Final answer:
The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)
Explanation:
The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.
Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.
What is the sum of the first 7 terms of the series −4+8−16+32−... ?
Enter your answer in the box.
we have that
−4+8−16+32−.....
a1=-2*(-2)-----> -4
a2=-4*(-2)-----> +8
a3=+8*(-2)-----> -16
a4=-16*(-2)----> +32
a5=+32*(-2)----> -64
a6=-64*(-2)-----> +128
a7=+128*(-2)-----> -256
The sum of the first 7 terms of the series is
[a1+a2+a3+a4+a5+a6+a7]-----> [-4+8-16+32-64+128-256]-------> -172
Why is circle 1 similar to circle 2?
Circle 1: center (2, 3) and radius 4
Circle 2: center (2, 3) and radius 12
Answer: The answer is given below.
Step-by-step explanation: The given circles are:
Circle 1: centre (2, 3) and radius 4
Circle 2: centre (2, 3) and radius 12.
The equations of circle 1 and circle 2 are respectively given as :
[tex](x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.[/tex]
These two circles are drawn on the graph as shown in the attached figure.
We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor
[tex]S=\dfrac{12}{4}=3.[/tex]
Thus, the two circles are similar.
What is the area of the circle if XY = 5.4 mm?
the answer would be 7.29π mm² because what you would do is
you would first divide 5.4 by two in order to get what the radius is
then you would multiply 2.7 times 2.7 in order to get 7.29
the reason that this is correct is because you have to make sure that you plug in the right values in the formula
What is the area of a circle whose radius is 5 ft? 5π ft² 10π ft² 20π ft² 25π ft²
Answer:
The area of the circle is equal to [tex]25 \pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=5\ ft[/tex]
substitute
[tex]A=\pi (5^{2})=25 \pi\ ft^{2}[/tex]
The area of a circle with a radius of 5 ft is equal to 25π ft² which is calculated using the formula A = πr². Below step-by-step calculation helps in understanding how to apply the formula correctly.
To find the area of a circle whose radius is 5 ft, we use the formula for the area of a circle: [tex]A = \pi r^2[/tex].
Step 1: Identify the radius (r) of the circle
[tex]r=5 \text{ ft}[/tex]Step 2: Plug the radius value into the formula
[tex]A &= \pi (5 \text{ ft})^2[/tex]Step 3: Square the radius
[tex](5 \text{ ft})^2 = 25 \text{ ft}^2[/tex]Step 4: Multiply this result by π (pi)
[tex]A = \pi \times 25 \text{ ft}^2[/tex]which gives [tex]A = 25 \pi \text{ ft}^2[/tex].
Therefore, the area of a circle with a radius of 5 ft is 25π ft².
You are paid $8.50/hr at your part-time job. Your deductions are FICA (7.65%), federal tax withholding (9.15%), and state tax withholding (7.5%). Your travel expenses are $6.00 per day worked. You work 16 hours over a 4-day period of time. What is your net income after travel expenses?,
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three?
The quotients are different because the order matters in division. When 3 is divided by 1/5 it becomes a multiplication problem with reciprocal of 1/5, yielding 15. However, when 1/5 is divided by 3, it becomes multiplication with reciprocal of 3 and yields 1/15.
Explanation:The reason that the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three is due to how division works in mathematics. To put it simply, the order of numbers in a division operation matters; it is not commutative like addition or multiplication.
When you divide 3 by 1/5, you're essentially asking, 'how many times does 1/5 fit into 3?'. Here, you're dealing with fractions and whole numbers. To perform the division, we multiply 3 by the reciprocal of 1/5, which is 5. The answer is 3 * 5 = 15.
But, when you divide 1/5 by 3, you're asking 'how many times does 3 fit into 1/5?'. Here, you need to multiply 1/5 by the reciprocal of 3, which is 1/3. The calculation is (1/5) * (1/3) = 1/15.
