Answer:
4/9 cubic units
Step-by-step explanation:
The volume of a rectangular prism is the product of its edge lengths:
V = LWH
V = (1/2)(2/3)(4/3) = (1·2·4)/(2·3·3) = 4/9 . . . . cubic units
Write the following sentence using mathematical symbols. The difference of z and two-thirds is the same as the product of z and two-thirds.
Answer:
Step-by-step explanation:
z - 2/3 = (2/3)z
A book shelf is 1 m wide. Joe wants to place a set of books across the shelf. He has 20 books. Each book is 5.2 cm wide. Will he have enough space for all the books?
Answer:
Only 19 books
Step-by-step explanation:
1m=100cm
1 book attains 5.2cm
x books attain 100cm
Do cross multiplication and then u will get answer as 19.23
books can't be in decimals
So answer is 19 books
Write the perimeter of the triangle as a simplified expression
Answer: 10y + 1
Step-by-step explanation:
The perimeter is the total distance round the figure.
Now, in this case it is going to be
Perimeter = 3y + 5 + 6y + y - 4
= 3y + 6y + y + 5 - 4
= 10y + 1
The perimeter of the given triangle is 10y + 1 units.
What is a triangle ?A triangle is formed by 3 non co-linear points it has three sides and three vertices.
A triangle is also a polygon with three sides.The sum of all the interior angles of a triangle is 180°.
In the given question
Equations of all the sides of the lengths of the triangle is given.
We know that the perimeter of a triangle is the sum of the lengths of all the sides.
∴ Perimeter of the given triangle
= (3y + 5) + (y - 4) + 6y
= 10y + 1 units.
Learn more about Triangles here :
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solve
10a -7 = 21 - ба
Answer:
A=1.75
Step-by-step explanation:
[tex]10a + 6a = 21 + 7 \\ 16a = 28 \\ divide \: both \: sides \: by \: 16 \\ a = 1.75 \: or 1 \ \frac{3}{4} [/tex]
Answer:
a = 7/4
Step-by-step explanation:
10a -7 = 21 - 6а
Add 6a to each side
10a+6a -7 = 21 - 6а+6a
16a -7 = 21
Add 7 to each side
16a+7-7=21+7
16a = 28
Divide each side by 16
16a/16 = 28/16
a = 7/4
Find the 7th term in the
sequence
-1, -3, -9,...
Answer:
The answer is 729
Step-by-step explanation:
to get the next term, the sequence multiples the previous number by -3
1 * -3 = -3
-3 * -3 = 9
and so on.
To get the 7th term:
-27 * -3 = 81 (5th term)
81 * -3 = -243 (6th)
-243 * -3 = 729 (7th)
Answer:
The seventh term in the sequence is -729.
Step-by-step explanation:
Notice that the sequence is not increasing linearly. Therefore, this is a geometric sequence.
Recall that the explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the first term, r is the common ratio, and n denotes the nth term.
From the sequence, we can see that our first term a is -1.
Because each term is thrice the previous, our common ratio r is 3.
By substitution:
[tex]x_n=-(3)^{n-1}[/tex]
Hence, the seventh term is:
[tex]\displaystyle \begin{aligned} x_7 & = -(3)^{(7)-1} \\ \\ & = -(3)^{6} \\ \\ & = -729\end{aligned}[/tex]
In conclusion, the seventh term is -729.
my hw write find an equation of the line passing through (-2,3) and (4,-5) I have to write the equation in slope-intercept form I need help
Answer:
The line passing through the given points is:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
in its slope-intercept form
Step-by-step explanation:
Start by finding the slope of the segment that joins the two given points using the slope formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
which for our case renders:
[tex]slope=\frac{3-(-5)}{-2-4}=\frac{8}{-6} =-\frac{4}{3}[/tex]
Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:
[tex]y=-\frac{4}{3} x+b\\3=-\frac{4}{3} (-2)+b\\3=\frac{8}{3}+b\\b=3-\frac{8}{3} \\b=\frac{9-8}{3} \\b=\frac{1}{3}[/tex]
Therefore, the equation of the line becomes:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 6 ← is in slope- intercept form
with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (1, 5) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = 5 + [tex]\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex] ← equation of perpendicular line
What’s the measure of x for the for each figure?
