frac{36}{45} =0.8[/tex]
Lastly, we will multiply it by 100 to find the percentage.
0.8 * 100 = 80%
Answer:
80% was correct.
Step-by-step explanation:
The total number of questions is 45 (36 + 9). The percentage is the part correct over the total.
36/45 = .8. The answer is given in the decimal form. To change a decimal to a percent, move the decimal two places to the right.
A zookeeper is monitoring the population of penguins. the group needs to have exactly two times more males than females for the population to thrive. the zoo only has room for a maximum of 10 female penguins. let x represent the number of female penguins and y represent the number of male penguins. write the constraints that represent the possible number of male and female penguins that can live in a thriving population at the zoo. 0 < x ≤ 10 and 0 < y ≤ 20 x > 0 and y > 0 0 < x ≤ 10 and y > 20 x > 0 and y < 10
Answer:
0 < x ≤ 10 and 0 < y ≤ 20.
Step-by-step explanation:
I did the test and got it right ma bois.
Answer: Its A
Step-by-step explanation:
if you rolled two dice what is the probability that you would roll a 4 or a 5
What is the period of y = 2cos(3x - 2п)?
Answer:
Periodicity of 2cos(3x-2π)=
[tex] \frac{2\pi}{3} [/tex]
Step-by-step explanation:
Greetings![tex]periodicity \: of \: 2 \cos(3x - 2\pi) \\ periodicity \: of \: a. \cos(bx + c) + d = \\ \frac{periodicity \: of \: \cos(x) }{|b|} \\ periodicity \: of \: \cos(x) \: is \: 2\pi = \frac{2\pi}{|3|} \\ simplify = \frac{2\pi}{3} [/tex]
Answer:
[tex]\sf Period=\dfrac{2}{3} \pi[/tex]
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
y = 2 cos (3x - 2π)
Therefore:
A = 2B = 3C = 2/3D = 0Period of given function:
[tex]\sf \implies Period=\dfrac{2 \pi}{B} = \dfrac{2 \pi}{3}[/tex]
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Find the missing length indicated.
The missing length of given right triangle is equal to 1500.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
Thus, if h²=m*n. You can write:
h²=900*1600
[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]
If h=1200, you can find x from Pythagorean Theorem.
x²=1200²+900²
x²=1440000+810000
x²=2250000
x=[tex]\sqrt{2250000}[/tex]
x=1500
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Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?
Considering the situation described, it can be graphed by the first function.
Which graph models the situation?Cities A, B and C are on a straight line.
On the first hour, they leave town B to town C, moving farther from Town A, hence the distance is increasing on the first hour.On the second hour, they stop for lunch, meaning that the distance remains constant at the point it was at the end of the first hour.Hence, the first graph is the correct one for this problem.
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PLease helppppppppp!!!
Answer:
437.068 28.019
Step-by-step explanation:
Not sure how to explain this one....it is what it is
7 ones = 7
3 tens = 30
4 hundreds = 400 added = 437
No tenths = 0
6 hudredths = .06
8 thousandths = .008 added to = 437.068
280 tenths = 280 * 1/10 = 28
19 thousandths = .019 summed = 28.019
8x + 2y =16
standard form
1) m=
2 y - intercept x - intercept
Answer:
m=-4
y-intercept=8
x-intercept=2
Step-by-step explanation:
Please see attachment.
y-intercept=8
The y-intercept is where the line crosses the y-axis.
x-intercept=2
The x-intercept is where the line crosses the x-axis.
m=-4
If you do not know how to find slope by looking at graph, use slope formula.
(y2-y1)/(x2-x1)
Choose 2 points. You may use the x and y intercepts.
(2,0) and (0,8)
(8-0)/(0-2)=8/-2=-4
Hope this helps!
A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach. to estimate support for firing the current head coach, a television news station provides a link on its website where fans of the team can respond to the question: "do you feel the current head coach should be fired?" after 2,367 votes on the website, 79% of those who responded felt the coach should be fired. which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall support for firing the coach?
This is voluntary response bias. The result overestimates true support for firing the coach.
What is voluntary response bias? When sample participants are self-selected volunteers, as in voluntary samples, voluntary response bias emerges.An illustration would be call-in radio programs that invite listeners to participate in polls on contentious issues (abortion, affirmative action, gun control, etc.).The sample that results tends to overrepresent people with strong opinions. In a random sampling technique, every component of the population has a known, non-zero probability of being chosen, and the selection of the sample unit is dependent only on chance.By removing voluntary response bias and protecting against undercoverage bias, random sampling aids in the production of representative samples.Random sampling underpins all probability sampling techniques.To know more about voluntary response bias with the given link
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Solve for n.
