Please someone help me with steps!
Answer:
96
Step-by-step explanation:
The formula for average = [tex]\frac{Sum \hspace{0.15cm} of\hspace{0.15cm} Items}{No.\hspace{0.15cm} of \hspace{0.15cm} Items}[/tex]
After taking 3 tests, the average is 88.
∴ 88 = Sum of Items / 3
Sum of Items = 88 x 3
= 264
This means Lenny's total score after 3 tests is 264.
We now have to calculate how many marks needs to be added to 264 so that after four tests, the average is 90.
Now the number of items (tests) = 4, and average = 90.
Let the marks required in 4th test = [tex]x[/tex]
∴ [tex]\frac{264 + x}{4} = 90[/tex]
264 + [tex]x[/tex] = 360
[tex]x[/tex] = 360 - 264
= 96
find the zeros of following quadratic polynomial and verify the relationship between the zeros and the coefficient of the polynomial f(x)=5x-4√3+2√3x²
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.
Dr. Shepherd - no, not that Dr. Shepherd, the other one-writes an order for ibuprophen 300 mg by mouth every 4 hours for pain. Pharmacy
dispenses 50 mg/2.5 mL. How many mL per dose?
000
a
b
C
d
5mL
50 ml
2.5 mL
15 mL
Answer: d
Step-by-step explanation:
divide 300 by 50 to get 6 then multiply 2.5 by 6 to get 15 therefore the answer is d 15ml
Find the equation of the line that is perpendicular to the graph of y=1/6x+3 and passes through (6.-6)
Answer:
y=−6x−36
Step-by-step explanation:
ez math
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥14), n=18, p=0.8
The probability is 0.2153.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]^{n}C_x* P^{x}* (1-p)^{n-x}[/tex]
n=18, p=0.8
So,
[tex]^{18}C_{14}* 0.8^{14}* (1-0.8)^{18-14}[/tex]
=0.2153
Hence, the probability is 0.2153.
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First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? Part A Part B Part C Part D Question 3(Multiple Choice Worth 5 points) (05.05 MC) Two systems of equations are shown below: System A System B 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 Which of the following statements is correct about the two systems of equations? They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A. The value of x for System B will be −5 times the value of x for System A because the coefficient of x in the first equation of System B is −5 times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −12 to the first equation of System A and the second equations are identical. Question 4(Multiple Choice Worth 5 points) (05.06 LC) To which graph does the point (−1, −4) belong? y ≤ −x + 4 y ≤ −x − 6 y ≤ 2x − 3 y ≤ 5x − 1 Question 5(Multiple Choice Worth 5 points) (06.04 MC) What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negative four. y = − (x − 3)2 + 1 y = − (x + 3)2 + 1 y = (x − 3)2 − 1 y = (x + 3)2 − 1 Question 6 (Fill-In-The-Blank Worth 5 points) (06.04 MC) A ball is thrown upward from the top of a building. The function below
The part that represents the solution to the inequality will be Part B shaded below first line and above second line.
How to depict the inequality?From the information given, the equation of the first line will be:
y - 3 = (-3 - 3/2 + 4)(x + 4)
y - 3 = -1(x + 4)
y + x = -4 + 3
x + y = -1
The equation of the second line will be:
y + 3 = -1(x + 4)
y = x + 4 - 3
y = x + 1
This is plotted on the graph attached.
From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.
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Help please!!! I will give 20 points to the correct answer !!!
Answer:
-3 and -7
Step-by-step explanation:
Factors of 21: 1, 3, 7, 21
3 and 7 add up to 10, but what about -10? Well, -3 * -7 is also 21, and -3 + -7 gives you -10.
Brainliest, please :)
Select the correct answer.
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
OA. The lines in a system cannot be parallel.
There are infinitely many solutions.
B.
OC. There is exactly one solution.
D. There is no solution.
Reset
Next
Answer:
Look below!
Step-by-step explanation:
From the picture, the answer is A.
From the points, calculate the slope using y2-y1/x2-x1
you will find that the slope is -1
parallel lines have the same slope
so y = -x+1 is the correct answer
now,
parallel lines never intersect
therefore, they have no solution.
Solve this for me please
Answer:
30.5
Step-by-step explanation:
here :
n represents the number of trials
p represents the probability of success
In a binomial distribution, The mean
is equal to the product of those two values.
In other words,
The mean = n × p
= 122 × 0.25
= 30.5
I need help please……
Answer:
f=- 6, x=-1
f = - 6, x=-3
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Simplify the expression by combining like
terms: Algebra 1
Answer:
The number in the green box should be 3.
