the first several multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 the first several multiples of 6 are 6: 12, 18, 24, 30, 36, 42, 48, 54, 60
Two polygons have a similarity ratio of 4:5. If the perimeter of the first one is 10 inches, then what is the perimeter of the second?
Group of answer choices
11 inches
8 inches
12.5 inches
15 inches
what is the slope of the line?
Answer:
1/2
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
We have two points on the line
(-1,3) and ( 1,4)
m = ( 4-3)/(1 - -1)
= (4-3)/(1+1)
= 1/2
Answer:
Start where the line meets a point. Then go up and over until it meets another.
The answer is 1/2
So go up one and over two. Then other problems such as this one should be pretty straight forward
- z > 8 equivalent inequality
Answer: z < -8
Step-by-step explanation:
Since z is negative, divide both sides by -1, which leaves you with z > -8.
Multiplying or dividing an inequality by a negative number flips the sign, thus the answer is z < 8.
Correct me if I am incorrect.
Alvin is 9 years older than Elga. The sum of their ages is 81. What is Elga's age?
Answer:
elga is 32 and alvin is 49
The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Use analytic methods to do each of the following: (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position? (c) Find the total distance traveled by the particle. v(t) = 5 (sint)^2(cost); 0 ≤ t ≤ 2π
Answer:
(a) The particle is moving to the right in the interval [tex](0 \ , \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2} \ , \ 2\pi)[/tex] , to the left in the interval [tex](\displaystyle\frac{\pi}{2}\ , \ \displaystyle\frac{3\pi}{2})[/tex], and stops when t = 0, [tex]\displaystyle\frac{\pi}{2}[/tex], [tex]\displaystyle\frac{3\pi}{2}[/tex] and [tex]2\pi[/tex].
(b) The equation of the particle's displacement is [tex]\mathrm{s(t)} \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex]; Final position of the particle [tex]\mathrm{s(2\pi)} \ = \ 3[/tex].
(c) The total distance traveled by the particle is 9.67 (2 d.p.)
Step-by-step explanation:
(a) The particle is moving towards the right direction when v(t) > 0 and to the left direction when v(t) < 0. It stops when v(t) = 0 (no velocity).
Situation 1: When the particle stops.
[tex]\-\hspace{1.7cm} v(t) \ = \ 0 \\ \\ 5 \ \mathrm{sin^{2}(t)} \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.3cm} \mathrm{sin^{2}(t) \ cos(t)} \ = \ 0 \\ \\ \mathrm{sin^{2}(t)} \ = \ 0 \ \ \ \mathrm{or} \ \ \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.85cm} t \ = \ 0, \ \displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2} \ \ \mathrm{and} \ \ 2\pi[/tex].
Situation 2: When the particle moves to the right.
[tex]\-\hspace{1.67cm} v(t) \ > \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ > \ 0[/tex]
Since the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is positive in the first and third quadrant or when [tex]\mathrm{t} \ \epsilon \ (0, \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2}, \ 2\pi)[/tex] .
*Note that parentheses are used to demonstrate the interval of t in which cos(t) is strictly positive, implying that the endpoints of the interval are non-inclusive for the set of values for t.
Situation 3: When the particle moves to the left.
[tex]\-\hspace{1.67cm} v(t) \ < \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ < \ 0[/tex]
Similarly, the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is negative in the second and third quadrant or [tex]\mathrm{t} \ \epsilon \ (\displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2})[/tex].
(b) The equation of the particle's displacement can be evaluated by integrating the equation of the particle's velocity.
[tex]s(t) \ = \ \displaystyle\int\ {5 \ \mathrm{sin^{2}(t) \ cos(t)}} \, dx \ \\ \\ \-\hspace{0.69cm} = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx[/tex]
To integrate the expression [tex]\mathrm{sin^{2}(t) \ cos(t)}[/tex], u-substitution is performed where
[tex]u \ = \ \mathrm{sin(t)} \ , \ \ du \ = \ \mathrm{cos(t)} \, dx[/tex].
