Answer:
[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]
To find the zeros, set the function to zero and solve for x using the quadratic formula.
[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]
Quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore,
a = 2√3b = 5c = - 4√3Substituting the values into the quadratic formula:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]
[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
The sum of the roots of a polynomial is -b/a:
[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]
The sum of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]
The product of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Answer:
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
To find the zeros, set the function to zero and solve for x using the quadratic formula.
Quadratic formula:
Therefore,
a = 2√3
b = 5
c = - 4√3
Substituting the values into the quadratic formula:
The sum of the roots of a polynomial is -b/a:
The sum of the found roots is:
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
The product of the found roots is:
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Factorise and evaluate
50 × 11 + 50 × 9
Answer:
1000
Step-by-step explanation:
50 × 11 + 50 × 9 ← factor out 50 from each term
= 50(11 + 9)
= 50(20)
= 1000
What is 1+1? 10 point if u get it right.
Answer:
11
Step-by-step explanation:
duh add 1 and 1 merge it together to get 11
that's a hard question imma go with 2 though
Step-by-step explanation:
for this problem let's let x=1 and y also =1 so x+y=2 hope this helps
Which of these could be the graph of F(x) = log₂ x?
A
A. Graph A
B. Graph B
C. Graph C
D. Graph D
The graph of the function is shown in the attached image.
The radius of a circle is 0.00012 * 10 ^ 5 * f * t . What is the area of the circle? Use the formula A = pi * r ^ 2
Answer: [tex]144\pi[/tex] square feet
Step-by-step explanation:
[tex]A=\pi(0.00012 \times 10^{5})^{2}=\boxed{144\pi \text{ ft}^{2}}[/tex]
pls help!!!
What is the range of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
Answer:
All real numbers greater than or equal to 2.
Step-by-step explanation:
To find the range, we look at the y values. Since all the y values never dip under 2 and also keep increasing to infinity, the range is [tex]y\geq 2[/tex].
Answer:
all real numbers greater than or equal to 2
Step-by-step explanation:
Edge
From Khan Academy Pre Algebra
Please Evaluate This Question:
answer is this in decimal form if this is what ur looking for 4.21900462…
hope it helps....
Answer:
17.8
Step-by-step explanation:
if the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle
Any help will do! Thank you!
Let's take this problem step-by-step:
First let's set up the equation for the cost for one week of renting the car
agency charges $230 per week[tex]charge = 230[/tex]
agency charges $0.25 per mile (lets set the number of miles as 'x')[tex]charge = 230 + 0.25x[/tex]
The total cost was 415, therefore:
[tex]415 =230 + 0.25x\\185 = 0.25x\\x = 740[/tex]
Therefore, you traveled 740 miles
Answer: 740 miles
Hope that helps!
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Find x and Y pls help
Answer:
Step-by-step explanation:
Comment
The angle supplementary to x and 3x are equal.
Supplementary angles = 180
Solution
x + 3x = 180
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
The angle supplementary to x is 3x
3x = 3*45
3x = 135
This angle is vertically opposite y. Vertically opposite angles are equal. So y = 135
Answer
x = 45
y = 135
Find the value of JN in the figure.
Answer:
JN = 32
Step-by-step explanation:
Δ JMN and Δ JKL are similar ( AA postulate )
then the ratios of corresponding sides are in proportion, that is
[tex]\frac{JM}{JK}[/tex] = [tex]\frac{JN}{JL}[/tex] ( substitute values )
[tex]\frac{24}{33}[/tex] = [tex]\frac{JN}{JN+12}[/tex]
[tex]\frac{8}{11}[/tex] = [tex]\frac{JN}{JN+12}[/tex] ( cross- multiply )
11 JN = 8(JN + 12)
11 JN = 8 JN + 96 ( subtract 8 JN from both sides )
3 JN = 96 ( divide both sides by 3 )
JN = 32
Solve the problem.
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is
198 feet, what are the room's dimensions?
Answer:
width is 30, and the length 69.
Step-by-step explanation:
In order to do this, we need to do ALGOOBRAA
lets say x is equal to the width of the room
then, that means the length is (9+2x) Sooooo,
198=2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you dont know what that is, then go search it up :/
so,
198=2x+18+4x
198=6x+18
180=6x
30=x
BAM
Now, we know that the width is 30, bro.
That means the length is 60+9, Which is 69.
Therefore, the width is 30, and the length 69.
Sry if im wrong btw.
The width of rectangle is 30, and the length is 69.
What is Rectangle?
A rectangle is a quadrilateral. The opposite sides of a rectangle are equal and parallel to each other. The interior angle of a rectangle at each vertex is 90°. The sum of all interior angles is 360°. The diagonals bisect each other.
Here, lets say x is equal to the width of the room
then, that means the length is (9+2x) So,
198 = 2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you don't know what that is, then go search it up :/
so,
198 = 2x+18+4x
198=6x+18
180=6x
30=x
Now, we know that the width is 30,
That means the length is 60+9, Which is 69.
Thus, the width of rectangle is 30, and the length is 69.
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Using side lengths only, could the triangles be similar?
Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.
