Answer:
[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]
Step-by-step explanation:
First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer
9y²+21-18=0
pls tell how to do
Hello,
I think it is 9y² + 21y - 18 = 0
we have a = 9 ; b = 21 and c = -18
∆ = b² - 4ac = 21² - 4 × 9 × (-18) = 1089 > 0
x1 = (-b - √∆)/2a = (-21 - 33)/9 = 6
x2 = (-b + √∆)/2a = (-21 + 33)/9 = 12/9 = 4/3
S = {4/3 ; 6}
Which of the following best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers?
A) the sum is a constant
B) the sum is a polynomial
C) the sum is an exponential expression
D) nothing can be determined about the sum without more information
The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
Sum of Polynomial expressionPolynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.
ax^2+bx+c and;
mx^2+nx+p
Take the sum of the polynomials
P(x) =. ax^2+bx+c
f(x) = mx^2+nx+p
Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.
Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
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CALLING ALL EXPERTS PLS ILL GIVE BRAINLIEST
On Monday, Gian spent 5 minutes watching videos. On Tuesday, he spent 25 minutes watching videos. Place points on the graph to show Gian's activity for Monday and Tuesday.
can someone please help mee (will give brainliest 20 points!!!)
A scientist studying insects starts with a population of 10. The population triples every hour. How many insects will there be after 20 minutes?
The population after 20 minutes is 14.
We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-
After 1 hour, the population is 3*10
After 2 hours, -> 3*3*10
After 3 hours, -> 3*3*3*10
Make a function from above observation in the increasing
number of the insects per hour
This can be generalized as a function of t, the time in hours:
f(t) = (3^t) * 10
putting the values in the function and get the desired answer,
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for
(1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.422 ≈ 14
The population after 20 minutes is 14.
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Answer:The population after 20 minutes is 14.
We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-
After 1 hour, the population is 3*10
After 2 hours, -> 3*3*10
After 3 hours, -> 3*3*3*10
Make a function from above observation in the increasing
number of the insects per hour
This can be generalized as a function of t, the time in hours:
f(t) = (3^t) * 10
putting the values in the function and get the desired answer,
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for
(1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.422 ≈ 14
The population after 20 minutes is 14.
Step-by-step explanation:
The coordinates of the vertices of △MER are M(3,2), E(3,−3), and R(9,−3). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. Answers;
A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
B) ME = 6; ER = 5, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 51°, m∠R ≈ 39°
C) ME = 6; ER = 5, MR = 11 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
D) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 40°, m∠R ≈ 50°
Please give a full explanation I would really appreciate it :)
Using the Pythagorean theorem and the law of sines, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are: A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
What is the Pythagorean Theorem?The theorem states that the square of the longest side of a right triangle equals the sum of the squares of the lengths of the other two smaller sides of the right triangle.
The points, M(3,2), E(3,−3), and R(9,−3) has been plotted on the graph which shows that angle E is a right triangle, therefore:
m∠E = 90 degrees.
Find ME and ER:
ME = 5 units
ER = 6 units.
Using the Pythagorean theorem, find MR:
MR = √(ME² + ER²)
MR = √(5² + 6²)
MR = √(25 + 36)
MR = 7.81 units
Using the law of sines, find m∠M:
sin M/ER = sin E/MR
sin M/6 = sin 90/7.81
sin M = (sin 90 × 6)/7.81
sin M = 0.7682
M = sin^(-1)(0.7682)
m∠M ≈ 50°
m∠R = 180 - 50 - 90
m∠R = 40°
Thus, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are:
A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
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Genevieve wants to verify that negative x is the simplified expression of one-fifth (5 x minus 20) minus one-half (4 x minus 8). which procedure can genevieve follow to verify this? add one-fifth (5 x minus 20) minus one-half (4 x minus 8) and negative x. put an equal sign between one-fifth (5 x minus 20) minus one-half (4 x minus 8) and one-fifth (5 x minus 20) minus one-half (4 x minus 8) and then solve for x. substitute 5 into the first expression, substitute 4 into the second expression, and evaluate them. substitute 5 into each expression and evaluate them.
Answer: -x
Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)
Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 4
Reorder and gather like terms: (x - 2x) + (- 4 + 4)
Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)
Calculate the sum or difference : - x + (- 4 + 4)
The sum of two opposites equals 0: -x
Answer: -x
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Answer:
D) Substitute 5 into each expression and evaluate them.
