Answer:
[tex]\sf 3^{-3x}=3^{(-4x+6)}[/tex]
[tex]\sf x=6[/tex]
Step-by-step explanation:
[tex]\sf Given \ equation: \left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]
[tex]\sf As \ \dfrac{1}{27}=\dfrac{1}{3^3} \ and \ \dfrac{1}{a^b}=a^{-b} \ then \ \dfrac{1}{27}=3^{-3}[/tex]
Therefore, we can rewrite the given equation with base 3:
[tex]\implies \sf (3^{-3})^x=3^{(-4x+6)}[/tex]
Apply the exponent rule [tex]\sf (a^b)^c=a^{bc}[/tex] :
[tex]\implies \sf 3^{-3x}=3^{(-4x+6)}[/tex]
[tex]\sf If \ a^{f(x)}=a^{g(x)} \ then \ f(x)=g(x)[/tex]
[tex]\implies -3x=-4x+6[/tex]
Add 4x to both sides to solve for x:
[tex]\implies \sf x=6[/tex]
Use the equation machine to help you solve the addition equation.
k=8
k=9
k=17
k=26
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 4)(0,4) and (2, 256)(2,256).
Answer:
Step-by-step explanation:
[tex]y=ab^x\\x=0,y=4\\4=ab^0\\4=a(1)\\a=4\\y=4b^x\\x=2,y=256\\256=4b^2\\b^2=\frac{256}{4} =64\\b=\pm8\\y=4(8)^x\\or\\y=4(-8)^x[/tex]
A man invests a sum of money ($8,000) in a bank that offers a rate of 5%. He invests the money for 2 years. Calculate the amount of money in the bank at the end of the 2-year period if invested at:
(a) simple interest
(b) compound interest.
Question 6 (6 marks)
The diameter of a circle is 10 cm (as shown in the diagram). Use π = 3.14 Calculate to 2 decimal places, the:
(a) circumference
(b) area
Answer:
(a) 8000 times 5 times 2 = 800
what is the answer for this also?
Answer:
64 cm^3
Step-by-step explanation:
V = lwh
V = 4 x 4 x 4
V = 64 cm^3
Hope this helps!
[tex] \huge\fbox\orange{ANSWER} [/tex]
[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]
[tex] \mathsf \pink{v = {4}^{3} }[/tex]
[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]
An angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6
The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of [tex](90^0)a[/tex]
Where a = positive odd integer,
We hyave given the given angle is,
[tex](870n)^0,[/tex]
What is terminal side?The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
[tex](870(3))^0=2610^0[/tex]
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
https://brainly.com/question/24680641
Answer:
a
Step-by-step explanation:
x=3 on edge
Answer below
due today at noon
Answer:
x = -3
Step-by-step explanation:
A vertical line has an equation of the form
x = a
where a is the x-coordinate of every point on the line.
Every point on the line has x-coordinate -3, so the equation is
x = -3
I want to know how to find EF and what the answer is.
[tex]\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}[/tex]
Step-by-step explanation:
5x+12=6x+7 (opposite sides of a parallelogram are equal) 12=x+7 (subtract 5x from both sides) x=5 (subtract 7 from both sides) Now put x in any of the equations-- 5(5)+12=37 or 6(5) +7=37Rowan has 3 pieces of yarn, as described below. *a red piece of yarn that is 3/4 foot long *a yellow piece of yarn that is 6/8 foot long * a blue piece of yarn that is 4/12 foot long Wich number sentence correctly compares the lengths of 2 of these pieces of yarn. A 3/4 < 3/6 B 4/12 < 3/4 C 3/4 > 6/8 D 4/12 > 6/8
Answer:
b
Step-by-step explanation:
because all the orher ones are wrong and not correct.
The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?
Answer:
between 222 and 223 days
Step-by-step explanation:
This relation includes the point (0, 2).
A proportional relation must include the point (0, 0).
This is not proportional, but it may be linear.
Points: (0, 2), (2, 20)
y = mx + b
20 = (20 - 2)/(2 - 0) × 2 + b
20 = 18/2 × 2 + b
b = 2
y = 18x + 2
When 4000 people know, y = 4000.
y = 18x + 2
4000 = 18x + 2
3998 = 18x
x = 3998/18
x = 222.111...
Answer: between 222 and 223 days
To determine the age of fossils, scientists use radiometric dating. This involves measuring quantities of certain radioactive isotopes and using mathematical equations to compare the amounts of each isotope present.
Suppose a scientist dates a piece of petrified wood and calculates that it is approximately 23,881,392.3102 years old. The petrified wood is later displayed in a museum.
What is the most reasonable way for the museum tour guide to describe the age of the wood to museum visitors?
