Answers
Answer:
a. t = 3 + √15 or t = 3 - √15
b. t = 6.87 or t = -0.87
Step-by-step explanation:
a.
Given : t² = 6t + 6
t² = 6t + 6 ⇔ t² - 6t + 6 = 0
USING THE QUADRATIC FORMULA:
[tex]t=\frac{6\pm \sqrt{\left( -6\right)^{2} -4\left( 1\right)(-6) } }{2}[/tex]
Then
[tex]t=\frac{6\pm \sqrt{36 +24 } }{2}[/tex]
Then
[tex]t=\frac{6\pm \sqrt{60 } }{2}[/tex]
Then
[tex]t=\frac{6\pm 2\sqrt{15 } }{2}[/tex]
Then
t = 3 ± √15
Then
t = 3 + √15 or t = 3 - √15
…………………………………………………
b.
t = 3 + √15 = 6.872983346207 ≈ 6.87
or t = 3 - √15 = -0.872983346207 ≈ -0.87
Related Questions
The figure below is a right rectangular prism.
X
W
४
M
N
x
Y
N
O
12
2x
T
Which expression represents the volume of the prism?
01x³
O
O
(+)
0 (x)
Answers
Answer:
1/2x^3
Step-by-step explanation:
The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).
Just plug the numbers (or in this case variables) into the formula:
v = x times x times 1/2x
v = 1/2 times x^3
v = 1/2x^3
Volume
LBH1/2x(x)(x)1/2(x)³Option A
How many zero pairs must be added to the function
f(x) = x2 – 10x – 4 in order to begin writing the function in vertex form?
4
10
21
25
Answers
1 zero pair of 25 was added to bring given function into vertex form.
What is a Zero Pair ?A zero Pair is the set of two numbers which when added together gives 0.
The function given is
f(x) = x² -10x -4
To convert it into the vertex form
y = a(x-h)² +k
f(x) = x² -10x +25 -25 -4
f(x) = x² -10x +5² -25-4
f(x) = (x-5)² -29
Therefore this is the given function's vertex form and
1 zero pair of 25 was added to bring it into that.
Therefore Option D is the answer.
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Which of the following triangles are right triangles? Select all that apply.
Triangle A:
101
20
Triangle A
Triangle B
Triangle C
89
15
Triangle B:
113
110
20
Triangle C:
29
21
B
Answers
So there is a possibility I read it wrong, or you typed it wrong. but from what I see, there are NO right triangles.
Step-by-step explanation:
a right triangle has a 90 degree angle. none of these have one.
Part 1 - Application Pick one of the two graphs below. Describe a situation which could be modeled by this polynomial graph. Be sure to label the x and y axis with what each will represent in your real life graph. Sample labels could include time, temperature, speed, distance and more. Be sure to add numbers to your axes as well and explain how you came up with your situation.
Answers
One good example of a situation that can be modeled by this Polynomial Graph is the price-time relationship between currency pairs being traded on the Foreign Exchange Market.
What is a Polynomial Graph?A polynomial parameter graph is essentially a smooth continuous curve.
Although the forex graph attached has sharp undulations, when regressed and viewed via Polynomial Regression Indicators, they exhibit strong polynomial qualities that meet the requirements of the definition above.
It is to be noted that the Y-Axis is indicative of the price of the currency pairs (which could be any currency against another) and the X-Axis expresses time. See the attached graphs for a better picture.
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What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?
(6, 31)
(−6, 31)
(6, −31)
(−6, −31)
Answers
Answer: (6, -31)
Explanation: See attachment
Find the volume of this sphere.
Use 3 for pie.
V≈ [?]cm³
V = πr³
10 cm
Answers
Answer:
V ≈ 500 cm³
Step-by-step explanation:
Volume of a sphere: ⁴⁄₃πr³ (where r is the radius)
π (pi) ≈ 3r (radius) = diameter/2 ⇒ 10/2 = 5 cmSubstitute the given values into the formula:
⇒ V = ⁴⁄₃πr³
⇒ V ≈ (⁴⁄₃)(3)(5)³
⇒ V ≈ (⁴⁄₃)(3)(125)
⇒ V ≈ (⁴⁄₃)(375)
⇒ V ≈ 500 cm³
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Given: [tex]\textsf{Diameter = 10 cm, Volume = 4/3} * \pi*r^3[/tex]
Find: [tex]\textsf{Determine the volume}[/tex]
Solution: First we need to determine the radius by dividing the diameter by 2 and after that we can plug in the information into the equation and simplify it until we get the volume.