Step-by-step explanation:
What is the equation I'm supposed to write?
The equation in slope intercept form is y = -4x/3 + 10
How to determine the equation?The representations are given as:
x represents peachesy represents applesSo, we have:
2 * x + 1.5 * y = 15
Evaluate the product
2x + 1.5y = 15
Subtract 2x from both sides
1.5y = -2x + 15
Divide through by 1.5
y = -4x/3 + 10
Hence, the equation in slope intercept form is y = -4x/3 + 10
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Geometry: Complete these proof, ASAP!!!
The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.
What is the transitive property of congruence?Transitive property:
If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.
I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.
What does the angle bisector theorem state?The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.
I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2
(where ∠B1 = ∠B2)
Given:The line BD bisects ∠ABC, AD║BC, and AB║CD
Proof:The line BD bisects ∠ABC. So,
∠B = ∠3 + ∠4
According to the angle bisector theorem, ∠3 ≅ ∠4.
Since AD║BC and AB║CD, the alternate angle are congruent.
I.e., ∠3 ≅ ∠1
Thus, by the transitive property of congruence,
∠1 ≅ ∠4
Hence proved.
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4. Find the missing side lengths. Leave the answers as radicals in simplest form.
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
(2, 12)
(2, 18)
(2, 7)
(3, 7)
Answer: (2, 18)
Step-by-step explanation:
When x=2, [tex]f(2)=2(3)^{2}=18[/tex].
So, it should pass through (2, 18).
Answer:
(2, 18)
Step-by-step explanation:
i posted this at 1:19 in the morning, good day
The double number line shows that 333 back-to-school packages contain 363636 pencils. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, two unlabeled tick marks, 3, another unlabeled tick mark. The line labeled Pencils, reads from left to right: 0, two unlabeled tick marks, 36, another unlabeled tick mark. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, two unlabeled tick marks, 3, another unlabeled tick mark. The line labeled Pencils, reads from left to right: 0, two unlabeled tick marks, 36, another unlabeled tick mark. Select the double number line that shows the other values of packages and pencils. Choose 1 answer: Choose 1 answer: (Choice A) A A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48. (Choice B) B A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 10, 22, 36, 52.
HELP MEEEEEEEEEEEEEEEEEEEE
The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.
What is a number line?It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.
In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information
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For each of the following distance matrices of graphs, identify the diameter, radius and center. Assume the graphs vertices are the numbers 1 through
For each of the following distance matrices of graph, the
The diameter = 3The radius of the graph is given as 2What is the diameter of the graph?This is used to refer to the fact that there would be a maximum distance that exists between the pair of vertices.
What is the radius of the graphThis used to refer to the minimum eccentricities of the vertices
What is the center of the graph?This is used to show all of the vertices that have minimum eccentricities.
How to solve the matrixWe have
e 1 = 3
e 2 = 3
e3 = 2
e4 = 3
e 5 = 3
e 6 = 3
e 7 = 3
e8 = 2
e 9 = 3
e 10 = 2
Then the the diameter = maximum eccentricity = 3
The radius = minimum eccentricity = 2
center = [3, 8,10]
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7,
24*
nswer:
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
Answer:
1/12
Step-by-step explanation:
the chances of rolling a 3 is 1/6
there are 3 numbers more than 3 on a number die, 4,5, and 6
which is 3/6 or 1/2 if you decide to simplify
to find the probability you want you have to multiply the fractions by each other
1/6x1/2=1/12
2. The Kenya Seed Company sold 6 460 t 760 kg of maize seeds to 95 farmers. The farmers bought equal masses of seeds. What mass of seeds did each farmer buy? fond his cous in equal
Using proportions, it is found that each farmer bought 68,008 kg.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:
6460 x 1000 + 760 = 6,460,760 kg
The amount per farmer is:
6,460,760/95 = 68,008 kg.
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y
T
N
9
6
U
3
M
What is the value of y?