[tex]s(t) \ = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ \mathrm{sin^{2}(t)} \, du \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ u^{2} \, du \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5u^{3}}{3} \ + \ C \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ C \\ \\ s(0) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(0)} \ + \ C \\ \\ \-\hspace{0.48cm} 3 \ = \ 0 \ + \ C \\ \\ \-\hspace{0.4cm} C \ = \ 3.[/tex]
Therefore, [tex]s(t) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex].
The final position of the particle is [tex]s(2\pi) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(2\pi)} \ + \ 3 \ = \ 3[/tex].
(c)
[tex]s(\displaystyle\frac{\pi}{2}) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(\frac{\pi}{2})} \ + \ 3 \\ \\ \-\hspace{0.85cm} \ = \ \displaystyle\frac{14}{3} \qquad (\mathrm{The \ distance \ traveled \ initially \ when \ moving \ to \ the \ right})[/tex]
[tex]|s(\displaystyle\frac{3\pi}{2}) - s(\displatstyle\frac{\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(\frac{3\pi}{2})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | (-1) \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{10}{3} \\ \\ (\mathrm{The \ distance \ traveled \ when \ moving \ to \ the \ left})[/tex]
[tex]|s(2\pi) - s(\displaystyle\frac{3\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(2\pi})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{3\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | 0 \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{5}{3} \\ \\ (\mathrm{The \ distance \ traveled \ finally \ when \ moving \ to \ the \ right})[/tex].
The total distance traveled by the particle in the given time interval is[tex]\displaystyle\frac{14}{3} \ + \ \displaystyle\frac{5}{3} \ + \ \displaystyle\frac{10}{3} \ = \ \displaystyle\frac{29}{3}[/tex].
PLEASE HELP -7y + 11 = 75 + y
Answer:
y = -8
Step-by-step explanation:
-7y + 11 = 75 + y
Bring the "y" variable on one side, and rest on the other.
Rearranging, we get,
-7y - y = 75 - 11
-8y = 64
-y = 8
y = -8
Hope it helps :)
The vertices of quadrilateral PQRS are listed.
P(3,7), Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS
A.
Quadrilateral PQRS is a square.
B.
Quadrilateral PQRS is a trapezoid.
C.
Quadrilateral PQRS is a rectangle.
D.
Quadrilateral PQRS is a parallelogram.
Answer:
It's C. for plato. It's a rectangle
Step-by-step explanation:
FILE BELOWAnswer:
its a rectangle .
Step-by-step explanation:
At the restaurant, Gordon packed 8 orders with 4 items per order
in the morning. In the afternoon, he packed 6 orders with 7 items
per order.
Answer:
what is the question?
Step-by-step explanation:
One side of a square garden is 8 feet long. How can you find the area of That is the
the garden?
Answer:
64 ft
Step-by-step explanation:
A square has to be equal on all 4 sides for it to be considered a square. Considering that it is 8 feet on one side it would be 8 feet on all the others as well. From there you multiply 8*8 and receive the solution of 84 feet for the area of the garden.
Could someone help me solve this please? With explanation?
Answer:
x=109 degrees
Step-by-step explanation:
By alternate interior angles, the measure of angle ADE is the same as that of EAB, both of which are 38.
Because ADE is an isosceles triangle, the measure angle EAD is equal to that angle EDA; let that measure be x.
Because the angles of a triangle add up to 180, x+x+38=180 -> 2x+38=180 -> 2x=142 -> x=71
That means that angle EDA is 180 degrees
Because x is supplementary to angle EDA, the measure of angle x is 180-71=109 degrees
3.
In parallelogram ABCD, M
m
Answer:
Please send a picture or explain properly
write 321.51 as word form
Answer:
three hundred twenty one and fifty one hundredths
Help pleaseee????????
it will be equal to the photo
median 5
lowerA basket of fruit contains 6 apples, 5 oranges, 3 bananas, and 2 limes.Which of the following statements about the fruits in the basket are true?Select the two correct statements.
