Answer:
4 < x < 12
Step-by-step explanation:
Given:
[tex]\displaystyle \large{9|x-8| < 36}[/tex]
Divide both sides by 9:
[tex]\displaystyle \large{|x-8| < 4}[/tex]
Theorem:
For [tex]\displaystyle \large{|x-a| < b}[/tex], since absolute is less than a constant, the interval or solution is:
[tex]\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}[/tex]
Therefore:
[tex]\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}[/tex]
Therefore, the solution is 4 < x < 12
Answer:
4 < x < 12
Step-by-step explanation:
9|x - 8| < 36
Divide both sides by 9:
|x - 8| < 4
Solution 1
(x - 8) < 4
Add 8 to both sides:
x < 12
Solution 2
-(x - 8) < 4
-x + 8 < 4
Subtract 8 from both sides:
-x < -4
Divide both sides by -1 (remembering to change the direction of the sign):
x > 4
Therefore, the solution to the inequality is 4 < x < 12
Who was one of the earliest non-king leaders of the Benin people?
A. Sakura
B. Oranyan
C. Ekewa
D. Sundiata
Answer:
the answer is d , sundiata!
Step-by-step explanation:
the
Given an interest rate of 12% compounded yearly, Find the equivalent rate per year compounded monthly.
Answer:
Answer below in the picture
I hope my answer helps.
HELP ME OUTT PPL (BRAINIEST)
Answer:
(0, 6)
Step-by-step explanation:
Point T is at (3, 4), and three units to the left would be (0, 4). They then tell us to go two points up, which would change the ordered pair to (0, 6).
I hope this was helpful! Have a lovely day! :D
help pretty please!
Cyrus lives 11 miles due south of Adriana, Adriana live 19 miles due west of Jane, Jane lives 12 miles due south of Madisyn.
The shortest distance between Cyrus' house and Jane's house is
•21.95
•481.802
•0.52
The shortest distance between Adriana's house and Madisyn's house is
•504.901
•22.47
•44.42
Answer:
A.) 21.95
B.)22.47
Step-by-step explanation:
A.) An easy way to solve this is to use the Pythagorean theorem. Since the only person between Cyrus and Jane is Adriana, we will use her as a measuring point. Adriana's distance to Jane is 19, we will set a = 19, Adriana also is 11 miles away from Cyrus, and we will set b = 11. Now we plug it into the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+11^2=c^2\\\sqrt{482} =\sqrt{c^2}\\ 21.95=c[/tex]
B.) Using the same principle but for Adriana and Madisyn, we will use Jane as she is between them. Adriana is 19 miles from Jane, so we will set a=19, Madisyn is also 12 miles from Jane, so we will set b=12. Plug it for the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+12^2=c^2\\505=c^2\\\sqrt{505}=\sqrt{c^2}\\ 22.47 = c[/tex]
Find the area of the plane figure :
Answer:
99.9 [tex]cm^{2}[/tex]
Step-by-step explanation:
Given, AB=13 cm, BC=4 cm
AC is the diagonal of parallelogram ABCD.
Also AC=16 cm
We know, △ABC≅△ACD [S−S−S Congruence]
Also, area of parallelogram ABCD = Area of △ABC + Area of △ACD
= 2 × Area of △ABC
= [tex]2\sqrt{s(s-13)(s-4)(s-15)}[/tex]
[tex]s= \frac{13+15+4}{2}[/tex] = [tex]2\sqrt{16(16-13)(16-4)(16-15)}[/tex]
= 16 = 99.9
Three students are sitting in a playground to make a circular path. They are sitting on the circumference, the co-ordinates of their position on the circle are (1, 2), (3, 4) and (3, 2). Find the co-ordinates of the point equidistant from their position. Also, find the equation of the locus.
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
How to derive the equation of the circunference associated with a playground
The center is the point that is equidistant to every point on the circumference. First, we need to determine the coefficients of the general equation of the circle, whose form is described below:
x² + y² + D · x + E · y + F = 0 (1)
We need three distinct points of the circumference to determine one solution.
