Answer:
90
Step-by-step explanation:
5x – 2y + (7x – y)
Combine like terms
12x -3y
Let x = 7 and y = -2
12(7) -3(-2)
84 +6
90
Answer:
90
Step-by-step explanation:
Hi there!
We are given this expression:
5x-2y+(7x-y) and we want to evaluate it if x=7 and y=-2
First, let's combine like terms, as that will make it easier for when we substitute the values into the expression
Open up the parentheses
5x-2y+7x-y
Combine like terms
12x-3y
Now substitute 7 as x and -2 as y into the expression
12(7)-3(-2)
Multiply
84+6
Add
90
Hope this helps!
What is the phase of y= -3cos (3x-pi) +5
Answer:
[tex]- \frac{\pi}{3}[/tex]
Step-by-step explanation:
Given
[tex]y = -3\cos(3x - \pi) + 5[/tex]
Required
The phase
We have:
[tex]y = -3\cos(3x - \pi) + 5[/tex]
Rewrite as:
[tex]y = -3\cos(3(x - \frac{\pi}{3})) + 5[/tex]
A cosine function is represented as:
[tex]y = A\cos(B(x + C)) + D[/tex]
Where:
[tex]C \to[/tex] Phase
By comparison:
[tex]C = - \frac{\pi}{3}[/tex]
Hence, the phase is: [tex]- \frac{\pi}{3}[/tex]
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
give the size of the letter figure below
Answer: 150 degrees
Step-by-step explanation: 10+ 20 = 30
180-30 = 150 degrees.
*20 points*
What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 14 red marbles, and 15 green marbles if the first marble is not replaced?
a. 192/1,849
b. 18/43
c. 21/205
Answer:
c: 21/205
Step-by-step explanation:
The probability of choosing a yellow marble first is 12/41 bc there are 12 yellow marbles and 41 marbles to choose from.
The probability of choosing a red marble is 14/40 bc there are 14 red marbles and 40 marbles to choose from( since you have removed the marble you first chose so there are 40 marbles left).
Multiplying these two together, 12/41 * 14/40 = 168/1640, simplified it's 21/205.
e movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. How could you correctly rewrite the equation 4(10+5) = 6(12 - 2) using the distributive property
9514 1404 393
Answer:
4·10 +4·5 = 6·12 -6·2
Step-by-step explanation:
Each outside factor multiplies each inside term.
4(10 +5) = 6(12 -2)
4·10 +4·5 = 6·12 -6·2
The smallest positive solution of tan bx = 2 is x = 0.3. Determine the general solution of tan bx = 2.
The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
From Trigonometry we remember that Tangent is a Transcendental Function that is positive both in 1st and 3rd Quadrants and have a periodicity of [tex]\pi[/tex] radians. The procedure consists in using concepts of Direct and Inverse Trigonometric Functions as well as characteristics related to the behavior of the tangent function in order to derive a General Formula for every value of [tex]x[/tex], measured in radians.
First, we solve the following system of equations for [tex]b[/tex]:
[tex]\tan bx = 2[/tex] (1)
[tex]x = 0.3[/tex] (2)
Please notice that angles are measured in radians.
(2) in (1):
[tex]\tan 0.3b = 2[/tex]
[tex]0.3\cdot b = \tan^{-1} 2[/tex]
[tex]b = \frac{10}{3}\cdot \tan^{-1}2[/tex]
[tex]b\approx 3.690[/tex]
Under the assumption of periodicity, we know that:
[tex]y = \tan bx[/tex]
[tex]b\cdot x \pm \pi\cdot i = \tan^{-1} y[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
[tex]b\cdot x = \tan^{-1}y \mp \pi\cdot i[/tex]
[tex]x = \frac{\tan^{-1}y \mp \pi\cdot i}{b}[/tex]
If we know that [tex]y = 2[/tex] and [tex]b \approx 3.690[/tex], then the general solution of this trigonometric function is:
[tex]x = \frac{0.352\pi \mp \pi\cdot i}{3.690}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
[tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
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I need help please can not figure out this problem
From September 1991 to September 1994 the enrollment at a particular school declined by 20 percent. If the number of students enrolled at that school in September 1994 was 720, what was the enrollment in September 1991
Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
Can someone do #4 and #5
Answer:
First, find two points on the graph:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]
16 + (-3) = 16 - 3 = 13
Three numbers form an arithmetic sequence whose
common difference is 3. If the first number is
increased by 1, the second increased by 6, and
the third increased by 19, the resulting three
numbers form a geometric sequence. Determine
the original three numbers.
Let x be the first number in the sequence. Then the first three numbers are
{x, x + 3, x + 6}
The next sentence says that the sequence
{x + 1, x + 9, x + 25}
is geometric, which means there is some fixed number r for which
x + 9 = r (x + 1)
x + 25 = r (x + 9)
Solve for r :
r = (x + 9)/(x + 1) = (x + 25)/(x + 9)
Solve for x :
(x + 9)² = (x + 25) (x + 1)
x ² + 18x + 81 = x ² + 26x + 25
8x = 56
x = 7
Then the three numbers are
{7, 10, 13}
write your answer in simplest radical form
Answer:
z = √3
Step-by-step explanation:
sin (30°) = z / 2√3
z = sin (30°) 2√3
z = √3
35 + 3 x n with n = 7
lim(x-0) (sinx-1/x-1)
9514 1404 393
Answer:
as written: the limit does not existsin(x-1)/(x-1) has a limit of sin(1) ≈ 0.841 at x=0Step-by-step explanation:
The expression written is interpreted according to the order of operations as ...
sin(x) -(1/x) -1
As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.
