The Solution:
We are required to find the force.
[tex]\begin{gathered} F\propto a \\ \text{This implies that:} \\ F=ka \end{gathered}[/tex]In this case,
F= force=30 N
a = acceleration = 3m/s
k = constant of proportionality = ?
We shall find the constant k by substituting the above values in the formula.
[tex]\begin{gathered} F=ka \\ 30=k(10) \end{gathered}[/tex]Dividing both sides by 10, we get
[tex]k=\frac{30}{10}=3[/tex]So,
The formula for finding Force is:
[tex]F=3a[/tex]To find the Force when a = 3m/s, we shall substitute 3 for a in the formula.
[tex]F=3\times3=9N[/tex]Therefore, the correct answer is 9 N
In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?A. CL=LDB. AL>LBC. CL⋅LD=ABD. BL>LA
The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L. In this case this means CL = LD
A triangle has 2 sides of length 15 and 19 what is the smallest possible whole number length for the 3rd side
We have a triangle with 2 sides of length 15 and 19.
We have to find the smallest possible whole number length for the 3rd side.
We can draw this as:
The third size is x.
If we reduce h, approaching to 0, x is minimized.
When h is very close to 0 (if h=0, the triangle cease to exist), the value of x can be written as a little bigger than the difference between the largest side (19) and the other side (15).
Then, x is, in the limit h-->0:
[tex]x+15>19\Rightarrow x>19-15=4\Rightarrow x>4[/tex]As x>4, the next whole number is 5.
NOTE: if x=4, the triangle does not exist, as there is no height or 3 angles.
Answer: The smallest whole number length for the 3rd side is 5.
What is the value of log4(1/64)?
log4 (1/64) = x
Rewrite in exponential form:
logb(x)= y
b^y = x
4^x = 1/64
Rewrite as equations with equal base
(2^2)^x = 2^-6
2^2x = 2^-6
Equal exponents:
2x = -6
Solve for x
x = -6/2
x = -3
81/50 as a percentage
Given:
[tex]\frac{81}{50}[/tex][tex]\begin{gathered} \frac{81}{50}=\frac{81}{50}\times100\text{ \%} \\ =162\text{ \%} \end{gathered}[/tex]Answer:
162%
Step-by-step explanation:
[tex]\frac{81}{50} (100)=1.62(100)=162[/tex]
Hope this helps
I need help with this please, thank you very much
1. translation 1 unit left and 6 units down
[tex]h(x)=6(2^x)-1[/tex]2. Stretch vertically by a factor of 6 and translate 1 unit down
[tex]j(x)=2^{6x}-1[/tex]3. Compress horizontally by a factor of 6 and translate 1 unit down
[tex]k(x)=2^{x+6}+1[/tex]4. Translation 6 units left and 1 unit up
find the average rate of change in the simplest form of the function over the interval 4
Suppose the function is f.
Then the average rate
f(4) = 5
and f(5) = 10
Hence,
[tex]\text{average rate of change =}\frac{f(5)-f(4)}{5-4}=\frac{10-5}{5-4}=\frac{5}{1}[/tex]Hence the average rate of change over the interval 4
3x - 9y = 94x - 12y = 36
3x - 9y = 9 --------------------------(1)
4x - 12y = 36 --------------------------(2)
Multiply equation (1) by 4 and then multiply equation(1) by 3
12x - 36y = 36 ---------------(3)
12x - 36y = 108 ------------------(4)
Subtract equation (4) from (3)
0 is not equal to -72
Hence the system has no solution
f(x)=(−x+3)(x+5)Use the Parabola tool by plotting the vertex first and then another point on the parabola.
Answer:
Explanation:
Here, we want to get the plot of the parabola
We start by getting its vertex
We have that as follows:
[tex]\begin{gathered} f(x)\text{ = (-x+3)(x+5)} \\ f(x)=-x^2-2x+15 \end{gathered}[/tex]We have the vertex form as follows:
[tex]\begin{gathered} f(x)\text{ = }-1(x+1)^2+16 \\ \text{compared with the general vertex form:} \\ f(x)=a(x-h)^2+k \\ \text{vertex is (h,k)} \end{gathered}[/tex]The vertex here is thus (-1,16)
To get the other point, we can equate the values in the brackets to zero and solve for x
We have that as:
[tex]\begin{gathered} -x+3\text{ = 0} \\ x\text{ = 3} \\ x+5\text{ = 0} \\ x=\text{ -5} \end{gathered}[/tex]The other points are thus (3,0) and (-5,0)
Thus, we can join (-1,16) with either (3,0) and (5,0) as shown below:
kyra brought a trick coin that landed on heads with a probability of 0.4. which frequency table would kyra most likely generate by flipping the coin many times ?
