Answers
Answer:
1) x = 6 + 2√19 or x = 6 - 2√19
2a) (x + 5)²
2b) (x + 5/2)²
3) x = 22 or 18
Step-by-step explanation:
1) x² - 12x = 40
First step is;
We take ½ of the x-term and square it.
Thus;
(½ × -12)² = (-6)² = 36
Second step is to add the result in step 1 to both sides;
x² - 12x + 36 = 40 + 36
x² - 12x + 36 = 76
On the left, is a perfect square that can be written as (x - 6)²
Thus, the new equation is;
(x - 6)² = 76
Taking square root of both sides gives;
x - 6 = ±√76
x - 6 = ±2√19
x = 6 + 2√19 or x = 6 - 2√19
2a) we want to find the value of c that makes x² + 10x + c the perfect square.
From completing the square in question 1 above, we see that;
c = (b/2)²
From ax² + bx + c, we can see that in this case, b = 10
Thus;
c = (10/2)²
c = 5²
c = 25
Thus, the trinomial is;
x² + 10x + 25
As a perfect square, it is;
(x + 5)²
2b) x² + 5x + c
Similar to 2a above;
b = 5
Thus; c = (5/2)²
c = 25/4
Trinomial is; x² + 5x + 25/4
As a perfect square, we have;
(x + 5/2)²
3) We want to solve x² - 40x + 396 = 0
This can be rewritten as;
x² - 40x = -396
First step is;
We take ½ of the x-term and square it.
Thus;
(½ × -40)² = 400
Second step is to add the result in step 1 to both sides;
x² - 40x + 400 = -396 + 400
x² - 40x + 400 = 4
On the left, is a perfect square that can be written as (x - 20)²
Thus;
(x - 20)² = 4
Taking square root of both sides gives;
x - 20 = ±√4
x - 20 = ±2
x = 20 + 2 or x = 20 - 2
x = 22 or 18
Related Questions
PLEASE HELP URGENTTTG HURRYYY
Answers
Answer:
4:1
Step-by-step explanation:
A is basically 4 times bigger than B
Find the intersection of the lines y = x +1 and 3y + 2x = 13 without drawing the graph.
Answers
Answer:
The intersection point is (2, 3)
Step-by-step explanation:
The given (linear) equations for the point of intersection is required are;
y = x + 1...(1)
3·y + 2·x = 13...(2)
To find the point of intersection without using graph, we note that the point of intersection is the point at which the values of both equations are equal
We find the values of 'x' and y-coordinates at the point of intersection as follows;
Making 'y' the subject of equation (2) gives;
y = (13 - 2·x)/3
When both lines intersect, the 'x' and y-values are the same;
y = x + 1 for the first line, and y = (13 - 2·x)/3 for the second line, therefore, at the intersection point, we have;
y = y
x + 1 = (13 - 2·x)/3
3·(x + 1) = 13 - 2·x
3·x + 3 = 13 - 2·x
3·x + 2·x = 13 - 3
3·x + 2·x = 5·x = 13 - 3 = 10
∴ 5·x = 10
Therefore, at the point of intersection, x = 10/5 = 2
x = 2
'y' is given in equation (1) by y = x + 1, therefore, at the point of intersection, 'x = 2', we get;
y = x + 1
∴ The value of 'y' at the point of intersection is y = 2 + 1 = 3
y = 3
Therefore, the (x, y) coordinate at the point of intersection is (2, 3) which can be written as follows;
The point of intersection = (2, 3).
In the figure provided, BDC is said to be
A. an inscribed angle
B. A central angle
C. a circumstance
D. a right angle
Answers
Answer:
circumscribed angle:
Step-by-step explanation:
circumscribed angle:
A circumscribed angle is the angle made by two intersecting tangent lines to a circle.
Explain why multiplying a fraction by 5/6 results in a value that is less than the original fraction
Answers
Answer:
Step-by-step explanation:
(5/6) itself is less than 1 (but greater than 0). Thus, anything multiplied by (5/6) will result in a smaller-by-magnitude quantity.
For example, (5/6)(3/4) is LESS than 3/4 because 5/6 is greater than zero but less than 1.
The fraction 5/6 is less than one anything multiplied to this number will be less than 1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the fraction is 5/6.
5/6 is less than 1 on its own (but greater than 0). Anything multiplied by (5/6) will provide a magnitude-less result. Because 5/6 is more than 0 but less than 1, it can be shown that (5/6)(3/4) is less than 3/4.
Therefore, the fraction 5/6 is less than one anything multiplied to this number will be less than 1.