Yes, StartFraction 0.5 Over 1 EndFraction = StartFraction 0.5 Over 1 EndFraction.
Yes, One-half = StartFraction 0.5 Over 1 EndFraction.
Yes, StartFraction 1.5 Over 1 EndFraction = StartFraction 2 Over 1.5 EndFraction.
The triangles are not similar as the ratios are different.
How to depict the triangle?ΔXYZ
XY = 1.5, XZ = 1, ZY = 2
Δ QSR
QR =1, RS = 1.5, SQ = 0.5
Ratios:
XY/SQ = 1.5/0.5
XZ/QR = 1/1
ZY/RS = 2/1.5
The answer is no because ratios are different
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Z varies directly as x^3 and inversely as y^3. If z=167 when x = 3 and y=10, find z if X=4 and y=6
Answer is 1832.7
step by step
z=kx^3 / y^3
167=27k/1000
k=16700/27
k=6185.2, then
z=6185.2×4^3/6^3
z=6185.2×64/216
z=1832.7
PLEASE HELP ASAP! Consider the scatter plot. Complete the equation that models the curve of best fit for this data.
curve of best fit: f(x)
The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Consider the scatter plot.
Then the equation that models the curve of best fit for this data will be
At (1.2, 3), then we have
[tex]\rm 3 =ab^{1.2}[/tex] ..........1
At (4, 16), then we have
16 = ab⁴ ..........2
By solving the equations 1 and 2, we have
a = 1.4646 and b = 1.818
Then the equation will be
y = 1.4646·(1.818)ˣ
Then the graph is drawn.
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Graphing a exponential decay function
The process of Graphing a exponential decay function is shown in detail below.
There are two types of exponential equations: exponential decay and exponential growth. The fundamental shape of an exponential function and its corresponding graphs must be understood in order to fully comprehend the distinctions between exponential growth and decay. The fundamental distinction between the two is that in an exponential decay connection, the output values rise quickly as the input value rises, but in an exponential growth relationship, the output rises noticeably faster as the input value rises. Furthermore, neither of the two functions is linear, hence their rate of change is not constant. What distinguishes one equation from the other when they both have the same precise form, y = abx?
The value of the constant "b" is the fundamental factor in deciding whether the exponential function is one of growth or decay:
If function y = ab^x and b > 1then the function is an exponential growth function.If the function y = ab^x and 0<b<1 then the function is an exponential decay function. As noted before, "b" can never be exactly 1.In this way we can graph a exponential decay function
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Given the two similar triangles below, which proportion is not true?
The proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
ProportionThe three sides of each of the rectangles should be proportional to each other
Triangle A : Triangle B
9 cm : 13.5 cm
= 9/13.5
14 cm : 21 cm
= 14 cm / 21 cm
6 cm : 9 cm
= 6 cm / 9 cm
Therefore, the proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
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A. 10%
B.15%
C.28%
D.25%
Answer: 10%
Step-by-step explanation:
She had a total of $16,800. Subtracting the $5700 standard deduction and the $3650 exemption, we get:
[tex]16800-5700-3650=7450[/tex]
Which falls within the 10% tax bracket.
How many full cases and additional items are needed to fulfill the order 80 6
The number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
80 units needed 6 units per case. What are the number of cases and the number of additional units?
Total number of units = 80 units
6 units per case
Number of case = 80/6 = 13.33 ≈ 13
Total units if the number of cases = 13
= 13×6
= 78
Additional units = 80 - 78 = 2 units
Thus, the number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
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A 7 x 8 array is 7 rows of ____
Answer:
8
Step-by-step explanation:
It's 7 rows of 8 items
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is t ≥ 0
The greatest concentration of the medication is 5mg/L
Given that:
C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t ≥ 0
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).
The slope of the line is
[tex]\frac{-3-1}{6-3}=\frac{-4}{3}[/tex]
Substituting into point-slope form using the point (3,1),
[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]
Answer: The equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex] +5.
Step-by-step explanation:
Point-slope formula : (y - y1) = m(x - x1)
y = y coordinate of second point
y1 = y coordinate of first point
m = slope
x = x coordinate of second point
x1 = x coordinate of first point
slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]
m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]
now put values in point-slope formula : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)
y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4
y = [tex]\frac{-4x}{3}[/tex] +5
So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.
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find the perimeter: (use 3.14 for pi):
Answer:
10.676 mm
Step-by-step explanation:
The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7, 2*3.14*1.7 = 10.676 mm.
Hope this helps!!! Please mark me as brainliest!!!
Write an algorithm to find Area of square?
Step-by-step explanation:
AREA OF SQUARE:
A square is simply a rectangle with equal sides. As a result, the length and breadth of a square are equal. As a result, the area of a square is the product of two square sides, or in simpler terms, squares of the side.
Area = Side^{2}Area=Side
2
We use the following formula to compute the area of a rectangle after being given the length and width of the rectangle as input.
ALGORITHM:
Step 1 : Start
Step 2: Input Side
Step 3: Area = Side \times× Side
Step 4: Print area
Step 5: Stop
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set
builder form using a compound inequality.