Since the probability of landing heads with the trick coin is 0.4, we have:
[tex]\begin{gathered} P(heads)=0.4=\frac{36}{90} \\ \\ \Rightarrow P(tails)=1-P(heads)=1-\frac{36}{90}=\frac{54}{90} \end{gathered}[/tex]therefore, the first frequency table represents the behavior of the trick coin.
Asuka is planting grass seeds on her new lawn. The dimensions of her lawn are 4 ft by 3 ft. The instructions to plant the grass seeds suggest planting 16 seeds for every squarefoot How many seeds should Asuka use to plant her entire lawn? foot
Since she can plant 16 seeds per square foot, then
We must find the area of the lawn
Since the lawn is shaped a rectangle of dimensions 4 ft and 3 ft, then
[tex]\begin{gathered} A=L\times W \\ A=4\times3 \\ A=12ft^2 \end{gathered}[/tex]Since 1 square foot = 16 seed, then
12 square feet = 12 x 16 = 192 seeds
She will need 192 seeds to plant the entire lawn
Mike rolls a die 30 times and gets the frequency shown in the table below. What is the relative frequency (experimental probability of rolling a 3 or a 4?
Given:
Number of times the die rolled = 30
Number of times got 3 = 7
Number of times got 4 = 6
Required: Experimental probability of rolling a 3 or a 4.
Explanation:
Experimental probability is defined as
[tex]P(\text{event\rparen=}\frac{\text{ Number of times event occur}}{\text{ Total number of events}}[/tex]Number of times got a 3 or a 4 = 7+6 = 13
So,
[tex]\begin{gathered} P(\text{rolling a 3 or a 4\rparen=}\frac{\text{ Number of times got a 3 or a 4}}{\text{ Total number of trials}} \\ =\frac{13}{30} \end{gathered}[/tex]Option C is correct.
Final Answer: Experimental probability of rolling a 3 or a 4 is 13/30.
In the diagram, m of angle Q= 75º and Measure of arc QS = 133 degrees. Find Measure of QR. PLEASE HELP!
It is given that angle Q is 75 degrees and arc QS is 133 degrees.
Use inscribed angle theorem on angle RQS to get:
[tex]\begin{gathered} \angle RQS=\frac{1}{2}mRS \\ m(RS)=2\angle RQS \\ m(RS)=2\times75=150^{\circ} \end{gathered}[/tex]It is known that the sum of all arcs of circle is 360 degrees so it follows:
[tex]\begin{gathered} m(QS)+m(RS)+m(RQ)=360 \\ 133+150+m(RQ)=360 \\ m(RQ)=360-150-133=77^{\circ} \end{gathered}[/tex]Hence the measure of arc QR is 77 degrees.
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find f(-3) for the equation below f(x)=-2x+3
In this problem, we are applying function notation. When we see a function written as
[tex]f(x),[/tex]we read it as "f of x" or "f as a function of x."
We will take the value of x and substitute it into the quation.
The function rule states
[tex]f(x)=-2x+3[/tex]Since we are given f(-3), we will substitute each x-value (inside parentheses), and simplify:
[tex]f(-3)=-2(-3)+3=6+3=9[/tex]Therefore, f(-3) = 9.
Lucas read 30% of his book containing 480 pages. What page is he going to read next? How many pages has he read so far?
First, calculate the number of page read by Lucas. Calculate the 30% of 480, as follow:
(30/100)(480) = 144
Next, subtract the previous result to 480:
480 - 144 = 336
Hence, Lucas is going to read 336 pages
a panel containing three on off switches in a row is to be set. assuming no restrictions on individual switches.use the fundamental counting principle to find the total number of possible panel settings.
