Use main properties of powers
(a^m)^n=a^{m\cdot n};(am)n=am⋅n;
\dfrac{1}{a^n}=a^{-n}an1=a−n
to simplify given equation.
1.
4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.
2.
\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.
3. Then the equation is
2^{2x}=2^{-3x-15}.22x=2−3x−15.
The bases are the same, so equate the powers:
2x=-3x-15,
2x+3x=-15,
5x=-15,
x=-3.
Answer: for x=-3.
Graph the system of inequalities. Then state whether the situation is infeasible, has alternate optimal solutions, or is unbounded. (Assume that x>0 y>0
Answer:
x
[tex]x \leqslant - y + 1[/tex]
Steps are show in the picture above.
Bond and DePaulo (2006) analyzed the results from 384 studies that tested the lie-detecting ability of more than 24,000 people and found that: Group of answer choices about 50% of people are especially clairvoyant and able to discern truths from lies. the accuracy rate of most people is barely above the 50% guessing level. most people can rather accurately guess whether they are told the truth or a lie. training people can substantially increase their lie-detecting ability.
Answer:
B: the accuracy rate of most people is barely above the 50% guessing level
Step-by-step explanation:
Bond and DePaul carried out a research and analysis on the accuracy of deception judgments in 2016.
This research involved synthesizing of results gotten from 206 research documents as well as a total of 24483 judges.
In this research and analysis, there were a couple of discoveries when people tried to discriminate lies from the truth and these discoveries include; average percentage of correct lie-truth judgments, percentage of those who correctly classified lies as deception and also percentage of those who classified truths as non-deceptive e.t.c. In conclusion, part of their discoveries was that the accuracy rate of most people is barely above the 50% guessing level.
This corresponds to option B.
Visualise 4.26 on the number line, up to 4 decimal places.
Answer:
is it 4.2626
Step-by-step explanation:
let me know if it right
The dot plot below represents this set of data:
30, 29, 30, 28, 28, 27, 22, 28, 28, 22, 27, 26, 25, 27
Answer:
True
Step-by-step explanation:
All of them match up
Joey has $400 in a bank account that earns 8% in annual interest. Would this equation be Linear or Exponential?
Exponential
The first year, he would earn 8% interest on the $400 deposited, so he'd have $432. The next year, he would earn 8% interest on the interest earned the previous year in addition to the amount deposited, so he'd have $466.56.
His bank balance would follow the compound interest equation which is exponential.
= 400 × 1.08^t
where t is the number of years since the deposit
see question in image
Answer:
b) 1/9Step-by-step explanation:
Rolling two dice, there are 6*6 = 36 outcomes
The outcomes with the difference of 4:
1&5, 2&6, 6&2, 5&1 - total of 4Required probability:
P = 4/36 = 1/9Correct choice is b
find the value of the trigonometric ratio
tan c =opposite÷ adjacent
tan c =36÷15
tan c = 12÷5
Hope made 3 different yo-yo's. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string
Answer:
See explanation
Step-by-step explanation:
Your question is different from the attachment
Statement 1
1 adult + 5 Children
$4 for adult and total of $16 for both adult and children
Let
Cost of children skating = x
The equation is
4 + 5x = 16
Statement 2:
Cost of making a bike bag= $4
Selling price of the bike bag = $5
Profit = $16
Let x = number of bike bag
Profit = selling price - cost price
16 = 5x - 4x
16 = x(5 - 4)
Also written as
(5 - 4)x = 16
Statement 3:
Initial temperature = 16°C
Change in temperature per hour = 4°C
Final temperature = 5°C
Let
x = number of hours it changes
16 - 4x = 5
Hope made 3 different yo-yos. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string for the second yo-yo, and a total of meters of string 4 1/3
length of first yo-yo = 1 3/4
length of second yo-yo = 1
Length of third yo-yo = x
Total = 4 1/3
Total length = length of first yo-yo + length of second yo-yo + length of third yo-yo
4 1/3 = 1 3/4 + 1 + x
4 1/3 = 2 3/4 + x
4 1/3 - 2 3/4 = x
13/3 - 11/4 = x
(52-33) / 12 = x
19/12 = x
x = 1 7/12
solve for w: 7w < -56
Lets solve
[tex]\\ \sf\longmapsto 7w<-56[/tex]
Take 7 to right side[tex]\\ \sf\longmapsto w<dfrac{-56}{7}[/tex]
Simplify[tex]\\ \sf\longmapsto w<-8[/tex]
Answer:
[tex]\boxed {\boxed {\sf w < -8}}[/tex]
Step-by-step explanation:
We are given an inequality and asked to solve for the variable w.
