Answer:
[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]
Step-by-step explanation:
Given equation:
[tex]t^2-10t+6=7[/tex]
When completing the square for a quadratic equation, the first step is to move the constant to the right side of the equation:
[tex]\implies t^2-10t+6-6=7-6[/tex]
[tex]\implies t^2-10t=1[/tex]
Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:
[tex]\implies t^2-10t+\left(\dfrac{-10}{2}\right)^2=1+\left(\dfrac{-10}{2}\right)^2[/tex]
Simplify:
[tex]\implies t^2-10t+\left(-5\right)^2=1+\left(-5\right)^2[/tex]
[tex]\implies t^2-10t+25=1+25[/tex]
[tex]\implies t^2-10t+25=26[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (t-5)^2=26[/tex]
Square root both sides:
[tex]\implies \sqrt{(t-5)^2}=\sqrt{26}[/tex]
[tex]\implies t-5=\pm \sqrt{26}[/tex]
Add 5 to both sides:
[tex]\implies t-5+5=\pm \sqrt{26}+5[/tex]
[tex]\implies t=5 \pm \sqrt{26}[/tex]
Therefore, the solutions of the given quadratic equation are:
[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]
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Choose the system for the graph.
Answer:
Step-by-step explanation:
(3x+4y<12
2x - 5y = 14
y = 3x+5
Answer:
x = -3
y = -4
Step-by-step explanation:
2x - 5y = 14 ⇒ ( 1 )
y = 3x + 5 ⇒ ( 2 )
First, let us find the value of x.
For that let us use equation ( 1 ) and replace y with (3x + 5 ).
2x - 5y = 14
2x - 5 ( 3x + 5 ) = 14
Solve the brackets.
2x - 15x - 25 = 14
Combine like terms.
-13x - 25 = 14
Add 25 to both sides.
-13x = 14 + 25
- 13x = 39
Divide both sides by -13.
x = -3
Let us find the value of y.
For that, use equation (2) and replace x with (-3).
y = 3x + 5
y = 3 × -3 + 5
y = - 9 + 5
y = -4
Identify the kind of equence hown: 2, -1, -4, -7, -10,. *
Arithmetic
Geometric
Neither
The kind of sequence shown 2, -1, -4, -7, -10, is definitely an arithmetic sequence.
What are sequences?In mathematics, a sequence is a collection of numbers or items that have been organised in a certain order in accordance with a set of rules. These sequences, which might be endless or finite, are useful for simulating a variety of real-world processes. In addition to its practical uses, sequences are an essential mathematical notion that allows us to analyse patterns and relationships between numbers. We may edit and examine sequences to better understand their characteristics and behaviour by applying mathematical operations. Sequences are frequently used to investigate patterns and relationships between numbers, as well as to solve problems in a variety of mathematical disciplines such as algebra, calculus, and geometry. Arithmetic sequences, geometric sequences, recursive sequence are a few examples of frequent sequence types.
How to solve?
In an arithmetic sequence, the difference between any two consecutive terms is constant.
In the given sequence, the difference between any two consecutive terms is -3. i.e.,
d = -10 - (-7) = -7 -(-4) = -4 - (-1) = -1 - (2) = -3
Therefore, the sequence is an arithmetic sequence.
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PLEASE HELP!! WILL MARK BRAINLIEST! What is m< C
Answer:
sometimes used to distinguish between the measure of the angle
Step-by-step explanation:
A regular polygon has its exterior angles all equal to 5⁰ Find the number of sides of the polygon.
calculate the size of the exterior and interior angles of all the different polygon.
Helpp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! GEOMETRY
Geometry is a topic that deals with shapes, lines and angles. The explanation below is required to show the reasons for the statements are given below:
A triangle has three straight sides and three internal angles. The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Triangles can generally be classifies with respect to the size of angles, or according to the length of sides. Some common types are; right angles, obtuse angled, acute angle, isosceles, equilateral and scalene.
A right angled triangle is a type which has two of its sides at [tex]90^{o}[/tex] to each other.
Therefore, the required statements and reasons to prove that <JLK ≅ <LJM are:
STATEMENT REASON
1. ΔJKL and ΔLMJ are right triangles Given
2. JK ≅ LM Hypotenuse-Leg (HL)
3. Jl ≅ LJ Reflexive property
4. ΔJKL ≅ ΔLMJ CPCTC
5. <JLK ≅ <LJM Symmetric property
Thus, <JLK ≅ <LJM
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At a distance of 6 meters, a person with average vision is able to clearly read letters 1.0 cm high.Approximately how large do the letters appear on the retina? (Assume that the retina is 1.7 cm from the lens.)
The size of the letters appear on the retina is 0.00289 cm
Given data:
To determine the size of the letters on the retina, use the concept of angular size and the relationship between object size, distance, and angular size.