Using the fundamental counting principal, we get that every switch has 2 options, on or off. So the total possible outcomes are:
[tex]2\times2\times2=2^3=8[/tex]Find the number of ways of arranging N people in a straight line, if two particular people must always be separate
Answer:
N! - 2(N - 1)!
Step-by-step explanation:
It’s the number of ways N people can be arranged in a straight line without restriction minus the number of arrangements in which the 2 people are together.
The number of ways N people can be arranged in a straight line without restriction = N!
The number of arrangements in which the 2 people are together = the number of possible positions for the left-hand person multiplied by the number of people who can be that person, multiplied by the number of possible arrangements for the other N - 2 people
= (N - 1) * 2 * (N - 2)!
= 2 (N - 1)!
So the number of ways N people can be arranged in a straight line if 2 particular people must be separated = N! - 2(N - 1)!
#SPJ1
Calvin and Sara went to the candy store. Calvin bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.Use the system of equations to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
We are given that Calvin bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. If the cost of each fudge is "f" and the cost of each gum is "g", then the equation representing the purchase for Calvin is:
[tex]5f+3g=5.7,(1)[/tex]This is our first equation.
We are also given that Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. The equation representing the purchase for Sara is
[tex]2f+10g=3.6,(2)[/tex]This is our second equation.
To solve the system we will solve for "f" in equation (1). To do that we will subtract "3g" from both sides:
[tex]\begin{gathered} 5f+3g-3g=5.7-3g \\ 5f=5.7-3g \end{gathered}[/tex]Now we divide both sides by 5:
[tex]f=\frac{5.7-3g}{5}[/tex]Now we substitute this value in equation (1):
[tex]2(\frac{5.7-3g}{5})+10g=3.6[/tex]Now we divide the equation by 2, we get:
[tex]\frac{5.7-3g}{5}+\frac{10g}{2}=\frac{3.6}{2}[/tex]Simplifying we get:
[tex]\frac{5.7-3g}{5}+5g=1.8[/tex]Now we multiply both sides by 5:
[tex]5.7-3g+25g=9[/tex]Now we add like terms:
[tex]5.7+22g=9[/tex]Now we subtract 5.7 to both sides, we get:
[tex]\begin{gathered} 5.7-5.7+22g=9-5.7 \\ 22g=3.3 \end{gathered}[/tex]Now we divide both sides by 22:
[tex]\begin{gathered} \frac{22g}{22}=\frac{3.3}{22} \\ \\ g=0.15 \end{gathered}[/tex]Now, we substitute this value in equation (1) where we have already solved for "f":
[tex]f=\frac{5.7-3g}{5}[/tex]Substituting the value of "g" we get:
[tex]f=\frac{5.7-3(0.15)}{5}[/tex]Now we solve the operations, we solve the product:
[tex]f=\frac{5.7-0.45}{5}[/tex]Now we solve the operations:
[tex]f=\frac{5.25}{5}=1.05[/tex]Therefore, the price of gums is $0.15 and the price of fudge is $1.05.
Use order of operations and the mathematical properties of numbers to simplify
these numbers.
6x7-7x3 =
Answer:
21
Step-by-step explanation:
[tex]6*7-7*3[/tex]
Utilizing PEMDAS, we know that all multiplication comes before subtraction.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Knowing this, multiply the four terms:
[tex]42-21[/tex]
Now subtract:
[tex]21[/tex]
Macy babysit the children in her neighborhood for each family she charges a flat fee plus a per hour charge as described by the data in the table. which equation represents the total amount macy charges for each family where x represents the number of hours she babysits
Solution
Babysitting pricing
Therefore the equation representing the function is
[tex]y=9x+7[/tex]Hence the answer is Option D
Find the x- and y-intercepts of the graph of the function f (x) = -2|x – 1| +6.Enter your answers as points, (a,b).Enter the x-intercepts in order of increasing x-value.
Given the function:
[tex]fx=-2|x-1|+6[/tex]Let's find the x-intercepts and the y-intercepts of the graph.
