Answer:
The correct answers are:
[tex]\sqrt{0}=0\\\sqrt{1.44} = \pm 1.2\\\sqrt{2.25} = \pm 1.5\\\sqrt{3.24} = \pm 1.8\\\sqrt{4.41} = \pm 2.1\\\sqrt{5.29} =\pm 2.3[/tex]
Step-by-step explanation:
Given the function:
[tex]y=p(x)=\sqrt{x}[/tex]
That means, the value that we give as input i.e. the value of x is square rooted and given as output.
Input is x and output is [tex]\sqrt x[/tex].
Now, calculating the outputs for different values of x:
1. x = 0, the square root of 0 is always 0.
so, y = p (0) = 0
2. x = 1.44
[tex]y = p(1.44)=\sqrt{1.44} \\\Rightarrow \sqrt{\dfrac{144} {100}}\\\Rightarrow \pm \dfrac{12} {10} = \pm 1.2[/tex]
Similarly other square roots can be calculated:
3. x = 2.25
[tex]y = p(2.25)=\sqrt{2.25} \\\Rightarrow \sqrt{\dfrac{225} {100}}\\\Rightarrow \pm \dfrac{15} {10} = \pm 1.5[/tex]
4. x = 3.24
[tex]y = p(3.24)=\sqrt{3.24} \\\Rightarrow \sqrt{\dfrac{324} {100}}\\\Rightarrow \pm \dfrac{18} {10} = \pm 1.8[/tex]
5. x = 4.41
[tex]y = p(4.41)=\sqrt{4.41} \\\Rightarrow \sqrt{\dfrac{441} {100}}\\\Rightarrow \pm \dfrac{21} {10} = \pm 2.1[/tex]
6. x = 5.29
[tex]y = p(5.29)=\sqrt{5.29} \\\Rightarrow \sqrt{\dfrac{529} {100}}\\\Rightarrow \pm \dfrac{23} {10} = \pm 2.3[/tex]
Hence, The correct answers are:
[tex]\sqrt{0}=0\\\sqrt{1.44} = \pm 1.2\\\sqrt{2.25} = \pm 1.5\\\sqrt{3.24} = \pm 1.8\\\sqrt{4.41} = \pm 2.1\\\sqrt{5.29} =\pm 2.3[/tex]
The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of the original dosage? Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve.
Answer:
It will take 4.84 hours for the drug to decay to 93% of the original dosage.
Step-by-step explanation:
We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.
The given exponential model is: [tex]A = A_0 e^{kt}[/tex]
Now, we know that A becomes half after 47 hours which means that;
[tex]A = 0.5 A_0[/tex]
Using this in the above equation we get;
[tex]A = A_0 e^{kt}[/tex]
[tex]0.5 A_0 = A_0 e^{(k\times 47)}[/tex] where t = 47 hours
[tex]\frac{0.5 A_0}{A_0} = e^{(47k)}[/tex]
[tex]0.5 = e^{47k}[/tex]
Taking log on both sides we get;
[tex]ln(0.5) = ln(e^{47k})[/tex]
[tex]ln(0.5) =47k[/tex]
[tex]k = \frac{ln(0.5)}{47}[/tex]
k = -0.015
Now, the time it will take for the drug to decay to 93% of the original dosage is given by;
[tex]0.93 = e^{kt}[/tex] where t is the required time
[tex]0.93 = e^{(-0.015 \times t)}[/tex]
Taking log on both sides we get;
[tex]ln(0.93) = ln(e^{-0.015t})[/tex]
[tex]ln(0.93) =-0.015t[/tex]
[tex]t = \frac{ln(0.93)}{-0.015}[/tex]
t = 4.84 hours
Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.
Need help solving. Prefer you show each step in solving.
Answer:
55
Step-by-step explanation:
For PQ and RS to be parallel, the two degrees must be equal.
3x - 65 = 2x - 10
(3x - 65) + 65 = (2x - 10) + 65
3x = 2x + 55
(3x) - 2x = (2x + 55) - 2x
x = 55
Clara would like to buy a toy for her baby sister that sells for
$12.49. How much will the toy cost after 13% tax? (Round to the nearest
cent)
A skateboard ramp has a slope of 5/6. What is the measure of the angle the ramp forms with the ground to the nearest degree
Answer:
39.8°
Step-by-step explanation:
We know slope is rise over run. That would mean our right triangle would have a horizontal leg of 6 and a vertical leg of 5. From there we use tan∅ to help solve ∅:
tan∅ = 5/6
∅ = tan⁻¹(5/6)
∅ = 39.8056
cot(45-A)=tan2A+ sec2A
Answer:
See picture.