Angular size is the measure of the angle subtended by an object as seen from a particular point, in this case, the eye.
Angular size = Object size / Distance
Object size = 1.0 cm
Distance = 6 meters
Angular size = 1.0 cm / 6 meters
To convert the distance to centimeters, multiply by 100:
Angular size = 1.0 cm / (6 meters * 100 cm/meter)
Angular size = 1.0 cm / 600 cm
Angular size = 0.0017 radians
The angular size of the letters is 0.0017 radians.
Now, to determine the size of the letters on the retina, calculate the linear size on the retina using the angular size and the distance from the lens to the retina.
Linear size on retina = Angular size * Distance from lens to retina
Angular size = 0.0017 radians
Distance from lens to retina = 1.7 cm
Linear size on retina = 0.0017 radians * 1.7 cm
Linear size on retina ≈ 0.00289 cm
Hence, the letters appear to be approximately 0.00289 cm in size on the retina.
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On a snow day, Logan created two snowmen in his backyard. Snowman A was built to
a height of 34 inches and Snowman B was built to a height of 46 inches. The next day,
the temperature increased and both snowmen began to melt. At sunrise, Snowman
A's height decrease by inches per hour and Snowman B's height decreased by 7
inches per hour. Let A represent the height of Snowman A t hours after sunrise and
let B represent the height of Snowman B t hours after sunrise. Write an equation for
each situation, in terms of t, and determine the interval of time, t, when Snowman A
is taller than Snowman B.
A
B =
Snowman A is taller than Snowman B when to
Equation for each situation are A = 59 -7t and B = 34 -2t and t<5 is the interval of time.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Snowman A starts at 59 inches and decreases height at 7 inches per hour.
The height can be represented as A = 59 -7t
Snowman B starts at 34 inches and decreases height by 2 inches per hour. That height can be represented by B = 34 -2t
A is taller than B.
A > B
59 -7t > 34 -2t
add 7t-34
25 > 5t
Divide by 5
5 > t
A will be taller than B when t < 5.
Hence, A = 59 -7t and B = 34 -2t are equation for each situation and t< is the interval.
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The number 651 is what percent of 700?
Answer:
93%
Step-by-step explanation:
651/700
Answer: 93%
Step-by-step explanation:= (
(651 × 100/700) × 1/100 = 93/100
Is the line through points P(8, 4) and Q(6, –1) parallel to the line through points R(1, –4) and S(4, 5)? Explain.
Answer:
No, the lines are not parallel
Step-by-step explanation:
They are not parallel because the slopes of the lines are not equal.
Many credit card companie chard a compound interet rate of 1. 8% per month Nelon owe 950 on a credit card
Following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27
What is a geometric sequence?A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
So, in this issue, the interest rate is as follows: 1.8%.
The debt will therefore be equal to the debt from the previous month multiplied by 100 + 1.8 = 101.8% = 1.018 each month, and the common ratio is as follows: 1.018.
In light of this, the terms of the series are as follows:
2nd term: 950 x 1.018 = $967.1
3rd term: 967.1 x 1.018 = $984.51
4th term: 984.51 x 1.018 = $1002.23
5th term: 1002.23 x 1.018 = $1020.27
Therefore, the following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27
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Complete question:
Many credit card companies chard a compound interest rate of 1.8% per month Nelson owes 950 on a credit card. If he makes no purchases or payments he will go deeper and deeper into debt.
Lei withdrew $50 from her bank account every day for a week. What was the change in her account in that week?
Please someone help me in 1985, there were 285 cell phone subscribers in the small town of glenwood. the number of subscribers increased by 75% per year after 1985. Find out the number of subscribers in 2008? I just need the equation not the full answer
The number of subscribers in 2008 will be 110845988.
How to calculate the value of the subscriber?From the information, in 1985, there were 285 cell phone subscribers in the small town of glenwood. the number of subscribers increased by 75% per year after 1985.
It should be noted that the number of years between 1985 and 2008 will be:
= 2008 - 1985
= 23 years.
Therefore, the number of subscriber in 2008 will be:
= 285 × (1 + 75%)^23
= 285 × 1.75^23
= 285 × 388933.29
= 110845988
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PLSSS HELP ASAP 30PTS
Consider parallelogram ABCD with vertices A(-6, 6), B(0, 10), C(2,4), and D(-4, 0). Classify the parallelogram and select ALL that apply.
MORE THAN ONE POSSIBLE ANSWER
The figure is neither a rhombus nor a rectangle since the sides are of varied lengths and are not at right angles. "None of the other" applies.
Given that,
Consider parallelogram ABCD with vertices A(-6,6), B(0,10), C(2,4) and D(-4,0).
We have to find the parallelogram is square, rectangle, rhombus and none of the above.
