Answer:
The two numbers are 20 and 60
Step-by-step explanation:
Two numbers: x and y
x + y = 80
x - y = 40
x = y + 40
Substitute x
y + 40 + y = 80
2y + 40 = 80
2y = 40
y = 20
Substitute y, so x = 60
If 2x - 8 = 0, find the value of x
Answer:
x = 4
Step-by-step explanation:
2x - 8 = 0
2x = 8
x = 8/2
x = 4
The side of one square is 2 centimeters longer than the side of the second square. If the sum of their
areas is 100cm?, find the length of the side of each square.
*DUE TOMORROW* please help
Answer:
Side length of first square is 10 cm
Side length of second square is 8 cm
Step-by-step explanation:
Let (x + 2) = side length of first square
Let x = side length of second square
Area of a square = (side length)²
⇒ area of first square = (x + 2)²
⇒ area of second square = x²
If the sum of their areas is 100 cm² then:
⇒ (x + 2)² + x² = 100
Expand the brackets:
⇒ x² + 4x + 4 + x² = 100
Collect and combine like terms:
⇒ 2x² + 4x + 4 = 100
Subtract 100 from both sides:
⇒ 2x² + 4x - 96 = 0
Divide both sides by 2:
⇒ x² + 2x - 48 = 0
Factor:
⇒ (x - 6)(x + 8) = 0
Therefore,
⇒ x = 6, x = -8
As distance is positive, x = 8 only.
Therefore, side length of first square is 10 cm
Side length of second square is 8 cm
Use the figure to solve the inequality
Answer:
c hope this help
Step-by-step explanation:
There are 90 students in a speech contest. Yesterday, 1/6 of them gave their speeches. Today, 2/5 of the remaining students gave their speeches. How many students still haven’t given their speeches?
Answer:
45 students still haven't given their speeches
Step-by-step explanation:
90/6 = 15
90-15 = 75
75/5 = 15
15*2 = 30
75-30 = 45
pls mark me brainliest
Family spends $240.000 per week on food. If this is 6% of their income,what is their income??
their income is "x", which oddly enough is the 100% of their income, we also know that 16% of it 240 bucks, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 240&16 \end{array}\implies \cfrac{x}{240}=\cfrac{100}{16}\implies 16x=24000 \\\\\\ x=\cfrac{24000}{16}\implies x=1500[/tex]
Can someone please help me out?
Answer:
11.5
Step-by-step explanation:
Coordinate values and side lengths are multiplied by the dilation scale factor. (Angle values remain unchanged.)
W'X' = (1/4)WX
W'X' = (1/4)(46) = 11.5
Which equations may be used to determine the 3 consecutive integers whose sum is 127?
Answer:
a and b.
Step-by-step explanation:
I’ll explain by giving an example.
Let’s say that: a=3;b=4;c=5; => they all are consecutive -> their sum is 12.
=> if we use a) n=3 => 3*n+3=3*3+3=12 => correct.
b) n+(n+1)+(n+2)= 3+4+5=12=> correct.
c)n+2n+3n=3+6+9=18=>incorrect.
d)3n=3*3=9=>incorrect.
4.
Spiral Review
3. Coach Clarke has 48 students
in his P.E. class. He places the
students in teams of 6 for an
activity. How many teams can
Coach Clarke make?
Answer:
8 teams
Step-by-step explanation:
48/6 = 8
Create an equation to solve the following word problem:
An electrician has placed two electric outlet boxes on each wall in a new home plus 5 additional electric outlet boxes in the garage. She installed 37 electric outlet boxes in total for the entire home (including the garage). On how many walls did she installed electric outlet boxes?
Answer:
2+5+30/2=18.5
or,
37/2=18.5
Write 0.54 as a fraction.
a fifty-four hundredths
b four and five-tenths
c fifty-four tenths
d five and four-tenths
[tex]\\ \tt\hookrightarrow 0.54[/tex]
Fifty-four hundredths[tex]\\ \tt\hookrightarrow \dfrac{54}{100}[/tex]
More simplify
[tex]\\ \tt\hookrightarrow \dfrac{27}{50}[/tex]
Solution:
Since there is two digits on the right of the decimals, it is called "the hundredths."
