Logarithmic are inverse of exponential functions. The point where graph of f and g intersect is (0, ∞)
Logarithmic functionLogarithmic are inverse of exponential functions. Given the following functions;
g(x)=log2x and g(x)=log10x
The point where the graphs intersect is the point where g(x) = g(x)
Equate
log2x = log10x
2x = 10x
The value of x that made them equal is 0
Determine the value of g(x)
g(0) = log2(0)
g(0) = ∞
Hence the point where graph of f and g intersect is (0, ∞)
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Simplify 3y²-4x² + xy - 2x² - 9y²
Answer:
-6x²+xy-6y²
Step-by-step explanation:
3y² - 4x² + xy - 2x² - 9y²
-4x²+ xy - 2x² - 6y²
-6y² + xy - 6y²
Answer:
−6x² + xy − 6y²
Step-by-step explanation:
Simplify 3y²-4x² + xy - 2x² - 9y²
Step 1
Subtract 9y² from 3y²
−4x² +xy −2x² −6y²
Step 2
Subtract 2x² from −4x²
−6x² + xy − 6y²
If you multiply four negative numbers, what is the sign of the product?
If you multiply five negative numbers, what is the sign of the product?
Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of
negative numbers in the expression.
Answer:
positive
Step-by-step explanation:
(-a) (-a) (-a) (-a) = a
(-a)(-a) = a
a (-a) = -a
-a (-a) = a --> positive sign
If you multiply four negative numbers, what is the sign of the product?
You can test this with numbers, the easiest with -1:
(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) = 1
General:
(-a)(-b)(-c)(-d) = abcd
The sign of the product of four negative numbers is positive.
If you multiply five negative numbers, what is the sign of the product?
Testing with -1:
(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1
General:
(-a)(-b)(-c)(-d)(-e) = -abcde
The sign of the product of five negative numbers is negative.
General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.
why the question “How many colors are there in the United States flag?” is NOT a statistical question.
Answer:
3
Step-by-step explanation:
blue, white, and red colors
If f(x) = 3x²+2 and g(x)=x2-9, find (f- g)(x).
Answer:
Step-by-step explanation:
Depending on whether or not the g(x) is x^2 or 2x, I have both ways.
If g(x) is x^2 - 9...
--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11
If g(x) is 2x...
--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11
Hope this helps!
The 2 main support rods for a barbeque grill are each 7.5 cm from the centre of the
grill. the grill is 60 cm in diameter, how long is each support rod?
Answer:
58.1 cm
Step-by-step explanation:
The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.
__
Pythagorean theoremThe theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...
c² = a² +b²
applicationFor the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.
30² = 7.5 +b²
b² = 900 -56.25 = 843.75
b = √843.75 ≈ 29.0473
The length of each support rod is twice this value, so ...
rod length = 2b = 2(29.0473) = 58.0947
Each support rod is about 58.1 cm long.
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From experience, an airline knows that only 70% of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that fewer than 7 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.
Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
p = 0.7, n = 8.
The probability that fewer than 7 of them show up is given by:
[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]
In which:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]
[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]
Then:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]
[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]
0.7447 = 74.47% probability that fewer than 7 of them show up.
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On last week math tests Mr.Jones class had an average of 82 points with a standard deviation of 10 points.Mrs.Potters class had an average of 79 points with a standard deviation of 3 points.Which class was more constant and how can you tell
Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.
What is a statistical dispersion?A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.
In Mathematics, there are four measures of dispersion for a data set and these include the following:
RangeInterquartile rangeVarianceStandard deviationIn this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.
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What shapes can the composite figure be decomposed into? Select two options.
A hexagon.
a rectangle and a triangle
a rectangle and two triangles
a square and two triangles
two rectangles
two trapezoids
Answer:
one of them is two trapezoids
Step-by-step explanation:
dependent or independent
The probability of coin landing with heads is an independent event.
The probability of winning 1st and 2nd prize is a dependent event.
What are independent and dependent events?
Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.
Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.
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Petra is making a batch of extra large donuts by stamping circles in dough using
a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out
a circle using a pastry stamp that has a diameter of 2 inches.
How many square inches of dough are left in the donut after the hole has been
removed?
Step 1 Find the radius of each circle
Step 2 - Find the area of the large circle
Step 3 - Find the area of the small circle
Step 4 - Area of large circle minus area of small circle
Area = Tr
The answer of the following questions is discussed below
What is area of circle?Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.
The radius of each circle
r1= 2.5 inches.
r2= 1 inches
Area of circle large circle,
= πr1²
=3.14*2.5*2.5
=19.625 inch²
Area of small circle,
= πr2²
= 3.14*1*1
=3.14 inch²
Area of large circle minus area of small circle,
= 16.485 inch²
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Solve for x.
40°
x + 71
75°
Answer:
x = -6.
Step-by-step explanation:
First thing to notice is that this is the third angle in a triangle, and all 3 angles have to equal 180.
Subtract 75 and 40 from 180 to get the missing angles value.
180 - 75 - 40 = 65
So now we know the missing angle has to be 65, or can be written as:
x + 71 = 65.
To solve this, just subtract 71 from both sides.
x = -6.
Expand (x^22-3x^5 + x^-2 - 7) * (5x^4).
Can someone please explain in detail how to remove the parentheses step by step?