Answer:
[tex]6 + 5 = 11 + 3 = 14 + 2 = 16[/tex]
[tex]6 \div 5 \div 3 \div 2 = 0.2[/tex]
[tex] 6 \times 5 \times 3 \times 2 = 180[/tex]
Step-by-step explanation:
If its addition add them, multiplication multiply them, division divided them.
Answer:
Step-by-step explanation:
i need help sorry no answer got u
HELP ASAP PLEASE!!!!
Answers:
c = 7d = 5=========================================================
Explanation:
For equation A, I'll transform the right hand side into a similar form as the left side. Throughout the steps below, the left hand side stays the same.
[tex]\sqrt{448x^c} = 8x^3\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{(8x^3)^2}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{3*2}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}*7x}\\\\\sqrt{448x^c} = \sqrt{64*7x^{6+1}}\\\\\sqrt{448x^c} = \sqrt{448x^{7}}\\\\[/tex]
Therefore, c = 7
Notice that 7/2 = 3 remainder 1. The quotient 3 is the exponent for the term outside the root for [tex]8x^3\sqrt{7x}[/tex] while the remainder 1 is the exponent for the x term inside the root.
---------------------------------------
We do the same idea for equation B.
[tex]\sqrt[3]{576x^{d}} = 4x\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{(4x)^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3*9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64*9x^{3+2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{576x^{5}}\\\\[/tex]
This must mean d = 5
Note: 5/3 = 1 remainder 2, which means [tex]\sqrt[3]{x^5} = x^1\sqrt[3]{x^2} = x\sqrt[3]{x^2}[/tex]
Approximately what portion of the box is shaded blue?
A.2/3. B.9/10
C.3/5
The Levine family has 10 gallons of gas in the car. The car uses 1 5/8 of a gallon each hour. How long can they drive on 10 gallons of gas?
Answer:
6.15
Step-by-step explanation:
10 gallons is 80/8
1 5/8= 13/8
80 divided by 13 is 6.15384615385 but rounded 6.15
6.15 hours
if its not that then keep rounding to 6.2 or 6hrs
A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
if we can assume the ball is being thrown from the ground upwards, then we can say that the inital height of it is 0, whilst its initial velocity is 80 ft/s, thus
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+80t+0\implies h(t)=-16t^2+80t[/tex]
need help with solving this please
Answer:
3/2
Step-by-step explanation:
Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio
s : 2s : sroot3
The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3
In this diagram the short leg is (root3)/2 .
(root3)/2 × root3 = 3/2
See image.
Make x the subject of the formula
t=
[tex] \sqrt{2(x - ut) \div a}[/tex]
[tex]t = \sqrt \frac{ {2(x - ut)} }{a} \\ = > t = \sqrt{ \frac{2x - 2ut}{a} } \\ = > {t}^{2} = \frac{2x - 2ut}{a} \\ = > a {t}^{2} = 2x - 2ut \\ = > \frac{ { - at}^{2} }{2ut} = 2x \\ = > \frac{ - at}{2u} = 2x \\ = > \frac{ - at}{2u \times 2} = x \\ = > \frac{ - at}{4u} = x[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Adelita, Elena, Betina, and Bianca each work as a doctor, lawyer, teacher, or banker. From these clues, decide who is the doctor.
Answer: betina or adelita
Step-by-step explanation: hope it helps
Martin, his 2 brothers, and his 5 sisters want to fairly share 3 bottles of water. How
much water will Martin get?
Answer:
3/8 bottle
Step-by-step explanation:
Fractions are just division.
Martin + 2sisters + 5bros
= 8 people
3bottles ÷ 8people
= 3/8 bottles per person
Martin is a person, so he gets 3/8 of a bottle, if they all share equally.