Step-by-step explanation:
[tex]c + 4 {c}^{2} - 2 + 2c - {c}^{2} + 5 = 3 {c}^{2} + 3c + 3[/tex]
What is the equation of the line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5)?
y=x+9
y=-3x-4
y=-x-13
y-x-1
Rewriting the equation of the given line in slope-intercept form,
[tex]2x-3y=13\\\\2x-13=3y\\\\y=\frac{2}{3}x-\frac{13}{3}[/tex]
Thus, the slope of the given line is 2/3. Since perpendicular lines have slopes that are negative reciprocals of each other, we want to find the line with a slope of -3/2.
Substituting into point-slope form,
[tex]y-5=-\frac{3}{2}(x+6)\\\\y-5=-\frac{3}{2}x-9\\\\\boxed{y=-\frac{3}{2}x-4}[/tex]
2) Sarah takes a small business loan for
$25,000. The term for repayment is 60
months and the interest rate is 5.75%.
formula,
Use the loan amortization
what is the estimated monthly
payment?
Using it's formula, it is found that the estimate monthly payment is of $480.42.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.The parameters are given as follows:
P = 25000, n = 60, r = 0.0575.
Hence:
r/12 = 0.0575/12 = 0.00479167.
Hence the payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]
A = 480.42.
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Find f(g(x)) and g(f(x)).
f(x)=x²-2 and g(x)=√x+1
Answer:
1. x - 1
2. [tex]\sqrt{x^2-1}[/tex]
Step-by-step explanation:
[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]
[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]
Determine which of the following statements about the given triangles is true.
Answer:
The answer be the 2 one
Step-by-step explanation:
I do it and it come right
A woman when working with her takes 2 hours to complete the housework, and takes 3 hours when working alone How long would it take the daughter to complete the housework if working alone?
A) 6 hours
B) 2 hours
C) 4 hours
D) 9 hours
E) 0 hours
Answer:
6 hours for daughter alone Answer A
Step-by-step explanation:
Rate of mom to clean one house = 1 house /3 hrs = 1/3
rate of daughter = 1/x
Now find the time to clean one house with their combined rates for one house
1 / (1/3 + 1/x ) = 2 hrs
1/3 + 1/x = 1/ 2
x + 3 = 3/2 x
3 = 1/2 x
x = 6 hrs daughter alone
What is the distance between the given points?
Answer:
√85 which is approximately 9.2195
Step-by-step explanation:
Find the equation of the line that
3
is perpendicular to y ===x+1
and contains the point (9,12).
4
4
Y = 3 x + [ ? ]
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!Which products result in a difference of squares? Select three options. a (x minus y)(y minus x) b (6 minus y)(6 minus y) c (3 + x z)(negative 3 + x z) d (y squared minus x y)(y squared + x y) e (64 y squared + x squared)(negative x squared + 64 y squared)
Answer:
By comparing all the expressions with the formula (a - b)(a + b) = (a² - b²), we find that c, d and e options are correct.
Step-by-step explanation:
Concept: The condition is that, the product should result in a difference of squares. In mathematics, we have such a formula which is (a - b)(a + b) = (a² - b²). So, we need to compare all the options with this relation.
(x - y)(y - x) = -(x² - 2xy + y²)
(6 - y)(6 - y) = 36 - 12y + y²
(3 + xz)(-3 + xz) = (xz + 3)(xz - 3) = x²z² - 9 . This expression is correct
(y² - xy)(y² + xy) = [tex]y^{4} - x^{2} y^{2}[/tex]. This expression is correct
(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²) = [tex]4096y^{4} -x^{4}[/tex]. This expression is correct.
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Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][1, \infty)[/tex]Range: [tex](-\infty, -2][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
For each relation decide whether or not it is a function
Answer:
Relation 1: FunctionRelation 2: FunctionRelation 3: Not a functionRelation 4: functionStep-by-step explanation:
A function is defined so that for each input, there is no more than one output.
Mary is going to roll a six-sided die. What is the probability that the die lands on the number 3? Input your answer in fraction form
Answer:
added in the picture
Step-by-step explanation:
added in the picture
K
178
219
J
Which of the following statements is true?
A. sin(J)> cos(L)
B. sin(L)
C. tan(J)=tan(Z)
Using the sine and cosine ratios, the true statement is: D. sin(J) = cos(L).
What is the Sine and Cosine Ratios?Sine ratio: sin ∅ = opp/hyp.
