The non-extraneous solutions are -6 and -5.
How to find non-extraneous solutions?By checking these solution values in the original equation.
[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]
Thus, -6 is non-extraneous.
[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]
Thus, -5 is non-extraneous.
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The following shape is only based on squares, semicircles and quarter circles. Find the Area and Perimeter of the shaded part. Answers in terms of pi.
The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have shown a square in which a one-fourth circle is shown and making an ellipse.
The perimeter of the circle = 2πr = 2π(8) = 16π cm
The perimeter of the one-fourth is circle = (16π)/4 = 4π cm
The perimeter of 2 one-fourth circle = 2(4π) = 8π cm
The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm
The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm
The area of the shaded region = 2(16π - 32) = 36.53 square cm
or
= 32(π - 2)cm²
Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
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A baker is making 41/8 batches of cookies. If each batch requires 3/4 of a stick of butter, how much butter will he need for all 41/8?
Answer: 123/32 or 3 27/32 sticks
Step-by-step explanation:
41/8*3/4 =
41*3/8*4 =
123/32 =
3 27/32
Find the exact values of the trigonometric functions of theta if theta terminated in quadrant 4. Tangent of theta = -3/4
Answer:
sin=-3/5
cos=4/5
tan-3/4
csc=5/-3
sec=5/4
cot=4/-3
Step-by-step explanation:
you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.
Please give an answer and solution.
Using proportions, it is found that 78 students would prefer long jump.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Out of 300 students, 26% would prefer long jump, hence the amount is given by:
n = 0.26 x 300 = 78 students.
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help please. been stuck on this for the past hour!!
Answer:
A) 100 terms, B) 63 terms, C) 101 terms==========================
Given sequences:A) 1, 4, 4², ..., 4⁹⁹B) 11, 15, 19, 23, ..., 259C) 44, 45, 46, ..., 144To findThe number of terms.SolutionA) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:
4⁰, 4¹, 4², 4³, ... , 4⁹⁹The number of terms from zero to 99 is:
99 + 1 = 100B) This is a AP with the first term of 11 and common difference of 4.
The nth term equation is:
aₙ = a₁ + (n - 1)dSubstitute the values and solve for n:
259 = 11 + (n - 1)*44(n - 1) = 259 - 114(n - 1) = 248n - 1 = 248/4n - 1 = 62n = 63C) Same as above, the sequence is AP, with the first term 44 and common difference 1.
Applying the nth term formula:
144 = 44 + (n - 1)*1n - 1 = 144 - 44n - 1 = 100n = 101Write this ratio as a fraction in simplest form without any units. 28 quarts to 9 gallons You can use the table below to help convert the units. Length Weight Capacity (Volume) 1 foot 12 inches 1 yard = 3 feet 1 pound = 16 ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts
Answer:
7/9
Step-by-step explanation:
In order to write the fraction without any units (as a pure number), we must have units in the numerator and denominator that are the same. Then the units cancel.
Convert to gallonsWe are given the conversion ...
4 quarts = 1 gallon
Multiplying by 7, we see ...
28 quarts = 7 gallons
RatioThis lets us write the desired fraction as ...
(28 quarts)/(9 gallons) = (7 gallons)/(9 gallons) = 7/9
The ratio in simplest form is 7/9.
Mia counts on in steps of 100 she starts at 946. Write the next number she says
Answer:
100+946=1046
Ao the next no. Is 1046
Question An old vinyl record is played on a turntable that turns at a rate of 45 rotations per minute. Find the angular speed in radians per second. Give your answer as a fraction and do not include units. Keep your answer in terms of if necessary.
The angular speed of the turntable is = 4.7 rad/sec.
Calculation of angular speedAngular speed can be defined as the rate at which angular displacement changes with respect to time.
Speed can be defined as the distance traveled by an object at a particular time interval.
The rate of rotation of the turntable = 45 rotations per minute.
That is, the time taken to complete one rotation in seconds = 1/45 ×60sec = 1.34secs
This is taken to be the period of rotation (T)
Therefore, the angular speed is calculated using the formula, 2π/T
= 2×3.14/1.34 = 4.7 rad/sec.
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Is the function one-to-one? {(-19,9),(-2,9),(-7,-16)}
Answer:
no
Step-by-step explanation:
the y coordinate 9 repeats twice
Geometry Perimeter and area
A)
B)
C)
Use a graphing calculator to find the value of the correlation coefficient r and determine if there is a strong correlation among the data.
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
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What is the value of x in the equation three-fourths (one-fourth x 8) minus (one-half x 2) = startfraction 3 over 8 endfraction (4 minus x) minus one-fourth?