Using proportions, it is found that Martin will get 0.375 of a bottle.
This question is solved by proportions, using a rule of three.Martin, his 2 brothers and 5 sisters combine to represent 8 people, which will share 3 bottles equally. How much will Martin, which is one person, get?The rule of three is:
1 person - x bottles
8 people - 3 bottles
Applying cross multiplication:
[tex]8x = 3[/tex]
[tex]x = \frac{3}{8}[/tex]
[tex]x = 0.375[/tex]
Martin will get 0.375 of a bottle.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
Pls help ASAP
Give the domain and range
Answer:
D: {-2, 0, 2}
R: {-1, 1, 3
Which graph shows a linear equation?
Answer:
The bottom right is a linear equation.
Step-by-step explanation:
Answer:
right side down one
Step-by-step explanation:
as you know linear means supplementary having 180 °
Luis goes out to lunch. The bill, before tax and tip, was $14.60. A sales tax of 9% was added on. Luis tipped 19% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Add the sales tax to the bill:
Bill with tax = 14.60 x 1.09 = $15.95
Multiply the total bill by the tip percentage:
Tip = 15.95 x 0.19 = 3.02
Tip = $3.02
a manufacturer has the following quality control check at the end of a production line. if at least 8 of 10 randomly picked articles meet all specifications, the whole shipment is approved. if in reality, 85% of a particular shipment meets all specifications, what is the probability that the shipment will make it through the control check?
Using the binomial distribution, it is found that there is a 0.8202 = 82.02% probability that the shipment will make it through the control check.
For each article, there are only two possible outcomes, either it meets the specifications, or it does not. The probability of an article meeting the specifications is independent of any other article, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
10 articles are picked, hence [tex]n = 10[/tex].85% of the articles meets all specifications, hence [tex]p = 0.85[/tex]The probability is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.85)^{8}.(0.15)^{2} = 0.2759[/tex]
[tex]P(X = 9) = C_{10,9}.(0.85)^{9}.(0.15)^{1} = 0.3474[/tex]
[tex]P(X = 10) = C_{10,10}.(0.85)^{10}.(0.15)^{0} = 0.1969[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2759 + 0.3474 + 0.1969 = 0.8202[/tex]
0.8202 = 82.02% probability that the shipment will make it through the control check.
For more on the binomial distribution, you can check https://brainly.com/question/24863377
Write an algebraic expression for the given scenario and define the variables.
Answer:
n($6.50) + m($5.50) + k($6.00) = p
Step-by-step explanation:
n = matinee ticket
m = drink
k = popcorn
p = total cost
Without knowing the exact amount that was bought we must put a variable to show an unknown number. All of this together makes an algebraic expression.
Approximately what portion of the beaker is filled?
A. 1/2
B. 1/4 C.3/4
Answer:
B. [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The whole beaker is 1. If you measure the beaker, you will notice you can fill up the beaker to the brim (whole, which is 1) if you use the current amount 4 times, and four times is [tex]\frac{1}{4}[/tex].
What is 10³?
10
100
1000
Answer:
1000
Step-by-step explanation:
Answer: 1000, hope it helps.
Step-by-step explanation:
Let f(x)=x* + 14x and g(x) = 6 - X. Find the domain off f + g. Determine the domain of f + g.
[tex]\begin{cases} f(x) = x^4+14x\\ g(x) = 6-x \end{cases}\qquad \qquad h(x) = f(x) + g(x) \\\\\\ h(x) = (x^4+14x)+(6-x)\implies h(x) = x^4+14x-x+6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x) = x^4+13x+6~\hfill[/tex]
now, if we graph h(x), Check the picture below, we can see that horizontally the line keeps on moving towards the left, going going and going towards -infinity, and it also keeps on moving towards the right, going going and going towards +infinity, and since the horizontal area used by the function is the domain of it, the domain for h(x) will be (-∞ , +∞).