Answer:
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Step-by-step explanation:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Keep in mind that a log is an exponent.
When you are asked for the log base 2 of 16, you are being asked for the exponent you need to raise 2 to, to get 16. The base in the log is the same base as in the exponential form.
In other words, the question "what is log base 2 of 16?" is the same as the question "what exponent do you raise the base 2 to to get 16?"
Need help with a math question
Answer:
360
Step-by-step explanation:
n=?
1800° = sum of interior angles
Pentagon = 5 sides
n = 1800° ÷ 5
n = 360
Answer: [tex]n=12[/tex]
Step-by-step explanation:
You can observe that the formula for the sum of the interior angles of a polygon is:
[tex]sum=(n-2)180[/tex]
Where "n" is the number of sides of the polygon.
You know that the sum of the interior angles of this polygon is 1,800 degrees. Therefore, you can find the number of sides by substituting this sum into the formula and then solving for "n".
Then:
[tex]1,800=(n-2)180\\\\\frac{1,800}{180}=n-2\\\\10=n-2\\\\10+2=n\\\\n=12[/tex]
Stephanie is a goalie on her soccer team, which means she tries to block any shots her opponents take on goal. During a tournament, she blocked 15 shots but allowed 4 goals. For every goal Stephanie allowed, she blocked nearly shots.
Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x4 - 9x3 + x - 7a = 7
We have [tex]f(7)=8918[/tex]. By the definition of continuity, we require that
[tex]\displaystyle\lim_{x\to7}f(x)=f(7)[/tex]
So for any [tex]\varepsilon>0[/tex], we want to find sufficient [tex]\delta[/tex] for which
[tex]0<|x-7|<\delta\implies|f(x)-8918|<\varepsilon[/tex]
We have
[tex]|5x^4-9x^3+x-7-8918|=|5 x^4 - 9 x^3 + x - 8925|=|x - 7||5 x^3 + 26 x^2 + 182 x + 1275|[/tex]
Suppose we let [tex]0<\delta\le1[/tex]. Then
[tex]|x-7|\le1\implies x\le8[/tex]
so that
[tex]|5 x^3 + 26 x^2 + 182 x + 1275|\le5|x|^3+26|x|^2+182|x|+1275\le6955[/tex]
[tex]\implies|5x^4-9x^3+x-7-8918|\le6955|x-7|<\varepsilon[/tex]
[tex]\implies|x-7|<\dfrac\varepsilon{6955}[/tex]
which suggests that it suffices to choose
[tex]\delta=\min\left\{1,\dfrac\varepsilon{6955}\right\}[/tex]
in order to meet the required condition.
PLEASE HELP!!!!
Question: ⇒ An object is launched from the ground. The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched. When will the object hit the ground after it is launched?
⇒ Explain how you found your answer.
⇒ No spam answers, please!
⇒ No wrong answers, please!
Thank you!
Answer:
it would take 5 seconds for the object to hit the ground after launched.
////////////////////////////////////////////////////////////////////////////////
1st step: (turn the quadratic function to a quadratic equation by setting the equal to zero): 0 = -16t2 + 80t + 0
2nd step: t = 0 & t = 5
(t = 0 is the time of launch. t = 5 represents the 5 seconds it took to hit the ground after the object was launched.)
Answer:
The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds
Suppose the population of a town is 2,700 and is growing 4% each year. Write an equation to model the population growth. Predict the population after 12 years
PLEASE HELP ME
CHOICE OPTIONS:
(7,5, 0.5)
(7, 0.5)
(7, 1)
(7, 0)
Answer:
(7, .5)
Step-by-step explanation:
From the origin, our intersection is 7 units to the right where x is positive, so x = 7. It appears that we are between y values of 0 and 1 at x = 7, so the coordinate that best represents the solution is (7, .5)
What is the equation and solution for the sentence?
The sum of a number and thirty-one is one hundred thirteen.
Write the equation as n-31=113 and subtract 31 from both sides. The answer is 82.
Write the equation as n+31=113 and subtract 31 from both sides. The answer is 82.
Write the equation as n+31=113 and add 31 to both sides. The answer is 144.
Write the equation as n-31=113 and add 31 to both sides. The answer is 144.
Answer:
Write the equation as n+31=113 and subtract 31 from both sides. The answer is 82.
Step-by-step explanation:
Let
n ----> the number
we have that
The equation is equal to
n+31=113
solve for n
subtract 31 both sides
n+31-31=113-31
n=82
Answer:Write the equation as n+31=113 and subtract 31 from both sides. The answer is 82.