Step-by-step explanation:
help i will give brainliest
Answer:
93°Step-by-step explanation:
[tex]\dfrac{|AC|}{\sin B}=\dfrac{|AB|}{\sin C}\\\\\dfrac{9}{\sin38^o}=\dfrac{11}{\sin C}\\\\\dfrac{\sin38^o}9=\dfrac{\sin C}{11}\\\\\sin C=\frac{11}9\sin38^o =\frac{11}9\cdot0,6157=0,7525(2)\\\\\sin C\approx0,7525\quad\iff\quad |\angle C|\approx48^o48'\\\\|\angle A|=180^o-|\angle B|-|\angle C|\\\\|\angle A|=180^o-38^o-48^o48'\\\\|\angle A|=93^o12'\approx93^o[/tex]
Angles that measure between 0 and 90 degrees are called_?
Answer:
Acute angles.
Step-by-step explanation:
Acute angles are from 0-90 degrees.
Hope this helps :)
Answer:
Acute angles
Step-by-step explanation:
Acute angles are measured between 0 and 90 degrees.
A polynomial is factored using algebra tiles. An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 15 tiles are in the Product spot in 3 columns with 5 rows: 1 is labeled + x squared, 2 are labeled + x, the 4 tiles below + x squared are labeled negative x, and the 8 tiles below the + x tiles are labeled negative. Which polynomial was factored? x2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4
Answer:
x² - 2x - 8
Step-by-step explanation:
Algebra tiles are tiles used to represent variables or numbers and are rectangular or square shaped.
1 is labeled + x squared, this gives x²
2 are labeled + x, this gives +x × 2 = +2x
4 tiles below + x squared are labeled negative x, this gives - x × 4 = - 4x
8 tiles below the + x tiles are labeled negative, this gives -1 × 8 = -8
Therefore to get the polynomial that was factored, we add all the terms. This gives :
+x² + (+ 2x) + (-4x) + (-8) = x² + 2x - 4x - 8 = x² - 2x - 8
Answer:
The answer is A, and if edge is being weird the answer is x^2-2x-8, Have fun dreamers!
Step-by-step explanation:
please help thanks !
Answer:
point slope form: y-3=[tex]-\frac{3}5}[/tex](x+2)
slope-intercept form: y=[tex]-\frac{3}{5}[/tex]x+[tex]\frac{9}{5}[/tex]
Step-by-step explanation:
so to find point-slope form, you first have to find the slope of the line
--slope =[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]=[tex]\frac{0-3}{3+2} =-\frac{3}{5}[/tex] (you have to use the two points shown: (-2,3) and (3,0) to plug in for y1, y2, x1, and x2 to find the slope.)
so your slope is [tex]-\frac{3}{5}[/tex].
Now all you have to do is use one of the points (-2,3) to sub in for y1 and x1 in the point-slope form equation.
Therefore, you get y-3=[tex]-\frac{3}{5}[/tex](x+2) for point-slope form.
Now for slope-intercept form, you already have the slope because you found it to complete the equation for point slope form
slope = [tex]-\frac{3}{5}[/tex]
Now slope intercept form is y=mx+b, where m is the slope and b is the y-intercept.
So, far we have y=[tex]-\frac{3}{5}[/tex]x+b
the easiet point to use for the x and y values is (3,0)
so, lets substitute: 0=[tex]-\frac{3}{5}[/tex](3)+b, which becomes 0=[tex]-\frac{9}{5}[/tex]+b
add [tex]-\frac{9}{5}[/tex] to both sides to get b=[tex]\frac{9}{5}[/tex]
Now you have both the slope and the y-intercept so you can now write the line in slope-intercept form.
You get [tex]y=-\frac{3}{5}x +\frac{9}{5}[/tex].
You are getting on an elevator that is already filled with several people. You wonder if your weight will put the elevator over the maximum weight limit. You know that your weight is 132 pounds. In the equation below, p is the weight of all the people already on the elevator, and t is the total weight inside the elevator after you get on. The relationship between these two variables can be expressed by the following equation: t=p+132. What is the dependent variable?
A.The total weight inside the elevator after you get on.
B.The weight of all the people already on the elevator.
Answer:
A
Step-by-step explanation:
T is the dependent variable
a dependent variable means it depends on something so if a number changes it will change the end result for T.
T is dependent on P since if the weight on the elevator changes the total weight will change. That is what makes it dependent.
Answer:
They are both dependent variables.
Step-by-step explanation:
I did this on Khan Academy and it worked.
can someone help me answer this
Answer:
A
Step-by-step explanation:
A magazine has 96 pages. There are ads on 75% of the pages. How many pages don't have ads?
Hey there! :)
Answer:
24 pages.
Step-by-step explanation:
Calculate how many pages 75% of 96 is:
96 × 0.75 = 72 pages.
Find how many pages do not have ads by subtracting the amount that have ads from the total:
96 - 72 = 24 pages.
Therefore, 1/4 of 96 or 24 pages do not have ads.
Explain how to determine the solutions to a quadratic equation, graphically.
Answer:
In a nutshell, you have to graph the parabola. Where the parabola intersects the x-axis is the solutions to the quadratic equation.
Approximately how many seconds would it take for the Mississippi River( 16,790 cubic meters per second) to fill the volume of the Gulf of Mexico(2,434,000,000,000,000)? Choice A : 1 *10^9 Choice B : 1* 10^10 Choice C : 1 * 10^11
Answer:
1 * 10^11
Step-by-step explanation:
Take the gulf of mexico and divide by the rate to get the number of seconds
2,434,000,000,000,000 / 16790
Change each to scientific notation
2 * 10 ^15/ 1.6 *10^ 4
Rounding
2 * 10^15 / 2 * 10^4
Dividing the numbers 2/2 =1
Dividing the exponents means subtracting the powers = 10 ^(15-4) = 10 ^1
1 * 10^11
hi can you help me i can’t move forward if i skip this question.
Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown. To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C. Which figures could Brian be constructing? equilateral triangle MNQ inscribed in circle C equilateral triangle ANP inscribed in circle C regular hexagon AMNBPQ inscribed in circle C square MNPQ inscribed in circle C square ANBQ inscribed in circle C
Answer:
equilateral triangle ANP inscribed in circle C
regular hexagon AMNBPQ inscribed in circle C
Step-by-step explanation:
By looking through our choices, we can eliminate which choices could be wrong and which choices could be right.
Δ MNQ does form a triangle, however, it DOES NOT form a equilateral triangle.
Δ ANP does form a triangle and it is ALSO an equilateral triangle.
Hexagon AMNBPQ does form a hexagon and it is ALSO a regular polygon as we can see all the sides and angles within the polygon are congruent to one another.
MNPQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.
ANBQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.
By looking through our observations, we can conclude that Δ ANP and hexagon AMNBPQ are the correct choices.
- 2022 Edmentum
The equilateral triangle ANP inscribed in circle C and the regular hexagon AMNBPQ inscribed in circle C. Then the correct options are B and C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C.
He labeled the points of intersection of the two circles as shown.
The equilateral triangle ANP inscribed in circle C and the regular hexagon AMNBPQ inscribed in circle C.
Then the correct options are B and C.
The complete question is attached below.
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ5
Abigail wants to make a tapestry in the shape of a parallelogram that is 24 inches across the bottom and 36 inches tall. If she pieces smaller similar parallelograms that are 2 inches at the base and 3 inches tall, how many will she need to make the tapestry?
Answer:
144
Step-by-step explanation:
Abigail wants to produce a tapestry that will be in the shape of a parallelogram
The tapestry is 24 inches across the bottom and 36 inches tall
She pieces smaller simlar parallelograms that are 2 inches wide and 3 inches tall
The first step is to find the area of the whole tapestry
Area = base × height
Base= 24 inches
Height= 36 inches
Area= 24×36
= 864 square inches
The next step is calculate the area of the smaller pieces
Area= base × height
Base= 2 inches
Height= 3 inches
Area= 2×3
= 6 square inches
Therefore, the value needed to produce the tapestry can be calculated by dividing the area of the whole tapestry by the area of the smaller pieces
= 864/6
= 144
Hence Abigail will need 144 smaller similar parallelograms to make the tapestry.
Answer:
144
Step-by-step explanation:
Of the four choices given, which two, when written as a system, have a solution of (–4, 5)? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. 2 x + y = negative 3 Negative 2 x + y = negative 3 A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8. 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. Negative 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8. Negative 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8.
Answer:
The answer is a.
Step-by-step explanation:
Hope this helps!
Answer:
It's A)
Step-by-step explanation:
Uma caixa na forma de um cubo tem medidas de arestas igual a 10,5 cm. O volume dessa caixa corresponde à: * 1 ponto a) 1157,625cm³ b) 1157,6cm³ c) 11,5627cm³ d) 115,7625cm³
Answer:
(A) [tex]1157,625$ cm^3[/tex]
Step-by-step explanation:
s = 10,5 cm.