Answer:
a)73
b)27
c)58
d)70
Pilar wanted to use estimation to solve a decimal addition problem. She correctly used estimation to rewrite the problem as 12 + 3 + 5 + 6. What could her original problem have been? Also it is written in decimals.
Answer:
Could be 11.9 + 2.9 + 4.9 + 5.9
Step-by-step explanation:
All the numbers above will round to 12 + 3 + 5 + 6. There are other answers too
Answer:
it would be Could be 11.9 + 2.9 + 4.9 + 5.9
Step-by-step explanation:
I’d rather draw a map than give someone Verbal directions true or false
Answer:
True because there would be more understanding
Step-by-step explanation:
Answer:
FALSE
Step-by-step explanation:
Drawing map takes a while but verbal directions are quite simple and easy to understand
Hope it helps!
(- 6x + 7) + (2x - 6) = - 4x + 1
Answer:
Step-by-step explanation:
-4x + 1 = -4x + 1
1 = 1
infinitely many solutions
Defining Terms
Warm-Up
Active
Reviewing Undefinable Terms
The intersection of plane R and plane P is
R
H
Point is not on plane P.
E and 8 intersect at point
P
Intro
Answers: line DB
H
D
Fill in the blank.
(5x)2
a0x2
Answer:[tex]a_0=25[/tex]
Step-by-step explanation:
It is given that, [tex](5x)^2=a_0x^2[/tex]
We need to find the value of [tex]a_0[/tex]
As [tex](5x)^2=a_0x^2[/tex]
Solving LHS
[tex]25x^2=a_0x^2[/tex]
Now comparing the coefficients of [tex]x^2[/tex]
In LHS the coefficient of [tex]x^2[/tex] is 25
In RHS the coefficient of [tex]x^2[/tex] is [tex]a_0[/tex]
It implies that, [tex]a_0=25[/tex]
So, the value of [tex]a_0[/tex] is 25.
What is the area of the parallelogram?
Answer:
A = 60 cm^2
Step-by-step explanation:
The area of a parallelogram is
A = bh
A = 14*5
A = 60 cm^2
[tex] area \: of \: parallelogram \: = \: base \times height[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: 14cm \times 5cm[/tex]
[tex]a \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 70 {cm}^{2} [/tex]
Solve the following equations
(a) tydt + (t + 1)dy = 0,
(b) y dy dt + t = 1,
(c) ty0 + y = y 2 , with the initial condition, y(1) = 1 2
Answer:
A) In y = - [ x-In (x+1) ] + c
B) [tex]\frac{y^2}{2} = t - \frac{t^2}{2} + c[/tex]
Step-by-step explanation:
A) tydt + ( t + 1 ) dy = 0
dy/y = - ( [tex]\frac{tdt}{t+1}[/tex] ) we have to integrate both sides of the equation
In y = - [ x- In (x +1) ] + c
B) y dy/dt + t = 1
we can express the equation as :
y dy = ( 1 - t ) dt
when we integrate the equation we have
[tex]\frac{y^2}{2} = t - \frac{t^2}{2} + c[/tex]
Write 5.42 as a mixed number in simplest form.
5.42 =
Answer: 5 21/50
Step-by-step explanation: 5.42 = 271/50 = 521/50 as a fraction
What's the perimeter of triangle ABC
Answer:
[tex]\Large \boxed{12.9}[/tex]
Step-by-step explanation:
BC = B’C’
BC = 2
The perimeter of a triangle is the sum of all its sides.
[tex]\sf \Rightarrow 5.1+5.8+2 \\\\\\ \Rightarrow 12.9[/tex]
The perimeter of the triangle is 12.9.
Answer:
12.9 is the perimeter
Step-by-step explanation:
BC is 2 since B’C’ is equal to BC.
Add all sides to get perimeter.
5.1+5.8+2=12.9
You’re welcome.