Determine the radius
[tex]\textsf{Radius = Diameter / 2}[/tex][tex]\textsf{Radius = 10 cm / 2}[/tex][tex]\textsf{Radius = 5 cm}[/tex]Plug in the values
[tex]\textsf{Volume = 4/3 } * \pi*r^3[/tex][tex]\textsf{Volume = 4/3 } * 3 * (5\ cm)^3[/tex]Simplify the expression
[tex]\textsf{Volume = (4 * 3)/3} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * 125\ cm^3[/tex][tex]\textsf{Volume = } 500\ cm^3[/tex]After completing the steps we were able to determine that volume of the sphere that was provided is 500 cubed centimeters.
Write the word phrases into an algebraic expression : 4 less than 5 times a number "p"
Answers
5 times ‘p’ = 5p
4 less than ‘p’ = p - 4
Therefore,
=> 5p - 4
)If 18th February, 2030 falls on Monday then what will be the day on 18th February, 2040
Who ever answers this quickly with explanation I will make then brainliest
Answers
The Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
18th February 2030 falls on Monday
To find what will be the day on 18th February 2040
Calculate the expression:
= Given date + Month code + (difference between years) + Numbe of leap year
Leap year = difference between years/4
= (2040-2030)/4
= 10/4 = 2.5 ≈2
= 18 + 3 + (2040-2030) + 2
= 33
Divide 33 by 7 the remainder will be 5
Day code = given day code + remainder
= 1 + 5
= 6 (saturday from the table attahced)
Thus, Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday.
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If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?
Answers
Answer:
26
Step-by-step explanation:
Define the variables:
2n = first even number2n + 2 = consecutive even numberGiven information:
2 times the sum of two consecutive even numbers is greater than 94Create an inequality from the defined variables and the given information:
⇒ 2(2n + 2n + 2) > 94
Solve the inequality:
⇒ 2(4n + 2) > 94
⇒ 8n + 4 > 94
⇒ 8n > 90
⇒ n > 11.25
Therefore:
2n > 22.52n + 2 > 24.5As 2n and 2n+2 are even numbers:
smaller number (2n) ≥ 24larger number (2n + 2) ≥ 26Therefore, the smallest possible value of the larger number is 26.
This table represents a quadratic function with a vertex at (1, 1). What is the
average rate of change for the interval from x = 5 to x = 6?
OA. 26
OB. 13
O C. 7
OD. 9
1
2
3
4
5
X
1
2
LO
5
10
17
y
Answers
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
How to find the average rate of change on the interval?
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
[tex]r = \frac{f(6) - f(5)}{6 - 5}[/tex]
[tex]f(x) = a*x^2 + b*x + c[/tex]
I we look at the table we see that:
[tex]f(1) = 1 = a + b + c[/tex]
[tex]f(2) =2 = 4a + 2b + c[/tex]
[tex]f(3) = 5 = 9a + 3b + c[/tex]
This is a system of equations.
If we subtract the second and first functions, we get:
[tex]2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c[/tex]
From that we take two relations:
[tex]1 - 3a = b\\2a = c[/tex]
Now we can replace these two in the last equations so we get:
[tex]5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1[/tex]
Now that we know the value of a:
[tex]c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2[/tex]
The quadratic equation is:
[tex]f(x) = x^2 - 2x + 2[/tex]
Evaluating this in x = 6 we get:
[tex]f(6) = 6^2 - 2*6 + 2 = 26[/tex]
And from the table we know that f(5) = 17, then the average rate of change is:
[tex]r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9[/tex]
The correct option is D.
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From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.
Answers
Answer:
a) 182.90 m
b) 203.85 m
Step-by-step explanation:
The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.
__
a)The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...
Tan = Opposite/Adjacent
Solving for the adjacent side, we have ...
BF = (90 m)/tan(26.2°) ≈ 182.90 m
The boat is about 182.90 meters from the foot of the cliff.
__
b)The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...
Sin = Opposite/Hypotenuse
BC = (90 m)/sin(26.2°) ≈ 203.85 m
The boat is about 203.85 meters from the top of the cliff.
Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answers
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
11 potters can make 143 pots in 8 days. How many potters will be required to make 169 pots in 4 days?
Answers
26 potters will be required to make 169 pots in 4 days.
Given: 11 potters can make 143 pots in 8 days.
Step 1:
1 potter makes 143 pots in 8 × 11 days.
1 potter can make 1 pot in
(8 × 11)/143 days.