[tex]7w < -56[/tex]
In order to solve for w, we must isolate the variable. It is being multiplied by 7. The inverse of multiplication is division, so we divide both sides of the inequality by 7.
[tex]\frac {7w}{7} < \frac {-56}{7}[/tex]
[tex]w < \frac{-56}{7}[/tex]
[tex]w < -8[/tex]
w is less than -8 or w < -8.
Alex cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces?
Answer:
61 seconds
Step-by-step explanation:
36 divided by 7 = 5.1 seconds so if you add 5 to 36 five more times you'll get the answer which is 61.
Height is 2ft. More than its width. If the total area is 99ft squared , determine the dimensions of the painting.
Answer: [tex]9\times 11\ ft^2[/tex]
Step-by-step explanation:
Given
Height is [tex]2\ ft[/tex] more than its width
Suppose the width is [tex]x[/tex]. So, height becomes [tex]x+2[/tex]
Area of the painting is [tex]99\ ft^2[/tex]
Area is the product of width and height
[tex]\therefore 99=x(x+2)\\\Rightarrow 99=x^2+2x\\\Rightarrow x^2+2x-99=0\\\Rightarrow x^2+11x-9x-99=0\\\Rightarrow (x+11)(x-9)=0\\\Rightarrow x=-11,9[/tex]
Neglect the negative values
[tex]\text{Width =}9\ ft\\\text{height =}9+2=11\ ft[/tex]
What is the solution, if any, to the inequality |3x|20?
all real numbers
solution
no
x>0
x
Answer:
20×2=40bnmcsshjvghjpiutewqadgjlmbcz
Answer: all real numbers
Step-by-step explanation:
In Natalie's class, 18 children listed math as their favorite subject while 15 said English was their favorite
subject. Eleven children liked both subjects equally well and 3 children didn't like either math or English. How
many children are in the class?
25 is your answer if i am sure, the question was confusing tho.
Thirty- five out of sixty students preferred to eat their lunch at school rather going home in lunch break. Express the numbers in decimal.
Answer:
0.583
Step-by-step explanation:
Use a caluclator
what is the x? please answer!
Answer:
x = 2
Step-by-step explanation:
1. distribute 9 in 9(x+1)
9x + 9 = 25 + x
2. subtract x from the right side to isolate x onto one side
8x + 9 = 25
3. subtract 9 from the left side
8x = 16
4. divide both sides by 8 to get x alone
x = 2
help please fast!! geometry coordinates
E is halfway between A and C
coordinates are
-2a , -2b
you could basically see it in the picture.
the formula is alrdy given, so I just gave you the solution
Which of the following is a point-slope equation of a line that passes through
the points (-1,4) and (8, -2)?
O A. y-1--3(x-1)
O B. y 4 = {(x+1)
O C. y-4--(x+1)
O D. y-4--2(x+1)
Answer:
y - 4 = -2/3 (x + 1)
Step-by-step explanation:
y2 - y1 / x2 - x1 -2 - 4 / 8 - (-1) -6/9 = -2/3
y - 4 = -2/3 (x + 1)
Determine the point of intersection of the lines x + y = 4 and 2x + 3y = 12
Answer:
(2,2)
Step-by-step explanation:
x=4-y
2 ( 4 - y )+ 3y= 12
2y = 12 -8
y= 2
substitute y in first eq. :
x=4 - 2
x= 2
What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)?
= –216+616–4116
= –216+616–4116
=216–616+4116
=216–616+4116
Answer: y= x^2/16-6x/16+41/16
Step-by-step explanation:
The equation of a parabola will be; y = x^2/16 - 6x/16 + 41/16
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
Otherwise, we had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
WE need to find the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)
Thus, the equation of a parabola will be;
y = x^2/16 - 6x/16 + 41/16
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
#SPJ2
21,5=13
7,9=8
36,2=19
1,7=?
find the value of ?
Answer:
4
Step-by-step explanation:
(21 + 5) : 2 = 13
(7 + 9) : 2 = 8
(36 + 2) : 2 = 19
(1 + 7) : 2 = 4
Need help asap, thanks :)
Answer:
937
425
Step-by-step explanation:
9 is the square of 3
7 is 1 more than 6, the double of 3
4 is the square of 2
5 is 1 more than 4, 2x 2
Is there more?
Answer:
425
Step-by-step explanation:
1st = 2^2
3rd = 2*2 + 1
look at image for question and answer
A spherical ball has a radius of 4 inches. What is the volume of this sphere, to the
nearest cubic inch.
Answer:
V = 267.9 in^3
Step-by-step explanation:
V = 4/3 * (pi) * r^3
V = 4/3 * 3.14 * 4^3
V = 4/3 * 3.14 * 64
V = 256/3 * 3.14
V = 803.84/3
PLEASE HELPPPPPPPP!!!!!!!!
Answer:
True
Step-by-step explanation:
tan B = sin B / cos B = 3/4 Let sin B =3 and cos B = 4
Cot B = cos B / sin B = 4/3
This is true
Rita offers to pay for 8 of her friends to play laser tag, but 3
of them don't want to play.
If laser tag costs $5 per person, how much will Rita spend on her friends?
Choose the correct expression and solution to this problem,
Last Option
Rita will spend $25
5(8-3)
Answered by Gauthmath must click thanks and mark brainliest
Answer: The correct answer is D.
Step-by-step explanation:
Since 3 of Rita's 8 friends don't want to play laser tag, Rita only has to pay for 5 of her friends to go.
So, the expression would be:
5 (8 - 3)
= 5 (5)
= $25
Hope this helps! :)
Cho biểu thức : A=(√x+1)/(√x-2) +(2√x)/(√x+2 )+(2+5√x)/(4-x)
a.Rút gọn A
b.Tính giá trị của A khi x=2
c.Tính giá trị của A khi X-5√x+6=0
Answer:
A= (3*X - 6[tex]\sqrt{x}[/tex])/(X-4)
A=(3*2 - 6[tex]\sqrt{2}[/tex])/(2-4)= -3+3[tex]\sqrt{2}[/tex]
A=(3*4 - 6[tex]\sqrt{4}[/tex])/(4-4) Unknown
Step-by-step explanation:
A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.
Answer:
A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.
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HELP ME PLS ITS PYTHAGOREAN THEOREM
Answer:
a= [tex]\sqrt{19}[/tex]
Step-by-step explanation:
Pythagorean Theorem: a^2+b^2=c^2
a^2+9^2=10^2
a^2+81=100
a^2=19
a=[tex]\sqrt{19}[/tex]
Answer:
b = 4.4 meters
kim is 10 years older than laura. laura is twice as old as melissa. if melissa will be 1o years old in 5 years, how old is kim now
Answer:
Kim is 20 years old
Step-by-step explanation:
We have to make equations;
Kim= laura+10 so L+10
Laura is twice as old as Melissa so Laura will be
2 X M = 2M
Melissa is 5 years old nowInput values in to the equation
2M = 2X5= 10 years old (Laura)As Kim is 10 years older than Laura it will be 10+10
which will give the answer of 20The age of Kim is 20 years.
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
Kim's age = laura' age +10 years
= x +10
As, Laura is twice as old as Melissa
Laura's age = 2*y
Now, Melissa is 5 years old now
So,
2y = 2X5= 10 years old
So, the Kim's age= 10+ 10 = 20 years old
Learn more about equation here:
https://brainly.com/question/10413253
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3. Find f(x) - g(x)
4 options to pick from
Answer:
Answer is 13x⁴ - x³ - 9x²( the last option)
Step-by-step explanation:
f(x) = 8x⁴ - x³ - 4x²
g(x) = -5x⁴ + 5x²
so,
f(x) - g(x)
=(substituting the value)
= (8x⁴ - x³ - 4x²) - (-5x⁴ + 5x²)
= 8x⁴ - x³ - 4x² + 5x⁴ - 5x²
= 8x⁴ + 5x⁴ - x³ - 4x² - 5x²
= 13x⁴ - x³ - 9x²
Answer:
The 4th option would be correct.
Step-by-step explanation:
No complex calculations are needed. Just pay attention to what the problem is asking for. Notice that f(x) is positive while g(x) is negative. So instead of adding, you're subtracting.
Now look at the last coefficients in each function. Notice that they're the same term, since both of their variables are x^2. Since we're subtracting, that 5x^2 in function g is actually going to be negative. This is why the answer would be the last option, since it's the only one that shows that -4x^2 and -5x^2 is being combined.
Also, at the start, I said no complex calculations are needed. This is because the problem didn't say 'Show your work' or something along those lines. Only do it if it asks, or if your teacher does.
