Answer:
Step-by-step explanation:
Discussion
The object of this is make w by itself on one side of the equation.
Equation
x = 3 (y + w) - 1 Add 1 to both sides of the equation.
x + 1 = 3(y + w) - 1 + 1 Combine
x + 1 = 3(y + w) Remove the Brackets
x + 1 = 3y + 3w Notice y and w are affected by the 3. Subtract 3y
x + 1 - 3y = 3y-3y + 3w Combine
x + 1 = 3w Divide both sides by 3
(x +1)/3 = 3w/3
(x + 1)/3 = w
Answer: (x + 1)/3 = w
Given the functions f(x) = log2(4x) and g(x) = 4x – 3, which of the following statements is true?
Both f(x) and g(x) have a common domain on the interval (0, ∞).
Both f(x) and g(x) have the same range of (–∞, 0].
Both f(x) and g(x) have the same x-intercept of (2, 0).
Both f(x) and g(x) increase on the interval of (–4 , ∞).
The true statement about the two functions is:
"Both f(x) and g(x) increase on the interval of (–4 , ∞)."
Which statement is true regarding the given functions?Here we have the functions:
f(x) = log₂(4x)
g(x) = 4x - 3
That can be seen in the graph at the end. In the graph the green one is the logarithmic function.
As you can see there, both of these have similar ranges that go from (-∞, ∞) and both are increasing functions.
Then the correct statement is:
Both f(x) and g(x) increase on the interval of (–4 , ∞).
Where f(x) is actually increasing on all it's domain which is (-∞, ∞), so the statement is true.
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Answer:
Both f(x) and g(x) have a common domain on the interval (0, ∞).
Step-by-step explanation:
The person explained it perfectly in this link shown below
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pls give me brainist for finding the answer
Also, the answer to the question
"What type of function is f(x) = 2x^3 – 4x^2 + 5?"
A) Exponential
B) Logarithmic
C) Polynomial
D) Radical
The answer is C) Polynomial
Explanation:
The exponential equation would look like this: f(x) = 2^x
with x for the exponent
The logarithmic equation would look like this: f(x) = log2 + 4
with log in the equation
The radical equation would look like this: f(x) = x^2 + 4x -1
3x^2 -9x +2
With divide by something
The area of the parallelogram below is
square meters.
9 m
2 m
Find the solutions to the equation below.
Check all that apply.
2x² +7x+3=0
A. x=2
B. x=4
C. x= 3
D. x=7
Ex=-3
F. x= -1/-2
Answer:
E and F.
Step-by-step explanation:
This can be written in quadratic formula.
x = -b +- √b² - 4ac/2a
The equation to solve is written as ax² + bx + c = 0.
a = 2, b = 7, c = 3
x = -7 +- √49 (7²) - 24 (4*2*3, or 4ac).
x = -7 +- √25
x = -7 +- 5
divide by 2a (4)
-7/4 = -1.75
5/4 = 1.25
now we do -1.75 +- 1.25
x = -1/2 (F.)
x = -3 (E.)
Sorry for the late response, I had made an error and had to fix it.
what is 8% of 40 as a decimal
Answer:
The answer is 3.2
Step-by-step explanation:
8 x 40________100 = 3.2can anyone help me find the area of these two pls ?
Pa answer po please,thank you po!!
brainliest>>>>>
Answer:
answer down below
Step-by-step explanation:
Select the correct answer from each drop-down menu. Graph shows 2 four-sided polygons in the first quadrant of a coordinate plane. First polygon is at A (3, 0), B (1, 0), C (1, 2), and D (3, 2). Second polygon is at A prime (6, 0), B prime (2, 0), C prime (2, 2), and D prime (6, 2). In the figure, polygon ABCD is transformed to create polygon A′B′C′D′. This transformation is a by a factor of .
This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2
How to determine the scale factor?The coordinates are given as:
First polygon: A (3, 0), B (1, 0), C (1, 2), and D (3, 2). Second polygon: A' (6, 0), B'(2, 0), C'(2, 2), and D'(6, 2)Calculate the distance AB and A'B' using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
This gives
[tex]AB = \sqrt{(3-1)^2 + (0-0)^2} = 2[/tex]
[tex]A'B' = \sqrt{(6-2)^2 + (0-0)^2} = 4[/tex]
Divide A'B' by AB to determine the scale factor (k)
k = 4/2
k = 2
Hence, this transformation is a by a factor of 2
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Lucy went on holiday for 10 days. These are the temperatures for each day. 21°C 24°C 29°C 23°C 24°C Calculate the median temperature 24°C 27°C 23°C 22°C 23°C
Answer:
Step-by-step explanation:
21 22 23 23 23 24 24 24 27 29
(23 + 24)/2= 47/2= 23.5 is the median temperature
Solve the system of equations:
3x-y= 17
5x + 3y = 5
A.(-4,5)
B.(4,-5)
C.(-4,-5)
D.(4,5)
Answer:
x=
1
3
y+
17
3
Step-by-step explanation:
This is all i can get so far, if can improve opon this let me know
It’s costs $79 to buy 5 tickets to a show.what is the cost of one ticket?
