Answers
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{1}{(t-2)^2}[/tex] = 6 + [tex]\frac{1}{(t-2)}[/tex] ( multiply through by (t - 2)²
1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify
1 = 6(t² - 4t + 4) + t - 2
1 = 6t² - 24t + 24 + t - 2
1 = 6t² - 23t + 22 ( subtract 1 from both sides )
6t² - 23t + 21 = 0 ← in standard form
(2t - 3)(3t - 7) = 0 → in factored form
Equate each factor to zero and solve for t
2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex] ← p
3t - 7 = 0 ⇒ 3t = 7 ⇒ t = [tex]\frac{7}{3}[/tex] ← q
Thus
p × q = [tex]\frac{3}{2}[/tex] × [tex]\frac{7}{3}[/tex] = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex] → B
Related Questions
In triangle $ABC,$ $AB = BC = 17$ and $AC = 16.$ Find the circumradius of triangle $ABC.$
Answers
Answer:
[tex]R = 9.63\ units[/tex]
Step-by-step explanation:
Given
[tex]AB = BC = 17[/tex]
[tex]AC = 16[/tex]
Required
Determine the circumradius, R
The circumradius is calculated as follows;
[tex]R = \frac{AB * BC * AC}{\sqrt{(AB + BC + AC)(AB + BC - AC)(AB + AC - BC)(AC + BC - AB)}}[/tex]
Substitute the values of AB, BC and AC
[tex]R = \frac{17 * 17 * 16}{\sqrt{(17 + 17 + 16)(17 + 17 - 16)(17 + 16 - 17)(16 + 17 - 17)}}[/tex]
Evaluate the denominator
[tex]R = \frac{17 * 17 * 16}{\sqrt{(50)(18)(16)(16)}}[/tex]
[tex]R = \frac{4624}{\sqrt{230400}}[/tex]
Take square root of 230400
[tex]R = \frac{4624}{480}[/tex]
[tex]R = 9.63\ units[/tex] (Approximated)
Hence, the circumradius is 9.63
Answer:
289/30
Step-by-step explanation:
Let the circumcenter be point O. We start by drawing line median BM. Since AB = BC, median BM is perpendicular to side AC.
Therefore, BM is part of the perpendicular bisector of AC and thus, must pass through point O.
We have AM = 8, so the Pythagorean Theorem applied to triangle ABM gives us BM = 15.
Let OA = x, our circumradius. Since O is equidistant from A and B, we have OB = x as well.
Therefore,
OM = BM - BO = 15 - x.
From right triangle OAM, we have (OA)^2 = (OM)^2 + (AM)^2.
Solving for x, we have 30x = 225 + 64.
So, x = 289/30.
arithmetic sequences are to linear functions as geometric sequences are to
Answers
Answer:
exponential functions.
Step-by-step explanation:
Determine which letter on the numberline best represents the radical(photo attached)
Answers
Answer:
The square root of 133 is 11.53. The closest to this number would be point D.
Please answer my question i will mark brainlyest.
Answers
Step-by-step explanation:
2 * 6 - 15 / 3 * 8
= 12 - 5 * 8
= 12 - 40
= -26.
8x + 20 = 36
8x = 16
x = 2.
Give two more examples of irrational numbers between 10 and 11.
Answers
Number 14 help I have to zoom with the answer in five minutes
Answers
Answer:
31 over -3
Step-by-step explanation:
4.7+1.6=6.3x 5 =31.5-.5=31
Answer: 28
Step-by-step explanation:
The histogram shows the heights in meters of trees in a certain section of a park.
How many trees are less than 16 meters tall?
A histogram titled Heights of Trees with Height in meters on horizontal x-axis and Frequency on vertical y-axis
5
9
16
12
Answers
Answer:
16
Step-by-step explanation:
someone please answer and give me a reason. hint: the answer isn’t 49.
Answers
Answer:
√37
Step-by-step explanation:
An irrational number is a number that never terminates nor repeats.
Let's go through each of the answer choices.