If we know that (x₁, y₁) = (1, 2), (x₂, y₂) = (3, 4) and (x₃, y₃) = (3, 2), then the system of linear equations is:
D + 2 · E + F = -5 (2)
3 · D + 4 · E + F = - 25 (3)
3 · D + 2 · E + F = - 13 (4)
The solution of the linear system is D = - 4, E = - 6 and F = 11.
Now we proceed to transform the expression into its standard form by completing the squares:
x² + y² - 4 · x - 6 · y + 11 = 0
(x² - 4 · x + 4) + (y² - 6 · y + 9) - 2 = 0
(x - 2)² + (y - 3)² = 2
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
To learn more on circumferences, we kindly invite to check this verified question: https://brainly.com/question/4268218
A car depreciates at a rate of 30% per year. How much will
a $20 000 car be worth after five years? (3 marks)
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 30\%\to \frac{30}{100}\dotfill &0.3\\ t=\textit{elapsed time}\dotfill &5\\ \end{cases} \\\\\\ A=20000(1 - 0.3)^{5}\implies A=20000(0.7)^5\implies A=3361.4[/tex]
Samantha collected 352 books to give to her students. If she gives 4 books to her students each day, how many days will it take her to give all of her books away?
Answer: 88
Step-by-step explanation:since we know 4 books are given each day and the total is 352 . 352 divided by 4 is 88
Answer:
the answer is 88
Step-by-step explanation:
352÷4=88
Which is greater -8.5 or -15
Answer:
-8.5
Step-by-step explanation:
this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.
Jessica needs 658 cups of flour for her recipe. The box she has only has 78 cup of flour left in it.
How many more cups of flour does she need?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
5 3/4 cups.
Step-by-step explanation:
Subtract the two amounts.
6 5/8 - 7/8
Make 6 5/8 an improper fraction by multiplying the 8 and 6 then adding 5.
8 x 6 = 48
48 + 5 = 53
53/8
53/8 - 7/8 = 46/8
Convert back into a mixed number by dividing.
46/8 = 5 6/8
reduce the fraction
5 3/4
Find AE. Round the answer to the nearest tenth.
A 9.7
B. 13.5
C. 16.1
D. 17.3
AE= 17.4 to nearest tenth
Step-by-step explanation:
Opposite + hypotenuse = SOH / sin
Sin 31 = 6/h
xh, then ÷ sin31
H= 6/sin31
H= 11.649....(a or b & 6 being a or b)
a^2 + b^2 = c^2
c = 13.1
Actually it's not a right-angle triangle
180 - 13+31 (or 44) = 136 degrees
Cosine rule: a^2=b^2+c^2 - 2bc cosA
AE = root 11.649...^2 + 7^2 - 2x11.649...x7xcos136
= 17.3791......
AE= 17.4 to nearest tenth
Hope this helps!
In a school theater performance, 150 tickets were sold, some for $30 and others for $20, how many tickets were sold of each price if the total sale was $3,500?
Answer:
85 tickets for 20 dollars and 60 for 30
Step-by-step explanation:
my smart friend in AP calc said so
How would you write 8^5 as a multiplication expression?
OA 8x5
ОВ.8x8x8x8x8
OC. 5x5x5x5x5x5x5x5
Answer:
The answer is B
Step-by-step explanation:
Because the exponent shows how many times you multiply that number
Example: 8^2 would be 8x8 because it is to the second power
Hopefully this helps
Answer:
Step-by-step explanation:
8•8•8•8•8 is the correct answer
emma had originally selected 8 intervals the interval that she put up for swap was not picked up nor did she show up to service it her technical issue had also prevented her from servicinfor 45 minutes emma was also 5 minutes late for two other intervals what was emma resulting ca percentage for the week
Answer:
83%
Step-by-step explanation:
mrs. vickers is covering her students work table with chalkboard paper. the table is a radius of 3.8 ft. How much paper will she need?
Answer:
How might the situation lead to bullying?
How might the situation lead to bullying?
How might the situation lead to bullying?
How might the situation lead to bullying?
