Answer:
y = -1/3x + 7
Step-by-step explanation:
x + 3y = 9 ⇒ y = -1/3x + 3
Use point-slope form and substitute the values:
[tex]y-y_1=m(x-x_1)\\y-5=-\frac{1}{3}(x-6)\\y-5=-\frac{1}{3}x+2\\y=-\frac{1}{3}x+7[/tex]
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]
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! :)
What is an equation for the line that passes through the coordinates (2, 0) and (0, 3)?
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%
A rectangle has a length of 12.6 m and a width of 6.3 m. A similar rectangle has a width of 2.1 m. What is the length of the similar rectangle?
Step-by-step explanation:
Please see the photo for the method
What is the area of the triangle ?
A) 64
B) 56
C) 48
D) 112
Answer:
[tex]\text{B) }56\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The area of a triangle with height [tex]h[/tex] and base [tex]b[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. By definition, the base and the height must intersect at a 90 degree angle. Therefore, the diagram gives a base of 14 cm and a height of 8 cm. Substituting these values, we get:
[tex]A=\frac{1}{2}\cdot 8\cdot 14=\boxed{\text{B) }56\:\mathrm{cm^2}}[/tex]
in the right triangle ABC mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Answer:
The length of the hypotenuse is 8 units
Step-by-step explanation:
Recall the notation SOH CAH TOA. This means that in aright angled triangle,
Sin A = a/c where a is the length of the opposite side and c is the length of the hypotenuse.
Given that sinA=1/2 and a = 4, the hypotenuse c
sin A = 4/c
1/2 = 4/c
cross multiply
c * 1 = 4 * 2
c = 8 units
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.
help please anyone ??
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]
Pls help school is almost over
Answer:
correct answer is c
Step-by-step explanation:
2.44x10^-3
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]
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
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
x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth
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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
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].
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
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)
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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.
HELP PLZ ALMOST DONE!!!
Answer:
A = 30 inches^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 10+5) * 4
A = 1/2 (15)*4
A = 30 inches^2
Answer:
Area of trapezoid is 30 inches ².
Step-by-step explanation:
Question :-A trapezoid having length of Base ¹ and Base ² are 10 in. and 5 in. and it's height is 4 in. Find the area of trapezoid.
Solution :-Area of trapezoid is given by
= 1/2 × ( B¹ + B² ) × h
Where, B¹ = 10 in.
B ² = 5 in.
h = 4 in.
substitute the values
Area = 1 / 2 × ( 10 in × 5 in ) × 4 in
multiplying the values
Area = 1 / 2 × 15 in. × 4 in
Area = 1 / 2 × 60 in ².
Area = 30 in².
Hence, Area of trapezoid is 30 inches ².
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
please help picture included
Match the verbal expression (term) with its algebraic expression (definition). Match Term Definition Some number A) a = 2 increased by two A variable decreased B) b + 2 by two Product of an C) y2 unknown value and two D) X - 2 Quotient of some number and two An unknown value E) 22 squared
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Answer:
B, D, E, A, C
Step-by-step explanation:
The main idea here is to use your English comprehension skill to determine the meaning of the phrase, then use your math understanding to write it in symbols. Turning off your brain at the sight of a "word problem" will not be productive.
The wording "some number" or "a variable" or "unknown value" all refer to a variable, typically represented by a single letter. Letters commonly use are {a, b, c, x, y, z}, but variables are not restricted to that set (nor to single letters, nor lower case letters).
In most cases, the math expression is a direct translation of the English expression using the usual math symbols. Values are generally increased by addition, decreased by subtraction, squared using an exponent of 2. A product is the result of multiplication, and a quotient is the result of division.
Top-to-bottom, the boxes on the left will be filled with B, D, E, A, C.
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)
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]
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]
Simplify the expression 35e^9/5e^8
[tex] \frac{35e {}^{9} }{5 {e}^{8} } \ \\ \\ \frac{7e {}^{9} }{e {}^{8} } \\ \\ \\ = 7e[/tex]
Step By Step Explanation:
Reduce: Reduce the fraction with 5Simplify: Simplify the expressionAlternate Forms:
19.02797☆彡Hannaa 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
HELPPPPP!!!
Jack and Joey went to the store to buy candy. Jack bought 5 Hershey bars and 2 packs of
starbursts for $12. Joey bought 3 Hershey bars and 4 packs of starbursts for $13.50. Let x equal the cost of one Hershey bar and y equal the cost of one pack of starbursts.
8a) Write a system of equations that describes the situation above.
8b) using the equations from part a, determine the cost of one Hershey bat and the cost of one pack of starburst in dollars and cents
Answer:
5x + 2y = 12
3x + 4y = 13.50
One Hersey bar = 1.5
One pack of Starburst = 2.25
Step-by-step explanation:
Let :
Cost of one Hersey bar = x
Cost of one pack of Starburst = y
System of equation :
For Jack :
5x + 2y = 12 - - - (1)
For Joey :
3x + 4y = 13.50 - - - (2)
To determine the cost per Hersey bar and pack of Starburst
5x + 2y = 12 - - - (1)
3x + 4y = 13.50 - - (2)
Multiply (1) by 3 and (2) by 5
15x + 6y = 36 - - - (3)
15x + 20y = 67.50 - - - (4)
Subtract (4) from (3)
-14y = - 31.50
y = 31.50 / 14
y = 2.25
Using (1)
5x + 2y = 12
Put y = 2.25
5x + 2(2.25) = 12
5x + 4.50 = 12
5x = 12 - 4.50
5x = 7.50
x = 1.5
Cual es la ecuación de la recta dado su pendiente m=2 y p(2,3)
Answer:
y=2x-1
Step-by-step explanation:
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
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