- bananamilkshake43
solve v = 1/3 bh for b the base of the cone
Answer:
[tex]b = \frac{3v}{h} [/tex]Step-by-step explanation:
[tex]v = \frac{1}{3} bh[/tex]First of all multiply through by 3
That's
[tex]3v = \frac{1}{3} \times bh[/tex]We have
[tex]3v = bh[/tex]Divide both sides by h to make b stand alone
That's
[tex] \frac{bh}{h} = \frac{3v}{h} [/tex]We have the final answer as
[tex]b = \frac{3v}{h} [/tex]Hope this helps you
Point A is the terminal point on the unit circle associated with real number pi/5. What are the coordinates of this point?
Answer:
In polar coordinates, we represent the points as:
P = (R, θ)
Where R is the radius and θ is the angle (depending on how you want to work, you can use θ in degrees or radians).
Then in this case we know that we are working with the unit circle, whose radius is R = 1.
And the angle is pi/5.
Then our point will be:
P = (1, pi/5).
Now we also could write it in rectangular coordinates, knowing that for a point (R, θ) we have:
x = R*cos(θ)
Y = R*sin(θ)
Then for our point the rectangular coordinates are:
x = 1*cos(pi/5) = 0.81
y = 1*sin(pi/5) = 0.59
Then the point is (0.81, 0.59)
PLEASE HELP ME SOLVE THIS QUESTION(PLS CHECK IMAGE)
20x4=10
30x13=12
10x12=3
40x11=
Answer:
440
Step-by-step explanation:
12. Write the first five terms of two different sequences that have 10 as the
second term. Describe the pattern in each of your sequences.
Answer:
a) The arithmetic sequence with common difference 2 that has 8 as the first term.
b) The arithmetic sequence of common difference -5 and first term 15.
Step-by-step explanation:
Let's use for example the arithmetic sequence with common difference 2 that has 8 as the first term. Then the first two terms of this sequence are:
8, and (8+2) = 10 Therefore the second term is 10.
Another arithmetic sequence of common difference -5 and first term 15. The firs two terms of this sequence are:
15, and (15 - 5) = 10. Therefore again a 10 as second term.
How to calculate the value of i=?
Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
HELP ASAP,,,,,,,,,,,,,,,
Answer:
3. it should be positive 3.5
4. (-2,4); (4,2); (6,-9)
Step-by-step explanation:
Consider a simple clock.
A. Find the measure of the angle swept by the hour hand between noon and 9:55 pm
B. Find the exact angle between the minute and hour hands at 1:25 pm
Answer:
A. 280degree
B. 137degree
miranda made some cupcakes for the school bake sale. Of the cupcakes 1/2 are choclate and 1/2 are strawberry. Of the strawberry cupcakes, 1/3 are frosted with vanilla frosting, and the rest are frosted with choclate frosting. What portion of the cupcakes are strawberry with chocalate frosting?
Answer:
2/3
Step-by-step explanation:
3/3 = 1 whole
3/3 - 1/3 = 2/3
State the domain and the range of each relation. Then determine whether the relation is a function. Write yes or no. {(2,7), (3,10), (1,6)}
A school has 1500 students. Given that 3% of them were late for school on a particular day, find the no of students who were punctual for school
Answer:
1455
Step-by-step explanation:
0.03% x 1500 = 45
therefore, 45 students were late
1500 - 45 = 1455 punctual
Vector a = 4i + 5j
Vector b = 3i + 6j
Find the dot product.
Step-by-step explanation:
a · b = (4)(3) + (5)(6)
a · b = 12 + 30
a · b = 42
Answer:
42
Step-by-step explanation:
a*b = 4*3 + 5*6 = 12 + 30 ( where i*i = j*j = 1)
∴ a*b = 42
imagine you and a friend are trying to rearrange the furniture in your classroom. You push on a desk with a force of 150 N to the right. Your friend pushes on the same desk with a force of 50 N to the left. What is the net force on the desk?
Answer:
100NStep-by-step explanation:
If I push on a desk with a force of 150 N to the right and my friend pushes on the same desk with a force of 50 N to the left, this means that I pushed the desk in the positive x direction and the force I applied is F1 = +150N; my friend pushes the desk in the negative x direction and the applied force will be F2 = -50N.
THe net force will the sum total of both forces acting on the desk.
Net force F = F1+F2
Given F1 = +150N and F2 = -50N
Net force F = +150N+(-50N)
Net force F = +150N-50N
Net force F = +100N
Hence the net force on the desk is 100N