Step-by-step explanation:
A tree of 14m height is broken by the wind so that its top touches the ground and makes an angle of 60° with the ground. Find the length of the broken part of the tree.
Please help me,
I'll will mark as BRAINLIEST...
Answer:
7.50 m
Step-by-step explanation:
The side lengths of the "special triangle" with angles 30°-60°-90° have the ratios 1 : √3 : 2. These ratios can be used to solve the problem.
__
The parts of the tree of interest correspond to the long side and the hypotenuse of a 30-60-90 triangle.
In terms of the above ratio units, the fraction of tree height that is broken off is ...
[tex]\dfrac{\text{hypotenuse}}{\text{hypotenuse $+$ long side}}=\dfrac{2}{2+\sqrt{3}}\approx0.535898[/tex]
So, the length of the broken part of the tree is ...
0.535898 × 14 m ≈ 7.50 m
What is the length of AB? I
Answer:
9 units
Step-by-step explanation:
Line O bissects AC at its midpoint, creating a right angle. So, we know that AB is exactly 1/2 of AC.
Algebraically:
AB = AC/2
AB = 18/2
AB = 9 units
Hope this helps!
Answer:
AB = 9
Step-by-step explanation:
Perpendicular line from the center of the cirlcle to the chord bisects the chord.
AB = 18/2
AB = 9
Help picture below problem 9
Answer:
sometimes...
Step-by-step explanation:
mark me brainliest
A parallelogram is sometimes a rectangle.
A) sometimes
Explanation:because the vertices join the adjacent sides at 90° angles and it has two sets of parallel sides and two pairs of opposite sides that are congruent. (a rectangle has all of the properties of a parallelogram.)
A printer can print 14 pages in 28 sec.
The rate in lowest terms is____?
Answer:
1/2 or 0.5 :)
Step-by-step explanation:
We can divide to see lower forns :)
14/28 = 7/14 = 1/2
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
2 pages every 7 seconds, divide by the common denominator which is 7 to get the answer
I’m not good at these I need help
Answer:
f(3) = 9
Step-by-step explanation:
From the table, when can see that when x is 3, f(x) is 9.
Therefore, f(3) = 9
Answer:
[tex]f(3)[/tex]=9
Step-by-step explanation:
[tex]f(x)[/tex] is x times a function.
so if you look at the table on the 'x' side and go down the table until you reach '3' and see what number on the 'f(x)' side corresponds with it, you will see '9'
so [tex]f(3) = 9[/tex]
and that means your answer is D
What would be the most logical first step for solving this quadratic equation?
x²+2x-11=4
A. Add 11 to both sides
B. Take the square root of both sides
C. Divide both sides by x
D. Subtract 4 from both sides
Answer:
D. Subtract 4 from both sides
Step-by-step explanation:
When you're solving a quadratic equation you want to use the quadratic formula [tex]\frac{-b+ \sqrt[]{b^{2} -4ac } }{2a}[/tex].
To get the quadratic equation into this form, you first need to convert it into [tex]ax^{2} +bx+c=0[/tex] which means the first step would be to subtract 4 on both sides.
Find the area of this parallelogram. A) 35 cm B) 75 cm C) 105 cm D) 150 cm
Answer:
B) 75 cm
Step-by-step explanation:
A = bh
(b =base & h = height)
therefore
area = 5 × 15
= 75 cm
I think this will helpful to you
give me a brainliest
Mae has 36 orange slices. She will fill each of
7 bags with the same number of orange slices.
How many slices will be in each bag? How many
slices will be left over?
Answer:
5 orange slices will be in each bag with 1 left over
Step-by-step explanation:
36 ÷ 7 = 5 with a remainder of 1
a
A map is drawn to scale so that a length of 1 centimeter on the map represents an actual distance of 5
kilometers. If two towns are 30 centimeters apart on the map, what is the actual distance between the two
towns?