3√3 units
6√3 units
O
9√3 units
O 12√3 units
The value of y from the given figure is 6√3
Pythagoras theoremFrom the given figure, according to the theorem;
H² = 6² - 3²
H² = 36 - 9
H² = 27
H = 3√3
Determine the value of y using the same theorem;
y² = 9² + ( 3√3)²
y² = 81. + 27
y = √108
y = 6√3
Hence the value of y from the given figure is 6√3
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Which table shows a function that is increasing only over the interval(-2,1),and nowhere else?
table 1, and table 2 are the answers.
we know that any function is increasing when for an increase in x-values, y-value should also increase
we will verify each table
table-1:
we can see that
x increase as -3, -2, -1 , 0, 1,2
y is also increasing -6,-3,-1,1,3,6
so, this is increasing
table-2:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but it is asking between -2 to 1
y-values are -4,-1,1,4.....which is increasing
so, this is increasing
table-3:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from -3 to -5 .....which is decreasing
so, this is not increasing
table-4:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from 7 to 1 .....which is decreasing
so, this is not increasing
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Which expressions represent the sum of exactly two terms?
Choose 2 answers:
A. xy
B. m^4+6m
C. 3+7s+t
D. a+c
Answer: D and B
Step-by-step explanation:
Formula for two terms = a + b
Therefore,
D and B have two terms aka one plus sign
D. a + c
B. m^4 + 6m
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The sum of two terms is what we get after adding these two terms.
If you add two positive terms, you put a + sign in between these terms.
[tex]\sf{Example\!\!:a+b}[/tex]
If you add two negative terms, you put a - sign in between these terms.
[tex]\sf{Example\!\!:a-b}[/tex] (this is the same as [tex]\sf{a+-b}[/tex])
Let's look at the provided choices to see which one works.
Choice A.Provided Expression = [tex]\sf{xy}[/tex]Does Choice A. work ??It doesn't, because [tex]\sf{xy\neq x+y}[/tex]. In this expression a number x was multiplied by a number y. So this one doesn't check.
One down, three to go.
Choice B.Provided Expression = [tex]\sf{m^4+6m}[/tex]Does Choice B. work ??It does, because [tex]\sf{m^4+6m\stackrel\checkmark{=}m^4+6m}[/tex]. A number m was multiplied by itself 4 times, and then the product of that samee number m and 6 was added to it.
So this one checks.
Choice C.Provided Expression = [tex]\sf{3+7s+t}[/tex]Does Choice C. work ??It doesn't. It is indeed a sum, but we need 2 terms, not 3
So this one doesn't work.
Choice D.Provided Expression = [tex]\sf{a+c}[/tex]Does Choice D. work ??It does, because [tex]\sf{a+c\stackrel\checkmark{=}a+c}[/tex]. So Choice D. also works.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{calligraphy}\star[/tex]
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
Applying the trigonometric ratios, the equations that can be used are:
sin 45 = BC/9
cos 45 = BC/9
How to Apply the Trigonometric Ratio?In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:
To find AC, use the cosine ratio, CAH.
To find BC, use the sine ratio, SOH.
sin 45 = opp/hyp = BC/9
sin 45 = BC/9
cos 45 = adj/hyp = BC/9
cos 45 = BC/9
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Answer: A, E
Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9
mr hassell came home to find that each of the 6 kit kat bars he brought had 1 bar eaten. They each had 3/4 in it.How many bars of kitkat are there in total.
The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars
AlgebraNumber of bars = 6Number of bars eaten = 1Number of bar in each KitKat = 3/4Total bars of KitKat = 6 × 3/4
= (6×3)/4
= 18/4
= 9/2
= 4 1/2 bars
Number of bar remaining after eating 1 bar = 4 1/2 - 1
= 3 1/2 bars
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Please find answers of 14 a, b, c and d
Q14)
a) The smallest prime number is 2. The smallest composite number is 4.
b) Rs 720 - 20 [as loss]
=> Rs 790 = SP
c) Rs 500 - 30 [as profit]
=> Rs 470 = CP
d) a° + b° = 180°
Hope it helps you!
Julie has 20 times as many bouncy ball as her brother her brother haves 4 balls how many does Julie have?
Answer:
80
Step-by-step explanation:
Answer:
80 balls
Step-by-step explanation:
Julie's brother's balls x 20 = Julie's balls
4 x 20 = 80
Brainliest, please :)
Please help and explain
Answer:
D
Step-by-step explanation:
Yep, what you did there is correct!
The expression was: [tex](\frac{5^2}{4} )^4[/tex]
So let's solve this step by step.
First the numerator
[tex](5^2)^4[/tex]
Is the same thing as
[tex]5^8[/tex]
Since the exponents are multiplied.
