You are given a square ABCD, and midpoints M and N are marked on BC and CD, respectively. Draw AM and BN, which meet at Q. Find the size of angle AQB.
Answers
- AB=BC (sides of square)
- BM=CN (half sides of square)
- angle B = angle C (adjacent sides of square are perpendicular)
=> triangles ABM and BCN are congruent (SAS)
Step: find angle AQB
- angle AQB = QMB+MBQ (exterior angles of a triangle)
= BNC+MBN (corresponding angles of congruent triangles)
= 90 degrees (exterior angle of triangle BNC)
A square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q. the size of angle AQB 90 degrees.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q.
To show triangles ABM and BNC are congruent
AB = BC
BM = NC
angle B = angle C
Thus, triangles ABM and BNC are congruent by (SAS).
To find ∠AQB
∠AQB =∠ QMB + ∠MBQ (exterior angles of a triangle)
= ∠BNC + ∠MBN (corresponding angles of congruent triangles)
= 90 degrees (exterior angle of triangle BNC)
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Related Questions
a paragraph of; compare savings and investments
Answers
Andy and alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid 20$ for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large sized prints cost
Answers
Final answer:
To find the cost of small and large prints, we create two equations based on Andy's and Alex's orders and solve for the two variables. The small 4x6 inch prints cost $0.50 each, and the large 8x10 inch prints cost $1.25 each.
Explanation:
To solve how much small and large sized prints cost, we can set up a system of linear equations based on the information given:
Andy's order: 40 small prints and 10 large prints for $32.50Alex's order: 20 small prints and 8 large prints for $20.00Let s represent the cost of a small 4x6 inch print, and let l represent the cost of a large 8x10 inch print. We can then form the equations:
40s + 10l = 32.5020s + 8l = 20.00By dividing the first equation by 2, we get:
20s + 5l = 16.25Subtracting the second equation from this result gives:
(20s + 5l) - (20s + 8l) = (16.25 - 20)-3l = -3.75l = 1.25With the cost of a large print found, we can plug this back into the second equation to find the cost of a small print:
20s + 8(1.25) = 2020s + 10 = 2020s = 10s = 0.50Therefore, the cost of a small 4x6 inch print is $0.50 and a large 8x10 inch print is $1.25.
A stained glass window is shaped like a semicircle the bottom edge of the window is 36 inches long what is the area of the stained glass window
Answers
so, if the semi-circle has a diameter of 36, then the radius is half that, or 18
[tex]\bf \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2}\quad \begin{cases} r=radius\\ -----\\ r=18 \end{cases}\implies A=\cfrac{\pi 18^2}{2}\implies A=\cfrac{324\pi }{2} \\\\\\ A=162\pi [/tex]
The perimeter of a quilt is 34 ft. If the quilt is 8 ft long, what is the area
Answers
2 x 8 = 16 (Finding out the length)
16 + 2w = 34 (Problem with the length)
-16 -16 (Using the subtraction property of equality to isolate the variable)
2w = 18 (New problem)
/2 /2 (Using division property of equality)
w = 9. (Width is found)
9 x 8 = 72. The area is 72 squared feet.
18÷2=9
8x9=72
a puppy pen is 4 square feet wide and 5 feet long. is 21 square feet of fabric large enough to make a mat for the pen? Explain
Answers
Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground
Answers
tan 65°=y/25------------> y=tan 65°*25 ( distance of the washer at the eye level)
[the window washer high above the ground]=[(tan 65°)*25+5.5]
[the window washer high above the ground]=[53.61+5.5]=59.11 ft
the answer is 59.11 ft
You track fuel accounts for q shipping line. One vessel consumes 2 1/2 tons of fuel per day during transport. About how many fuel in tons should the vessel consume during 15-day transport?
Answers
2 1/2
Rewriting we have:
2.5 ton / day
The total amount after 15 days is:
(2.5) * (15) = 37.5 Ton
Rewriting we have:
37 1/2 Ton
Answer:
the vessel should consume 37 1/2 Ton during 15-day transport
Determine the x-intercept of 5x -6y =10
Answers
This is a linear equation...
A typical linear equation is written in the form
y=mx+c
Where m=gradient
And c=intercept
So all you have to do is to express y in terms of x "make y the subject of the formula"
Therefore 5x-6y=10
6y=5x-10
Divide through by 6
6y/6 = 5x/6 - 10/6
The intercept here is = - 10/6
Gradient = 5/6-----the coefficient of x....
Hope this helped.....???