1) √100 is just 10. This is not irrational.
2) √81 is just 9. This is again not irrational.
3) √64 is 8. Not irrational.
4) √49 is 7. Again, not irrational.
5) √37 is 6.08276253... This number will never end and it doesn't repeat. Therefore, √37 is irrational.
And this is our answer.
And we're done!
Simplify:
(XY3Z4)4
A.xy3z16
B.xy3z8
C.x4y12z16
D.x5y7z8
Answers
Answer:
C
Step-by-step explanation:
(xy^3z^4)^4 =
(x)^4 = x^4
(y^3)^4 = y^12
(z^4)^4 = z^16
Therefore the answer is C. x^4 y^12 z^16
What is the equivalent equation to: -6=3y
Answers
the answer for your question is y=−2
Find the value of X on the equation below. Please explain step by step and I will mark you brainliest.
g=x-c+y
Answers
g = x - c + y
First, let's add c to both sides.
g + c = x + y
Now, let's subtract y from both sides.
g + c - y = x
z−4/9−1/3=5/9 Enter your answer as a fraction in simplest form in the box. z =
Answers
Answer:
z=12/9 or 4/3 or 1 1/3
Step-by-step explanation:
1/3 needs to have a denominator of 9 so 3/9 because 3x3=9 and you have to multiply the numerator by 3 also
z-4/9-3/9=5/9
add -4/9 and -3/9 because you add two negative numbers
new equation
z-7/9=5/9
add 7/9 to 5/9
z=12/9 or 4/3 or 1 1/3
Enter a fraction equivalent to 0.8. Use only whole numbers for numerator and denominator.
Answers
Answer:
4/5
Step-by-step explanation:
=>0.8
=>8/10
=>4/5
all linear pairs and vertical pairs share the same...?
Answers
Answer:
Lines
Step-by-step explanation:
In both linear and vertical pairs share at least one line.
Hope This Helps :)
All linear pairs and vertical pairs share the same supplementary angle.
Linear pairs and vertical pairs are both types of angle pairs formed by intersecting lines or by the intersection of a line and a transversal.
1. Linear Pairs: A linear pair consists of two adjacent angles formed by two intersecting lines. The two angles in a linear pair are always supplementary, meaning their measures add up to 180 degrees. In other words, if one angle in a linear pair measures x degrees, then the other angle will measure (180 - x) degrees.
2. Vertical Pairs: Vertical angles are formed by the intersection of two lines. They are opposite angles that share a common vertex but are formed by different pairs of intersecting lines. Vertical angles are congruent, meaning they have the same measure. If one vertical angle measures x degrees, then the other vertical angle formed by the same pair of intersecting lines will also measure x degrees.
Therefore, both linear pairs and vertical pairs share the same property of having angles with equal measures. In the case of linear pairs, the angles are supplementary (their measures add up to 180 degrees), while in vertical pairs, the angles are congruent (they have the same measure).
To know more about linear pairs, refer here:
https://brainly.com/question/34190098
#SPJ2
Of the 400 employees,5% of them are park managers.How many managers does the park employee?
Answers
Answer:
16/5
Step-by-step explanation:
1600 diviudes by 100=16
Multiply total People by percentage:
400 x 0.05 = 20
There are 20 managers
Do the following ratios form a proportion? 5/8, 9/14 OR 10/16, 18/28 BRAINLIEST AND 30 POINTS
Answers
Answer:
18/28
Step-by-step explanation:
If angle 1 and angle 2 form a linear pair and angle 1 is 18 degrees less than five times the measure of angle 2, then the angle 1 is _____ degrees
Answers
Answer:
Angle 1 is 147 degrees
Step-by-step explanation:
When two angles form a linear pair, then we have the intersection of two lines
So what this mean is that both angles lie on a straight line and the sum of both angles is 180.