• x-intercepts:
To find the x-intercept, substitute 0 for f(x) and solve for x:
[tex]\begin{gathered} 0=-2|x-1|+6 \\ \end{gathered}[/tex]Subtract 6 from both sides:
[tex]\begin{gathered} 0-6=-2|x-1| \\ \\ -6=-2|x-1| \end{gathered}[/tex]Divide both sides by -2:
[tex]\begin{gathered} \frac{-6}{-2}=\frac{-2|x-1|}{-1} \\ \\ 3=|x-1| \\ \\ x=\pm3+1 \\ \\ x=3+1,-3+1 \\ \\ x=-2,\text{ 4} \end{gathered}[/tex]Therefore, the x-intercepts are:
x = -2, 4
• y-intercept:
To find the y-intercept, set the value of x to zero and solve for f(x).
[tex]\begin{gathered} f(x)=-2|x-1|+6 \\ \\ f(0)=-2|0-1|+6 \\ \\ f(0)-2|-1|+6 \\ \\ f(0)=-2(1)+6 \\ \\ f(0)\text{ =}-2+6 \\ \\ f(0)=4 \end{gathered}[/tex]Yes, therefore, the y-intercept is:
y = 4
ANSWER:
• x-intercepts: x = -2, 4
,• y-intercept: y = 4
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=25,900(0.86)^t Find the intial value of the car and the value after 13 years. Round your answers to the nearest dollor as necessary.
To find the initial value of the car replace when t=0
[tex]\begin{gathered} V(0)=25,900(0.86)^0 \\ V(0)=25,900 \end{gathered}[/tex]To find the value after 13 years use t=13
[tex]\begin{gathered} V(13)=25,900(0.86)^{13} \\ V(13)=3645.69\approx3646 \end{gathered}[/tex]PLEASE HELP :Order the following numbers below in ascending order(smallest to largest) -10/2 , 2 1/2 , -0.52, 51.5%
Arranging in ascending order we have,
[tex]\frac{-10}{2},\text{ -0.52, 51.5\%, 2}\frac{1}{2}[/tex]What answer was rounded to the tenths place 4.1,4.100,or 4
Answer:
4.1
Explanation:
In the number:
[tex]1.234[/tex]• The place value of 2= 2 tenths
,• The place value of 3= 3 hundredths
,• The place value of 4= 4 thousandths
The digit rounded to the tenths place is that which have just a digit after the decimal sign.
The correct choice is 4.1
find the values of x and y if l || m.
Explanation
Step 1
when a lines intersects a pair of parallel lines , diverse angles are created
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent,so ( in the image yellow angles are corresponding, so)
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \end{gathered}[/tex]solve for x
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \text{subtrac 5x in both sides} \\ (5x+14)-5x=(7x-30)-5x \\ 14=2x-30 \\ \text{add 30 in both sides} \\ 14+30=2x-30+30 \\ 44=2x \\ \text{divide both sides by 2} \\ \frac{44}{2}=\frac{2x}{2} \\ 22=x \end{gathered}[/tex]Step 2
now, yellow angle and ble angles are supplementary( Two Angles are Supplementary when they add up to 180 degrees),so
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ \end{gathered}[/tex]let
x=22
and solve for y
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ 3y+11+124=180 \\ 3y+135=180 \\ \text{subtract 135 in both sides} \\ 3y+135-135=180-135 \\ 3y=45 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{45}{3} \\ y=15 \end{gathered}[/tex]I hope this helps you
A quilt maker sews both large and small quilts. A large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric. How many of each size quilt did she make if she used a total of 90 yards of fabric to make 15 quilts?
Answer:
The number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]Explanation:
Given that a large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric.
Let x represent the number large quilt and y the number of small quilt.
If she used a total of 90 yards of fabric to make 15 quilts then we have;
[tex]\begin{gathered} 8x+3y=90\text{ ---------1} \\ x+y=15\text{ ----------2} \end{gathered}[/tex]let us solve the system of equations by substitution. From equation 2;
[tex]x=15-y[/tex]substituting into equation 1;
[tex]\begin{gathered} 8x+3y=90 \\ 8(15-y)+3y=90 \\ 120-8y+3y=90 \\ 120-5y=90 \\ 5y=120-90 \\ 5y=30 \\ y=\frac{30}{5} \\ y=6 \end{gathered}[/tex]substituting the value of y;
[tex]\begin{gathered} x=15-y \\ x=15-6 \\ x=9 \end{gathered}[/tex]Therefore; the number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]Solve the following trigonometric equation on the interval [0, 2π]12sin2x−3=0
Given the expression:
[tex]12sin^2(x)-3=0[/tex]To solve the expression, follow the steps below:
Step 01: Add 3 to both sides.