How many outcomes are there in the sample space for rolling 1 die?
Answers
Answer:
6
Step-by-step explanation:
find the surface area of the toolbox
Answers
Which number line represents the solution set for the inequality-4(x+3)<-2-2x
Answers
The inequality -4(x+3)<-2-2x simplifies to x > -5. Therefore, the number line representing this solution should shade the values greater than -5, thus, highlighting that x is any value greater than -5.
Explanation:Let's solve the inequality -4(x+3)<-2-2x step by step:
Distribute -4 through (x+3) to get -4x-12<-2-2x. Add 4x to both sides to isolate x, which leads to -12 < 2x - 2. Finally, add 2 to both sides to isolate x to get -10 < 2x or equivalently, x > -5.
As a result, the number line that represents this solution is one where the values greater than -5 are shaded. This means the value of x is anything greater than -5. Any number line visualization should start at -5 and include everything to the right of that point.
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Zakai cuts a piece of birthday cake as shown below.
What is the volume of the piece of cake?
Answers
A=10*18/2
A=90
V=A*H
V=90*6
V=540
What is the mean of the values in the stem-and-leaf plot? Enter your answer in the box.Key: 2|5 means 25
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with leaf values of 5 and 8, a stem value of 2, a stem value of 3, a stem value of 4 with a leaf value of 6, a stem value of 5 with leaf values of 0, 0, 0, 0, 7, a stem value of 6, a stem value of 7, a stem value of 8, and a stem value of 9.
Answers
The mean of the values in the stem-and-leaf plot is 42.
To find the mean of the values in the stem-and-leaf plot, we first need to interpret the plot correctly. Here's the stem-and-leaf plot description:
Stem | Leaves
1 | 5, 8
2 |
3 |
4 | 6
5 | 0, 0, 0, 0, 7
6 |
7 |
8 |
9 |
Let's list the individual values from the plot:
- From stem 1: Leaves are 5 and 8
- From stem 4: Leaf is 6
- From stem 5: Leaves are 0, 0, 0, 0, 7
Now, we calculate the mean (average) of these values.
Step-by-step calculation:
1. List of values:
- Values from stem 1: 15, 18
- Values from stem 4: 46
- Values from stem 5: 50, 50, 50, 57
2. Count the number of values:
- There are 2 values from stem 1, 1 value from stem 4, and 5 values from stem 5.
- Total count = 2 + 1 + 5 = 8
3. Calculate the sum of all values:
- Sum = 15 + 18 + 46 + 50 + 50 + 50 + 50 + 57
- Sum = 336
4. Calculate the mean:
- Mean = Sum / Count
- Mean = 336 / 8
- Mean = 42
Therefore, the mean of the values in the stem-and-leaf plot is [tex]{42} \).[/tex]
Find geometric mean of the pair of number 6 and 10
Answers
6 x 10 = 60
2nd step find the square root
sqrt(60) = 7.745
round the answer as needed.
The Geometric mean of the pair of number 6 and 10 is [tex]7.74[/tex]
Geometric mean :The geometric mean of two number m and n is given as,
[tex]G.M=\sqrt{m*n}[/tex]
Geometric mean of the pair of number 6 and 10 is,
[tex]G.M=\sqrt{6*10} =\sqrt{60} \\\\G.M=7.74[/tex]
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Please help me out with #8 surface area and please explain
Answers
angle symbol is meant to connect to the vertical line closest to us.
What's all the writing to the left and right. What does it say?
Finally what do you know? Can you find area using Heron's Formula for area. I'm going to hold off saying much. You can put a remark somewhere. The magic editor will pick it up and tell me you've done it.
A gardener plants a bed of flowers such that he plants twenty day lilies in the first row, twenty-six day lilies in the second row, and thirty-two day lilies in the third row. He continues to plant lilies in the bed with this pattern for a total of twelve rows. How many day lilies did he plant?
Answers
There are 86 lilies he did plant in 12th row of the garden.
What is Arithmetic Sequence?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
Here, The number of lilies plants in first, second third,..., and last row are respectively.
20,26,32,........
the number of rows of lilies plants is 12.
The sequence 20,26,32,........ is an A.P. with first term a =20, common difference d = 6 and n =12
formula for nth term.
∴aₙ = a+(n−1)d
aₙ=20+ (12-1).6
aₙ = 20 + 11 X 6
aₙ = 86
Thus, there are 86 lilies he did plant in 12th row of the garden.