To know more about an expression follow
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what is the final answer
Answers
Answer:
y=3x-2 (d)
Step-by-step explanation:
First, we need to look at the y-intercept, we can see that when x = 0, y= -2. So then our equation has to be y=mx+b, and b is -2. next we find our slope, we can see that we go up by 3, then over 1, so our slope is 3/1 or 3. so the final equation is y=3x-2.
Hope this helps!
:)
Answer:
D
Step-by-step explanation:
You can use desmos graphing cacluator for this
What integer values satisfy both inequalities? -1 < x ≤ 2 -2 ≤ x < 3
Answers
Answer:
0,1and2 brainliest me plsss po
Given csc(A) = 65/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!
Answers
Answer:
secA = [tex]\frac{65}{63}[/tex]
Step-by-step explanation:
cscA = [tex]\frac{65}{16}[/tex] = [tex]\frac{hypotenuse}{opposite}[/tex]
This is a right triangle with hypotenuse = 65, opposite = 16 and
adjacent = [tex]\sqrt{65^2-16^2}[/tex] = 63
Then
secA = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{65}{63}[/tex]
1. Classify the number as rational or irrational.
32
Answers
Answer:
32 is rational number.
Step-by-step explanation:
Because it can be expressed as the quotient of two integers : 32/1
if one person tells another 10 people and then each of those 10 people tell another 10 people and so on we get rapid spreading of a message video photo news item of the product across internet
level 0 1 _ etc
spread (b) +10 + 100 +
powers 10 to the power of 0 (c) 10 to the power of 2
Answers
Answer:
If you did these this is what it would look like
10
100
1000
10000
100000
1000000
and so and so on
Match each radical expression on the left with an equivalent expression on the right. Help me please
Answers
hope it helps you ♡
see the attachment for further information
15
A spinner on a board game has a radius of 3 inches and spins on a circular region as shown in the
figure.
3 in
The center of the circular region is the origin and the spinner's initial position is on the positive
x-axis. Rachel flicks the spinner, causing it to rotate 600°. What are the coordinates of the tip of
the spinner when it stops?
3
313
А
2
2
313
3
B
2
2
V3
с
1
2'
2.
V3
1
D
)
2
2
Answers
Answer:
Option A ( -3/2 , [tex]\frac{-3\sqrt{3} }{2}[/tex] )
Step-by-step explanation:
According to Question, The Spinner Rotate 600* Thus after Completing 360* it Comes Exactly Where It Started . Now again rotate It 180* .Now We Are on ( -X axis ) & Completed 360*+180*=540* RotationNow After Rotate It 60* More we come in Third Quadrant & Here In Third Quadrant Only Tangent & Cotangent Is Positive .(Sine & Cosine is Negative)(For Diagram, Please Find in attachment)
Now In Triangle OAB
Cos60* = OA / OB1/2 = -X / 3 Thus X= -3/2
Sin60* = AB / OB[tex]\sqrt{3}[/tex]/2 = -Y / 3 Thus Y = -[tex]\sqrt{3}[/tex] * 3 /2
Which of the following does NOT give you congruent angles?
CPCTC
Midpoint
Alternate Interior Angles
Triangle Sum Theorem
Answers
Answer:
Triangle Sum Theorem
Step-by-step explanation:
These do not give you congruent angles
2. What is the probability of spinning an A on the first spinner and an odd number
on the second spinner? *
Answers
Answer:
1/10
Step-by-step explanation:
All spinners have equal areas & circumference on each outcome, so spinning an A is one out of five, or 1/5. The probability of spinning any number is 1/6. Since 1, 3, and 5 are all odd numbers, the probability of spinning an odd number is 3/6, or 1/2.
The probability of spinning both spinners successfully (an A AND an odd number) can be found by the product rule, which is the product of the two probabilities, namely 1/5 * 1/2 = 1/10.
The gross annual salary of a teacher is $54 750, what's his gross monthly salary
Answers
Answer:
4562.50 per month
Step-by-step explanation:
To find the monthly salary, divide by the number of months ( which is 12)
54750/12
4562.50 per month
What is the value of the expression 3^2 . (2^3 +4) _____________ 2^2
Answers
Answer:
The answer is [tex]3^3\times 2^2[/tex].
Step-by-step explanation:
According to the rules of exponents
a^n = a x a x a x .... n times
So,
[tex]3^{2}\times (2^{3}+4)\\\\=9\times (8 +4)\\\\=108\\\\=3^{3}\times 2^{2}[/tex]
Pls pls pls pls pls help
Answers
What’s the value of x?
Answers
Answer:
x = 4.5
Step-by-step explanation:
thesetwo triangles are similar to we can create a proportion from corresponding sides as follows:
4/9 = 2/x
cross-multiply:
4x = 18
x = 4.5
A rectangle has a length of 9 mm. A similar rectangle is drawn using a scale of 1:3. What is the length of the second rectangle?
