By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
How to find the zeroes of a second order polynomial
A value of x is a zero of a polynomial if and only if [tex]\sum\limits_{i=0}^{n} c_{i}\cdot x^{i} = 0[/tex], the quadratic formula for second order polynomials of the form a · x² + b · x + c = 0 is presented below:
[tex]x =\frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
If we know that a = 1, b = -20 and c = 32, then the roots of the second order polynomial are:
[tex]x = \frac{20 \pm \sqrt{(-20)^{2}-4\cdot (1)\cdot (32)}}{2\cdot (1)}[/tex]
[tex]x = 10 \pm 2\sqrt{17}[/tex]
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
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(10/2)x7+5-4 whats the answer
Answer:
36
Step-by-step explanation:
Question:
[tex] \bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]
Solution:
Here, we need to use PEMDAS rule, where:
P = parenthesise = exponentsm = multiplicationD = divisiona = additions = subtractionThere's a rule as well, the sum given is need to solved from the left, whichever sign is there.
Solved:
[tex]\bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]
Solve for parentheses first:
[tex] = 5 \times 7 + 5 - 4[/tex]
Then multiplication of course:
[tex] = 35 + 5 - 4[/tex]
Then addition:
[tex] = 4 0 - 4[/tex]
[tex] =36[/tex]
Hence, the answer is 36.
Someone is thinking of two numbers that are natural, and one is bigger than the other one by 10, if you multiply those two numbers you get 375 what are those two numbers.
Answer:
So the two numbers are {15, 25}.
Step-by-step explanation:
Simultaneous Equations:
xy = 375
x = y + 10
Subsitute the Second One into the First:
(y + 10)y = 375
y^2 + 10y - 375 = 0
y = 15 [and not -25 (natural numbers are not negative)]
Solve for x by Substituing y in the Second Equation:
x = 15 + 10
x = 25
Solution:
So the two numbers are {15, 25}.
Answer:
15 and 25
Step-by-step explanation:
The given relations between the two numbers allow you to write a system of equations. Algebraic solution of the system involves the solution of a quadratic equation. The numbers are "natural numbers", so are both positive integers.
__
setupLet x and y represent the smaller and larger of the two numbers, respectively. The given relations are ...
y = x +10 . . . . . . the larger is 10 more than the smaller
xy = 375 . . . . . . their product is 375
solutionSubstituting for y in the second equation, we have ...
x(x +10) = 375
Adding (10/2)² will complete the square.
x² +10x +25 = 375 +25 . . . . add 25
(x +5)² = 400 . . . . . . . . . . . write as a square
x +5 = √400 = 20 . . . . . . positive square root
x = 20 -5 = 15
y = x +10 = 25
Those two numbers are 15 and 25.
__
The attachment shows a graphical solution of the equations.
_____
Additional comment
Your number sense tells you that both numbers end in 5. Their geometric mean is √375 ≈ 19.4, so the first numbers that deserve consideration are numbers ending in 5 that are either side of this value: 15 and 25.
You can also consider their arithmetic mean. If that is represented by z, then we have (z-5)(z+5)=375 ⇒ z²-25=375 ⇒ z²=400 ⇒ z=20, and the two numbers are 20±5.
A book is chosen randomly. complete the steps to find the probability that the book is nonfiction given that it is hard-covered. find the probability that a chosen book is nonfiction and hard-covered. p(n ∩ h) = find the probability that a chosen book is hard-covered. p(h) = calculate the conditional probability. startfraction p (n intersection h) over p (h) endfraction =
The probability that the book is nonfiction given that it is hard-covered is 4/11
How to determine the probability?From the complete question, we have:
Total = 20
n(H ∩ N) = 4
n(H) = 11
This means that:
P(H ∩ N) = n(H ∩ N)/Total
So, we have:
P(H ∩ N) = 4/20
The conditional probability is then calculated using:
P(N | H) =4/20 ÷ 11/20
Evaluate
P(N | H) = 4/11
Hence, the probability that the book is nonfiction given that it is hard-covered is 4/11
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Answer:
Step-by-step explanation:
4/20
11/20
4/11
yw :)
Find the value of x for which l is parallel to m 105 (3x-18)
The value of x for which the lines m and l are parallel is 31 degrees
Parallel linesThe given diagram includes two parallel lines m and l, since the line are parallel hence the sum of the angles 105 and 3x - 18 are supplementary that is;
105 + 3x - 18 = 180
Simplify for the value of x
87 + 3x = 180
3x = 180 - 87
3x = 93
x = 93/3
x = 31
Hence the value of x for which the lines m and l are parallel is 31 degrees
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jamie is shopping for sports equipment. he purchases equipment worth 202 bout pays only 168. What is the discount amount?