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1. A ball is dropped from a height of 225 feet. The ball’s height y (in feet) after t seconds can be modeled by y = 225-16t2 . After how many seconds does the ball hit the ground?
What number should be placed in the box to help complete the division calculation?
helppppppppppppppppppppppppppppppppppp
An unlabeled hierarchical diagram of various astronomical bodies is shown below. The labels A, B, C and D can be used to represent the galaxy, Mars, universe, moon, and solar system.
Part 1: Which four astronomical bodies would you choose to represent the four labels in the diagram?
Part 2: Explain why the hierarchical level D is different from the rest.
The four astronomical bodies represents here are A represents Universe, B represents Galaxy, C represents Solar System, and D represents Mars.
The hierarchical level D is different from the rest is because Mars is a planet and unlike all other astronomical bodies it does not hold other astronomical bodies with in it.
What are astronomical bodies?"Astronomical bodies are objects in space like sun, moon, planets, and stars. They form a part of the vast universe we live in and are very far from Earth."
What is Universe?"The universe includes all space, time, and their objects that also includes planets, stars, galaxies, and other forms of matter and energy."
What is Galaxy?"Galaxy is a vast collection of dust, gas, billions of stars with their solar systems that are all held together by gravity."
What is Solar System?"Solar System is a gravitationally bound system of eight planets, their moons in orbit round the sun with small bodies like comets, meteoroids, and asteroids."
What is Mars?"Mars is the fourth planet from the sun and the second smallest planet in the Solar System."
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What is the value of c such that x2 + 10x + c is a perfect square trinomial?
The value of c that makes x² + 10x + c a perfect square trinomial is c = 25.
What value of c makes the equation a perfect square trinomial?Given the equation in the question:
x² + 10x + c
A perfect square trinomial is of the form (ax² + bx + c), and it can be factored into (px + q)², where p and q are constants.
To find the value of c such that x² + 10x + c is a perfect square trinomial, we need to factor it as (px + q)².
Note that, the coefficient of x in the given trinomial is 10, so 2pq must equal 10.
Also, the coefficient of x² is 1, so p² must equal 1.
Hence, we have:
2pq = 10
p² = 1
From equation (2), we know that p could be either 1 or -1, after taking the square of both sides:
If p = 1, from equation (1) we have:
2pq = 10
2(1)q = 10
2q = 10
q = 10/2
q = 5
So, if p = 1 and q = 5, the perfect square trinomial is (x + 5)².
Let's expand to check:
(x + 5)² = x² + 10x + 25
Therefore, the value of c is 25.
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simplify the expression. write the answer using scientific notation 4(6.2x10^11)
The correct answer is 2.48*10^12.
The supply and demand curves reflect data for a specific brand of sunglasses. Which circumstance best explains the shift of the demand curve from D to D1?
a. An ad campaign highlights the sustainable resources used to make the sunglasses.
b. Consumer reports indicate that the sunglasses break easily.
c. Fuel costs increase, making it more costly to produce the sunglasses.
d. Tax incentives encourage the producer to hire more workers.
Since there is a decrease in quantity and supply the answer would be Consumer reports indicate that the sunglasses break easily.
Answer "A" is definitely wrong
Please help asap!!! 12 points
Find the volume v of the described solid s. a right circular cone with height 7h and base radius 3r
The volume of a right circular cone with height 7h and base radius 3r is ⅔ 9r² h.
Explanation:The volume of a right circular cone can be calculated using the formula V = ⅔ ² h, where r is the radius of the base and h is the height of the cone.
In this case, the height of the cone is 7h and the base radius is 3r.Plugging in the values, we have V = ⅔ (3r)² (7h) = ⅔ 9r² h.
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what is the probability that a card picked at random from a 52-card deck of playing cards is a club or a jack?