7 + 2n
||
=
submit
Answer:
2
Step-by-step explanation:
7+2n = 11
2n = 11-7
2n = 4
n = 4/2
therefore n = 2
In a scale drawing of a painting, 2 centimeters represents 7 inches.
The height of the real painting is 35 inches. What is the height of the painting in the scale drawing?
The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.
Find the height of the painting in the scale drawing:Here in the question it is given that,
In a scale drawing of a painting, 2 centimeters represents 7 inchesThe height of the real painting is 35 inchesThus we can say that, scale of the painting is 2 cm : 7 in
Ratio of scale drawing and real painting is 2 : 7
⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.
We can say that,
2 cm/7 in = x cm/35 in
where x is the height of the painting in the scale drawing
2 cm × 35 in /7 in = x cm
x = 2 × 5 cm
x = 10 cm
Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.
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The local gym is offering this new promotion: An enrollment fee of $40 and a monthly fee of $30. Which of the following expressions represents the cost of the gym membership for m months?
40+30m=c40 plus 30 m is equal to c
30+40m=c30 plus 40 m is equal to c
40+30m40 plus 30 m
30+40m
The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The local gym is offering this new promotion:
An enrollment fee of $40 and a monthly fee of $30.
Let m be the total number of months
Total monthly fee = 30m
Total cost(including the enrollment fee of $40) = 40 + 30m
Let the total cost is c:
c = 40 + 30m
If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.
Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
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Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
What is the distance?Distance is a measurement of time and speed.
The distance equals speed multiplied by time.
Data and Calculations:Distance between Alice and Bob = 1,000 feet
Distance between the bird and Bob = 1,000 feet
Speed of Alice and Bob = 10 feet per second, respectively
The combined speed of Alice and Bob = 20 feet per second
Since the two are running directly toward each other, the distance each will cover at the meeting point is 50 feet (1,000/20)
The time covered at the meeting point = 20 seconds (1,000/50)
Speed of the bird = 20 feet per second
The distance covered by the bird towards Bob at their meeting point is 40 feet (20 feet x 20 seconds)
Thus, the total distance covered by the bird at the meeting point is 40 feet.
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19/23 x 50
HELP ME Giving BRAINLIEST ALSO 30 POINTS
[tex]\boldsymbol{\sf{\dfrac{19}{23}\times50 }}[/tex]
We express 19/25 x 53, as a single fraction as follows:
[tex]\boldsymbol{\sf{\dfrac{19\times50}{23} \ \ \longmapsto \ \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{950}{23} }}[/tex]
Like the fraction 950/23, it cannot be further simplified, so it remains that way, therefore
[tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ \frac{950}{23} }}}}[/tex]
2(x+1)=10 what's x please best example
Answer:
x = 4
Step-by-step explanation:
1.Distribute
2. Subtract 2 from both sides
3. Simplify
4. Divide both sides by same factor
5. Simplify
x = 4
Answer: 4
Step-by-step explanation:
We have to try getting x by itself to solve for it. Since we have two sides that are equal to each other, we can add, subtract, multiply, and divide anything on both sides to try to isolate x.
[tex]2(x+1)=10[/tex]
We can first divide the left side and the right side by 2. This would remove the 2 being multiplied on the outside.
[tex]\frac{2(x+1)}{2}=\frac{10}{2}\\x+1=10\div 2\\x+1=5[/tex]
Now, we have a + 1 on the left side that we need to remove to get x by itself. If we are adding something, we can remove that by subtracting the same thing. Hence, we can subtract 1 from both sides to remove the + 1.
[tex]x+1=5\\x+1-1=5-1\\x+0=4\\x=4[/tex]
After all that simplifying, we get that x equals 4.
4x+10=-2x + 4
y - 4 (2y - 5) = -4
Solve the 2 equations
(ignore image)
The solutions to the equations are x = 7/3 and y = 24/7
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
4x + 10 = -2x + 4
y - 4(2y - 5) = -4
Considering the first equation
4x + 10 = -2x + 4
Collect the like terms
4x + 2x = 10 + 4
Evaluate the like terms, by adding them
6x = 14
Divide both sides of the equation by 6
x = 7/3
Considering the second equation
y - 4(2y - 5) = -4
Expand the bracket in the above equation
y - 8y + 20 = -4
Collect the like terms
y - 8y = -20 -4
Evaluate the like terms, by adding them
-7y = -24
Divide both sides of the equation by -7
y = 24/7
Hence, the solutions to the equations are x = 7/3 and y = 24/7
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Let a and b be 3 by 3 matrices with det (a) = 3 and det (b) = 5. find the value of det(ab).