Answer:
Discount amount = 34
Step-by-step explanation:
Discount amount = 202 - 168 = 34
write in standard form
(2×10³)+(4×10²)+(4×10¹)+(4×1)
can somebody answer this please.
c:
Answer: 2,444
Step-by-step explanation: We can find the answer to this problem by simplifying the scientific notation, and then adding. You would end up with 2,000 + 400 + 40 + 4 if done correctly. Hope this helps!
A ball is kicked upward with an initial velocity of 52 feet per second. The ball's height, h (in feet), from the ground Is
modeled by h= -16t^2 +52t where t is measured in seconds. How much time does the ball take to reach its highest
point? What is its height at this point?
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+52}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 52}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (52)^2}{4(-16)}\right) \implies \left( - \cfrac{ 52 }{ -32 }~~,~~0 - \cfrac{ 2704 }{ -64 } \right)[/tex]
[tex]\left( \cfrac{13}{8}~~,~~\cfrac{169}{4} \right)\implies \underset{\stackrel{\uparrow \hspace{3em}}{seconds\qquad }}{\stackrel{\stackrel{\qquad feet}{\hspace{3em}\downarrow }}{\left( 1\frac{5}{8}~~,~~42\frac{1}{4} \right)}}[/tex]
The mean test score of 12 students is . 42
A student joins the class and the mean becomes .43
Find the test score of the student who joined the class.
Answer:
45 becasue it has to be over 43
Step-by-step explanation:
The test score of the student who joined the class will be;
⇒ 55
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mean test score of 12 students = 42
And, A student joins the class and the mean becomes 43.
Now,
Total score for 12 students is,
⇒ x / 12 = 42
⇒ x = 42 × 12
⇒ x = 504
Here, A student joins the class and the mean becomes 43.
Let the student who join = y
So, We get;
⇒ (504 + y) / 13 = 43
⇒ 504 + y = 43× 13
⇒ 504 + y = 559
⇒ y = 559 - 504
⇒ y = 55
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bobs snowplow business charges 300$ per season plus 10$ for each walkway shoveled, while mikes snow removal charges 250$ per season plus 15$ per walkway.
using technology, how many walkways must be shoveled to result in equal billing from both companies?
The number of walkways that must be shoveled to result in equal billing from both companies is 10
Calculating costFrom the question, we are to determine how many walkways must be shoveled to result in equal billing from both companies
Let the number of walkways be x
From the given information,
Bobs snowplow business charges 300$ per season plus 10$ for each walkway shoveled
∴ If x walkways are shoveled
the billing will be $300 + $10x
For Mikes snow removal
Mikes snow removal charges 250$ per season plus 15$ per walkway
∴ If x walkways are shoveled
the billing will be $250 + $15x
Now, we are to determine the value of x for which the billings from both companies will be equal,
That is,
$300 + $10x = $250 + $15x
$15x - $10x = $300 - $250
$5x = $50
x = $50 / $5
x = 10
Hence, the number of walkways that must be shoveled to result in equal billing from both companies is 10.
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Student attendance at football games
sampling method
results of survey
collin surveys 63 students by randomly choosing names from the school
69% attend football games.
directory.
karl surveys 30 students that were sitting near him during lunch. 87% attend football games.
collin's method is (select) v than karl's method. karl's method picks students who
(select)
Collin's sampling method will better represent the entire population.
Missing part of the questionDetermine which sampling method will better represent the entire population.
How to determine the better method?From the question, we understand the Collin selected random names from the school directory.
While Karl surveyed only the students sitting close to him.
Karl's method is biased because students sitting far from him do not have a chance of being surveyed.
Hence, Collin's sampling method will better represent the entire population.
