The diagram shows a rectangle ABCD.The point A is (2,14) , Bus (-2,8) and C lies on the x-axis.
Find
(i) the equation of BC.
(ii) the coordinates of Cand D.
Using linear function concepts, it is found that:
i) The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].
ii) The coordinates of C are C(0,10) and the coordinate of D are D(14,6).
What is the missing information?The diagram is missing, and is shown in the graph at the end of the answer.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the coordinates are given as follows:
A(2, 14), B(-2,8) and C(x,0).
From the diagram, AB and BC are perpendicular, meaning that the multiplication of their slopes is of -1.
Given two points, the slope is given by change in y divided by change in x. Hence the slope of AB is given as follows:
mAB = (8 - 14)/(-2 - 2) = 3/2.
The slope of BC is given as follows:
mBC = (0 - 8)/(x - (-2))
mBC = -8/(x + 2).
The multiplication of the slopes is of -1, hence:
mAB x mBC = -1
-12/(x + 2) = -1
- x - 2 = -12
x = 10.
Hence, the slope of BC is:
mBC = -8/(x + 2) = -8/12 = -2/3.
Then:
y = -2/3x + b.
When x = 10, y = 0, hence we can find b as follows:
0 = -2/3(10) + b
b = 20/3.
Hence:
The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].
From the diagram, we also have that AB and CD are parallel, meaning that they have the same slope, hence, considering D(x,y), we have that:
mCD = mAB
y/(x - 10) = 3/2
y = 1.5(x - 10)
y = 1.5x - 15.
AD and BC are also parallel, hence:
mAD = mBC
(y - 14)/(x - 2) = -2/3
Since y = 1.5x - 15, we have that:
(1.5x - 15 - 14)/(x - 2) = -2/3
(1.5x - 29)/(x - 2) = -2/3
3(1.5x - 29) = -2(x - 2)
4.5x - 87 = -2x + 4.
6.5x = 91
x = 91/6.5
x = 14.
y = 1.5x - 15 = 1.5(14) - 15 = 21 - 15 = 6.
Hence:
The coordinates of C are C(0,10) and the coordinate of D are D(14,6).
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Mia is making smoothies. Each smoothie uses 1/2 cup of yogurt. How much yogurt
does she need to make 7 smoothies?
To solve, we'll need to _______
because we know the SIZE of the groups and the _______
but we don't know the ______
Answer: 3.5 cups
To solve, we'll need to multiply because we know the SIZE of the groups and the amount of groups but we don't know the total amount.
What is 75 Of 625 percent
Answer:
75 * (625 percent) = 468.75
Step-by-step explanation:
A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon.
Based on the calculations, the perimeter of this regular polygon is equal to 7.5 units.
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
TriangleQuadrilateralPentagonHexagonHeptagonOctagonNonagonHow to determine the perimeter of this regular polygon?Since this polygon is a regular polygon with each of its sides being equal, we have:
3(x - 1) = 5x - 6
3x - 3 = 5x - 6
5x - 3x = 6 - 3
2x = 3
x = 3/2
x = 1.5.
The measure of each of its sides is given by:
3x - 3 = 5x - 6
3(1.5) - 3 = 5(1.5) - 6
4.5 - 3 = 7.5 - 6
1.5 = 1.5
Each side, a = 1.5 units.
Now, we can determine the perimeter of this regular polygon:
Perimeter of pentagon = 5a
Perimeter of pentagon = 5 × 1.5
Perimeter of pentagon = 7.5 units.
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what is the 15th term of the general term
n(n+1)
______
2
Answer:
a₁₅ = 240
Step-by-step explanation:
to find the 15 th term substitute n = 15 into the general term
a₁₅ = 15(15 + 1) = 15(16) = 15 × 16 = 240
-12 - ([tex]\frac{2}{3} \[/tex]=
Answer:
[tex]-\frac{38}{3}[/tex]
Step-by-step explanation:
[tex]-12-\frac{2}{3}\\-12 = \frac{-36}{3} = \left(-36\right) \div 3\\\frac{-36}{3}-\frac{2}{3}\\=\frac{-36-2}{3}\\=\frac{-38}{3}[/tex]
Hope this helps!