Note: To type in the sign, type <= or use the Math Quill by clicking the yellow arrow.
Answer:
Domain: Interval notation is [tex](-3, 4][/tex], set builder is [tex]\{x|-3 < x\leq4 \}[/tex]Range: Interval notation is [tex][0, 3)[/tex], set builder is [tex]\{y|0\leq y < 3\}[/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Suppose a jar contains 12 red marbles and 12 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red
The probability that both are red marbles is 0.2391
How to determine the probability?The given parameters are:
Red =12
Blue = 12
Total = 24
The probability of selecting the first red marble :
P(Red) = 12/24
Now, there are 11 red marbles and 23 marbles in all
The probability of selecting the second red marble :
P(Red) = 11/23
The required probability is:
P = 12/24 * 11/23
Evaluate
P = 0.2391
Hence, the probability that both are red marbles is 0.2391
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What is the surface area of a square prism with sides that measure 8 units?
O254 units²
O 300 units²
0314 units²
0384 units²
Answer:
384 units²
Step-by-step explanation:
The area of one face is (8)(8)=64.
Multiplying this by the six faces, we get 64(6)=384
Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!
The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.
Distance of each truck from the fireUsing sine rule, we find the length of AB and BC as shown in the image.
a/sin A = b/sin B = c/sin C
Angle C = 180 - (58 + 52) = 70⁰
1.3/(sin 70) = b/(sin 52)
b = (1.3sin 52) / (sin 70)
b = 1.09 mile
c = (1.3sin 58) / (sin 70)
c = 1.1732 miles
Bisect angle C, and use sine rule again to find the lengths of bisected line AB.
1.09/(sin 90) = x/[sin (90 - 58)]
1.09/(sin 90) = x/(sin 32)
x = (1.09 sin 32)/(sin 90)
x = 0.578 mile
Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile
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Steve is ordering burgers and individual pizzas for $1000. He plans to buy not more than 80 items. The costs of each burger and each pizza are $7 and $4. Select the inequality that describes this situation. Use the given numbers and the following variables. x = the number of burgers. y = the number of pizzas.
[tex]x+y\leq 80[/tex]
[tex]7x+4y=1000[/tex]
The number of burgers = [tex]x[/tex]
the number of pizzas = [tex]y[/tex]
the cost of each burger = $[tex]7[/tex]
the cost of each pizza = $[tex]4[/tex]
not more than 80 items: [tex]x+y\leq 80[/tex]
total price =[tex]7x+4y=1000[/tex]
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The Gross Domestic of a country in the first quarter of 2014 was $1.3299×10×8.
GPD=$
The GDP of the country for 2014 is $5.3196 × 10⁸.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given the Gross Domestic of a country in the first quarter of 2014 was $1.3299×10⁸. Therefore, the GDP of the country for that year will be,
GDP = 4 × (Gross Domestic for a single quarter)
= 4 × ($1.3299×10⁸)
= $5.3196 × 10⁸
Hence, the GDP of the country for 2014 is $5.3196 × 10⁸.
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Examine the following three premises: i. All kids who have a smartphone play mobile legends.
ii. All people who play mobile legends enjoy life.
iii. Some college instructors enjoy life. Now consider each of the following six conclusions. For each conclusion, determine whether the argument formed by the three premises and the conclusion is valid or invalid.
1. Therefore, some college instructors have a smartphone.
2. Therefore, some college instructors play mobile legends.
3. Therefore, some kids who play mobile legends are college instructors. Examine the following three premises :
i . All kids who have a smartphone play mobile legends .
ii . All people who play mobile legends enjoy life .
iii . Some college instructors enjoy life . Now consider each of the following six conclusions . For each conclusion , determine whether the argument formed by the three premises and the conclusion is valid or invalid .
1. Therefore , some college instructors have a smartphone .
2. Therefore , some college instructors play mobile legends .
3. Therefore , some kids who play mobile legends are college instructors .
Answer:
The increasing number of students who are hooked on playing online mobile games (OMG) is alarming. As such, this study was realized to address the problem. This study assessed the gaming profile towards OMG and its relation to the academic performance of the engineering students of Eastern Visayas State University Tanauan Campus (EVSUTC). Specifically, the study investigated the correlation between student's number of hours spent on playing OMG (at school and home), commonly played OMG (at school and home), reasons for playing OMG and attitudes on playing OMG with academic performance utilizing Eta and Pearson r correlation analyses. A random sample of 134 student respondents were selected through purposive sampling of those who are playing OMG using their mobile phones. Descriptive correlational research design was utilized and a validated survey instrument was employed to gather the needed information. The findings revealed that majority of the students played mobile legends and spent mostly 2 hours playing OMG for a reason of boredom. The overall attitudes of the students on playing OMG were interpreted as Less Favorable (M=2.58, SD=1.13). Out of the independent variables being set in the study, the number of hours spent on playing OMG at home (r=-0.188, p=0.039) and commonly played OMG at school (r=0.203, p=0.045) were found significantly correlated with student's academic performance. Hence, the students' time spent on playing OMG at home and the type of games that students played at school have significant bearing to their academic performance. As such, delimiting student's usage of internet can be made to address the problem.