Volume do cubo = [tex]s^3[/tex]
[tex]=10,5^3\\=1157,625$ cm^3[/tex]
O volume do cubo é [tex]1157,625$ cm^3[/tex]
I need help!!!
Use the rational zero theorem, which of the following could not be a rational zero of: 6x^5+ax^3=bx+12? 1/2 -3/4 -2
Answer: x = -3/4 can not be a rational zero of the polynomial.
Step-by-step explanation:
We have the polynomial:
6x^5 + ax^3 -bx -12 = 0.
The theorem says that:
If P(x) is a polynomial with integer coefficients, and p/q is a zero of P(x) then p is a factor of the constant term (in this case the constant term is -12) and q is a factor of the leading coefficient (in this case the leading coefficient is 6.).
The factors of -12 (different than itself) are (independent of the sign).
1, 2, 3, 4 and 6.
So p can be: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6.
The factors of 6 are:
1, 2 and 3, so q can be 1, -1, 2, -2, 3, -3.
Then the option that can not be a zero of the polynomial is
x = -3/4
because the number in the denominator must be a factor of the leading coefficient, and 4 is not a factor of six.
John is standing at the point (-4,-8) and his friend Victor is standing at the point (-4,12). Find the distance between them. A. 20 units
B. -20 units
C. 28 units
D. -28 units
Answer:
20 unitssolution,
Let the points be A and B
A(-4,-8)--->(X1,y1)
B(-4,12)---->(x2,y2)
Now,
[tex]ab = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \: \: \: = \sqrt{ {( - 4 - ( - 4)}^{2} + 12 - ( - 8) ^{2} } \\ \: \: \: \: = \sqrt{ {( - 4 + 4)}^{2} + {(12 + 8)}^{2} } \\ = \: \: \: \: \sqrt{ {(0)}^{2} + {(20)}^{2} } \\ \: \: \: \: = \sqrt{0 + 400} \\ \: \: \: = \sqrt{400} \\ \: \: = \sqrt{ {(20)}^{2} } \\ \: \: = 20 \: units[/tex]
Hope this helps..
Good luck on your assignment...
What is the distance from point (-5,-4) to (9,2)?
Answer:
radical 232
Step-by-step explanation:
14^2+6^2=x^2
196+36= 232
radical 232
Answer: Distance is 15.2
Step-by-step explanation:
[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]
[tex](x2-x1) = (9 - -5) = 14[/tex]
[tex](y2-y1) = (2 - -4) = 6[/tex]
[tex](14)2 + (6)2 = 196 + 36 = 232[/tex]
[tex]\sqrt{232} =15.2315[/tex]
round to the nearest 10th
PLEASE HELP ASAP WITH MATH
Answer:
t =5
g = 15
Step-by-step explanation:
t = tennis balls
g = golf balls
70 = 5t+3g
85 = 2t+5g
Multiply the first equation by -2
-2(70 = 5t+3g)
-140 = -10t -6g
Multiply the second equation by 5
5(85 = 2t+5g)
425 = 10t + 25g
Add these new equation together to eliminate t
-140 = -10t -6g
425 = 10t + 25g
-------------------------------
285=0t+19g
Divide by 19
285/19 = g
15 = g
Now find t
85 = 2t+5g
85 = 2t +5(15)
85 = 2t + 75
10= 2t
t =5
Let the cost of a can of tennis balls be $x and that of a sleeve of golf balls be $y.
5x + 3y = 70
2x + 5y = 85
(5x + 3y) x 2 = 70 x 2
10x + 6y = 140
(2x + 5y) x 5 = 85 x 5
10x + 25y = 425
10x + 25y -10x - 6y = 425 - 140
19y = 285
y = 15
2x + 5y = 85
2x + 75 = 85
2x = 10
x = 5
Therefore the cost of a sleeve of golf balls is $15 and that of a can of tennis balls is $5.
Each unit on the coordinate grid represents 1 yard. The rectangular pool and triangular hot tub shown are both in need of covers. How much total material is needed to cover both? square yards
Answer:
29 square yards
Step-by-step explanation:
see attachment for the graph
Vertices of rectangular pool are A(3,2),B(7,8),C (4,10), and D (0,4).