(A): 2.3881×107 years old
(B): 24 million years old
(C): 23.8813923102 mega years old
(D): 23 billion years old
Answer:
B 24 million years old
Step-by-step explanation:
i did this quiz a long time ago tho so it might be B or D
Answer 11-12 it’s ok if your don’t no one of them. Please do at least one. Thanks.
[11]
Equation: 180° - 75°
Measure: 105°
A straight line has an angle measurement of 180°. Since we have GFB, 75°, we can find EFB this way.
[12]
Equation: 90° - 40°
Measure: 50°
The little box in the angle shows that it is equal to 90°. Since they give us HGB, 40°, we can solve for EFB using this information.
Pls help thanks to who ever does and please do NOT put links
Answer:
C
Step-by-step explanation:
Remark
The way to solve the problem is to figure out how many cubic feet would be present if the window was not there and then calculate the volume of the window and subtract it. That is the general method used to obtain the answer to the question you have asked.
Volume Original Shape
Each side of the figure is one side of a square.
So the volume of the square face is 6 by 6 or 6*6 = 36 (no window)
The window is 2*2 which is 4.
The volume of the original shape is 36 - 4 = 32
Volume new shape
Each side of the figure is 12 by 12 = 144 With no window
The size of the window is 4 by 4 = 16 With the window (Subtract)
The size of the modified figure is 128
Answer and discussion
The question is a bit ambiguous. I think the question means that the wall has gone from 32 to 128 cubic feet. So you need Subtract to find the difference..
Answer: 128 - 32 = 96 which is C.
I just need help on this one :) could u please try quickly
-3 x 2-1
I got -7. I tried probably wrong
Will give BRAINLIEST!! Write a polynomial and show all the steps you would take to factor this polynomial completely. Please explain each step thoroughly.
I am not accepting links. Thank you:)
Step-by-step explanation:
Consider this polynomial,
[tex]8 {x}^{2} + 2x - 3[/tex]
First, I do the AC memethod. To find my two numbers,
That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C
And that will also add to 2, my middle term.
So using that
[tex]8 \times - 3 = - 24[/tex]
So let find factors of-24:
Factors can be positve or negative
The factors of 24 are : 1,2,3,4,6 8,12,24.
So which one of these add up to 2.
[tex]6 + ( - 4) = 2[/tex]
and
[tex]6 \times - 4 = - 24[/tex]
So six and negative four is our numbers.
Now, let set up our binomials
Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.
Disclaimer: The placement of these numbers doesn't matter.
So we have
[tex]8 {x}^{2} + 6x - 4x - 3[/tex]
Step 2: Group the first two terms and last two terms
[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]
Factors the first group by finding the GCF.
x is the greatest common variable, and 2 is the gcf so we have
[tex]2x(4x + 3) + ( - 4x - 3)[/tex]
Next, factor the next group by -1.
[tex]2x(4x + 3) - 1(4x + 3)[/tex]
Combine the outside factors.
[tex](2x - 1)(4x + 3)[/tex]
So those are the factors.
Does anyone know the answer to these?
JL and MO are parallellines.
Which angles are alternate exterior angles?
Answer:
<N and <K
Step-by-step explanation:
Alternate exterior angles are a pair of angles on the outer side of the two parallel lines and are opposite of each other yet their measure is equal to each other.
The pair of angles that meet these requirements mentioned above are angle N and angle K.
(5) to the 7 over 3 power
[tex]5^{7/3} = 42.75[/tex] (approximately)
using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem
so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75
Simplify −4(x+1)+6x . Write your answer in factored form.
Answer:
2(x - 2)
Step-by-step explanation:
- 4(x + 1) + 6x ← distribute parenthesis by - 4
= - 4x - 4 + 6x ← collect like terms
= 2x - 4 ← factor out 2 from each term
= 2(x - 2)
=================================================
Let's simplify this expression.
The first step is to use the distributive property, which states:-
[tex]\bigstar{\boxed{a(b+c)}[/tex]
Simplify:-
[tex]\bigstar{\boxed{-4(x+1)}[/tex]
[tex]\longmapsto\sf{-4x-4}[/tex]
Add 6x:-
[tex]\longmapsto\sf{-4x+6x-4}[/tex]
Combine Like Terms:-
[tex]\longmapsto\sf{2x-4}[/tex]
Now, we should write our answer in factored form, so we factor 2 out:-
[tex]\longmapsto\sf{2(x-2)}[/tex]
=============================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Help me answer this question about congruent triangles. 50 points available.
Answer:
B
Step-by-step explanation:
No these triangles are not congruent.