Step-by-step explanation:
In the final round of trivia competition, contestants were asked to name as many states that begin with the letter M as they could in 15 seconds. The bar graph shows the number of states the contestants were able to name. How many contestants participated in the final round of the competition?
A) 6
B) 8
C) 14
D) 20
Answer:
D) 20
Step-by-step explanation:
The sum of the heights of the bars (numbers of contestants) is ...
1 + 1 + 5 + 6 + 4 + 2 + 1 = 20
The correct answer is A) 6.
To determine the number of contestants who participated in the final round of the competition, we need to analyze the bar graph provided in the question. Since the actual bar graph is not available in the text, we will assume that the number of states named by each contestant is represented by a separate bar in the graph.
The question states that the contestants were asked to name as many states that begin with the letter M as they could. The states that begin with the letter M are Montana, Minnesota, Missouri, Mississippi, Massachusetts, and Michigan. There are a total of 6 such states
Given that there are 6 states that start with the letter M, the maximum number of states any contestant could have named correctly is 6. Therefore, each contestant is represented by a bar on the graph that corresponds to the number of states they were able to name, with the maximum possible value being 6.
Since the question asks for the number of contestants and we have established that there are 6 states beginning with the letter M, it follows that there must be 6 bars on the graph, each representing one contestant. Thus, 6 contestants participated in the final round of the competition.
In conclusion, by understanding the context of the question and the constraints provided (the number of states beginning with the letter M), we can deduce that the number of contestants who participated in the final round is equal to the number of states that start with the letter M, which is 6. Hence, the correct answer is A) 6.
Suppose xy > 0. Describe the points whose coordinates are solutions to the inequality.
Answer:
all points in the 1st and 3rd quadrants (not including the x- and y-axes).
Step-by-step explanation:
The product of positive numbers will be greater than 0, as will the product of two negative numbers. Both coordinates are positive in the first quadrant; both are negative in the third quadrant.
The quadrant boundaries, x=0, y=0, are excluded from the solution set.
Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of whyrot be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.
Step-by-step explanation:
There are six unique letters. Any of the six could be the first letter. Once we've picked a first letter, that leaves 5 letters that could go second. So on and so forth. So the number of ways they can be arranged is:
6×5×4×3×2×1 = 720
The correct unscrambling is "worthy". So the probability of randomly selecting this order from the 720 possible combinations is 1/720.
please help asap giving brainliest to all of the questions i ask
I have to build a box for my scouting project with a volume of 36 cubic centimeters. The base of the box is 6 cm long and 2 cm wide.
How high should I build the box? in centimeters
Answer:
3 cm
Step-by-step explanation:
Volume = Length x Width x Height
given that the volume = 36 cm³ ,length = 6 cm and width = 2 cm
Height = volume / (length x width) = 36 / (6x2) = 3 cm
Answer:
Volume is length x width x height.
The base is 12. (2x6)
Then you do 36/12
Finally your answer is 3.
Step-by-step explanation:
Sarita has to solve the problem below for homework
2x+3y=25
4x+2y=22
Which variable should she choose to solve for so that she can use substitution to solve the system?
A. Sarita should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
B. Sarita should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
C. Sarita should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
D. Sarita should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Answer:
Option A is correct.
Step-by-step explanation:
2x+3y=25
4x+2y=22
Option A
2y = 22-4x
y = 11 -2x
Option B
2x = 25 -3y
x = 25/2 -3/2y
Option C
3y = 25 - 2x
y = 25/3 -2/3x
Option D
4x = 22 - 2y
x = 22/4 -2/4y
x = 11/2 -1/2y
In Option B,C and D we have fractions and for substitution the calculations will be complex.
But Option A has no fractions and solving by putting the value of y in equation 1 is easy.
So, Option A is correct.
Answer:
A
Sarita should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Step-by-step explanation:
Maria found the least common multiple of 6 and 15. Her work is shown below. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . Multiples of 15: 15, 30, 45, 60, . . . The least common multiple is 60. What is Maria's error?
Answer:
she overlooked 30
Step-by-step explanation:
The number 30 appears on both her lists. Maria apparently overlooked that value.
Two fair dice are rolled.
What is the PROBABILITY that the FIRST lands on a 6 and the SECOND lands on an ODD number?
SHOW YOUR WORK! Use the sample space from question 8 to assist you! Write your answer in SIMPLIFIED FRACTION form.
Answer:
1/12
Step-by-step explanation:
There are two dices being rolled. A dice has six faces numbered from one to six. A fair dice means that the probability of each number to appear is equal. Thus the probability of any number showing up is:
P(a number appears on the dice) = how much times the number has been displayed on the dice/number of faces of the dice.