Let the angle 2 be x
We are told that angle 1 is 18 degrees less than 5 times the measure of angle 2;
What we are saying here is that; angle 1 = 5x - 18
So let’s add both together to give 180
angle 1 + angle 2 = 180
x + 5x -18 = 180
6x = 180+ 18
6x = 198
x = 198/6
x = 33 degrees
But angle 1 is 5x -18 = 5(33) -18 = 165 -18 = 147 degrees
is this a. a function but no one-to-one B. a one-to.one C. not a function
Answers
===================================================
Explanation:
It is a function because it passes the vertical line test. We cannot draw a single vertical line through more than one point on the red curve. Any x input leads to exactly one and only one y output.
A similar test is the horizontal line test. We cannot draw a single horizontal line through more than one point on the red curve, so this red curve passes the horizontal line test. Each y is only paired with one x value only. This helps set up an inverse function.
-----------
In short:
If the curve passes the vertical line test, then we have a function
If the curve passes the horizontal line test, then it is one-to-one.
A contractor bought 34 loads of soil each weighing 12 tonnes at $13 per tonne. What was the total cost?
Answers
Answer:
$5304
Step-by-step explanation:
One load of soil is 12 tons.
Multiply 34 with 12: 34 x 12 = 408 tonnes in all.
Next, multiply the cost per tonne with the amount of tonnes:
408 x 13 = 5304
$5304 is the total cost.
~
8 blocks can build a house. Jimmy has 165 blocks, how many houses can he build? How many blocks will he have left?
Answers
Answer:
He can build 20 houses. He will have 5 left over.
Step-by-step explanation:
8 x 20 = 160
165 (total blocks) - 160 (highest possibility) = 5 (not enough to build a house, which is why they are left over)
2. The seventh grade class is putting on a variety show to raise
money. It cost $700 to rent the banquet hall that they are going to
use. If they charge $15 for each ticket, how many tickets do they
need to sell in order to raise at least $1000?
Answers
Answer:
67
Step-by-step explanation:
15 x 10 = 150
150 x 6 = 900
15 x 7 = 105
900 + 105 = 1005
closest to 1000 without decimals
with decimals 66.6666666667
Please mark brainliest
$1000 ÷ 15 = 66.67 ~ 67 tickets
what is 21000 take away two thirds
Answers
Answer:
7000
Step-by-step explanation:
21000/0.667
=14000
21000-14000
=7000
what is the slope of (-5,4) and (7,8)
Answers
-2x-10x+12=18
Help me plz
Answers
Answer x= - [tex]\frac{1}{2}[/tex]
Step-by-step explanation: -12x + 12 = 18 move constant to the right hand side and change its sign ( its + 12 :0)
-12x = 18- 12 caculate 18-12
-12x = 6
then divide both sides then you will get -1/2
-12x=18-12
-12x=6
x= -6/12
x= -1/2
A. 20% increase
B. 10% increase
C. 20% decrease
D. 10% decrease
Answers
Answer:
C. 20% decrease
Step-by-step explanation:
[tex]Saturday = 50\\Sunday =40\\\\50-40 =10\\\\\frac{10}{50} \times \frac{100}{1} \\= \frac{1000}{50} \\\\Cross \:cancel common \:factor; 50\\\\= 20[/tex]
-2(2u-3)+3u=3(u+8)
u=?
Answers
You get -4u+6+3u=3u+24
And if you simplify that you get:
-u+6=3u+24
Now you need to solve this equation to find u
First bring 3u to the other side to -u-3u (the positive changes to negative)
Now the equation is
-4u+6= 24
Take 6 of both sides
-4u=24-6= 18
-4u= 18
So u= -18/4
Which simplifies to -9/2
Answer: -9/2
Find the height H of solid
Answers
Is −2x=38 a literal equation?
Answers
Steps to solve:
-2x = 38
~Divide -2 to both sides
x = -19
Since this equation is solvable, it is a literal equation
Best of Luck!
Please help!,! Once again
Answers
Answer:
the answer is "dilation by a scale factor of 2 and a rotation of 90° counter clock wise about the origin"
Would anyone happen to know this?! I need help please ASAP
Answers
Answer:
nope
Step-by-step explanation: