Answers
Answer: his is a simple as well as an interesting question. CASE I: y = 25. Consider this a² = |a|. Given y = 25, we can write like this way,. y = -5/2.
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
We are given the exponential equation:—
[tex]\displaystyle \large{125=(\frac{1}{25})^{y-1}}[/tex]
First, use a law of exponent [Quotient Rules] to convert RHS:—
[tex]\displaystyle \large{125=(25^{-1})^{y-1}}[/tex]
Then convert both bases to base 5:—
[tex]\displaystyle \large{5^3 = (5^{-2})^{y-1}}[/tex]
Use another law of exponent [Power] to multiply the exponent of RHS:—
[tex]\displaystyle \large{5^3 = 5^{-2y+2}}[/tex]
Now that both sides have same base, solve the equations with exponent:—
[tex]\displaystyle \large{3=-2y+2}\\\displaystyle \large{1=-2y}\\\displaystyle \large{y=-\frac{1}{2}}[/tex]
Therefore, the value of y is:—
[tex]\displaystyle \large{\boxed{-\frac{1}{2}}}[/tex]
__________________________________________________________
Summary
This section includes an important or necessary explanation, summary or formulas that was used in the explanation above.
Laws of Exponent
Power of Power Rules:—
[tex]\displaystyle \large{(a^m)^n = a^{mn}}[/tex]
Quotient Rules:—
[tex]\displaystyle \large{a^{-n}=\frac{1}{a^n}}[/tex]
Note that the above, Quotient Rules, is derived from:—
[tex]\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}[/tex]
But when m = 0 the numerator becomes 1.
Exponential Equation
When solving an Exponential Equation, the goal is to convert both sides having the same base.
When both sides have same base, take both exponents of both sides to solve the equation.
__________________________________________________________
If you have any questions regarding this problem or need clarification, do not hesitate to ask in comment! Good luck on your assignment and have a nice day!
Related Questions
28. What is the simplified form of (12y+16)/(3y-2)? (1 point)
a. 4y - 8
b. 8y - 8
c. 4 + 8/3y-2
d. 4+ 24/3y-2
Answers
Answer:
OPTION D
Step-by-step explanation:
You can use long division
3y-2 4 /12y+16
-(12y-8)
24 (remaining)
we can write the expression as 4+24/3y-2
John is buying a new work uniform. He used a 25% off coupon on a pair of boots that were $80. He also bought a belt that was 15% off. In total, John spent $120.25.
How much was the original price of the belt?
Answers
Answer:
$70.88
Step-by-step explanation:
He bought the boots for $80*75% = $80*0.75 = $60
Let x = the original price of the belt
He spent x * 85% = 0.85x for the belt
total cost = 60 + 0.85x = 120.25
0.85x = 120.25 - 60 = 60.25
x = 60.25/0.85 = $70.88
How many squares u can actually count in this given picture?
Answers
Answer:
I counted 24.
Step-by-step explanation:
Its probably a trick question though
Answer: I counted 36.
(edit) But the answer is 40.
Step-by-step explanation:
Count all the "normal" squares. 16.
Then all the 2x2 normal squares. 9.
Then count all the tiny squares. 8.
Then the 2 big squares the tiny squares make. 2.
Then the giant square, which is all the squares. 1.
And I agree this probably is a trick question.
16 + 9 + 8 + 2 + 1 = 36 squares in total
*EDIT*
Apparently 3x3 squares exist so...
3x3 squares . 4
so 36 + 4 = 40 squares in total
(thanks to the person who asked the question in the first place for telling me about those 3x3 squares)
whats (x-3/4)^2 - 5 = 4 using the square root property?
please have an explanation; will give brainliest
answer: -9/4 and 15/4
Answers
Answer:
x = {-9/4, 15/4}
Step-by-step explanation:
To use the square root property to solve the quadratic, you need to get it to a form where the square root function can be usefully applied. That will mean having a square of a binomial on one side of the equal sign, and a constant on the other side of the equal sign.
We can get that from the given equation by adding 5 to both sides.
(x -3/4)^2 -5 = 4 . . . . . . given
(x -3/4)^2 = 9 . . . . . . . add 5 to get the square by itself
x -3/4 = ±3 . . . . . . . . . take the square root
x = ±3 +3/4 = {-9/4, 15/4} . . . . add 3/4 and expand the result
Ethan is randomly choosing a letter from the word “SKIP” and rolling a standard 6-sided die.
Calculate the following:
P (consonant, even number) =
Give your answer as a decimal.
(Hint: A consonant is any letter besides (a, e, I, o, u)
Answers
=====================================================
Work Shown:
A = P(consonant)
A = 3/4 since there are 3 consonants out of 4 letters in the word "SKIP".
B = P(even number)
B = 3/6
B = 1/2
P(consonant, even number) = A*B
P(consonant, even number) = (3/4)*(1/2)
P(consonant, even number) = 3/8
P(consonant, even number) = 0.375
In the given figure, O is the centre of a circle, TN is a Tangent, AN = 12 cm and OE = 5 cm. Find the length of NE.
Answers
Answer:
NE = 8 cm
Step-by-step explanation:
Radius OA = OE = 5 cm
In right triangle OAN, OA² + AN² = ON²
5² + 12² = ON²
ON² = 25 + 144 = 169
so ON = 13 cm
NE = ON - OE = 13 - 5 = 8 cm
( (-3/4)5)2 simplified
Answers
Answer:
3 4/5
Step-by-step explanation:
Zoe invested $16,000 in an account paying an interest rate of 3.6% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 20 years?
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 3.6\%\to \frac{3.6}{100}\dotfill &0.036\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=16000\left(1+\frac{0.036}{4}\right)^{4\cdot 20}\implies A=16000(1.009)^{20}\implies A\approx 19100[/tex]
PLEASE HURRYYYYYY!!!!!
A salesman sold $65,100 in bikes. He eared a 20% Commission, How much did he earn?
explain your answer please
Answers
Answer:
$13,020
Step-by-step explanation:
65,100 * 20% = 65,100 * 0.20 = 13,020
A flower pot has a circumference of 47 inches. What is the approximate length of the radius of the flower pot? Use 3.14 for .
please answer
Answers
Answer:
7.48
Step-by-step explanation:
C=2πr
Solving for
r=C
2π=47
2·π≈7.48028
Answer:
Step-by-step explanation:
Circumference = 47 inches
[tex]2\pi r = 47\\\\2*3.14*r = 47\\\\6.28*r = 47\\\\r = \dfrac{47}{6.28}\\\\[/tex]
r = 7.48 in
Help help math math ASAP ASAP
Answers
❑ Twσ triαnglєѕ αrє cσnѕidєr cσngruєnt if єαch αnd єvєrч ѕidє αѕ wєll αѕ αnglєѕ σf σnє triαnglє iѕ єquαl tσ thє cσrrσѕpσnding ѕidєѕ αnd αnglєѕ σf tht σthєr triαnglє.
❑ cσngruєnt ѕhαpєѕ cαn cσíncídє wíth єαch σthєr pєrfєctlч íf σvєrlαppєd.
[tex]\rule{7cm}{1 mm}[/tex]
the sum of three consecutive numbers is 12 find the small number
Answers
Answer:
3
Step-by-step explanation:
Numbers include 3,4,5
smallest is 3
For functions f(x)=5x2-1 and g(x)=4x-1, find (f.g)(1)
Answers
I believe this is the answer I’m so sorry if it isn’t
What is evaluate of 6a+2b
If a= -2, b=6 and c=5
Answers
-12 + 12
0
i don’t see no C btw
of the 140 in a book, 25% of them have illustrations. How many pages have illustrations
Answers
h e l p m e p l e a s e
Answers
Answer:
(a) 105
(b) 105
(c)105
Step-by-step explanation:
(a) You can subtract 75 from 180 to find your answer
(b) This angle is corresponding with (a)
(c) This is a consecutive exterior angle with the 75 degree one in 4th street and King Ave, therefore it will be 105
Write a mixed number to describe the length of the ribbon shown in the figure below.
Answers
Step-by-step explanation:
what did we learn in the other question ?
there are 8 equal sub-segments of 1/8 length between neighboring whole numbers.
so, each little line is 1/8.
the marker goes first to 1, and then one little line towards 2.
therefore, that number is 1 1/8.
In the formula l2 = h2 +r2, l=25 and r=7, then the value of h is
Answers
Answer:
18
Step-by-step explanation:
I2=h2+r2
25(2)=h2+7(2)
50=h2+14
-14 -14
36=h2
÷2 ÷2
18=h
4 What advice would you give a Grade 10 learner who is
Mathematical Literacy on how to draw Bar graphs.
Give them at least TWO tips
Answers
Answer:
taena mo bobo mo sa math hindi ka mag kakajowa sa February 14 hahahhahahah
good estimate of the length of a standard bed pillow
Answers
Answer:
I would say 2 ft
Step-by-step explanation:
Have amazing day!
Please rate!
What is the value of X ?
Answers
Answer:
26.6
Step-by-step explanation:
because you are multiplying a couple of numbers
solve the inequality |x+6-|3x+6||+|x+2|-x-4 less then or equal to 0
Answers
It looks like the inequality is
[tex]\bigg|x + 6 - |3x + 6|\bigg| + |x + 2| - x - 4 \le 0[/tex]
or equivalently,
[tex]\bigg|x + 6 - 3 |x + 2|\bigg| + |x + 2| - x - 4 \le 0[/tex]
Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
By this definition, we have
[tex]|x + 2| = \begin{cases} x + 2 & \text{if } x + 2 \ge 0 \\ -(x + 2) & \text{if } x + 2 < 0 \end{cases} = \begin{cases} x + 2 & \text{if } x \ge -2 \\ -x - 2 & \text{if } x < -2 \end{cases}[/tex]
Suppose [tex]x < -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (-x - 2)| + (-x - 2) - x - 4 \\\\ = |4x + 12| - 2x - 6[/tex]
By definition of absolute value,
[tex]|4x + 12| = 4 |x + 3| = \begin{cases} 4x + 12 & \text{if } x \ge -3 \\ -4x - 12 & \text{if } x < -3 \end{cases}[/tex]
so we further suppose that [tex]x < -3[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (-4x - 12) - 2x - 6 \\\\ = -6x - 18 \le 0 \\\\ \implies x \ge -3[/tex]
but this is a contradiction, so this case gives no solution.
If instead we have [tex]-3 \le x < -2[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (4x + 12) - 2x - 6 \\\\ = 2x + 6 \le 0 \\\\ \implies x \le -3[/tex]
and [tex]-3 \le x[/tex] and [tex]x \le -3[/tex] means that [tex]\boxed{x = -3}[/tex].
Now suppose [tex]x \ge -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (x + 2)| + (x + 2) - x - 4 \\\\ = |-2x| - 2 \\\\ = 2 |x| - 2[/tex]
If we further suppose that [tex]-2 \le x < 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = -2x - 2 \le 0 \\\\ \implies x \ge -1[/tex]
Otherwise, if [tex]x \ge 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = 2x - 2 \le 0 \\\\ \implies x \le 1[/tex]
Taken together, this case gives the solution [tex]\boxed{-1 \le x \le 1}[/tex]
So, the overall solution to the inequality is the set
[tex]\boxed{\left\{ x \in \mathbb R : x = -3 \text{ or } -1 \le x \le -1 \right\}}[/tex]
find the value of x in the triangle. 45-45-90. PLASE HELP!!!
