The pyramid shown below has a square base, a height of 7, and a volume of 84 cubic units.
What is the length of the side of the base?
12
36
6
18
x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth
9514 1404 393
Answer:
x ≈ 2.87
Step-by-step explanation:
We can subtract 6 to put the equation into a form easily solved.
x^2 +2x +1 = 15
(x +1)^2 = 15
x +1 = √15 . . . . . for the greatest solution, we only need the positive root
x = √15 -1 ≈ 2.87
Kate lanes a letter against her house to get to the roof. The house is 25 feet tall and I put a ladder is 15 feet away from the side of the house. What is the angle that the latter makes with the ground?
Answer:
this is the correct answer
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
5
60°
10
x
Not drawn to scale
Answer:
D
5 sq.rt. 3
Step-by-step explanation:
use the pythagorean theorem: a^2 + b^2 =c^2
5^2 + x^2 = 10^2
25+ x^2 =100
x^2 = 100 - 25
x^2 =75
x = [tex]\sqrt{75}[/tex]
x = 5 [tex]\sqrt{3}[/tex]
QueSLUIT Consider the universal set U of all the integers from 2 to 20, including both 2 and 20. Let B be the set of multiples of 2, not counting 2 itself. Find Bº. Write your answer in standard set notation, for example {1,2,3,4,5). Do not use the notation B° = in the answer
Step-by-step explanation:
{2,3,5,7,9,11,13,15,17,19}
Please solve for angle C
Answer:
29
Step-by-step explanation:
tan c = opposite / adjacent
c = tan -1 (25/45) = 29
Answer:
Step-by-step explanation:
tan C = opp/adj
sin C = 25/45
sin C = 0.5556
C = sin^-1 0.5556
= 33.75
lim x->1+( sin(1-x)-(e^(x-1))+1)/ lnx
We're given the one-sided limit,
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]
Evaluating the limand directly at x = 1 gives the indeterminate from
(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0
so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]
what is 2,799.89 x 4,984.76
!please answer i want to know!
Answer:
13,956,779.6764
Answer:
13956 779.7 (•‿•) this is my ans.
Cual es la ecuación de la recta dado su pendiente m=2 y p(2,3)
Answer:
y=2x-1
Step-by-step explanation:
PLEASE HELP ME!!!
WILL BE WORTH 10 POINTS!!!
I WILL MARK BRAINLIEST!!!
Please answer the 3 questions on the picture.
I would appreciate it so much!
A drone is originally priced at 110$. The online retailer gives a discount and the drone is now $88 . enter the percentage discount for the cost of the drone.
Answer:
20%
Step-by-step explanation:
Decrease in amount = original - new amount
Decrease in amount = 110 - 88 = $22
Decrease % = decrease/original x 100%
= 22/110 x 100%
= 20%
Find the volume of the given prism.
A) 6,336
B) 3,568
C) 1,784
D) 1,920
Answer:
[tex]\text{D. }1,920}\:\mathrm{in^3}[/tex]
Step-by-step explanation:
The volume of a rectangular prism is given by [tex]A=l\cdot w\cdot h[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is width, and [tex]h[/tex] is height.
Therefore, the area of the given prism is equal to [tex]8\cdot 12 \cdot 20=\boxed{\text{D. }1,920\:\mathrm{in^3}}[/tex].
AB = 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
12 cm
55°
6 cm
Answer:
12.7 cm
Step-by-step explanation:
We can obtain CB using Pythagoras :
CB = √12² - 6²
CB = √108
CB = 10.39
Using CB,
We can apply trigonometry on triangle BCD to obtain the length of CD
Sin θ = opposite / hypotenus
Sin 55 = CB / CD
Sin 55 = 10.39 / CD
CD = 10.39 / sin 55
CD = 12.68
CD = 12.7 cm
A student needs 12 minutes to solve an algebra problem how many minutes does the student need to solve 6 problems
Answer:
72
Step-by-step explanation:
12 * 6 = 72
of course, IRL not every problem takes the same amount of time
Answer: if they are all algebra questions then 72
Step-by-step explanation:
12 + 12 + 12 + 12 + 12 + 12= 70
QUESTION 14 · 1 POINT
Translate the English phrase into an algebraic expression: 6x less than 81xsquared
Answer:
Step-by-step explanation:
81x² - 6x
Answer:
81x² - 6x
Step-by-step explanation:
81x² - 6x
estimate the quotient for the following problems. 482 ÷ 5
Answer:
100
Step-by-step explanation:
482 ÷ 5 = 96.4
96.4 -> 100
Hope this helps! Brainliest?
Answer:
Quotient: 96
Step-by-step explanation:
482/5= 96R2
Quotient: 96
Remainder: 2
help please anyone ??
The Isosceles Trapezoid is part of an Isosceles triange with a 32° vertex angle. What is the measure of an acute base angle of the trapezoid?
Answer:
[tex]b = 74^o[/tex] --- acute base
Step-by-step explanation:
Given
See attachment for the figure
Required
The acute base angle of the trapezoid
From the question, the isosceles triangle and the trapezoid share the same base.
Represent the base angle with b.