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factor, x^4y+8x^3y-6x^2y^2-48xy^2
Answers
[tex]\boxed{\boxed{((((x^4)*y)+((8*(x^3))*y))-((6*(x^2))*(y^2)))-(24*3xy^2)}} \\ \\ (let's \ simplify \ some \ number's \ down) \\ \\ \boxed{\boxed{ ((((x4)*y)+((8*(x3))*y))-((2*3x2) *y2))-(24*3xy2)}} \\ \\ \\ Pull \ out \ like \ factors : \\ \\ \boxed{\boxed{ x4y + 8x^3y - 6x2y^2 - 48xy^2 = xy * (x3 + 8x^2 - 6xy - 48^y) }} \\ \\ \\ (TAKE \ NOTICE) \swarrow\swarrow\swarrow\swarrow \swarrow\swarrow\swarrow\swarrow\swarrow\swarrow \\ \\ \\ [/tex]
[tex]\boxed{\boxed{\boxed{ (((((x^4)*y)+(23x^3*y))-(2*3x2y2))}}} \\ \\ \\ \boxed{\boxed{\boxed{-(24*3xy2))-xy*(x3+8x2-6xy-48y) = \boxed{0}}}}}[/tex]
I hope this helps you!
see attached picture for steps:
Hdc produces microcomputer hard drives at four different production facilities (f1, f2, f3, and f4) hard drive production at f1, f2, f3, and f4 is 20%, 25%, 15%, and 40%, respectively. quality control records indicate that 1.5%, 2%, 1%, and 3% of the hard drives are defective at f1, f2, f3, and f4, respectively.
a. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f2?
b. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f4?
c. if an hdc hard drive is picked at random, what is the probability that it is non-defective? g
Answers
a. Probability defective hard drive from F2 ≈ 0.3226.
b. Probability defective hard drive from F4 ≈ 0.7742.
c. Probability non-defective hard drive ≈ 0.9785.
To solve this problem, we can use Bayes' theorem, which states:
[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]
Where:
- [tex]\( P(A|B) \)[/tex] is the probability of event A happening given that event B has occurred.
- [tex]\( P(B|A) \)[/tex] is the probability of event B happening given that event A has occurred.
- [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex] are the probabilities of events A and B, respectively.
Let's solve each part of the problem:
a. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F2?
Let:
- A be the event that the hard drive is defective.
- B be the event that the hard drive was produced at F2.
We need to find [tex]\( P(B|A) \)[/tex], the probability that the hard drive was produced at F2 given that it is defective.
[tex]$\begin{aligned} & P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ & P(A \cap B)=P(A \mid B) \times P(B)=0.02 \times 0.25=0.005 \\ & P(A)=P(A \cap F 1)+P(A \cap F 2)+P(A \cap F 3)+P(A \cap F 4) \\ & P(A)=0.015 \times 0.20+0.02 \times 0.25+0.01 \times 0.15+0.03 \times 0.40=0.0155 \\ & P(B \mid A)=\frac{0.005}{0.0155} \approx 0.3226\end{aligned}$[/tex]
b. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F4?
We need to find [tex]\( P(F4|A) \)[/tex], the probability that the hard drive was produced at F4 given that it is defective.
[tex]\[ P(F4|A) = \frac{P(A \cap F4)}{P(A)} \][/tex]
[tex]\[ P(A \cap F4) = P(A|F4) \times P(F4) = 0.03 \times 0.40 = 0.012 \][/tex]
[tex]\[ P(F4|A) = \frac{0.012}{0.0155} \approx 0.7742 \][/tex]
c. If an HDC hard drive is picked at random, what is the probability that it is non-defective?
Let P(non-defective) = P(non-defective at F1) + P(non-defective at F2) + P(non-defective at F3) + P(non-defective at F4)
P(non-defective) = [tex](1 - 0.015) \times 0.20 + (1 - 0.02) \times 0.25 + (1 - 0.01) \times 0.15 + (1 - 0.03) \times 0.40[/tex]
P(non-defective) = [tex]0.985 \times 0.20 + 0.98 \times 0.25 + 0.99 \times 0.15 + 0.97 \times 0.40[/tex]
P(non-defective) = 0.197 + 0.245 + 0.1485 + 0.388 = 0.9785
So, the probability that an HDC hard drive picked at random is non-defective is approximately [tex]\( 0.9785 \)[/tex].
Michael will be travelling out of town for business. During his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. His employer will pay him for these meals at the following rate: $ 22.65 for dinner, $ 10.95 for lunch, and $ 6.53 for breakfast.