Answer: 150 kilometers
Step-by-step explanation:
if it's 30 units of 5 kilometers then you multiply it
5x30=150
help me please :( I need this rlly badly no cap
Answer:
given below
Step-by-step explanation:
1 a. Sample space : 2 green, 1 red, 10 blue
b. Sample space : top surface, bottom surface, curved surface ( side)
c. shooting a free throw in a basketball game ( sorry I dont know this one )
On a given planet the weight of an object varies directly with the mass of an object. Suppose that an object whose mass is 3kg weighs 21N. Find the weight of an object whose mass is 7kg
x= 1+ root 2. find (x-1/x)³
I m in grade 9
Answer:
2√2 / (5√2 + 7)
Step-by-step explanation:
Given :
x = 1 + √2Expanding
(x - 1 / x)³(1 + √2 - 1)³ / (1 + √2)³(√2)³ / (1 + √2)³2√2 / 1 + 2√2 + 3(1)(√2)(1 + √2)2√2 / 1 + 2√2 + 3√2 + 62√2 / (5√2 + 7)Answer:
[tex]-14\sqrt{2}+20[/tex]
Step-by-step explanation:
[tex]\textsf{Substituting}\quad x=1+\sqrt2\quad\textsf{into}\quad\left(\dfrac{x-1}{x}\right)^3[/tex]
[tex]\implies \left(\dfrac{(1+\sqrt2)-1}{(1+\sqrt2)}\right)^3[/tex]
[tex]\implies \left(\dfrac{\sqrt2}{1+\sqrt2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule}:\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{(1+\sqrt2)^3}[/tex]
Expand numerator:
[tex](\sqrt{2} )^3=\sqrt{2}\sqrt{2}\sqrt{2}=2\sqrt{2}[/tex]
Expand denominator:
[tex]\begin{aligned}(1+\sqrt2)^3 & = (1+\sqrt2)(1+\sqrt2)(1+\sqrt2)\\ & =(1+\sqrt2)(1+2\sqrt{2}+2)\\ & =1+2\sqrt{2}+2+\sqrt{2}+2\sqrt{2}\sqrt{2}+2\sqrt{2}\\ & = 7+5\sqrt{2}\end{aligned}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{7+5\sqrt2}[/tex]
Substituting expanded numerator and denominator:
[tex]\implies \dfrac{2\sqrt{2}}{7+5\sqrt2}[/tex]
[tex]\textsf{Mulitply by conjugate :}\quad\dfrac{7-5\sqrt2}{7-5\sqrt2}[/tex]
[tex]\implies \dfrac{2\sqrt{2}(7-5\sqrt2)}{(7+5\sqrt2)(7-5\sqrt2)}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{49-50}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{-1}[/tex]
[tex]\implies -14\sqrt{2}+20[/tex]
Using proportions to solve for missing sides.
BCD~GEF, find BD.
Answer:
BD = 19
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so we have ...
BD/GF = BC/GE
(2x -7)/57 = (x +4)/51 . . . . use the values marked on the diagram
17(2x -7) = 19(x +4) . . . . . . . . multiply by 969
34x -119 = 19x +76 . . . . . eliminate parentheses
15x = 195 . . . . . . . . . add 119-19x
x = 13 . . . . . . . . . . divide by 15
BD = 2(13) -7 . . . . use the found value of x in the expression for BD
BD = 19
Sandy wants to carpet the game room in her house. How many square feet of carpet will she need to complete her project if the diameter of the semicircle portion of her room is 10 ft and the base of the triangle is 5 ft? Carpet is only sold in whole number quantities.
Answer:
52ft²
Step-by-step explanation:
Explanation is in photo
What is 25.4 x 10 to the 4th power?
Answer:
254,000
Step-by-step explanation:
What is 25.4 x 10 to the 4th power?
Translate:
25.4 * 10⁴
25.4 * 10,000
When multiplying numbers by 10s, 100s, 1,000s, and so on, all you have to do is move the decimals left (for dividing) or right (for multiplying). The number of spaces you move the decimal is based on the number of zeros following the 1. For example, *100 means moving the decimal two times to the right, and /100 means moving the decimal two places to the left. No calculator is really needed.Here, we will be moving the decimal four times to the right:
25.4 * 10,000
254,000
Note: if you're not sure, you can always use a calculator to double check :)
Hope this helps!