Step 2:
Let the number of potters required be x, then
x potters can make 1 pot in (8 × 11)/( 143 × x) days
x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days
Step 3:
The number of days given is 4. Hence equating the above equation to 4.
(8 × 11 × 169)/(143 × x ) = 4
Step 4:
Solve for x
14872/(143x) = 4
572x = 14872
x = 14872/572
x = 26
Thus, 26 potters will be required to make 169 pots in 4 days.
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A school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket
Answers
Using a system of equations, it is found that the price of a student ticket is of $3.49.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Price of a student ticket.Variable y: Price of an adult ticket.Considering the revenues and the number of tickets sold, the equations are given as follows:
180x + 110y = 1345.100x + 90y = 935.From the second equation:
90y = 935 - 100x
y = (935 - 100x)/90
y = 10.39 - 1.11x
Replacing in the first equation:
180x + 110y = 1345.
180x + 110(10.39 - 1.11x) = 1345
57.9x = 202.1.
x = 202.1/57.9
x = 3.49.
The price of a student ticket is of $3.49.
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Use the following information for problems 5-8.
f(2, 33) = 5.5, p < 0.01
1) how many groups were in this study?
a) 34
b)33
c) 3
d) 2
how many participants were in this study?
a) 36
b) 33
c) 3
d) 2
what is the f ratio?
a) 5.5
b) 2
c) 33
d) 0.01
Answers
The number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
f(2, 33) = 5.5, p < 0.01
From the above details, we can find the number of groups:
5) Number of groups = df for groups + 1
Number of groups = 2+ 1 = 3
Option (c) is correct.
6) Number of participants =2 + 33 + 1 = 36
Option (a) is correct.
7) f ratio = 5.5
Option (a) is correct.
8) True; as the p-value is less than the 0.01 level.
Thus, the number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
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What is the domain of the function shown in the
mapping?
Ox|x=-5, -3, 1, 2, 6}
O lyly=-9, -6, 0, 2, 4)
O {x|x=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Oyly=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Answers
Domain is the set of values for which the given function is defined. The correct option is A.
What is domain and range of a function?Domain is the set of values for which the given function is defined, therefore the are values that the function can take.
Range is the set of all values which the given function can produce an output.
Domain of a function is the range of the inputs which the function can take, therefore, the domain of the function shown in the mapping is,
x|x= -5, -3, 1, 2, 6}
Hence, the correct option is A.
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Clem's credit score is 733, while ingrid's credit score is 688. according to the
following table for a $150,000 mortgage, how much more would ingrid have
to pay per month than clem?
fico
interest monthly
score
rate
payment
720-850
5.59% $860
700-719
5.71% $872
675-699
6.25% $924
620-674
7.40% $1039
560-619
8.53% $1157
500-559
9.29% $1238
Answers
Ingrid would have to pay 64 per month more than clem.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given;
fico interest monthly score rate
720-850 5.59% $860
700-719 5.71% $872
675-699 6.25% $924
620-674 7.40% $1039
560-619 8.53% $1157
500-559 9.29% $1238
Clem's score is 733 which is 924 on the chart.
Ingrid's score is 688 which allows her to pay 860 per month.
924 - 860 = 64
Hence,
Ingrid would have to pay 64 per month more than clem.
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Please help if you can
Answers
Wkwkkekekwkwkkskskwkw
Here are three studies:
a: june asks eight of her friends if they plan on buying a school lunch that day.
b: sam selects a random sample of coins from his coin bank to see how many of them are older than 1982.
c: peyton randomly selects six eggs from a carton. she randomly assigns three of them to be boiled for 10 minutes and the other three are boiled for 15 minutes. after they have cooled she compares how easy they are to peel.
for which of these studies can we draw conclusions of cause and effect?
a
b
c
none of them
Answers
Answer:
The answer is C
Step-by-step explanation:
Just got it.
can someone please help mee(10 points)
Answers
Answer:
(2,-3)
Step-by-step explanation:
Thats where the parabola is the lowest at
Which term describes the point where the perpendicular bisectors of the three sides of a triangle intersect? OA. Incenter OB. Centroid OC. Circumcenter D. Orthocenter
Answers
Answer: Circumcenter (choice C)
Explanation:
The circumcenter is useful to form a circle that passes through all three points of a triangle. It is the smallest circle possible that doesn't go inside the triangle.
The incenter is formed by intersecting at least two angle bisectors, which means we can rule out choice A. The centroid is the result of intersecting two or more medians, which allows us to cross off choice B. Choice D is out because the orthocenter is the intersection of the altitudes.