Let's see
[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]
Use distributive law
a(b+c)=ab+ac[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]
[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]
Answer:
[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
Step-by-explanation:
Given expression:
[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]
Use the Distributive Property Law (b ± c)a = ab ± ac
to remove the parentheses:
[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]
Simplify by multiplying the coefficients of each term:
[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:
[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]
[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
Julia buys a spool with 12 yards of wire. The students in
her jewelry-making class use 4 yards 2 feet of the wire
for one project and 7 feet of the wire for another
project. How many feet of wire does Julia have left?
What is the algebraic equation of the sum of 28?
Answer:
There can be alot of equations for this since you didn't say anything specific. But since u didnt say anything specific, this can be one of the equations: 20 + 8, 30 - 2, 4 x 7
Cos W =0.53
Does anybody know this
Answer:
58°
Step-by-step explanation:
Apply trig inverse properties
W = arccos(0.53)
W = 2[tex]\pi[/tex] - arccos(0.53)
Solve for the coordinates of the midpoint of (13, 27) and (-31, 53). Show your work to receive full credit.
Answer:
-9,40
Step-by-step explanation:
Midpoint Formula:
[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]
Answer:
Midpoint = (−9,40)
Step-by-step explanation:
The product of 7 and x is the same as the sum of nine and three and two. What is the value of x?
Answer:
Given:
The product of 7 & x is the same as the sum of 9 and 3 and 2.To Find:
The value of x ?Solution:
According to the question:
(1) The product of 7 & x
➝ 7x
(2) The sum of 9 and 3 and 2
➝ 9 + 3 + 2
➝ 14
From (1) and (2) , we get:
➝ 7x = 14
➝ x = 14 ÷ 7
➝ x = 2
Let's Check:Let's check whether our answer is correct or not:
• To check our answerer, let's putting the value of x :
♣ 7(2) = 14
♣ 14 = 14 ✅
Thus, our answer is correct....The value of x is 2.
how to determine area of the following,in some cases leave the answer in term of x ABJH
Answer:
x²
Step-by-step explanation:
The area of rectangle ABJH is the product of its dimensions.
__
The dimensions are given as ...
AB = x
AH = x
The area of ABJH is ...
area = length × width = (x) × (x) = x²
The area of ABJH is x².
Please help, this is due by 2:18pm est
71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.
71 + y = 180
y = 109
The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.
109 + 46 + x = 180
x = 25
Answer: x = 25 degrees
Hope this helps!
help me with this question
Answer:
a) 150
b) 2650
Step-by-step explanation:
6% of 2500 is 150
150 + 2500 = 2650
HELP PLS I'LL MARK U BRAINLIST !!
Answer:
angles in a triangle add up to 180°
5:12:13 = 30
180 ÷ 30 = 6
6 × 5 = 30°
6 × 12 = 72°
6 × 13 = 78°
angles = 30°, 72°, 78°
What is the probability of getting tails and then tails
3. Here is a list of questions about the students and teachers at a school. Select all the
questions that are statistical questions.
A. What is the most popular lunch choice?
B. What school do these students attend?
C. How many math teachers are in the school?
D. What is a common age for the teachers at the school?
E. About how many hours of sleep do students generally get on a school night?
F. How do students usually travel from home to school?
education Roman Catholic School one five two weeks
Here is an equilateral triangle. The length of each side is units. A height is drawn. In an equilateral triangle, a line drawn from one corner to the center of the opposite side represents the height. 1. Find the exact height. 2. Find the area of the equilateral triangle. 3. (Challenge) Using for the length of each side in an equilateral triangle, express its area in terms of .
1. Height of the equilateral triangle is: √3 units
2. Area of the equilateral triangle = √3 units²
3. Area = √3/4 x², when each side is x.
What is an Equilateral Triangle?A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.
1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:
h = √(2² - 1²)
h = √(4 - 1)
h = √3
2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)
Area of the equilateral triangle = √3 units²
3. If x is the side length of the equilateral triangle, we would have:
height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x
Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²
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A side of the triangle below has been extended to form an exterior angle of 131°. Find the value of x. 131⁰ to 112º
Answer:
[tex]x = 49degrees[/tex]
Step-by-step explanation:
[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]
The required value of x for the given figure is 49°.
What is a straight line?A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.
The sum of the angles on a straight line is always 180°.
In the given figure the angles 131° and x° are on the same straight line.
Since, the sum of the angles on a straight line is 180°.
The following equation can be written for the given figure,
x + 131 = 180
=> x = 180 - 131
= 49
Hence, the value of x for the given figure is 49°.
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Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
Triangle A B C is shown. Angles A B C and B C A are congruent.
Which would prove that AB ≅ AC?
converse of the isosceles triangle theorem
substitution
definition of congruency
converse of the triangle parts relationship theor
The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.
The complete answer is given below and the figure is attached with the answer.
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.
What is the missing reason in the proof?
the converse of the triangle parts relationship theorem
substitution
definition of congruency
the converse of the isosceles triangle theorem
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Isosceles triangle two sides of the triangle are equal and their opposite angles too.
Given
△ABC with ∠B ≅ ∠C
Prove that
AB ≅ AC
How to give a conclusion?
From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.
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1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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Carlos spent a total of $40 at the grocery store. Of this amount, he spent $14 on fruit. What percentage of the total did he spend on fruit?
bivariate data is the type of data that a scatterplot is used to analyze?
True
or
False
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