Answer:
79÷5=15.8So the answer is (15.8)
Sketch a drawing of a square. Describe the properties of a square.
All four sides of a square are congruent and they all equal 90 degrees
Find the volume of a
cone with a base radius of 5 yd and a height of 7 yd.
Write the exact volume in terms of Tt, and be sure to include the correct unit in your answer.
Answer:
[tex]\textsf{Volume}=\sf \dfrac{175}{3} \pi \:yd^3[/tex]
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
radius (r) = 5 ydheight (h) = 7 ydSubstituting the given value into the formula:
[tex]\begin{aligned}\implies\textsf{Volume} &=\sf \dfrac{1}{3} \pi (5^2)(7)\\\\&=\sf \dfrac{1}{3} \pi (25)(7)\\ \\&=\sf \dfrac{1}{3} \pi (175)\\ \\&=\sf \dfrac{175}{3} \pi \:yd^3\\\\\end{aligned}[/tex]
Answer:
To find :-The volume of cone
Given :-radius (r) = 5 yd
height (h) = 7 yd
Solution :-The volume of cone
[tex] = \frac{1}{3} \pi {r}^{2} h[/tex]
Substituting the value of 'r' and 'h' in the formula.
[tex] = \frac{1}{3} \times \frac{22}{7} \times {5}^{2} \times 7 \\ = \frac{1}{3} \times 22 \times 5 \times 5 \\ = \frac{550}{3} {yd}^{3} [/tex]
Result :-[tex] \text {The volume of cone is} \frac{550}{3} {yd}^{3} [/tex].
[tex] \mathcal {BE \: \: BRAINLY} [/tex]
Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 3 starting from 10. Rule 2: Subtract 7 starting from 58. What is the first term that appears in both sequences?
A.30
B.55
C.60
D.180
The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the Sun is 60°. Find the angle of elevation of the Sum at the time of the longer shadow.
Answer:
[tex]30^{\circ}[/tex].
Step-by-step explanation:
Let [tex]\theta[/tex] denote the unknown angle of elevation. Let [tex]h[/tex] denote the height of the tower.
Refer to the diagram attached. In this diagram, [tex]{\sf A}[/tex] denotes the top of the tower while [tex]{\sf B}[/tex] denote the base of the tower; [tex]{\sf BC}[/tex] and [tex]{\sf BD}[/tex] denote the shadows of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex] and [tex]\theta[/tex], respectively. The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]; [tex]\angle {\sf ACB} = 60^{\circ}[/tex], [tex]\angle {\sf ADB} = \theta[/tex], and [tex]{\sf BD} = 3\, {\sf BC}[/tex]..
Note that in right triangle [tex]\triangle {\sf ABC}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ACB}[/tex]. At the same time, segment [tex]{\sf BC}[/tex] (shadow of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex]) is adjacent to [tex]\angle {\sf ACB}[/tex].
Thus, the ratio between the length of these two segments could be described with the tangent of [tex]m\angle {\sf ACB} = 60^{\circ}[/tex]:
[tex]\begin{aligned}\tan(\angle {\sf ACB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AB}}{{\sf BC}}\end{aligned}[/tex].
[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BC}} = \tan(60^{\circ}) = \sqrt{3}\end{aligned}[/tex].
The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]. Rearrange this equation to find the length of segment [tex]{\sf BC}[/tex]:
[tex]\begin{aligned} {\sf BC} &= \frac{{\sf AB}}{\tan(\angle ACB)} \\ &= \frac{h}{\tan(60^{\circ})}\\ &= \frac{h}{\sqrt{3}} \\ &\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}{\sf BD} &= 3\, {\sf BC} \\ &= \frac{3\, h}{\sqrt{3}} \\ &= (\sqrt{3})\, h\end{aligned}[/tex].
Similarly, in right triangle [tex]{\sf ABD}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ADB}[/tex]. Segment [tex]{\sf BD}[/tex] (shadow of the tower, with [tex]\theta[/tex] as the angle of elevation of the sun) is adjacent to [tex]\angle {\sf ADB}[/tex].