=> 1 digit on the right of decimal - tenths=> 2 digits on the right of decimal - hundredths=> 3 digits on the right of decimal - thousandths=> 4 digits on the right of decimal - ten thousandthsNow, we can recite 0.54 as 54 hundredths. The word "54 hundredths" defines 54/100. Hence, Option A is correct.
Further Simplification
=> 54/100 = 27/50Please help me thanks
Answer:
y= 1/4x - 3
Step-by-step explanation:
You want to build a skateboard ramp that is 12 feet long and reaches a
height of 3 feet. What is the angle of elevation of the ramp? Round your
answer to the nearest tenth.
Answer:
14.0362 degrees (round to 14.0 degrees)
Step-by-step explanation:
1. Assume that the math can be deduced by the sides of a triangle due to the "sightline" nature of the problem. This is a classic trig problem you will see.
2. The base of the triangle would be 12 feet and one of the legs of the triangle will be 3 feet.
3. Arctangent will provide the angle of elevation. The equation can be written as arctan(h/b), in this case h = height and b = base.
4. The calculation will be arctan(3/12) which translates to 14 degrees which is, fortunately, the angle of elevation.
I recommend trying this method out with another example such as the angle of elevation between you and the next plane you see in the sky. For example, the height difference between you and the plane is 7 miles and the plane is x miles away. Again we can create a simple triangle to discover many interesting details.
3/4 divided by 1/2 is
Answer:
Pictured this you have 3/4 of a sandwich and eat half of that 3/4 of the sandwich. you know have eaten 3/8 of a full sandwich and have 3/8 left.
if we were to actually divide 3/4 by 1/2 we would get 1.5 or 1 1/2 which would not make sense, so instead, we multiply and get 3/8
Use synthetic division to solve (x cubed minus x squared minus 17 x minus 15) divided by (x minus 5). What is the quotient?
x squared + 4 x + 3
x squared minus 6 x + 13 minus StartFraction 80 Over x minus 5 EndFraction
x cubed + 4 x squared + 3 x
x squared minus 6 x + 13 minus StartFraction 80 Over x + 5 EndFraction
Answer: A
Step-by-step explanation:
The quotient is x² + 4x +3. Then the correct option is A.
What is the quotient?A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.
The quotient is calculated as:-
x - 5 ) x³ - x² - 17x -15 ( x² + 4x + 3
-x³ + 5x²
_________________
4x² - 17x - 15
-4x² + 20x
_________________
3x -15
-3x + 15
_________________
0
Hence, the quotient is x² + 4x +3.
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Colin got 16 out of 80 correct in his test.
What fraction of the marks did he get wrong?
Give your answer in its simplest form.
Answer:4/5
Step-by-step explanation:
=80 out of 80 - 16 out of 80
=64 out of 80
Answer:
4/5
Step-by-step explanation:
substract the number of questions he got correctly from the total number of the questions to yield 80-16=64
then set the fraction as number of incorrect questions as the numerator and the total number of questions as the denominator
64/60=4/5
how do i do this, my son is struggling and he needs help
Answer:
32
Step-by-step explanation:
angle a is the outside angle. It creates a circle that will always equal 360 degrees. Since the outside angle is 302, the inside angle must be 58 degrees (360-302). The top square angle will be 90 degrees (a square angle is always 90 degrees). Since the angles in a triangle always add up to 180 degrees, we need to add 58 and 90, and then subtract it from 180, which equals 32. So, angle x equals 32.
Answer:
x = 32°
Step-by-step explanation:
The triangle is 58°. I know this because the question stated that "a" is 302. A full circle is 360. So you can subtract 360 - 302 = 58. There is a small corner of a square in the other side of the triangle. With that we know that, that side has to be 90°. A triangle is 180° total. So we can subtract:
180 - 90 - 58 = 32
Therefore, x = 32°
1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26 seconds, and the average height of the bottle is 12 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 6 feet. A cosine function can model the movement of the message in a bottle in relation to the height.
Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points)
Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? (5 points)
Part C: Based on the graph of the function, after how many seconds will it reach its lowest height? (5 points)
Show/Explain answer for each Part for the answer please
Answer:
See below for answers and explanations (along with a graph attached)
Step-by-step explanation:
Part A
The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet
Part B
The graph's function would be in the form of [tex]y=acos(bx+c)+d[/tex] where [tex]a[/tex] is the amplitude, [tex]\frac{2\pi}{b}[/tex] is the period, [tex]-\frac{c}{b}[/tex] is the phase/horizontal shift, and [tex]d[/tex] is the average/midline.
We already know our amplitude of [tex]a=3[/tex] from part A.
Since our period is given to us as 26 seconds, then we can use the equation [tex]\frac{2\pi}{b}=26[/tex] to find [tex]b[/tex], which happens to be [tex]b=\frac{\pi}{13}[/tex].
Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity [tex]sin(x)=cos(x-\frac{\pi}{2})[/tex] which shifts the cosine graph [tex]\frac{\pi}{2}[/tex] units to the right. This means that [tex]c=-\frac{\pi}{2}[/tex], making our phase shift [tex]-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5[/tex], or 6.5 feet to the right
Our average/midline would be [tex]d=12[/tex] as given as the average height by the problem.
Therefore, the function is [tex]f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12[/tex]
Part C
Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).
Part A
The distance from the highest and lowest point is 6 feet. Cut this in half to find the amplitude: 6/2 = 3. The amplitude represents the vertical distance from the midline (aka average height) to either the peak or valley points.
The period is 26 seconds because this is the time difference from one max height to the next max height. This is one of a few ways to measure a full cycle. Another way is from min height to the next min height.
Answers:Amplitude = 3 feetPeriod = 26 seconds==========================================================
Part B
In this case, the template for cosine is
h = Acos(B(t-C))+D
We found the amplitude A = 3 from the previous section.
The period is T = 26 which means B = 2pi/T = 2pi/26 = pi/13
D = 12 because the average height is 12 feet. The average height is always on the midline.
We are told that t = 0 leads to h = 12, so,
[tex]h = A\cos\left(B\left(t-C\right)\right)+D\\\\h = 3\cos\left(\frac{\pi}{13}\left(t-C\right)\right)+12\\\\12 = 3\cos\left(\frac{\pi}{13}\left(0-C\right)\right)+12\\\\3\cos\left(\frac{\pi}{13}\left(-C\right)\right) = 0\\\\\cos\left(\frac{\pi}{13}C\right) = 0\\\\[/tex]
Let's isolate the C term
[tex]\cos\left(\frac{\pi}{13}C\right) = 0\\\\\frac{\pi}{13}C = \arccos(0)\\\\\frac{\pi}{13}C = \frac{\pi}{2}\\\\C = \frac{\pi}{2}*\frac{13}{\pi}\\\\C = \frac{13}{2}[/tex]
Answer: [tex]h = 3\cos\left(\frac{\pi}{13}\left(t-\frac{13}{2}\right)\right)+12\\\\[/tex]==========================================================
Part C
A full period is 26 seconds.
At t = 0 the bottle is at a height of 12 feet
26 seconds later, the bottle is back again at 12 feet to repeat another cycle indefinitely.
At every quarter cycle, the object is either at a min point, max point, or at the average (midline).
So every 26/4 = 6.5 seconds the object will be in one of those places.
In this case, the object starts at 12 feet, goes up to the max 15 feet when t = 6.5
Then another 6.5 seconds later it's back to the midline again. Another 6.5 seconds later (total time is now 6.5*3 = 19.5 seconds) the bottle dips down to the min height of 9 feet. You should see that (19.5, 9) is one of the infinitely many minimum points on this particular cosine curve.
Answer: 19.5 secondsDetermine the smallest integer value of x in the solution of the following inequality.
3x - 10> -4
answer:
3
explanation:
3x-10 > -4
3x > 6
x > 2
hence, the smallest integer value of x is 3.