The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level. How many grams of fat are recommended daily? Round to the nearest whole number.
The daily recommended grams of fat is? ...
The daily recommended grams of fat by the nutritional label is 98 grams.
How to find the grams of fat recommended daily?The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level.
let
the recommended level = x
Therefore, the product of the percentage and the required daily recommendation level is equals to the 3 grams.
grams of fat = 3.06% × x
3 = 3.06% × x
3 = 3.06 / 100 × x
3 = 3.06x / 100
cross multiply
3 = 3.06x / 100
300 = 3.06x
300 = 3.06x
divide both sides by 3.06
300 / 3.06 = 3.06x / 3.06
x = 98.0392156863
x = 98 grams
Therefore, the daily recommended grams of fat by the nutritional label is 98 grams.
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Write the expression as a number in scientific notation.
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
4.2 x 1010
3.4 x 1010
4.2 x 105
3.4 x 105
The expression as a number in scientific notation is 4.2 * 10^5
How to write the expression as a number in scientific notation?The expression is given as:
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
Rewrite properly as:
[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]
Evaluate the product of 7 and 5.4
So, we have:
[37.8* 10^3 * 10^4]/[9 * 10^2]
Evaluate the product of 10^3 and 10^4
So, we have:
[37.8* 10^7]/[9 * 10^2]
Evaluate the quotient of 37.8 and 9
So, we have:
[4.2 * 10^7]/[10^2]
Evaluate the quotient of 10^7 and 10^2
So, we have:
4.2 * 10^5
Hence, the expression as a number in scientific notation is 4.2 * 10^5
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how to write and solve; two times the quantity of 7x plus 5 equals -32?
Answer: x = -3
Step-by-step explanation:
First, we will write an equation.
two times ➜ 2 *
7x plus 5 ➜ 7x + 5
equals -32 ➜ -32
2(7x+5) = -32
Next, we will solve by isolating the x variable.
2(7x+5) = -32
14x + 10 = -32
14x = -42
x = -3
HELPPPPP ASAPPPP PLS
Answer:
-1/6
Step-by-step explanation:
Homework Task 3: Item C
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Bookwork code: K90
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Give your answer as an integer or as a fraction in its simplest form.
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Answer
Answer:
Step-by-step explanation:
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PLEASE HELP
A TV show had 5.6 x 105 viewers in the first week and 4.1 x 105 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 1010
9.7 x 105
4.85 x 1010
4.85 x 105
The average number of viewers over the two weeks is 4. 85 x 10^5. Option D
What is average?Average is simply a number taken as the representative of a list of numbers.
It is determined by taking the sum of the numbers divided by the number of listed numbers.
Given the number of viewers as;
5.6 x 105 viewers and 4.1 x 105 viewers
Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2
Average = 9. 7 x 10^5 / 2
Average = 4. 85 x 10^5
The average number of viewers over the two weeks is 4. 85 x 10^5
Thus, the average number of viewers over the two weeks is 4. 85 x 10^5. Option D
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Evaluate the following expression when n = 2.
A. -1
B. 0
C. 4
D. 5
14n-61 +1-31
The value of expression is -61
In the given question is that:
Evaluate the expression when n = 2
and, Equation is = 14n - 61 + 1- 31
Now, According to the question :
Put the value of n= 2 in above equation:
then, 14 x 2 - 61 +1 - 31
= -61
Hence, The value of expression is -61
Composition of Functions:
The composition of function is the process of creating another function by applying a function as an input to another function.
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Tell whether the value is a solution of the inequality 5 − x < 8; x = −3
Answer:
The value is not a solution of the inequality.
Step-by-step explanation:
5 - x < 8
1. Substitute the variable, x, with -3: 5 - - 3 < 8
2. Use the KCC (keep,change,change) method to turn subtraction into addition: 5 + + 3 < 8
3. Add the numbers on left side of the inequality to get the answer: 8 < 8 - False statement - 8 is not less than 8.
A CD storage rack it's sold to stores at a wholesale price of $18 if the store has a 150% markup what is the retail price of the CD rack?