[tex]\begin{aligned}\tan(\angle {\sf ADB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AD}}{{\sf BD}}\end{aligned}[/tex].
[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BD}} = \tan(\theta) \end{aligned}[/tex].
Since [tex]{\sf AB} = h[/tex] while [tex]{\sf BD} = (\sqrt{3})\, h[/tex]:
[tex]\begin{aligned}\tan(\theta) &= \frac{{\sf AB}}{{\sf BD}} \\ &= \frac{h}{(\sqrt{3})\, h} \\ &= \frac{1}{\sqrt{3}}\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}\theta &= \arctan\left(\frac{1}{\sqrt{3}}\right) \\ &= 30^{\circ}\end{aligned}[/tex].
In other words, the angle of elevation of the sun at the time of the longer shadow would be [tex]30^{\circ}[/tex].
Mrs Ferguson is mailing a package that weighs 12.5 pounds. The post office charges by the ounce to mail a package. How much does the package weigh in ounces?
F. 187 ounces
G. 200 ounces
H. 192.5 ounces
J. 100 ounces
Answer: G
Step-by-step explanation:
1 pound equals =16 ounces
12.5 * 16=200
so 200 ounces.
Turn 6% into a decimal
Answer:
0.06
Step-by-step explanation:
Answer:
.06
Step-by-step explanation:
If 1 is 100%, then .06 is 6%.
Hope this helps!
simplify 3 (3a - 6) help please
Step-by-step explanation:
Simplify the expression by using the Distributive Property.
For this expression, we'll be distributing. In simpler terms, multiplying 3 into the values inside the parentheses.
Think of the expression as;
[tex]3(3a-6)=(3 \times3a)+(3 \times -6)[/tex]
Multiply;
[tex]3 \times 3a=9a[/tex] (Multiply the whole number.)
[tex]3 \times -6=-18[/tex]
Your simplified expression is [tex]9a-18.[/tex]
could i have some really really quick help?
Answer:
1125 m
Step-by-step explanation:
Given equation:
[tex]h=-5t^2+150t[/tex]
where:
h = height (in metres)t = time (in seconds)Method 1
Rewrite the equation in vertex form by completing the square:
[tex]h=-5t^2+150t[/tex]
[tex]\implies h=-5t^2+150t-1125+1125[/tex]
[tex]\implies h=-5(t^2-30t+225)+1125[/tex]
[tex]\implies h=-5(t-15)^2+1125[/tex]
The vertex (15, 1125) is the turning point of the parabola (minimum or maximum point). As the leading coefficient of the given equation is negative, the parabola opens downward, and so vertex is the maximum point. Therefore, the maximum height is the y-value of the vertex: 1125 metres.
Method 2
Differentiate the function:
[tex]\implies \dfrac{dh}{dt}=-10t+150[/tex]
Set it to zero and solve for t:
[tex]\implies -10t+150=0[/tex]
[tex]\implies 10t=150[/tex]
[tex]\implies t=15[/tex]
Input found value of t into the original function and solve for h:
[tex]\implies -5(15)^2+150(15)=1125[/tex]
Therefore, the maximum height is 1125 metres.
Convert to vertex form y=a(x-h)²+k
h=-5t²+150t+1125-1125h=-5t²+150t-1125+1125h=-5(t²-30t+225)+1125h=-5(t-15)²+1125Vertex at (15,1125)
As a is negative parabola is opening downwards hence vertex is maximum
Max height=1125mThe size of angle BAC is:
B= 75 degrees
A= 55 degrees
C=?
Answer:
[tex]C=20degrees[/tex]
Step-by-step explanation:
[tex]75 -55=20[/tex]
or [tex]20+55=75[/tex]
So the degrees of Angle C is [tex]20[/tex]
100 points!To solve the problem cos-1(cos(-pi/6)), find the angle in the interval (0,pi) whose cosine is sqrt3/2.
[tex]cos^{-1}[cos(\omega)]\implies \omega \\\\[-0.35em] ~\dotfill\\\\ cos\left( -\frac{\pi }{6} \right)\implies \stackrel{symmetry~identity}{cos\left( \frac{\pi }{6} \right)} \\\\\\ cos^{-1}\left[ cos\left( -\frac{\pi }{6} \right) \right]\implies cos^{-1}\left[ cos\left( \frac{\pi }{6} \right) \right]\implies \cfrac{\pi }{6}[/tex]
why did we use the positive version of π/6?
well, the inverse cosine function has a range of [0 , π], and -π/6 is on the IV Quadrant, out of the range for it, however it has a twin due to symmetry on the I Quadrant, that is π/6, thus the reason.