AB=[tex]\sqrt{(7-3)^{2}+(8-2)^{2}}= \sqrt{16+36}=\sqrt{52}[/tex] yard=CD
BC= [tex]\sqrt{(7-4)^{2}+(8-10)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]yard=DA
In order to find the area of rectangular pool =Length × Breadth
=√52 ×√13=13×2=26 sq. yard
Vertices of triangle given are: P(5,2),Q(7,2) and R(7,5).
PQ= 2 units, QR= 3 units
Area of right triangle PQR=1/2 ×PQ×PR
=1/2×2×3= 3 sq. yards
Next is to find total material needed to cover( that includes bot rectangular pool and triangular hot tub)
= Area of rectangle + Area of right triangle
=26+3=29 square yards
Answer:
29
Step-by-step explanation:
I just did my homework
Help me !!! please 50 points!!
A system of equations is shown below: 1. Equation A: 4c = d − 8 Equation B: c = 5d + 8 Which of the following steps should be performed to eliminate variable d first? (5 points)
Multiply equation B by 4. Multiply equation A by −5. Multiply equation A by 4. Multiply equation B by 5. 2 . A system of equations is shown below: n = 3m + 7 n − 2m = 1 What is the solution, in the form (m, n), to the system of equations? (5 points)
(3, 7) (1, 8) (−3, −2) (−6, −11) 3. A system of two equations is shown below: Equation C: a = 3b + 6 Equation D: a = 7b − 1 What value of a can be substituted into equation D to solve the system of equations? (5 points)
Answer:
the first step to eliminate d is to multiply equation B by 5
second :(m,n) (-6,-11)
value of a can be substituted into equation D to solve the system of equations is 7b-1
Step-by-step explanation:
first equation:
4c=d-8 or 4c-d=-8
c=5d+8 or c-5d=8
so the first step to eliminate d is to multiply equation B by 5
second equation :
n=3m+7 or n-3m=7
n-2m=1
n-3m=7
solve :
1-eliminate n by subtracting two equation : : n-2m-(n-3m)=1-7
-2m+3m=-6
m=-6
substitute m: n-3(-6)=7 , then n+18=7
n=7-18=-11
third :
a=3b+6 or a-3b=6
a=7b-1
find a
a-3b=6
value of a can be substituted into equation D to solve the system of equations is 7b-1
Enter values to complete the table below.
Answer: The answers are in the steps
Step-by-step explanation:
x y value of y/x
-3 -3 1
1 1 1
3 3 1
Which is the graph of f(x)=2(3) to the x power?
Answer:
Use a graphing calc.
Step-by-step explanation:
Find the median of the distribution
Frequences
Mark
0,1,2,3,4,5
Answer:
2.5
Step-by-step explanation:
The median is the middle value of the data set. If there is no exact middle value then it is the average of the 2 values either side of the middle.
0 , 1 , 2 , 3 , 4 , 5
↑ middle of data
Thus median = [tex]\frac{2+3}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5
Diana serves 8 kg of fried rice for 12 persons. How many persons can eat 20 kg of
fried rice?
Answer:
30 persons
Step-by-step explanation:
Let's create a proportion using the following setup:
persons/rice=persons/rice
We know that 12 persons can eat 8 kilograms of fried rice.
12 persons/ 8 kg of rice= persons/rice
We also know that x (unknown) persons can eat 20 kilograms of fried rice.
12 persons/ 8 kg of rice= x persons/ 20 kg of rice
12/8=x/20
x is being divided by 20. The inverse of division is multiplication. Multiply both sides of the equation by 20.
20(12/8)=(x/20)20
20*12/8=x
20*1.5=x
30=x
30 persons can eat 20 kilograms of fried rice.
Answer:
30 people
Step-by-step explanation:
1) Set up a proportion, 8kg/12 = 20kg/x
2) Do cross multiplication to solve for x
3) x = 30 people
Two fair dice are rolled 3 times and the sums of the numbers that come up is recorded. Find the probability of these events. A) the sum 10 on each of the three rolls? B) the sum is 10 exactly twice in three rolls?
Answer:
A) P(10 on three rolls) = 1/1728 = 0.0005787
B) P(10 in two of three rolls) = 11/1728 = 0.0063657
Step-by-step explanation:
Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.
To find a sum of 10, the cases are:
(4,6), (5,5) and (6,4).
So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:
P(10) = 3/36 = 1/12
A)
If we want the sum of 10 in each of the three rolls, the probability is:
P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787
B)
If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:
P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12
So we have:
P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)
P(10 in two of three rolls) = 11/1728 = 0.0063657