Answers
Answer:
2) X = 14 and y = 19.8
3) X = 25.45
5) X = 5.66
6) X = 7.07
Step-by-step explanation:
2) tan45° = 14/x
x(tan45) = 14
x = 14 / tan45
x = 14
[tex] y = \sqrt{14 ^{2} + 14 ^{2} } [/tex]
y = 19.79
3) cos45 = 18/x
x(cos45) = 18
x = 18/cos45
x = 22.45
5) cos45 = x/8
8(cos45) = x
x = 5.66
6) cos45 = x/10
10(cos45) = x
x = 7.07
What is the exact area of the following circle? *
Answers
Answer:
B
Step-by-step explanation:
Radius = 15/2 = 7.5 cm
Area = π*7.5² = 56.25π cm²
that is B
After 1/4 hour there are about 7 mg of medicine left. After 3/4 hour there are about 3,5
mg of medicine left. About how many mg of medicine are left after 1 3/4 hours? Explain
how you know.
Answers
Answer:
1.5
Step-by-step explanation:
From comparing the difference in the amounts of medicine in 1/4 and 3/4, we can see that 1.5 mg is taken away every 1/4 hours. Why you may ask? This is because the scenario said 3/4, not 2/4. 1.5 + 1.5 is 3.5. So, with that, we can say without any hours, there was originally 8.5 mg. Then we minus that by 1.5 7 times, as 1 and 3/4 = 7/4, and get our answer, 1.5. Hope this helped!
evaluate the expression 10^2+(3+5)^2-5
Answers
Hey there!
10^2 + (3 + 5)^2 - 5
= 10 * 10 + (3 + 5)^2 - 5
= 100 + (8)^2 - 5
= 100 + (8 * 8) - 5
= 100 + 64 - 5
= 164 - 5
= 159
Therefore, your answer is: 159
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
10² + (3 + 5)² - 5 = 159
Step-by-step explanation:
Given expression,
→ 10² + (3 + 5)² - 5
Evaluating the expression,
→ 10² + (3 + 5)² - 5
→ 10² + 8² - 5
→ 100 + 64 - 5
→ 100 + 59
→ 159
Hence, the answer is 159.
The area of the parallelogram is 17.6 cm 2 . What is the length of the base?
Answers
Answer:
The length of the base is 4.4 cm
area of parallelogram: base x height =
1) first you do 17.6=4 x h, which gives you 17.6/4
Answer:
area of parallelogram: base x height = 17.6 cm sq
}4 x h = 17.6
⇒h = 17.6/4
⇒h= 4.4 cm
Step-by-step explanation:
Hope it helps
PLEASE HURRY!!!!
Find the area of the figure below.
8 in.
11 in.
9 in
8 in
11 in
Answers
Answer:314 in squared
Step-by-step explanation:
99+44+99+72
Container A and container B are right circular cylinders. A has a radius of 4 inches and a height of 5 inches while container B has a radius of 2 inches and a height of 10 inches. Sarah pours equal amounts of oil into both containers and finds that the height of the oil in container A is 2 inches. What is the height of the oil in container B?
Okay I know I have to find the volume of both which I did (container A’s volume is 80pi and container B’s volume is 40pi) but I don’t know what to do after that. Can someone help me out?
Answers
Answer:
8 in
Step-by-step explanation:
RA = 4 in, RB = 2 in
oil height in A = hA = 2 in
Find oil height in B = hB
volume of oil in A = VA = π*RA² * hA
equal amount means volume of oil in B VB = VA
But VB = π*RB² * hB
so π*RA² * hA = π*RB² * hB
then
hB = hA *(RA/RB)² = 2 * (4/2)² = 8 in
The circumference of a roll of party streamers is 11 inches. The circumference decreases by 3 inches after you use the streamers to decorate for a birthday party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.
Answers
Answer:
2.55
Step-by-step explanation:
First take 11 and subtract it by 3 to get 8.
Then divide it by 3.14 and get 2.547770701...
After that round it to 2.55