Answer:
C. Circumcenter
Step-by-step explanation:
Hope this helps.
10. A In the adjoining Figure, ab is perpendicular to bc and ed is to cd while bc=cd . prove i) triangle abc is corresponding to triangle edc
ii)ab = cd
Answers
Part (i)
1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)
2) Angles ABC and CDE are right angles (perpendicular lines form right angles)
3) Angles ABC and CDE are equal (all right angles are equal)
4) Angles ACB and DCE are equal (vertical angles are equal)
5) Triangles ABC and EDC are congruent (ASA)
Part (ii)
6) AB = DE (corresponding parts of congruent triangles are equal)
Each staple is made from 0.21 g of metal.
How many staples can be made from 1 kg of metal?
Answers
Answer:
4762
Step-by-step explanation:
0.21g x 10,000= 2100
0.21 x 5,000= 1050
0.21 x 4,000= 840
0.21 x 4700 = 987
0.21 x 4760 = 999.6
0.21 x 4762= 1000.02
( how much it's made from x the quantity = the grams or kg)
MATHHH. Probability section!!! HELP!
please give the right answer.
Answers
Answer:
10% or 1 /10
Step-by-step explanation:
'Fish' is on the spinner in one slot out of 10 slots
one out of 10 = 1/10 = 10%
Answer:
10%
Step-by-step explanation:
There are 10 possible areas to land on fish is only shown once meaning there is a 1/10 chance which is = to 10%
Rewrite in simplest terms: (4x+5)+(−5x−1) pls help
Answers
Answer:
-x + 4
Step-by-step explanation:
(4x+5)+(−5x−1)
4x+5−5x−1 [Remove the parentheses]
-x + 4 [Combine Like Terms]
Answer:
-x+4
Step-by-step explanation:
Given:
(4x+5)+(−5x−1)
Solution:
To re-write this in it's simplest terms:
4x+5-5x−1Combine like terms:
4x-5x+5-1-x+4Hence the simplest form is -x+4.
Done.
The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 58 yd, find its length and width.
Answers
Answer:
Length = 16 yds
Width = 13 yds
Step-by-step explanation:
P = 2w + 2l
l = w + 3
58 = (2w + 2(w + 3))
58 = 4w + 6
52 = 4w
w = 13
L = w + 3
= 13 + 3
= 16
The length and width of the rectangle are 16,13yd.
The Length and Width of the rectangle can be found as:
Given:The length of the rectangle is 3yds longer than the width which means length = w+3
and the perimeter is given by 58yd
Let W be the width and L be the length
We know that the perimeter of a rectangle is 2(L+w)
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle
By simplifying we get2(w+w+3)=58
2(2w+3)=58
2w=29-3
w=13
then the length of the rectangle will be w+3
13+3 = 16
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Find the range for the given domain: {-2, 0, and 1}and the function is y = 3x + 1.
Answers
Answer:
It's the first option: -5, 1 and 4
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
Answers
The correct answer is option B which is y > 3x + 2.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)
The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).
Therefore the correct answer is option B which is y > 3x + 2.
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If you apply the changes below to the quadratic parent function, f(x) = x²,
which of these is the equation of the new function? Shift 1 unit left.
Vertically stretch by a factor of 5.
Reflect over the x-axis.
A. g(x) = -5(x-1)²
B. g(x) = -5x² - 1
C. g(x) = -5(x + 1)²
D. g(x) = (-5x + 1)²
Answers
Answer:
Step-by-step explanation:
Comment
Do the most mechanical part first. Moving 1 unit left will mean that x becomes (x + 1). It is anti intuative, but that is the correct answer.
So far what you have is y = a(x + 1)^2
The reason that you want to do it this way is any answer with a minus sign is wrong which eliminates A and B
When you stretch the parabola, a becomes 5 so now you have another part of the puzzle. and the equation becomes
y = 5(x + 1)^2
The 5 goes on the outside of the brackets which eliminates D
When you reflect this over the x axis, you invert the parabola which means you turn it upside down. The sign in front of the 5 becomes a minus.
Answer
y = - 5(x + 1)^2 or C.
Joe kept track of how much TV she watched each day for two weeks how many hours did she spend watching TV
Answers
The total hours joe spent watching TV each day for two weeks is 12 1/2 hours
Total hours spent watching TVTotal hours spent watching TV for two weeks = Number of hours × days
= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)
= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2
= 8 + (1+2+9+6) / 4
= 8 + 18/4
= 8 + 4 2/4
= 8 + 4 1/2
= 12 1/2 hours
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