We know that,
In the attached figure, which shows the number of grid squares for each side, we can see that one side is the diagonal of a 23 rectangle and the other side is the diagonal of a 13 rectangle. This reveals two things to you: The sides are not at perfect angles to one another and are of varied lengths. The slopes of the segments would be opposing reciprocals (if the sides were perpendicular).
Therefore, The figure is neither a rhombus nor a rectangle since the sides are of varied lengths and are not at right angles. "None of the other" applies.
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50, ...
The nth term of the given quadratic sequence is 2n².
What is quadratic sequence?
The ordered sets of numbers known as quadratic sequences are based on the rule n^2 = 1, 4, 9, 16, 25,.... (the square numbers). Every quadratic sequence has a n^2 term.
Consider, the given quadratic sequence
2, 8, 18, 32, 50, ...
we have to find nth term of this quadratic sequence ; 2 , 8 , 18 , 32, 50, ...
To find the nth term, we have to find the relation between the given terms.
here we see,
1st term = 2 = 2 × 1 × 1 = 2 × 1²
2nd term = 8 = 2 × 2 × 2 = 2 × 2²
3rd term = 18 = 2 × 3 × 3 = 2 × 3²
4th term = 32 = 2 × 4 × 4 = 2 × 4²
similarly 5th term = 2 × 5² = 2 × 25 = 100
...........
so nth term = 2 × n² = 2n²
Hence, the nth term of the given quadratic sequence is 2n².
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"opt-in" organ donation programs, where adults can choose to enroll in the program, have approximately 15% participation rates; "opt-out" organ donation programs, in which adults are enrolled by default and can choose to decline participation in the program, have approximately 90% participation rates. What best explains this difference?
It explains that people don't want to donate their organs in opt out because the probability of non donation public are greater.
As we know people who wants to donates their is organs opt out are approximately around 15 %
And we also know that people who don't want to donate their organs are approx. 90 %
In countries such as Australia, laws make organ donation the default option at the time of death, and so people must explicitly “opt out” of organ donation. In these so-called opt-out countries, more than 90% of people register to donate their organs.
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Write the equation of the line that passes through the given points (0 1) and (2 2).
The equation for the line connecting the two points is as follows y = 2x + x.
What is an example of an equation?A mathematical statement known as an equation is comprised of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Briefing:Equation of a line:
y = mx +b
Where;
m = slope
b = y-intercept
You are given the y-intercept from the point (0,2). When x = 0, y = 1
You can then see from the Eq: y = mx + b
that b = 1
By dividing the change in y by the change in x, or "rise over run," one may get the slope, m.
m = (y1-y2)/(x1-x2)
One of the points is (x1, y1) and the other (x2, y2)
m = (1-(2)) / (0 -(2))
m = (-1)/(-2) = 1/2
The equation for the line connecting the two points is as follows:
y = 2x + x.
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in a wildlife park, there were 20 gray wolves. after a few years, there were 38 gray wolves what is the percent gain
The percent gain in the number of wolves is 90%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
From the information, in a wildlife park, there were 20 gray wolves. after a few years, there were 38 gray wolves.
The percent gain will be:
= Increase in wolves / Previous number × 100
= (38 - 20) / 20 × 100
= 18/20 × 100
= 90%
Therefore, it should be noted that based on the information illustrated above, the percentage gain will be 90%.
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A company charges $2 for the first minute of tech
support and 50¢ for every minute after that. Is this
an example of a proportional relationship?
Answer:
No.
Step-by-step explanation:
No.
In a proportional relationship, every minute has the same charge.
What is the vertex of g(x) = -6.3|x|
The table below shows the linear relationship between
the distance in feet below sea level and the time in
seconds traveled by a submarine.
What is the rate of change low of the distance in the feet below sea level with respect to time that the box submarine traveled?
The rate of change of the distance with respect to time that the box submarine traveled is 11 feet per second
How to determine the rate of change of the distance with respect to time the box submarine traveled?A rate of change describes how one quantity changes in relation to another quantity.
Mathematically, it is defined as the change in one quantity divided by the change in the other quantity.
In this case, we have:
rate of change = change in distance / change in time
Use the data in the table:
rate of change = 545-380/15-0
rate of change = 165/15 = 11
Note: You can pick any 2 data points for the calculation
Therefore, 11 feeet per second is the rate of change of the distance in feet below sea level with respect to time that the box submarine traveled
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2X-Y=4
x=4-y
please explain each step
Step-by-step explanation:
2X-Y=4 ---------(1)
x=4-y---------(2)
since x = 4 – y just substitute for eqn 1
2(4–y) – y = 4
8 – 2y –y=4
8 –3y = 4
–3y=4–8
–3y=–4
y=–4/–3
y= 4/3
since y = 4/3 just substitute for y in eqn (2)
x=4–4/3
multiply both sides by 3
3x=12–4
3x=8
x=8/3 or 2 2/3
Complete the equation describing how
x and y are related.