[tex]\begin{gathered} 12sin^2(x)-3+3=0+3 \\ 12sin^2(x)=3 \end{gathered}[/tex]Step 02: Divide both sides by 12.
[tex]\begin{gathered} \frac{12sin^2(x)}{12}=\frac{3}{12} \\ sin^2(x)=\frac{1}{4} \end{gathered}[/tex]Step 03: Take the square root of both sides.
[tex]\begin{gathered} \sqrt{sin^2(x)}=\pm\sqrt{\frac{1}{4}} \\ sin(x)=\pm\frac{1}{2} \end{gathered}[/tex]Step 04: Evaluate the results.
First, let's evaluate sin(x) = 1/2.
Sin(x) is positive in the first and in the second quadrant. Then,
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=x \\ x=\frac{\pi}{6},x=\frac{5}{6}\pi \end{gathered}[/tex]Second, let's evaluate sin(x) = -1/2.
Sin(x) is negative in the third and in fourth quadrant. Then,
[tex]\begin{gathered} sin^{-1}(-\frac{1}{2})=x \\ x=\frac{7}{6}\pi,x=\frac{11}{6}\pi \end{gathered}[/tex]Answer:
[tex]x=\frac{\pi}{6},x=\frac{5}{6}\pi,x=\frac{7}{6}\pi,x=\frac{11}{6}\pi[/tex]You roll a 6-sided die two times.What is the probability of rolling an odd number and then rolling a 1?Simplify your answer and write it as a fraction or whole number.
The sample space for rolling a die twice is shown below
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Total number of outcomes = 36
Outcomes involving an odd number followed by 1 = 1,1 3,1 5,1
Thus, number of favorable outcomes = 3
Probability = number of favorable outcomes/total number of outcomes
the probability of rolling an odd number and then rolling a 1 = 3/36
the probability of rolling an odd number and then rolling a 1 = 1/12
As a Nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patients doctor indicated that you should mix 150 milligrams of Medication A with 225 milligrams of Medication B. However this week, the doctor said to only use 165 milligrams of Medication B. How many milligrams of Medication A should be mixed this week? Answer_____milligrams
Answer: This problem can be solved using the concept of mathematical proportions, the equation that can be constructed for the problem is as follows:
[tex]\begin{gathered} \frac{A_1}{B_1}=\frac{A_2}{B_2} \\ \\ \\ \frac{A_{1}}{B_{1}}=\frac{150mg}{225mg} \\ \\ \\ \frac{A_{2}}{B_{2}}=\frac{A_2}{165mg} \\ \\ \therefore\Rightarrow \\ \\ \\ \frac{150mg}{225mg}=\frac{A_{2}}{165mg}\Rightarrow(1) \end{gathered}[/tex]Solving equation (1) gives the answer, the solution to the equation (1) is as follows:
[tex]\begin{gathered} \begin{equation*} \frac{150mg}{225mg}=\frac{A_2}{165mg} \end{equation*} \\ \\ \\ A_2=(\frac{150}{225}\times165)mg=110mg \\ \\ A_2=110mg \end{gathered}[/tex]Therefore the answer is 110mg.
Please help hurry please. No explanation needed just answers please
Given the angles:
• (3x + 27) degrees
,• 96 degrees
Let's solve for x
The given angles are vertical angles and vertical angles are congruent.
Hence, we have the equation:
(3x + 27) = 96
Let's solve for x from the equation.
3x + 27 = 96
Subtract 27 from both sides:
3x + 27 - 27 = 96 - 27
3x = 69
divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{69}{3} \\ \\ x=23 \end{gathered}[/tex]ANSWER:
x = 23
1) if b is a root of a polynomial equation then (x-b) is a ______of the polynomial2). polynomial equation y=x^2+x-6 root=2 ,factor=__
If b is a root of a polynomial equation then (x - b) is a FACTOR of the Polynomial
Question 2
polynomial y = x^2 + x + 6
If root = 2
Then the factor is iven by
(x - 2)