The value of x in the equation is x=-44.
The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].
An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.
Firstly, apply the distributive property as a(b+c)=ab+ac and get
[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]
Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as
[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]
Further, simplify the above expression by taking L.C.M as
[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]
Then, multiply both sides with 4 and get
[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]
Furthermore, cross multiply both sides and get
[tex]x=-44[/tex]
Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.
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Simplify the slope of AC.
B (b,c)
C (a+b, c)
Al(0, 0)
D (a,0)
Enter the value that
belongs in the green box.
Slone Formula: Y2-1
[?]
+b
Answer:
[tex] \boxed{\bf \cfrac{\boxed{c}}{\boxed{a }+ b}} [/tex]
Step-by-step explanation:
Given:
[tex] \tt (x_1,y_1) : A (0,0)[/tex]
[tex]\tt (x_2,y_2) : C (a+b, c) [/tex]
[tex]\boxed{\tt Slope= \cfrac{y_2,y_1}{x_2,x_1}} [/tex]
[tex]\tt \cfrac{c - 0}{a + b - 0} [/tex]
Add zero (Anything plus zero gives itself).
[tex] \tt \cfrac{c}{a + b + 0} [/tex]
[tex]\tt \cfrac{c}{a + b} [/tex]
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
Leroy wants to tile the floor in his kitchen. The floor is 10 feet by 12 feet. Each tile is 6 by 8 inches. How many tiles will he need to finish the job?
a. 124 tiles
b. 360 tiles
c. 412 tiles
d. 514 tiles
Answer:
B
Step-by-step explanation:
Convert everything to inches first
The floor is 120 inches by 144 inches
The floor can be covered with (120/6) * (144/8) tiles
(120/6) * (144/8) = 20*18=360 tiles, hence b.
How to solve the inequality of ...
Answer:
x<3−√11 /2 or x > 3 +√11/2
Step-by-step explanation:
Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Which linear inequality is represented by the graph?
Answer: 3
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each value to the correct expression.
8
5
0
27
15
22
Using PEDMAS, the value of each expressions are:
a. 1 + 5 × 2 + (1 + 3)² = 27
b. 0.25 × 4³ - 1 = 15
c. 4 + 8(1/4 + 2) = 22
How to Apply PEDMAS in Evaluating an Expression?PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.
Let's evaluate the expressions using PEDMAS:
a. 1 + 5 × 2 + (1 + 3)²
1 + 5 × 2 + (4)²
1 + 5 × 2 + 16
1 + 10 + 16
= 27
b. 0.25 × 4³ - 1
0.25 × 64 - 1
16 - 1
= 15
c. 4 + 8(1/4 + 2)
4 + 8(9/4)
4 + 18
= 22.
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Estimate the average rate of change from x=4 to x=5 .
Answer:
Average rate of change = 4/3
Step-by-step explanation:
We have to calculate the average rate of change of the graph at x = 2 to x = 5.
From the graph attached,
At x = 2,
f(2) = 3
At x = 5,
f(5) = 7
Since, average rate of change of the function between x = a and x = b is defined by,
Average rate of change = f (b)-f (a) / b - a
Therefore, average rate of change of the function represented by the graph will be =7-3/5-2
= 4/3
calculate a four day moving average for a price of the stock for the end of day 7.day1=32,day2=56,day3=50,day4= 60, day5=59 ,day6 =55,day7=59,day8=63
The moving average of the stock for the end of day 7 is 53
How to determine the averageNote that
Average = Day 1 + Day 2 + Day3 + Day 4 = Day 5 + Day 6 + Day 7/ 7
We have
Average = 32 + 56 + 50 + 60 + 59 + 55 + 59 /7
Average = 371/ 7
Average = 53
Therefore, the moving average of the stock for the end of day 7 is 53
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(b) Solve the trigonometric equation and verify that its solutions are the x-coordinates of the maximum and minimum points of f. (Calculus is required to find the trigonometric equation. For each solution, give an exact answer and then round to four decimal places. Enter your answers from smallest to largest.)
The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.
We have
[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]
[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]
[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x) - 1 = 0[/tex]
[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]
In the interval [tex]0\le x< 2\pi[/tex], we have
[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]
and
[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]
In order from smallest to largest, that's
[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]
The solution to the Trigonometric equation is given as below.
What is a Trigonometric equation?A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.
The solution to the above problem is?The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.