If the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
Given that the value of determinant a is 3, determinant b is 5.
We are required to find the value of determinant ab.
Determinant of a matrix is the scalar value computed for a given square matrix.It means the matrix which is not square does not have a determinant value. It is denoted by IAI.
We know that,
IaI*IbI=IabI
So we have to just put the values in the above formula to get the determinant of ab.
IabI=3*5
=15
Hence if the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
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At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of 30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
Answer:
The average price of a ticket is $25.
Step-by-step explanation:
Lets us say 100% = 1
0.75 x 30 + 0.25 x 10 = 25
By selling 20 oranges for#1.35 a trader makes a profit of 8% what is the percentage gain or loss if he sells the same 20 oranges for#1.10?
Answer:
12% loss
Step-by-step explanation:
The selling price is the sum of the cost price and the markup. Here, the markup (profit) is expressed as a percentage of the cost price.
Cost priceThe relation between selling price and cost price is ...
selling price = cost price + cost price × markup fraction
selling price = cost price × (1 + markup fraction)
Then the original cost price is ...
cost price = (selling price) / (1 + markup fraction)
cost price = #1.35 / (1 +8%) = #1.25
ProfitAfter the change in selling price, we can find the markup fraction (profit rate) to be ...
1 + markup fraction = (selling price)/(cost price)
markup fraction = (selling price)/(cost price) -1
markup fraction = #1.10/1.25 -1 = 0.88 -1 = -0.12
The trader has a 12% loss when selling the oranges at #1.10.
Sumalee and Julio are selling cheesecakes for a school fundraiser. Customers can buy pecan
cheesecakes and apple cheesecakes. Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285. Find the cost each of one pecan cheesecake and one apple cheesecake.
The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
According to the statement
we have given that the Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285.
And we have to find that the cost each of one pecan cheesecake and one apple cheesecake.
So, for this purpose,
Let x be the cost of each pecan cheesecake.
and y be the cost of each one apple cheesecake.
Then The equation become
6x + 12y = 270 -(1)
12x + 9y = 285 -(2)
From elimination method
multiply (1) by 12 and (2) by 6 then
72x + 144y = 3240
72x + 54y = 1710
Now eliminate x from them then the equation become
90y = 1530
here y = 17
then the x become
6x + 12y = 270
6x + 12(17) = 270
6x = 270-204
6x = 66
and x become 11.
So, The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
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Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5
2 months
5 months
3 months
4 months
It would take 2 months for the membership of both clubs to be the same
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total cost of dues over x months, hence given that:
y = 3x - 5 (1)
Also:
4x - 3y = 5
y = (4x - 5)/3 (2)
For the membership of both clubs to be the same:
3x - 5 = (4x - 5)/3
9x - 15 = 4x - 5
x = 2
It would take 2 months for the membership of both clubs to be the same
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The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?
The possible base and height of a second triangle are:
B = 5 H = 12What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To find the base and height of the triangle:
First, we must find the constant of variation (k).
The problem indicates that the base of each triangle varies inversely with the height.
So, this can be represented as below:
B = k/H
B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.When we clear "k", we obtain:
B = k/H k = BxH k = 10x6 k = 60Now, we have:
B = 60/HWe can give any value to "H" and you will obtain the base of the second triangle.
If H = 12, then:
B = 60/H B = 60/12 B = 5Therefore, the possible base and height of a second triangle are:
B = 5 H = 12Know more about triangles here:
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Solve this system of equations by using the elimination method. x+4y=9 2x-4y=-6
Answer:
[tex]x=6[/tex]
[tex]y=\frac{3}{4}[/tex]
Step-by-step explanation:
Given the following question:
[tex]x+4y=9[/tex]
[tex]2x-4y=9[/tex]
To solve using the elimination method we will add the two equations together to find the two individual values.
[tex]x+2x=3x[/tex]
[tex]4y-4y=0[/tex]
[tex]9+9=18[/tex]
[tex]3x=18[/tex]
[tex]\frac{3x}{3} =x[/tex]
[tex]18\div3=6[/tex]
[tex]x=6[/tex]
[tex]x+4y=9[/tex]
Substitute six in for x:
[tex]x=6[/tex]
[tex]6+4y=9[/tex]
Solve for y:
[tex]6-6=0[/tex]
[tex]9-6=3[/tex]
[tex]\frac{4y}{4} =y[/tex]
[tex]3=\frac{3}{4}[/tex]
[tex]y=\frac{3}{4}[/tex]
x is equal to 6, and y is equal to 3/4.
Hope this helps.