Answers
4 dinners = 22.65 x 4 = $90.60
one lunch = 10.95
5 lunches = 10.95 x 5 = $54.75
one breakfast = 6.53
3 breakfasts = 6.53 x 3 = 19.59
Total = $90.60 + $54.75 + $19.59 = $164.94
what is the probabilaty getting a sum of 7 if you rolled a pair of dice?
Answers
Out of these, six {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} give a sum of 7.
Therefore the probability of rolling a sum of 7 is 6/36=1/6
Which shows how the distributive property can be used to evaluate 7×84/5?
Answers
84/5 gives 16 4/5. I don't know how much saving in work there is in doing this but you could do this.
7 ( 16 + 4/5)
You still have to do something with 28/5 when you get done, but it is one way to do it.
With a short time remaining in the day a delivery driver has to make deliveries at 5 locations among the 6 locations remaining. How many different routes are possible
Answers
So, you need to use permutation for this problem. The calculation would be:
6P5= 6!/ (6-5)!= 720 different routes
To find the number of different routes the delivery driver can take to make the deliveries at 5 out of 6 locations, we can use the concept of permutations.
Explanation:To find the number of different routes the delivery driver can take, we can use the concept of permutations. Since the delivery driver has to make deliveries at 5 out of the remaining 6 locations, we need to calculate the number of ways to arrange these locations.
We can use the formula for permutations to find the number of different routes:
nPr = n! / (n - r)!
Using this formula, we can calculate the number of different routes as:
6P5 = 6! / (6 - 5)! = 6! / 1! = 6 × 5 × 4 × 3 × 2 × 1 / 1 = 720
Therefore, there are 720 different routes the delivery driver can take to make the deliveries.
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.20.2, 0.30.3, and 0.50.5, respectively. what is the standard deviation of this customer's book purchases?
Answers
μ = average
σ = standard deviation
V (X) = Variance
σ = (V(X)) ^ 0.5
E [X] = X * P (x)
Assuming that the number of books purchased is a discrete random variable with mean μ = E [X]
Then the variance of X can be written as V (X) = E [X-μ]^2
We started finding the average μ
μ = 0 * 0.20 + 1 * 0.30 + 2 * 0.50
μ = 1.3
Once the average is found, we can calculate the value of the variance
V (X) = 0.20 * (0-1.3) ^ 2 + 0.30 * (1-1.3) ^ 2 + 0.50 * (2-1.3) ^ 2
V (X) = 0.61
Now we know that from the variance the standard deviation can be obtained by doing:
σ = (V (X)) ^ 0.5
Finally
σ = 0.781
The standard deviation of the customer's book purchases is 0.72.
The standard deviation of a discrete probability distribution can be calculated using the following formula:
σ = √(p[tex](x - \mu)^2[/tex])
where:
σ is the standard deviation
p(x) is the probability of the event x
μ is the mean of the distribution
In this case, the probabilities of the customer purchasing 0, 1, or 2 books are 0.2, 0.3, and 0.5, respectively. So, the mean of the distribution is:
μ = (0 * 0.2) + (1 * 0.3) + (2 * 0.5) = 1.2
The standard deviation is then:
σ = √([tex](0 - 1.2)^2 (0.3)^2[/tex] + [tex](1 - 1.2)^2 (0.3)^2[/tex] + [tex](2 - 1.2)^2 (0.5)^2)[/tex] = 0.72
So, the standard deviation of the customer's book purchases is 0.72.
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describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Answers
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Final answer:
The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.
Explanation:
The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).
On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.
Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.
ASAP Select the statement that correctly describes the expression below.
(2x+5)^2
a) the sum of the square of 2 times x and 5
b)the square of the sum of 2 times x and 5
c)the square of 2 times the addition of x and 5
d)the sum of 2 times x and the square of 5
Answers
Answer:
Option B
Step-by-step explanation:
The given expression is ( 2x + 5)²
We have to form a statement to describe the expression given.
(2x + 5)² square of sum of 2 times x and 5
Option B is the correct answer.
What is the measure of angle z in this figure?
Enter your answer in the box.
z = ___°
Answers
I've attached a photo for reference.
Lines A and B form straight angles, which measure 180 degrees. That means that -
m∠x + m∠y = 180°
m∠y + m∠z = 180°
m∠z + 43° = 180°
43° + m∠x = 180°
Since you're trying to find z, use the solvable equation with z in it:
m∠z + 43° = 180°
180 = z + 43
137 = z
Answer:
m∠z = 137°
How many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code?