Answer: y = 1x+4
the related between the x and y is x plus one and y plus 4
Step-by-step explanation:
Tyler has two cube-shaped storage spaces in his apartment building, one large and one
small. The small storage space has a volume of 12 ft". Tyler wants to know the total
volume of both storage spaces.
What is the total volume of both storage spaces if one side of the large storage spaces is 4 feet long?
Answer:
76 ft^3
Step-by-step explanation:
A volume of small box = 12 ft^
A volume of large box = 4×4×4= 64 ft^
the sum of volume = 12+64=76 ft^3
At a hospital, out of 10 doctors, 3 are on duty on Saturday, 4 on Sunday, and 2 on both days. If one of these doctors is randomly selected, what is the probability that she or he is on duty on Saturday or Sunday?
The probability distribution that she or he is on duty on Saturday or Sunday will be 0.7
What is probability distribution ?
A frequency distribution that has been idealised is a probability distribution.
An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each potential value of a variable appears.
The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:
Zero denotes impossibility.1 denotes a certainty.A value will occur more frequently in a sample the higher its likelihood.
The probability of a value is more particularly the relative frequency in an indefinitely large sample.
Probability distributions are theoretical since it is not feasible to obtain infinitely large samples in practise.
They are idealised frequency distributions that are intended to represent the population from which the sample was taken.To characterise the populations of real-world variables, such as coin tosses or the weight of chicken eggs, probability distributions are utilised. They are also used to calculate p values in hypothesis testing.Let the people work on Sunday = sun = 4
Let the people work on Saturday = sat = 3
total no. of doctors are 10
so the probability distribution of people work on either Sunday or Saturday will be :
= Sun + sat / total no of doctors
= 3+4/10
=0.7
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n a coordinate plane, Triangle XYZ is rotated 90 degrees counterclockwise about the origin to form Triangle X'Y'Z'. Which conclusion is always true?
△X'Y'Z' is transformed form △XYZ. If △XYZ rotated 90 degrees counterclockwise about the origin, then YZ ⊥ Y'Z'. Hence option B is the correct option.
What is transformation?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given that,
△XYZ is rotated 90 degrees counterclockwise about the origin to form △X'Y'Z'.
Each side of △XYZ is rotated 90 degrees counterclockwise.
Then the angle between corresponding sides of △XYZ and △X'Y'Z' are 90 degrees.
Therefore
XY⊥X'Y'
YZ ⊥Y'Z'
ZX ⊥ Z'X'.
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1/10 of the m&m in the bag are red and 1/5 are blue. What fraction of alll the m&m are red and blue
Step-by-step explanation:
we need to bring them to the same denominator. in this case : 10
so, 1/10 of everything are red.
1/5 = 2/2 × 1/5 = 2/10 of everything are blue.
so, we now just add these two :
1/10 + 2/10 = 3/10
so, 3/10 are red and blue (rather red or blue, because none are red and blue)..
(im giving brainliest for real answer)
The constant of proportionality of y and x in the graph is given as follows:
k = 3/4.
How to obtain the constant of proportionality?In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:
k = y/x.
A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.
The marked point on the graph has the coordinates given as follows:
(4,3).
Meaning that the constant of proportionality of y and x in the graph is calculated as follows:
k = y/x = 3/4.
(division of the value of the y-coordinate by the value of the x-coordinate).
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A concrete drain is 10m long, with an outside diameter of 1m and an inside diameter of 0.8m. Determine the volume of the concrete required to make the drain, to the nearest tenth of a cubic metre
Answer: To calculate the volume of the concrete required to make the drain, we need to find the volume of the cylinder formed by the outside diameter of the drain and subtract the volume of the cylinder formed by the inside diameter of the drain.
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
The radius of the base of the outside cylinder is 0.5m (the diameter of 1m divided by 2) and the height is 10m. The radius of the base of the inside cylinder is 0.4m (the diameter of 0.8m divided by 2) and the height is also 10m.
So the volume of the outside cylinder is:
V = π * 0.5^2 * 10 = 15.7 m^3
and the volume of the inside cylinder is:
V = π * 0.4^2 * 10 = 12.6 m^3
To find the volume of the concrete required to make the drain, we subtract the volume of the inside cylinder from the volume of the outside cylinder:
15.7 m^3 - 12.6 m^3 = 3.1 m^3
So the volume of concrete required to make the drain is approximately 3.1 cubic metres. To the nearest tenth of a cubic metre, this is 3.1 m^3.
There are 25 girls and 16 boys on the swim team. What percentage of the team is made up of boys?
Answer:
16/41 or 39%
Step-by-step explanation:
add both boys and girls and divide boys by that number