Thus,
18 sin (x) cos (x) - 9 sin (x) = 0
8 sin(x) = 0 or 2 cos (x) - 1 = 0
Sin (x) = 0 or Cos (x) = 1/2
Given the interval of 0 ≤ x ≤ 2π
→ Sin (x) = 0 → x = 0 or x = π
and
Cos (x) = 1/2
→ x = π/3 or x = 5π/3
Arranging the values from the smallest to the largest, we have:
x = 0 or x = π/3
x = π or x = 5π/3
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A 20-foot ladder is leaning against a building. The ladder forms an angle of 55" with the ground.
Part A: How far away from the building is the bottom of the ladder? Round the answer to the nearest tenth.
Part B: How far up the building does the ladder go? Round the answer to the nearest tenth.
Part C: If the ladder is repositioned, and the base is now 9 feet from the building, what is the new angle that the ladder makes with the ground? Round the answer to the nearest tenths place.
Pls help! Geometry
What is the perimeter of the shape above?
What is the area of the shape above?
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
What is the range of the function f(x)=1/2√x?
A. all real numbers
B. all real numbers greater than but not equal to 0
C. all real numbers less than or equal to 0
D. all real numbers greater than or equal to 0
Answer:
D. all real numbers greater than or equal to 0
Step-by-step explanation:
The range is the set of y-values.
A recent survey found that 4% of the population of the United States is unemployed. If Charlotte, North Carolina, has 26,440 unemployed, what is the population of Charlotte?
The population of Charlotte is 661,000.
What is the population of Charlotte?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The population of Charlotte = number of unemployed people / percentage of unemployed
26,440 / 0.04 = 661,000
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Factoring Inequalities,
Please help as I do not know how to progress after this.
The factored inequality is [tex]x^2-3x+6\geq 0[/tex]
Factoring InequalitiesThe given inequality is:
[tex]-x^2+3x-6\leq 0[/tex]
This can be further simplified as:
[tex]-(x^2-3x+6)\leq 0[/tex]
The inequality can be re-written as:
[tex]x^2-3x+6\geq 0[/tex]
Since the question does not state that we should solve the inequality, the simplest we can get after factoring is [tex]x^2-3x+6\geq 0[/tex]
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Consider the limaçon with equation r = 3 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop?
If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.
Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.
Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.
formula of polar graph is similar to r= a+ b cos (θ).
Case 1. If a<b or b/a>1
then the curve is a limacon with inner loop.
Case 2. If a>b or b/a<1
Then the limacon does not have an inner loop.
Here given that [tex]r=3+4cos[/tex] (θ)
It is observed that , a<b or b/a>1
Therefore the curve is limacon with an inner loop.
Hence because b/a>1 the curve is a limacon with an inner loop.
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Answer:
The answer is B
Step-by-step explanation:
50 POINTS! Should I buy an Eric Emanuel hoodie or a Cdg Hoodie
Answer:
Step-by-step explanation:
In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests,
Paul has scored 91, 88, and 93 on the first three. What range of scores on the fourth test will give Paul a C for the
semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.
Express your answer in interval notation.
Answer:
[8, 44]
Step-by-step explanation:
The average of equally-weighted values is their sum divided by their number.
SetupFor some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...
70 ≤ (91 +88 +93 +x)/4 ≤ 79
SolutionMultiplying by 4, we have ...
280 ≤ 272 +x ≤ 316
8 ≤ x ≤ 44 . . . . . . . . . . subtract 272
Paul will get a C if his fourth test score is in the interval [8, 44].
Rhoda is asked to graph this system of equations:
5x-6y=4
3y+2x=7
How many times will the lines intersect?
A. The lines will not intersect
B. The lines will intersect once.
C. There is no way to tell without graphing the lines first.
D. The lines will intersect infinitely many times, because they are identical.
Answer back fast!
I will award Brainliest too!
Answer: B. The lines will intersect once.
Step-by-step explanation:
Multiplying the bottom equation by 2, we get 6y+4x=14.
Adding this to the first equation, this gives 9x=18, and thus x=2.
Therefore, since this means there will be 1 solution, the lines will intersect once.
A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:
P(At least 8 have the disease) ≈ 0.4378P(At most 4 have the disease) ≈ 0.0342How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
X = B(n,p)
The probability that out of n trials, there'd be x successes is given by
P(X=x) = [tex]^nC_xp^x(1-p)^{n-x}[/tex]
Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.
Let we say
Success= Probability of a diseased person tagged as diseased by the clinic
Failure = Probability of a diseased person tagged as not diseased by the clinic.
Then,
P(Success) = p = 72% = 0.72 (of a single person)
P(Failure) = q = 1-p = 0.28
Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)
Calculating the needed probabilities, we get:
a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)
P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]
P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378
b) P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)
P (X ≤ 4) =
[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]
[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]
P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719
P (X ≤ 4) = 0.0342
Thus,
The probabilities of considered events are:
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