The angle in the interval (0, pi) whose cosine value is √3 / 2 is π/6 radians.
What is Cosine of an Angle?Cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse of a right angled triangle.
We have to find the angle in the interval (0, π) such that the cosine of the angle is √3 / 2.
We know that, ratio of sides of 30-60-90 triangle is 1 : √3 : 2.
Hypotenuse = 2x
Adjacent side to 30° = √3 x
Cos (30°) = Adjacent side / Hypotenuse
= √3 x / 2x
= √3 / 2
30 degrees is equivalent to 30 × (π/180) = π/6 in radians
Hence π/6 is the angle in the interval (0, π) whose cosine value is √3 / 2.
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If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (/) as the fraction bar
Answer:
7/10
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are two points on the line
m = ( 24-17)/(25-15)
= 7/10
= 7/10
Determine the measure of the missing angle
50 degrees
60 degrees
180 degrees
360 degrees
Answer:
x = 60
Step-by-step explanation:
Let x = ?
120 + 95 +85 +x =360
x +300 =360
x = 360-300
x = 60
A town has a population of 2000 and grows at 4% every year.
What will be the
population after 15 years, to the nearest whole number?
Answer:
3602 people in 15 years
Step-by-step explanation:
2000 ( 1 + .04)^n .04 is 4% n = years
2000 ( 1.04)^15 = 3602 people
What is the measure of the unknown angle?
Image of a full circle divided into two angles. One angle is one hundred twenty degrees and the other is unknown
Group of answer choices
210°
220°
Answer:
The answer is 240 degrees
Step-by-step explanation:
A full circle is 360 degrees.
We know one angle is 120 degrees.
360-120=240 degrees
Simplify (sin? 0 + cos² O) (sin 0 + cos O)
[tex](\sin^2 \theta + \cos^2 \theta)(\sin \theta + \cos \theta)\\\\=1 \cdot(\sin \theta + \cos \theta)\\\\=\sin \theta + \cos \theta[/tex]
Answer:
D: cos^3(O)
Step-by-step explanation:
Quadrilateral H is a scaled copy of quadrilateral G.
40
32
40
32
Quadrilateral H
45
Quadrilateral G
What is the value of i?
Answer:
36
Step-by-step explanation:
[tex] \frac{40}{32} = \frac{45}{?} \\ \frac{32 \times 45}{40 } = 36[/tex]
If quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given that Quadrilateral H is a scaled copy of quadrilateral G.
Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
The sides are proportional.
40/32 = 45/i
We have to find the value of i
Apply cross multiplication
40i=45(32)
40i = 1440
Divide both sides by 40
i = 1440/40
i = 36
Hence, if quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.
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Calculate the perimeter of a football field measuring 80m by 50m
Answer:
260m
Step-by-step explanation:
the length and the width of a football field is 80m and 50 meters.
perimeter- (80+50)×2= 260m
hope it helps
An amateur soccer ball is priced at
$19.50. This is 3/4ths the price of a
professional ball. What is the price of
the professional ball?
Answer: $26
Step-by-step explanation:
If $19.50 is 3/4, we need to find 4/4.
3/4 -> 0.75
4/4 -> 1
We will set up a proportion and solve.
[tex]\frac{19.5}{0.75} =\frac{x}{1}[/tex]
19.5 = 0.75x
26 = x
The professional ball is $26.
Answer:
$26
Step-by-step explanation:
19.50 = 3/4
so
to find 1/4, we do 19.50 / 3 = 6.5
6.5 = 1/4
so the price of a professional ball would be 4/4 (1 whole)
6.5 x 4 = 26
Hope this makes sense.
- profparis
What is the length of the missing leg?
Answer:
2.3
Step-by-step explanation:
4²+b²=4.6²
16+b²=21.16
-16 -16
b²= 5.16
b=√5.16
b= 2.3
Answer:
2.27 in ~2.3 in to the nearest tenth
Step-by-step explanation:
It is a right triangle ....so yo can use pythagorean theorem
4^2 + b^2 = 4.6^2
b = 2.27
Deanna uses only fruit juice and sparkling water to make
punch for a school dance. She uses 6 1/2 liters of fruit
juice. She uses 0.6 as much sparkling water as fruit
juice.
How much fruit punch does she make?
A : 3.9
B : 7.1
C: 9.4
D 10.4
I appreciate it thank you
May Allah bless you