Left triangle
Shortest side = 6 cm
Longest side = 13 cm
3rd side = unknown but < 13
Right triangle
Shortest side = 6 cm
Longest side = unknown but > 13
3rd side = 13 cm
Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.
We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.
Question 4 of 10
You have $10.00 and want to buy all of the items below. How much change
will you have left after you make your purchase? Do not include $ in your
answer.
COST
ITEM
Pancake Mix
Eggs
Syrup
$2.18
$2.28
$3.98
PLS HELP!’
Answer: 1.56
Step-by-step explanation:
Add all the cost together, the subtract the ten dollars.
2.18 + 2.28+ 3.98 = 8.44
10.00 - 8.44 = 1.56
A survey asked 100 seventh graders if they have either a cell phone or a tablet. Of the 32 students that have a cell phone, 19 do not have a tablet. Of the 70 students that have a tablet, 57 do not have a cell phone. A total of 11 students stated they do not have a cell phone or a tablet. Some of this information is included in the frequency table.
help please
Answer:
I don't know sir actually I didn't understand your question no need to reply to my answer bye
Answer:
13
Step-by-step explanation:
if you read through the paragraph and pot your data on the table, the answer will show and is 13
A four sided sandbox has exactly 2 right angles to side lengths 5 feet what geometric shape as described shape of the sandbox
Answer:
The sandbox is most likely in the shape of a kite. As it has only two right angles, it cannot be a square or other form of rectangle. It also cannot be a parallelogram, which has no right angles, nor is it a rhombus- all four sides are not of the same length.
A kite, however, has two pairs of equal-length sides that are adjacent to each other. It also has two sets of equal-measure angles, one of which can be 90° if it is a cyclic kite.
What is the value of In e^4
a 0
b 1
c 2
d 4
Answer:
[tex]4[/tex]
Step-by-step explanation:
[tex]\ln e^4= 4\ln e = 4 \log_e e = 4 \times 1 = 4[/tex]
a fast food chain surveyed a random sample of students to determine what pizza they prefer.cheese pizza was preferred by 40 students.pepperoni pizza was preferred by 28 students.based on the results,how many of 340 student can be expected to prefer cheese pizza
Answer:
12%, 0.12, 5/17, or as a ratio: 5:17
Step-by-step explanation:
To find the percentage:
Take the 40 students who prefer cheese and divide it by 340:
0.11764705882 rounded would be 0.12.
Convert 0.12 into 12% of students prefer cheese pizza.
To find the decimal, to the same exact thing I did up there, but, don't turn it into a percent, just leave it as 0.12.
To find the fraction, turn it into:
40/340
Then simplify it:
5/17 prefer cheese pizza.
For ratio, do the same as fraction, but, instead of the slash mark, turn it into a colon like this: 5:17.
:)
What is the area of this figure?
Answer:
234 mm^2
Step-by-step explanation:
These questions are tricky but to make them easier, try to break down the shape into smaller regular shapes and work them out.
I would divide this shape into 2 rectangles and one triangle
Area of small bottom rectangle: 4 x 11 = 44mm^2
Area of rectangle in the middle: 14 x 8 = 112mm^2
Area of triangle: 12 x 13/2 = 78mm^2
Add all the areas together = 44+112+78 = 234mm^2
solve for x use the trig to find angle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's solve, using Trigonometry ~
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{54}{72} [/tex]
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{3}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 37 \degree[/tex]
Answer:
[tex]\displaystyle 36,9[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
OR
[tex]\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
What is the slope-intercept equation for this line?
Answer:
y=-2x-1
Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.
Jasmine is trying to replace the flooring in her rectangular bedroom. When she measured the width and length of the floor, she found that the length is 5 ft. longer than the width. If the perimeter of the room is 50 ft., how much flooring will she need to replace the existing flooring in her room?
Answer:
150ft^2
Step-by-step explanation:
FINDING THE LENGTHS
50 = x + 5 + x + x + 5 + x
50 = 4x + 10
50 - 10 = 4x
40 = 4x
40/4 = x
10ft = x
AMOUNT OF FLOORING
area = l x b
= (10 + 5) x 10
= 15 x 10
= 150ft^2
These triangles are similar. Solve for the scale factor.
Answer:
Scale factor = 3
Step-by-step explanation:
A - B = 1-3
3 - 1 = 2
A' - B' = 3-9
9 - 3 = 6
6 / 2 = 3
A figure is made up of a triangle and a rectangle. The triangle has a height of 8 inches and a base of 9 inches. The rectangle has dimensions of 7 inches×9 inches. What is the area of the figure?
Step-by-step explanation:
area of triangles
1/2*9*8= 36
area of.rectangle
8*9= 72
36+72=108 square inches