Cosine ratio: cos ∅ = adj/hyp.
In the image given, find sin(J) using the sine ratio:
∅ = J
Opposite = KL = √(219² - 178²) = 127.6 [Pythagorean theorem]
Hypotenuse = LJ = 219
Sin(J) = 127.6/219
Find cos(L) using the cosine ratio:
∅ = L
Adj = KL = 127.6
Hypotenuse = LJ = 219
Cos(L) = 127.6/219
Therefore, the true statement is: D. sin(J) = cos(L).
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a drone traveling horizontally at 120m s over a flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground the trajectory of the package is given by x 120t y 4.9t 2 4500
The packet should be dropped 3636.55 horizontal meters before the target in order to hit the target
What is a Trajectory ?Trajectory is the path followed by a moving object when it is falling under gravitational force.
x = 90 t
y = -4.9 t²2 + 4500
t ≥ 0
y = 0
-4.9t² + 4500 = 0
4.9t²2 = 4500
[tex]\rm t = \sqrt {\dfrac{4500}{4.9}}[/tex]
t = 30.30 seconds
substituting the value to determine the horizontal distance
x = 120 * 30.30
x = 3636.55 meters
Therefore the packet should be dropped 3636.55 horizontal meters before the target in order to hit the target
The complete question is
a drone traveling horizontally at 120m s over a flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground the trajectory of the package is given by x 120t y 4.9t 2 4500 where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.
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URGENT
due in 1 hour! For 50 points!!
Pic is the question
Answer:
21 grandchildren
Explanation:
2/7ths + 5/7th = all
5/7ths = 15 <- divide both sides by 3 to get 1/7th
1/7th = 3 (multiply both sides by 7 to get "1")
7/7ths = 21
so, eva has 21 grandchildren
Answer:
21
Step-by-step explanation:
If 2/7th of Eva's grandchildren live in one location, we know that 5/7th (the remaining portion of Eva's grandchildren) must live in the other location
Wales + Australia = all of the kids (100% = 1/1 (which is equal to 7/7) )
Wales + Australia = 7/7ths
{x is the total number of kids}
Australia = 5/7ths
15 = [tex]\frac{5}{7}x[/tex] {multiply both sides by 7 to get rid of fraction}
105 = 5x {divide both sides to find 1x}
21 = x
check:
2/7th of 21 = 6
5/7th of 21 = 15 {which we know}
6 + 15 = 21
21 = 21
(TRUE)
So, Eva has 21 grandchildren
hope this helps!!
Multiply or divide the following expression: Reduce all answers to lowest terms. Factor the following completely.
Let f(x) = -x^2-4x+5
f(-3) = _______
f(3) + f(-3) = _______
A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,
f(-3) = -(-3)² - 4(-3) + 5
f(-3) = -9 + 12 + 5
f(-3) = 8
Now, the value of f(x) when the value of x is 3 is,
f(3) = -(3)²-4(3)+5
f(3) = - 9 - 12 + 5
f(3) = -16
further, the value of f(3) + f(-3) is,
f(3) + f(-3) = -16 + 8
f(3) + f(-3) = -8
Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
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Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?
Answer: y = 3x - 21
Step-by-step explanation:
If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).
The slope of AB is [tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]. This means that the slope of BC is 3.
Substituting into point-slope form,
[tex]y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}[/tex]
Please answer all the questions txxxx
What formula should be entered in A3 to compute A1 times B1?
A =A1 B1
B =A1/B1
=B1*83
=A1*B3
123
2
A B
2
10
8
8458
U375
C
The formula that should be entered in A3 is = A1 * B1
How to determine the formula?The question implies that:
A3 = A1 times B1
In mathematics, the term "times" means *
So, we have:
A3 = A1 * B1
Remove the variable A3
= A1 * B1
Hence, the formula that should be entered in A3 is = A1 * B1
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Two regular polygons X and Y are such that the number of sides of X is
3 more than the number of sides of Y. If the sum of the exterior angles
of X and Y is 117°, how many sides has .X?
Based on the indices of the regular polygons, the number of sides that X has is 8. See the computation below.
What is the analysis for the above solution?Assuming that X has G number of sides; and
Y has H number of sides, this means that:
G-H = 3 ...........1
Recall that the formula for the exterior angles is:
360/n; where n is number of sides
X = 360/G
Y = 360/H
(360/G) + (360/H) = 117°.......2
Solving 1 and 2 simultaneously, we obtain:
G= 8 and
H = 5
Thus, X has 8 sides.
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