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rotate 90 dgrees answer me
Step-by-step explanation:
here, given points are
(-2,-1),(-5,-3),(-5,-4)
now
(X,y)________ (-y,X)
(-2,-1)________ (1,-2)
(-5,-3)________ (3,-5)
(-5,-4)________ (4,-5)
now plot the points in the graphs
a shopkeeper purchased a TV at ₹15,000 and gives a discount of 20% on its marked prize and still got a profit of 8% . find the marked prize of the TV .
[tex]\huge\sf\underline{Answer} [/tex]
[tex]\sf\longrightarrow selling \: prize \: = \frac{100 + profit\%}{100} \times cp[/tex]
[tex]\sf\longrightarrow \frac{108}{100} \times 15000 = 16200[/tex]
Let the marked prize of the TV be x .
[tex]\sf\longrightarrow discount = 20\% \: of \: x \: = \frac{20}{100}x = \frac{x}{5} [/tex]
We have SP = MP - Discount
[tex]\sf\longrightarrow 16200 \: = \: x - \frac{x}{5} [/tex]
[tex]\sf\longrightarrow 16200 \: = \frac{4x}{5} [/tex]
[tex]\sf\longrightarrow x \: = \: 20250[/tex]
Hence , The marked prize of the TV is ₹20,250 .
Hope it helps ~
please help!!!!!!!!!!
i can, first add then take away and u done!
Step-by-step explanation:
What is the circumference, in centimeters, of the circle? Use 3.14 for π. Enter your answer in the box. (the diameter is 24cm)
The circumference of the circle is 75.36 cm.
Step 1: Given data:Diameter of the circle is 24 cm,
[tex]\pi = 3.14[/tex]
Step 2: Formula used and calculation:Circumference of the circle is [tex]2\pi r[/tex].
So, Radius, r = 24/2 = 12 cm.
Now, Putting the value in the above formula, we get
2 × 3.14 ×12 = 3.14 × 24 = 75.36 cm.
Hence, the circumference of the circle is 75.36 cm.
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12.34
the measure of one interior angle of a rhombus is [tex]79^{\circ}[/tex] . what are the measures of the other three interior angles?
Step-by-step explanation:
a rhombus is a parallelogram with 4 identical sides.
it has therefore two pairs of equal angles.
as any quadrilateral the sum of all interior angles is 360°.
(and yes, as add-on, the diagonals bisect each other at right angles).
so, one interior angle is 79°.
that means it has a twin that is also 79°.
together they have 79×2 = 158°.
that leaves
360 - 158 = 202°
for the other 2 angles (they must be equal too).
so, each of them has
202/2 = 101°
so, the other 3 angles are
79°, 101°, 101°
Anna makes a pot of the soup. She is using a ¼ cup measuring cup. How many times will Anna need to fill the measuring cup to measure ⅞ cup of turnips? Show your work.
Answer:
2/7 ?
Step-by-step explanation:
Because 1/4 divided by 7/8th is 1/4. Hope this works
Work out 21 as a fraction of 12
Answer:
see below
Step-by-step explanation:
1 9/12 = > 1 3/4
........
solve for x
4x + 9
16x - 9
Answer:
9
Step-by-step explanation:
Vertical lines are parallel so the given interior angles are supplementary and their sum is equal to 180:
4x + 9 + 16x - 9 = 180 add like terms
20x = 180 divide both sides by 20
x = 9
Angles A and B are complementary. If sin A = 5x + 9 and cos B = 3x + 21, what is the value of x? (1 point) 2 6 15 39
The value of x is 6.
What are complementary?Complementary angles are angles that sum up to 90°.
Analysis:
For angles A and B, to be complementary, the sine of angle A must be equal to the cosine of angle B.
sin A = cos B
5X+9 = 3x+21
5x - 3x = 21 - 9
2x = 12
x = 6
In conclusion, the value of x to make angles A and B complementary is 6.
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Johnny is a very picky eater, so he likes to use a lot of condiments. He has ketchup, salt, pepper, and shredded cheese at his disposal. His mother tells him he may only make two additions to his meal (i.e., he can add condiments only twice, regardless of whether or not he already used them). How many different ways can Johnny improve his meal?