Since all numbers appear once, and there are six sides of a dice. therefore:
P(a number appears on the dice) = 1/6. Thus, P(6 appears on a dice) = 1/6.
As far as the odd numbers are concerned, there are three even numbers and three odd numbers on the dice. So P(odd number appears on the dice) = 3/6 = 1/2.
Assuming that the probabilities of both the dices are independent, we can safely multiply both the probabilities. Thus:
P(first dice lands on a 6 and second dice lands on an odd number) = 1/6 * 1/2 = 1/12.
Thus, the final probability is 1/12!!!
People who have a college degree tend to live longer than those who do not have a college degree. This is true for both men and women, and it is true across many different ethnicities and in many different geographical regions. This phenomenon is easily explained because it has been proven that people who have attended college have lifestyles and habits that are well known to increase lifespan: they eat balanced meals, they exercise often, they consider themselves happy, and they tend to have strong relationships. Therefore, if you want to have a longer lifespan, you should get your college degree.Which of the following, if true, weakens the argument above?a) Some people who attend college do not get their college degree.b) People with those four habits and lifestyles are more likely to go to college than those without them.c) People with college degrees tend to have more heart attacks than those without one.d) Women tend to live much longer than men do.e) People from certain geographical regions and certain ethnicities tend to have longer lifespans.
Answer:
pepple with college degree live longer
Step-by-step explanation:
people with college degree live longer because they get to have a good job wich gives good income
Solve each exponential equation by using properties of common logarithms. When necessary, round answers to the nearest hundredth.
7(^3x) - 1 = 5(^x - 1)
A. x ≈ 12.33
B. x ≈ -3.09
C. x ≈ 0.08
please help!!!!
Answer:
The answer is C
Step-by-step explanation:
Just graph these functions lol...
Which number line represents the solutions to |x – 2| = 6?
Answer:
The solutions are x=8 and x=-4
Step-by-step explanation:
we have
[tex]\left|x-2\right|=6[/tex]
step 1
Find the first solution
case positive
[tex]+(x-2)=6[/tex]
[tex]x=6+2=8[/tex]
step 2
Find the second solution
case negative
[tex]-(x-2)=6[/tex]
[tex]-x+2=6[/tex]
[tex]x=2-6=-4[/tex]
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
5, -3, and -1 + 2i
Answer:
x^4 - 15x^2 - 38x - 60.
Step-by-step explanation:
Writing it in factor form:
( x - 5)(x + 3) ( x - (-1 + 2i) )(x - (-1 - 2i))
There are 4 parentheses because complex roots occur in pairs.
( x - (-1 + 2i) )(x - (-1 - 2i))
= ( x + 1 - 2i) )(x +1 + 2i))
= x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i + 4
= x^2 + 2x + 4.
So our polynomial is
( x - 5)(x + 3)( x^2 + 2x + 4)
= (x^2 - 2x - 15)(x^2 + 2x + 4)
= x^4 + 2x^3 + 4x^2 - 2x^3 - 4x^2 - 8x - 15x^2 - 30x - 60
= x^4 - 15x^2 - 38x - 60.
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not mixed number or decimal.
Answer:
The slope is:
[tex]m=-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope m of a line is calculated using the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points belonging to the straight line
Notice in the graph that the line passes through the points
(0, 2) and (2, -1)
Then the slope is:
[tex]m=\frac{-1-2}{2-0}[/tex]
[tex]m=\frac{-3}{2}[/tex]
Darlene's room measures 12feet on ones side and 9 feet on another, help her calculate the area of her room. The area if a rectangular room is a product of its length and width
Answer:
108 ft²
Step-by-step explanation:
The product of length and width is ...
(12 ft)(9 ft) = 12·9 ft·ft = 108 ft²
For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?
A. 3/7
B. 7/3
C. 10
D. 21
Answer:
D. 21
Step-by-step explanation:
The equation tells you xy = k. Substituting the given values, you get ...
7·3 = k
21 = k
Answer:
D) 21
Step-by-step explanation:
The given inverse variation equation is x.y = k, where k is the constant of proportionality.
Given: x = 7 and y = 3.
We need to find the constant variation, k.
To find the constant variation, k, plug in x = 7 and y = 3 in the given equation and simplify.
k = 7*3
k = 21.
Therefore, the constant of variation k = 21.
Answer is D) 21.
Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
8,000 + 24x
8,000 - 24x
8,000 + 2x
8,000 - 2x
Answer:
8,000 - 24x
Step-by-step explanation:
Let
y ----> depreciated value of the car
x---> rate of depreciation
t ----> the time in months
we know that
The linear equation that represent this situation is
y=8,000-xt
For
t=2 years=2*12=24 months
substitute
y=8,,000-x(24)
y=8,000-24x
Answer: 8,000 - 24x
Step-by-step explanation:
Find the point that lies on the following linear equation: y = -2x + 1.