PLEASE HELP ASAP I WILL GIVE BRAINSLET TO THE CORRECT ANSWER!!!!!!!!!!
Answer:
The solution to the system of equation is
[tex]y=-\frac{19}{11} \\\\x= -\frac{232}{11}[/tex]
1. Find the area of the composite figure.
picture at the bottom
Square root of y^2 over y^21
Answer:
The answer is 1/y^7
[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{7} }{ {y}^{21} } } [/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{0} }{ {y}^{21 - 7} } } [/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{0} }{ {y}^{14} } } [/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf \sqrt{ \dfrac{ 1}{ {y}^{14} } } [/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf \dfrac{1}{ {y}^{7} } [/tex]
Jenna picked a pumpkin at the pumpkin patch that weighed 8 and 1 half pounds, Her little sister, sandy, picked a pumpkin that weighed one half of that amount, how much did sandys pumpkin weigh
Answer:
4 pounds and 1/4 ounces
Step-by-step explanation:
8 and 1 half pounds = 8.5 Ibs
One half of 8.5 = 8.5/2 = 4. 25 Ibs or 4 & 1/4 or 4Ibs 4 ounces.
find the value of x.
Answer:
22
Step-by-step explanation:
The two transversals of a parallelogram equally divides each other, therefore,
x+40 = 2x+18
(collect the "x" to one side, and integers the other side of the equation)
2x-x = 40-18
x = 22
Can someone help me find the diameter?
also what is a diameter even?
Answer:
24
Step-by-step explanation:
area of circle = πr²
πr² = 144π
Cancel out π
r² = 144
r = √144
r = 12
diameter = 2 x radius
diameter = 2 x 12
diameter = 24m
* diameter is the "width of a circle", the distance from the widest points of the circle
8x18÷4+15 use pemdas right answers only please
Answer:
51
Step-by-step explanation:
PEMDAS means parenthesis (there are none), exponents (there are none), multiplication. So you multiply 8x18 to get 144. Then you have division, so 144/4 is 36. Finally, you add this number to 15 to get 51 as your final answer.
By PEMDAS, the solution of the expression 8x18÷4+15 is 51.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Given:
An expression,
8x18÷4+15.
In order to solve the problem by PEMDAS:
First, solve the multiplication operation,
144÷4+15
Now, solving division operations,
36 + 15
Applying addition operation,
51
Therefore, 51 is the solution to the expression.
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cuanto es 74032+891+31143
74032+891+31143 = 106066
The picture shows a triangular island:
65
d
e
Island
f
Which expression shows the value of e? (1 point)
O
a
f sin 650
Ob
fcos 65
OC
d
COS 65°
Od
d
sin 65°
Work Shown:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(65^{\circ}) = \frac{d}{e}\\\\e\cos(65^{\circ}) = d\\\\e = \frac{d}{\cos(65^{\circ})}\\\\[/tex]
A school bus can hold 39 students. A school district has 24 buses. Use compatible numbers to estimate about how many students the buses can transport.
You can multiply
39 • 24 and it gives you = 936
What is the probability of rolling a prime number of a standard 20-sided die? (1 is not a prime number.) a. 7/20 b. 2/5 c. 9/20 d. 1/2 Please select the best answer from the choices provided A B C D
Answer: Answer: 2/5. Step-by-step explanation: The prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. A total of 8. ... = 2/5. Still stuck? Get 1-on-1 help
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What is the probability of rolling a prime number of a standard 20-sided die? (1 is not a prime number.)
a.
7/20
b.
2/5
c.
9/20
d.
1/2
What is 1/6 ÷ 6 =
SHOW YOUR WORK
Answer:
1/36
Step-by-step explanation:
6 can be put over 1.
Our equation:
[tex]\frac{1}{6} \div\frac{6}{1}[/tex]
Find the reciprocal (opposite) of 6/1, then change to sign to multiplication:
[tex]\frac{1}{6} \times\frac{1}{6} =?[/tex]
Solve:
[tex]\frac{1}{6} \times\frac{1}{6} =\frac{1}{36}[/tex]
Your answer is 1/36.