Answers
Answer:
3mm brainliest please
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
9mm times 1:3 of the rectangle is 245
Determine the general rule (Tn)
Answers
Claire is driving a car traveling a steady of 63 miles per hour She drives for 3 hours. How far does she drive?
Answers
Answer:
189 miles
Step-by-step explanation:
63 miles per hour means 63 miles every hour, if she went at this speed for three hours, just multiply 63*3 and you get 189 miles. :)
Answer:
189 miles
Step-by-step explanation:
Claire drives at 63 miles in 1 hour.
Therefore in 3 hours she drives 63 × 3 = 189 miles
Which number is larger
Answers
Answer:
9
Step-by-step explanation:
When there are any negatives they will always be less then a positive.
-10,-9-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10
The larger the negative the less it is since its so far away from the middle (0)
-Greatest to least
-8,-5,3,9
Meagan bought 18 apples for $8.10. Whats the unit price?
Answers
Answer:
The unit price is .45
Step-by-step explanation:
You divide the price by the item
- 8.10÷18=.45
What is the image point of (0,-6) after the transformation D 1/2 or y-axis?
Answers
1/2(0)= 0
1/2(-6)= -3
(0,-3)
2x - y = 7 find the x and y intercept of each equation. graph the equation using its intercepts.
Answers
Which statement correctly describes the graph of g(x) = f(x - 9) ? x = 6 A. Function ghas the same horizontal and vertical asymptotes as function f. OB. Function g has the same horizontal asymptote as fand a vertical asymptote at . OC. Function g has the same horizontal asymptote as fand a horizontal asymptote at x = 9. D. Function ghas the same vertical asymptote as fand a horizontal asymptote at y = - 5 .
Answers
Answer:
-5
Step-by-step explanation:
The correct statement describing the graph is ''Function has the same horizontal asymptote as fand a vertical asymptote at x = 6''.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here,
We have to determine:
Which statement correctly describes the graph of g(x) = f(x - 9)?
According to the question
Graph; g(x) = f(x - 9)
here, we have,
The straight-line x=6 is a vertical asymptote of the graph of the function g(x) = f(x - 9) if at least one of these conditions is true:
we have,
A vertical asymptote occurs in rational functions at the points when the denominator is zero and the numerator is not equal to zero.
we know,
Vertical asymptotes are the vertical lines corresponding to the zeroes of the denominator of the rational number, to calculate the vertical asymptotes simply put the denominator of the rational number to zero, and solve for x, this is the required vertical asymptotes, if the denominator of the rational number is a quadratic, cubic types equations or any other polynomial then simplify put the whole equation to zero and simplify used any method for x, this is the required vertical asymptotes.
Hence, Function has the same horizontal asymptote as fand a vertical asymptote at x = 6.
To know more about Function click the link given below.
brainly.com/question/1491466
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8. On what day did Alfonso run faster? Day Distance (m) Time (min) Monday 1,020 6 Wednesday 1,554 9 a. Wednesday b. Monday
Answers
Ok
Estimate the product of 8.82 x 9.41 by rounding each factor to the nearest whole number.
Answers
Answer: The estimated product is 81
8.82 and 9.41 are both 9 rounded to the nearest whole number
Therefore, 9*9=81.
Find the value of x in the triangle shown below 3.5 4 3.5 x• 55•
Answers
Answer:
Step-by-step explanation:
Since this is not a right triangle, we will use the Law of Sines. For us that looks like this:
[tex]\frac{sin55}{3.5} =\frac{sinx}{4}[/tex] and cross multiply to get
4sin55 = 3.5sinx and solve for sinx:
[tex]sinx=\frac{4sin55}{3.5}[/tex] so
sinx = .9361737 Use the 2nd button on your calculator and the sin button to find that the angle
x = 69.4°. Not sure how you need it rounded. It's actually 69.4186°
Answer:
It is 70
Step-by-step explanation:
Khan Academy
8. Which of the following statements
about the box plot is true?
HHH
0 2 4 6 8 10 12 14 16 18 20
♡ Minimum: 4
B Maximum: 16
© First quartile: 8
0 Third quartile: 16
1
IAS
Answers
Explanation:
Box = 12
A + C = 4 + 8 = 12
B - A = 16 - 4 = 12
D - A = 16 - 4 = 12
(C + D)/2 = (8 + 16)/2 = 24/2 = 12
(B + C)/2 = 24/2 = 12
Who has the most blue sweets?
chris 1/2
sam 1/4
raj 3/4
jade 1/3
Answers
Answer:
raj
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Have a nice day