So:
[tex]b + b + 32^o = 180^o[/tex] --- angles in a triangle
[tex]2b = 180^o-32^o[/tex]
[tex]2b = 148^o[/tex]
Divide by 2
[tex]b = 74^o[/tex]
Does this a graph show a function? Explain how you
know.
O A. Yes; there are no y values that have more than one x-value.
O B. No; there are y-values that have more than one x-value.
O C. Yes; the graph passes the vertical line test.
O D. No; the graph fails the vertical line test.
Answer:
D. No; the graph fails the vertical line test.
Step-by-step explanation:
If any vertical line intersects a graph more than once it is NOT a function
In the accompanying diagram of circle o, chords AB and CD
intersect at E. If AE = 3, EB = 4, CE = x, and ED = x +1,
find CE
Answer:
x = 3
Step-by-step explanation:
Given :
AE = 3, EB = 4, CE = x, and ED = x +1,
Equating chord AB and CD
AE*EB = CE*ED
3*4 = x*(x+1)
12 = x² + x
x² + x - 12 = 0
x² +4x - 3x - 12 = 0
x(x + 4) - 3(x + 4)
(x + 4) = 0 or (x - 3) = 0
x = - 4 or x = 3
Distance can't be negative :
x = 3
Find the Laplace Transform of the following function.
f(t) = 10 cos (12t+ 60°) u(t)
Answer:
L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]
Step-by-step explanation:
f ( t ) = 10 cos ( 12t + 60°) u(t)
attached below is a detailed solution of the given problem
L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]
This college has one of the highest median graduation rates and the best consistency in graduation rates over time.
Answer:
70 has the most groups
Step-by-step explanation:
from the graph
Answer:
Step-by-step explanation:
The dark blue graph illustrates these two requirements. The rates represented there have the highest median.
Same graph illustrates consistency in outcomes, as the graduation rates vary little from their median.
A parallelogram is shown below: A B A 2 foot D с 3 feet Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
9514 1404 393
Answer:
Part A: 2 ft²
Part B: draw a diagonal (AC, for example); 1 ft²
Step-by-step explanation:
Part A:
The area of a parallelogram is given by the formula ...
A = bh
where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.
Using the numbers shown on the diagram, the area is ...
A = (3 ft)(2/3 ft) = 3·2/3 ft²
A = 2 ft² . . . . . area of the parallelogram
__
Part B:
Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.
The area of a triangle is given by the formula ...
A = 1/2bh
A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²
A = 1 ft² . . . . . . . . area of each triangle
_____
Additional comment
It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.
a phone company uses the expression 1.25 + 0.10m to calculate the cost of a phone call that lasts m minutes. what is the cost of a call that lasts 20 minutes?
Answer:
[tex]f(20) =3.25[/tex]
Step-by-step explanation:
Given
[tex]f(m) = 1.25 + 0.10m[/tex]
Required
[tex]f(20)[/tex]
We have: [tex]f(m) = 1.25 + 0.10m[/tex]
Substutute 20 for m
[tex]f(20) =1.25 + 0.10*20[/tex]
[tex]f(20) =1.25 + 2[/tex]
[tex]f(20) =3.25[/tex]
Find the value of x. Leave your answer in simplest radical form.
a rectangular room is 15ft long, 14ft wide and 8.0ft high. what is the length of the longest diagonal from one corner to another of the room
Answer:
20.51ft
Step-by-step explanation:
Given data
Length= 15ft
Width= 14ft
Height= 8ft
Because we want to find the diagonal, let us use the Length and the width
We can get the diagonal by applying the Pythagoras theorem
z^2= x^2+y^2
z^2= 15^2+ 14^2
z^2= 225+ 196
z^2= 421
square both sides
z= √421
z=20.51 ft
Hence the diagonal is 20.51ft
x−9≥−12 Express your answer as an inequality.
Answer:
x ≥ −3
Step-by-step explanation:
Step One : Add 9 to both sides.
x − 9 + 9 ≥ −12 + 9
x ≥ −3
There is no more to be done, that is our answer. x ≥ −3.
Hope this helps, please mark brainliest! :)
Which graph shows Point Pin Quadrant II and Point Q as (3,-4)
Answer:
p would be up top on the negative side (left)
q would be at the bottom on the positive side (right)
What is an equation for the line that passes through the coordinates (2, 0) and (0, 3)?
In the accompanying diagram of circle O, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x + 1, find. CE.
Answer:
CE = 3
Step-by-step explanation:
Given:
AE = 3
EB = 4
CE = x
ED = x + 1
Required:
CE
Solution:
First we need to determine the value of x by generating am equation as follows:
CE × ED = AE × EB (Interacting Chords Theorem)
Substitute
x × (x + 1) = 3 × 4
x² + x = 12
Subtract 12 from each side
x² + x - 12 = 12 - 12
x² + x - 12 = 0
Factorize to find the value of x
x² + 4x - 3x - 12 = 0
x(x + 4) -3(x + 4) = 0
(x - 3)(x + 4) = 0
x - 3 = 0
x = 3
Or
x + 4 = 0
x = -4
Let's use the positive value of x
CE = x = 3