10
6
12
16
Answer:
see the attachment photo!
The different ways Johnny can improve his meal is 16
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Given;
Mother tells him he may only make two additions to his meal
First addition; 1C4
Second addition; 1C4
1C4=4
=4x4
=16
Therefore, by combinations and permutations their will be 16ways
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Please help I’m begging you!!
Answer:
Here is the ans ...hope it helps:)
Determine when both options will cost you the same amount and how much is that?
Answer:
after 25 months both options cost $2000
Step-by-step explanation:
the options are the same at the point of intersection of the 2 lines
the lines intersect at (25, 2000)
That is after 25 months both options will cost $2000
what are the least common denominators for 4 and 6
Look at the top 3 banking activities done via mobile banking vs. online banking. what characteristics do you
notice for both?
The characteristics I notice in top 3 mobile banking vs. online banking. is that:
They are both flexible.They are both used for transferring fundsThey can both be used to Online bill pay.Both can be used to monitor account.What are the top 3 banking activities done via mobile banking?They are:
Checking of an account balance or checking recent transactions.Downloading of mobile banking app.Transferred money between two accounts.The top 3 banking activities done via online banking are:
Transferring of fundsLooking at account balances at any time.Looking or printing statements.Therefore, the characteristics I notice in top 3 mobile banking vs. online banking. is that:
They are both flexible.They are both used for transferring fundsThey can both be used to Online bill pay.Both can be used to monitor account.Learn more about banking activities from
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(x + 8/3)^2 + y^2 = 1 What is the center of the circle? what is the radius?
(x+8/3)²+y²=1
(x+8/3)²+y²+0²+2×0y=1
(x+8/3)²+(y+0)²=(V1)²
->center: C(8/3,0)
-> radius: V1
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
What is the probability of drawing a red marble out of the bag without looking?
[tex]|\Omega|=1+2+3+3=9\\|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33,3\%[/tex]
Which of the following is NOT a rational number?
A
√121
B
√12.1
C
√1.21
D
√0.0121
Answer:
A rational number is a number that can be expressed as a fraction (the ratio of two integers).
Integer: A whole number that can be positive, negative, or zero.
To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:
[tex]\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}[/tex]
[tex]\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}[/tex]
Therefore, [tex]\sf \sqrt{12.1}[/tex] is not a rational number.
There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the
probability that the mystery books are next to each other, the romance books are next to each other, and the
poetry books are next to each other? (For example, MMRRPP).
Answer:
Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you 1. 2 M, 2R, 2 P are placed in shelf randomly P(similar a…
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Transcribed image text: Your Turn Find the probability using permutation with repetition 1. There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the probability that the mystery books are next to each other, the romance books are next to each other, and the poetry books are next to each other? (For example, MMRRPP). 2. The school jazz band has 4 boys and 4 girls, and are randomly lined up for a yearbook photo. Find the probability of getting all of the boys grouped together.
Step-by-step explanation:
CORRECT ME IF IM WRONG
A population of 175 snails is increasing at an annual rate of 12%. what will the population
of the snails be in 10 years? round to the nearest hundreths place.
an...
snails
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &175\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A=175(1 + 0.12)^{10}\implies A=175(1.12)^{10}\implies A\approx 543.52[/tex]
Find the measure of the indicated angle to the nearest degree.
7
9
12
?
49⁰
O53⁰
41°
37⁰
Answer:
[tex]41^{\circ}[/tex]
Step-by-step explanation:
[tex]~~~~~~\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \cos \theta = \dfrac{9}{12}\\\\\\\implies \theta = \cos^{-1} \left( \dfrac 9{12} \right)\\\\\\\implies \theta \approx 41^{\circ}[/tex]
Answer:
41°
Step-by-step explanation:
Since the adjacent side and the hypotenuse are given, let's take the cosine ratio of the missing angle.
cos θ = adjacent side / hypotenuse
===========================================================
Given :
⇒ Adjacent side = 9
⇒ Hypotenuse = 12
===========================================================
Solving :
⇒ cos θ = 9/12
⇒ cos θ = 0.75
⇒ θ = cos⁻¹ (0.75)
⇒ θ = 41.4096221....
⇒ θ = 41° (to the nearest degree)