Next is the denominator
[tex]4^4[/tex]
This can stay the same, since solving it as 4 x 4 x 4 x 4 will only make the fraction more complicated. Also, the answer choices below show that the denominator stays in exponential form.
==> [tex]\frac{5^8}{4^4}[/tex] is our final answer!
So the answer to this question is D. You got the question correct! :)
I hope that helped!!
The wall around a playground is 410 m.if one wall along the length is 80 m what is the length of the wall along the breadth what is the area of playground.
The length of the wall = 125m
The area of the Playground = 10000[tex]m^{2}[/tex]
What is geometry?
A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.
Given data:
Perimeter of the playground=410m
length of the wall = 80m
The playground's width can be calculated as follows if its length is 80 meters:
(Formula of Perimeter of a rectangle)
P=2(L+B)
410=2(80 +B)
410= 160 + 2B
2B= 410-160
2B= 250
B= 125 m
This results in a 125 m length for the playground.
The area of playground.
Area = Length x Width
Area = 80 x 125
area = 10000[tex]m^{2}[/tex]
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There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. The events are dependent events.
Given that there are five vowels, which come from the letters A, E, I, O, and U, the likelihood of drawing a vowel is:
5/26
since there are a total of 26 alternatives available. After choosing that, we are left with 25 alternatives, 4 of which are vowels, thus the probability is:
4/25
The final likelihood is thus:
5/26 * (4/25) = 0.031
In other words, the likelihood is 3.1% when choosing a vowel and then another (without replacement).
The first event has an impact on the second event since there are fewer vowels and overall possibilities, hence the events are dependent.
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PLEASE HELP MEEEEe
jhchnthnht
The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x
Which method can be used to find the equation of the perpendicular bisector?The slope, m, of the line BC is calculated as follows;
m = (2 - 1)/(4 - (-2)) = 1/6The slope of the perpendicular line to BC is -1/(1/6) = -6
The midpoint of the line BC is found as follows;
[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]
The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.
The equation of the perpendicular bisector in point and slope form is therefore;
(y - 1.5) = -6•(x - 1)
y - 1.6 = -6•x + 6
y = -6•x + 6 + 1.6 = 7.6 - 6•x
Which gives;
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What's 2 divided by X
Answer:
2/x
Step-by-step explanation:
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. (round your answer up to the nearest whole number.) the answer is not 384. i already submitted that answer and it was incorrect
The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.
Given margin of error of 0.05 and confidence interval of 95%.
We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.
Margin of error is the difference between real values and calculated values.
The formula of margin of error is as under:
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where
z is the critical value of z for given confidence level
n is sample size
σ is population standard deviation
We have not given population standard deviation so we will use the following formula:
Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]
We have to find z value for 95% confidence level.
z value=1.96
We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2
put [tex]\sqrt{p(1-p)}[/tex]=1/2
Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]
0.05=1.96*0.5/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=0.98/0.05
[tex]\sqrt{n}[/tex]=19.6
squaring both sides
n=384.16
After rounding off we will get
n=384.
Hence the sample size needed to obtain a margin of error of 0.05 is 384.
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Can someone help me please
Answer:
10. 20.9°
11. 73.2°
Step-by-step explanation:
The inverse sine function is used to find the angle from its sine value.
10.In each case, the equation is of the form ...
a/sin(x) = b/c
Multiplying both sides by c/b·sin(x), we find the solution is ...
sin(x) = ac/b . . . . . find sin(x)
x = arcsin(ac/b) . . . . . find the corresponding angle
For the given values a=7.2, b=13, c=sin(40°), we have ...
x = arcsin(7.2sin(40°)/13) ≈ 20.9°
11.For the given values a=6.53, b=√40, c=sin(68°), we have ...
x = arcsin(6.53sin(68°)/√40) ≈ 73.2°
Select the correct answer. An experiment consists of rolling a six-sided die to select a number between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1, 2, 3, ... 10. Which event definition corresponds to exactly one outcome of the experiment?
Answer:
Step-by-step explanation:
Solution
You want to find the probability of one certain event happening. For example, you want the die to come up 5 and you want the 6 to be drawn from the cards.
The total number of outcomes is 6 (for the die) times 10 for the cards.
One 1 outcome is possible.
So the vent probability is 1/6*10 = 1/60. You will have to translate this to the choices you have been given. 1/60 = 0.0167 is another possibility.
Answer
1/60 or 0.0167