The retail price of the CD rack is $45.
How to calculate the value?From the information, the storage rack it's sold to stores at a wholesale price of $18 and the store has a 150% markup.
The retail price will be:
= $18 + (150% ×$18)
= $18 + $27
= $45
Therefore, the retail price of the CD rack is $45.
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Evaluate the expression when x = 5:
10|7−x|
A. -120
B. -20
C. 20
D. 120
Answer:
C. 20
Step-by-step explanation:
10|7−x| here we are asked to find the absolute value.
x is given as 5 so if we just rewrite the expression:
10|7-5| = 20 because absolute value cannot be negative.
quantity a: the number of prime numbers between 0 and 100, inclusive. quantity b: the number of prime numbers between 101 and 200, inclusive.
The correct option is Quantity a: the number of prime numbers between 0 and 100, inclusive is greater.
What is a prime number?A prime number is a natural number greater than 1 that is not the sum of two lesser natural numbers (or a prime). Any natural number greater than one that is not prime is referred to as a composite number. For instance, the product 1 5 and 5 1 are the only two ways to write the number 5, making it a prime. The fact that it is the sum of two smaller integers (2 x 2), 4, however, makes it composite. Primes play a significant role in number theory because of the fundamental theorem of arithmetic, it states that any natural number greater than one is either a prime number itself or may be factored as a unique prime product up to the order of the primes. the prime number (or a prime).
The number of primes reduces almost exponentially as we move up the number line. The prime numbers between 0 and 100 are therefore far more numerous than those between 101 and 200. It is crucial to understand this general number theory point, but it may also be rapidly illustrated by attempting to find some primes in these two groups.
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I WILL GIVE BRAINLIEST SND 59 POINTS PLS ANSWER ALL OF THE QUESTIONS At a bargain store, Tanya bought 4 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but each was $1.75 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Tanya's items
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences
What is the greatest common factor of 3 and 13?
Answer: 1
Step-by-step explanation:
In order to find GCF, take the prime factorization of 3 and 13.
3: 1*3 ==> Prime factorization of 3
13: 1*13 ==> Prime factorization of 3
The common factor is 1.
GCF of 13 and 3 is 1
the sum of two numbers is 56 . the larger number is 16 more than the smaller number. what are the numbers?
The numbers are 20 and 36.
As per the information in question, let the smaller number x. So, according to question, large number will be (x + 16).
Now, writing the equation that will form -
x + x + 16 = 56
Performing addition of variables on Left Hand Side
2x + 16 = 56
Shifting the number from Left Hand Side to Right Hand Side
2x = 56 - 16
Performing subtraction on Right Hand Side
2x = 40
Shifting 2 to denominator on Right Hand Side
x = 40÷2
Performing division to find the value of x
x = 20
So, smaller number is 20.
Larger number = x + 16
Larger number = 20 + 16
Larger number = 36
Hence, the numbers are 20 and 36.
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Use synthetic division to divide.
(6x³ +3x + 9) \ (x + 2)
Answer:
Step-by-step explanation:
HELP PLS FAST ITS EZZ ALEBRA
And the correct graph is the one in option b.
What is the correct graph of the function?
We know that you have 8 cups of flour, and it takes one cup of flour to make 24 cookies.
Then the linear function:
c(f) = 24*f
Relates the number of cookies that we can make using f cups of flour.
Then the possible domain of this function (the possible values of f) is given by:
0 ≤ f ≤ 8
The maximum number of cookies that can be made is:
24*8 = 192
And the range is:
0 ≤ c ≤ 192
With that in mind, we can see that the correct graph is the one in option b.