( 3, 5 )
( 3, -5 )
( 3, 6 )
( 3, -6 )
Answer:
(3,-5
Step-by-step explanation:
x=3 y=-2*3+1=-5
Type the correct answer in the box. Mr. Jensen is a salesperson for an insurance company. His monthly paycheck includes a base salary of $2,175 and a commission of $250 for each policy he sells. Write an equation, in slope-intercept form, that represents the total amount, y, in dollars, of Mr. Jensen's paycheck in a month when he sells x policies. Do not include dollar signs in the equation.
Answer:
y= 250x + 2175
Step-by-step explanation:
the slope intercept form is y = mx + b so you would put 250 for the M because it depends on each policy he sells which is X so y = 250x + b and B is the fixed price of 2,175 so you would get Y = 250x + 2175 as your answer
Answer:
The required answer is [tex]y = 250x + 2175[/tex].
Step-by-step explanation:
Consider the provided information.
The base salary of Mr. Jensen is 2175.
The commission per policy is 250.
The slope intercept form is:
[tex]y = mx + c[/tex]
Where, m is slope and c is y intercept.
Let "x" be the number of policy Mr. Jensen sells and "y" is the total paycheck including the commission.
[tex]y = 250x + 2175[/tex]
Therefore, the required answer is [tex]y = 250x + 2175[/tex].
Find the x- and y-intercept of Y
Answer:
Step-by-step explanation:
x intercepts include
(-1/2,0)
y intercepts include
(0,-3)
Hope that Helps!
Need help with a math question
Answer:
Z =7
Step-by-step explanation:
The middle segment theorem of a triangle says that: A middle segment connecting two sides of a triangle is parallel to the third side and is half its length.
In this case, the middle segment connecting two sides of a triangle is Z.
This means that
[tex]Z = 0.5(14)[/tex]
Finally we have that:
[tex]Z =7[/tex]
The length of the middle segment is 7 units
Un árbol ha sido partido por un rayo en dos partes formando un triangulo rectángulo la parte superior del árbol forma con la horizontal un ángulo de 36 grados mientras que la parte inferior no fue da?ada y mide 5 m ?Cuánto media el árbol antes de ser partido
Answer:
13,506 m
Step-by-step explanation:
Applying the trigonometric relation between opposite leg and hypotenuse
[tex]sin(\alpha)=\frac{Op}{h}[/tex]
isolating the variable [tex]sin(\alpha)=\frac{Op}{h} \longrightarrow h=\frac{Op}{sin(\alpha)}\longrightarrow h=\frac{5m}{sin(36^o)}=8,506m[/tex]
the total height is the sum to the hypotenuse and the opposite leg
[tex]h_{total}=hypotenuse+h=8,506m+5m=13,505m[/tex]
PLEASE HELP ASAP The diagram shows squares 1,2, and 3 constructed on the sides of a right triangle.
Answer: Area of 1+Area of 2=Area of 3
I just took the test
Step-by-step explanation:
Answer:
Option D
Step-by-step explanation:
Since the given triangle is a right angle triangle and it has been given that squares 1, 2 and 3 are constructed on its respective sides.
Since the triangle is the right angle triangle so it will follow Pythagoras theorem.
Hypotenuse² = (height )² + (base)²
since hypotenuse is the one side of square 3
so area of square 3 = Hypotenuse²
similarly height² = area of square 1
Base² = area of square 2
so area of 1 + area of 2 = area of 3 will be defined by the Pythagoras theorem.
Therefore, Option D. is the answer.
Find all angles, 0 ≤C<360 that satisfy the equation below, to the nearest tenth of a degree.
Move all the terms involving the sine to one side, and all the numbers to the other:
[tex]9\sin(c)-2=\sin(c)-7 \iff 8\sin(c) = -5\iff \sin(c)=-\dfrac{5}{8} \iff c = \arcsin\left(-\dfrac{5}{8}\right)\approx 321.3[/tex]
Im timed i need the answer NOW
Find the distance between point A(0,4) and point B (-2,-7) rounded to the nearest tenth.
A.3.6
B. 11.1
C.11.2
D.3.7
Answer:
C.11.2
Step-by-step explanation:
The distance between 2 points is given by
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( ( -2-0)^2 + (-7-4)^2)
= sqrt( (-2)^2 + (-11)^2)
= sqrt( 4 + 121)
= sqrt(125)
= 11.18033989
To the nearest tenth
11.2