Answers
[tex]2^0=1_2[/tex]
[tex]2^1=10_2[/tex]
[tex]2^2=100_2[/tex]
and so on. Observe that [tex]n+1[/tex] digits are required to represent the [tex]n[/tex]-th power of 2 in binary.
Also observe that
[tex]\log_2(2^n)=n\log_22=n[/tex]
so we need only add 1 to the logarithm to find the number of binary digits needed to represent powers of 2. For any other number (non-power-of-2), we would need to round down the logarithm to the nearest integer, since for example,
[tex]2_{10}=10_2\iff\log_2(2^1)=\log_22=1[/tex]
[tex]3_{10}=11_2\iff\log_23=1+(\text{some number between 0 and 1})[/tex]
[tex]4_{10}=100_2\iff\log_24=2[/tex]
That is, both 2 and 3 require only two binary digits, so we don't care about the decimal part of [tex]\log_23[/tex]. We only need the integer part, [tex]\lfloor\log_23\rfloor[/tex], then we add 1.
Now, [tex]2^9=512<1024=2^{10}[/tex], and 999 falls between these consecutive powers of 2. That means
[tex]\log_2999=9+\text{(some number between 0 and 1})[/tex]
which means 999 requires [tex]\lfloor\log_2999\rfloor+1=9+1=10[/tex] binary digits.
Your question seems to ask how many binary digits in total you need to represent all of the numbers 0-999. That would depend on how you encode numbers that requires less than 10 digits, like 1. Do you simply write [tex]1_2[/tex]? Or do you pad this number with 0s to get 10 digits, i.e. [tex]0000000001_2[/tex]? In the latter case, the answer is obvious; [tex]1000\times10=10^4[/tex] total binary digits are needed.
In the latter case, there's a bit more work involved, but really it's just a matter of finding how many number lie between successive powers of 2. For instance, 0 and 1 both require one digit, 2 and 3 require two, while 4-7 require three, while 8-15 require four, and so on.
Final answer:
To represent the decimal numbers from 0 to 999 in binary code, we require 10 bits. This is determined by finding the binary equivalent of the largest number, 999, which necessitates at least 10 powers of 2 (from [tex]2^0 \ to \ 2^9[/tex]).
Explanation:
To determine how many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code, we need to find the binary equivalent of the largest number in that range, which is 999. In binary, this would require the highest power of 2 that is less than or equal to 999. The largest power of 2 less than 999 is 512 (29), and we continue to add powers of 2 to represent the number:
512 (29)
256 (28)
128 (27)
64 (26)
32 (25)
16 (24)
8 (23)
4 (22)
2 (21)
1 (20)
Adding these up, we see that we need at least 10 bits to represent the number 999 in binary, because adding powers of 2 from 20 to 29 will give us the required range. Therefore, we need 10 bits to represent any number from 0 to 999 in binary.
Solve and plot your answer on the number line below: 7.08 + 2x=15.96
Answers
-7.08. -7.08
-------------------------
2x=8.88 divide each by 2
X=4.44
You would plot it in between 4 and 5 but on one of the line marks depending on what there value are
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5
Answers
x^2 - 4 x = 5
Subtract 5 from both sides:
x^2 - 4 x - 5 = 0
x = (4 ± sqrt((-4)^2 - 4 (-5)))/2 = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2:
x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (4 + 6)/2 or x = (4 - 6)/2
(4 + 6)/2 = 10/2 = 5:
x = 5 or x = (4 - 6)/2
(4 - 6)/2 = -2/2 = -1:
Answer: x = 5 or x = -1
Answer:
x = 5 or x = -1
Step-by-step explanation:
x^2 – 4x = 5
Solve it by completing the square method
In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it
-4/2 = -2
square it (-2)^2 = 4
Now add 4 on both sides
x^2 – 4x +4 = 5+4
x^2 – 4x +4 = 9
Now factor the left hand side
(x-2)(x-2)=9
(x-2)^2 = 9
Take square root on both sides
x-2 = +-3
x-2 = 3 , so x= 5
x-2 = -3, so x= -1
Grace has 2 cups of strawberries and plans to divide this amount into equal parts to make 3 strawberry pies. What fraction of a cup of strawberries will be used for each pie?
Answers
[tex] \frac{2}{3} [/tex]
cups for each individual pie.
Number of cups of Strawberries are there for 3 pies =2
Now we apply unitary method here to find how many strawberries are need for 1 pie.
Number of cups of Strawberries required for 1 pie = 2/3
Answer: So Grace would require 2/3 cups of Strawberries for making one pie.