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An artist is selling children's crafts necklaces cost 2.25 each, and brackets cost 1.50 per each select all the combinations of necklaces and braclets that the artist could sell for exactly 12.00
Answer: 4 necklaces 2 bracelets. 8 bracelets. 2 necklaces 5 bracelets
Step-by-step explanation:
v=pi r^2 h
solve for pi
Answer: π=v/(hr^2)
Step-by-step explanation:
v=pi r^2 h solve for pi
v=πhr^2 solve for π
v/h=πhr^2/h
v/h=πr^2
1/r^2 * v/h = πr^2 * 1/r^2
v*1/(h*r^2) = πr^2/r^2
π=v/(hr^2)
Earth is approximately 5x10^9. For which of these ages could this be an approximation
If earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Given,
The age of Earth = 5×[tex]10^{9}[/tex] years old
We know,
5×[tex]10^{9}[/tex]= 5000000000 years old
From the given option the closest number to 5×[tex]10^{9}[/tex] is 4,953,000,000 years old
Hence, if earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Complete question is:
Earth is approximately 5x109 years old. For which of these ages could this be an approximation? Select all that apply.
A. 4.37 x 100 years
B. 4.679999999 x 10º years
C. 4,953,000,000 years
D. 4,625,800,000 years
E. 50,000,000,000 years
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An Internet service company earned $770 in setup fees for new homes in a neighborhood. They charged $35 for each new setup. How many new setups did they perform? Responses 19 setups 19 setups 22 setups 22 setups 25 setups 25 setups 26 setups
The number of new setups the internet service company perform in the neighborhood is 22 setups.
The correct answer is option B
Find the number of new setups the internet service company performTotal amount the internet service company earned = $770Amount the internet service company charge per new setup = $35Number of new setups the internet service company perform = Total amount the internet service company earned ÷ Amount the internet service company charge per new setup
= $770 / $35
= 22 setups
Therefore, the number of new setups the internet service company perform in the neighborhood is 22 setups.
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Which is an example of the associative property?
–5 + 7 = 7 + (–5)
–(18 + 3) = –18 + (–3)
(–8 + 10) + 4 = –8 + (10 + 4)
–17 + 0 = –17
–5 + 7 = 7 + (–5) is an example of the associative property. Option A
This is further explained below.
What is associative property?Generally, The associative property is a rule in mathematics that states that the product of a multiplication problem does not depend on the method in which the elements that are being multiplied do not vary.
In conclusion, Even if the numbers on each side of the equal sign are written in the opposite direction, adding -5 to 7 still results in the same answer: 7 plus (-5).
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what is the equation of the line that passes through the points (-8,1) and (7,1)
Answer:
y = 1
Step-by-step explanation:
the equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through
the line passes through (- 8, 1 ) and (7, 1 )
both with y- coordinates of 1 , then
y = 1 ← is the equation of the line
Emmett made sand art bottles to sell at his school's craft fair. He wanted to use 9 different colors of sand. So, he bought 1 pound of each color. Then, he filled as many 6-ounce bottles as he could. How many sand art bottles did Emmett make?
The number of bottles will be 24 bottles.
How to calculate the value?It should be noted that 1 pound = 16 ounces.
Since he bought 1 pound of each color, the total pounds will be:
= 1 × 9 = 9 pounds.
The number of sand art will be:
= 9 pounds / 6 ounce
= (9 × 16) / 6
= 24 bottles
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The function g(x) is a transformation of the cube root parent function,
f(x)=√x. What function is g(x)?
5-
1
-5-
1
g(x)
f(x)
5
O A. g(x)=√x+2+1
B. g(x)=√x-1+2
O C. g(x)=√x-2+1
O D. g(x)=√x+1+2
By using horizontal and vertical translations, we find that the expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)
What kind of transformations have been done on a parent function to generate another function?
The picture presents us the graphs of two functions. The blue function represents the parent function f(x), whose form is [tex]f(x) = \sqrt[5]{x}[/tex], whereas the black function is the transformed function g(x), which is the result of applying two transformations:
Horizontal translation 2 units in +x direction.Vertical translation a unit in +y direction.Then, we must apply the following definition involving the concepts of horizontal and vertical translations:
g(x) = f(x - 2) + 1 (1)
If we know that [tex]f(x) = \sqrt[5]{x}[/tex], then the complete expression of the function is:
g(x) = [tex]\sqrt[5]{x-2}[/tex] + 1
Hence, by using horizontal and vertical translations, we find that the resulting expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)
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