__
Maybe you intend ...
sin(x -1)/(x -1)
This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...
The limit is about 0.841 at x=0.
What is the first step to solve the equation 16x-21 = 52?
1 Add 52 to both sides
2 Add 21 to both sides
3 Subtract 21 from both sides
4 Subtract 52 from both sides
Answer:
2) Add 21 to both sides
Step-by-step explanation:
When solving [tex]16x-21=52[/tex] for [tex]x[/tex], our goal to isolate [tex]x[/tex] such that we have [tex]x[/tex] set equal to something.
Therefore, we want to start by adding 21 to both sides. This leaves us with [tex]16x=73[/tex] and we are one step closer to isolating [tex]x[/tex].
Hi. I need help with part b thank you so much if you can do so
9514 1404 393
Answer:
Yes, that distance is the hypotenuse of a right triangle whose sides are known
Step-by-step explanation:
The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.
Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)
PLZ ANSWER QUESTION IN PICTURE
Answer: y = 3x + 6
Step-by-step explanation:
(x-intercept of -2: (-2,0))
(slope = m)
y = mx + b, (-2,0), m = 3
[tex]y=mx+b\\0=3(-2)+b\\0=-6+b\\b=6\\y=3x+6[/tex]
strontium-90 is a radioactive material that decays according to the function A(t)=A0e−0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium-90.
(a) What is the decay rate of strontium-90?
(b) How much strontium-90 is left after 30 years?
(c) When will only 100 grams of strontium-90 be left?
(d) What is the half-life of strontium-90?
(a) The decay rate of strontium-90 is nothing%.
(Type an integer or a decimal. Include the negative sign for the decay rate.)
Answer:
Step-by-step explanation:
The decay rate of strontium-90 is -.0244 as given.
For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.
[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to
A(t) = 400(.4809461353) so
A(t) = 192.4 g
For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:
[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:
[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:
[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:
ln(.25) = -.0244t and divide by -.0244:
61.8 years = t
For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:
[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:
[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:
[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:
ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):
[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:
[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and
H = 28.4 years
Find the area of a triangle as a mixed number.
Answer:
I believe the answer is 4 37/50!
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
Area and perimeter please?
Answer:
Area = 240 cm²
Perimeter = 80 cm
Step-by-step explanation:
✔️ Area of the triangle = ½*base*height
base of the triangle = 24 cm
height = 20 cm
Plug in the known values
Area = ½*24*20
= 12*20
Area = 240 cm²
✔️Perimeter of the triangle = sum of all the three sides that make up the triangle
Perimeter = 22 + 24 + 34
= 80 cm
if my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
$240
Step-by-step explanation:
A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240
Answer:
x+1/5x
Step-by-step explanation:
Because the eqaution would be x+10%=x+1/10+10%=1/5+x
Then the equation equals x+1/5
Conan puts tennis balls into tubes after gym class. There are 17 tennis balls, and each tube holds 3 balls. How many tubes does Conan completely fill? How many tennis balls are left?
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
(x/4) + (2x/7 =135 solve it
Answer:
the ans is 252................
Find the derivative on the value of x=-4
[tex]y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]
[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]
[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]
[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]
[tex]\\ \sf\longmapsto y=-1015i[/tex]
Use the order of operations to simplify 3/4+8(2.50-0.5).
Answer:
16[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Part b c and d please help
Answer:
b) Y =5.73X +4.36
C) =5.73225*(21)X +4.359
124.73625
D) 163.728 = 5.73X +4.36
X = (163.728 - 4.36)/5.73
X = 27.81291449
Year would be 2027
Step-by-step explanation:
x1 y1 x2 y2
4 27.288 16 96.075
(Y2-Y1) (96.075)-(27.288)= 68.787 ΔY 68.787
(X2-X1) (16)-(4)= 12 ΔX 12
slope= 5 41/56
B= 4 14/39
Y =5.73X +4.36
A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
Answer:
dv = surface area * dh
so
dv/dt = surface area * dh/dt
width at surface = 40 + (80-40)(30/40)
= 40 + 30 = 70 cm = 0.70 m
so
surface area = 9 * .7 = 6.3 m^2
so
.3 m^3/min = 6.3 m^2 * dh/dt
and
dh/dt = .047 meters/min or 4.7 cm/min
Step-by-step explanation:
in each figure below find m<1 and m < 2 if a||b
please help i don't have a lot of time I will give brainliest if you help
Answer:
m∠1 = 105°
m∠2 = 75°
Step-by-step explanation:
From the picture attached,
Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.
Therefore, m∠2 = 75° [Corresponding angles measure the same]
m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]
m∠1 + 75° = 180°
m∠1 = 105°