[tex] |\Omega|=52\\
|A|=\underbrace{13}_{\text{clubs}}+\underbrace{4}_{\text{jacks}}-\underbrace{1}_{\text{jack of clubs}}=16\\\\
P(A)=\dfrac{16}{52}=\dfrac{4}{13}\approx31\% [/tex]
Answer:
A. 4/13
Step-by-step explanation:
4/13 in percent is 30%(30.7692308 percent)
For Plato Users
GIVING BRAINLIEST TO THE FIRST RIGHT ANSWER!!!!
The following is the correct way to show the product for 0.453 × 8.1:
True
False
Answer:
true
Step-by-step explanation:
find the equation of the straight line passing throughthe point (3,5) which is perpendicular to the line y=3x+2
please explain
1. What is the simplest form of the radical expression? 4 fourth root of two x+ 6 fourth root of two x (1 point) 10fourth root of two x 10 fourth root of four x 20 fourth root of two x not possible to simplify,
Mark's father travels 463 miles every month for his job. How many miles does he travel in 8 months?
The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student takes latin?
A.)1
B.)1/2
C.)
1/4
Answer: B ) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given: The number of students in junior class n(S)= 50
The number of students take only Latin n(L-F)= 15
The number of students take only French n(F-L)=25
The number of students take both = n(F∩L)=10
The number of students take Latin n(L)=n(L-F)+n(F∩L)=15+10=25
Therefore, the probability that the student takes Latin is given by :-
[tex]\text{Probability(Latin)}=\frac{\text{number of students take latin}}{\text{Total students}}\\\\=\frac{25}{50}=\frac{1}{2}[/tex]
Do two triangles with the same base and height have the same area
solve for x: 7/8-1/x=3/4
x = 1
x = 2
x = 4
x = 8
9514 1404 393
Answer:
x = 8
Step-by-step explanation:
[tex]\dfrac{7}{8}-\dfrac{1}{x}=\dfrac{3}{4}\\\\7x-8=6x\qquad\text{multiply by $8x$ to clear fractions}\\\\\boxed{x=8}\qquad\text{add $8-6x$}[/tex]
__
If you don't mind dealing with fractions, you can add 1/x -3/4 to get ...
7/8 -3/4 = 1/x
1/8 = 1/x . . . . . . . simplify
x = 8 . . . . . . . . . . take reciprocals; equivalently, multiply by 8x.
To solve 5(2^x+4)=15, first divide each side by
Answer:5
Step-by-step explanation:
Find n (write in simplest radical form)
1. The center of a circle is located at (5, −5) . The radius of the circle is 3.
What is the equation of the circle in general form?
x^2+y^2+10x−10y+47=0
x^2+y^2+10x−10y+41=0
x^2+y^2−10x+10y+47=0
x^2+y^2−10x+10y+41=0
2.The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
x^2+y^2−10x−12y−62=0
x^2+y^2+10x+12y+62=0
x^2+y^2−10x−12y+60=0
x^2+y^2+10x+12y+60=0
Sigma Notation: Need Help!!
Problem 1:
Evaluate the summation of 3 times negative 2 to the n minus 1 power, from n equals 1 to 5.
Choices:
A.-93
B.-33
C.33
D.93,
Final answer:
To solve the sigma notation problem, we individually calculate each term for n from 1 to 5 and sum them up, resulting in a total value of 33. Thus, the correct answer is C.33.
Explanation:
The problem involves evaluating a series using sigma notation. Specifically, we're looking at the summation of 3 × (-2)n-1, with n going from 1 to 5.
To find the solution, we need to calculate each term separately for each value of n, and then sum all of the calculated terms together.
For n=1: [tex]3 \times (-2)^{1-1[/tex] = 3 × 1 = 3For n=2: [tex]3 \times (-2)^{2-1[/tex] = 3 × (-2) = -6For n=3: [tex]3 \times (-2)^{3-1[/tex] = 3 × 4 = 12For n=4: [tex]3 \times(-2)^{4-1[/tex] = 3 × (-8) = -24For n=5: [tex]3 \times (-2)^{5-1[/tex] = 3 × 16 = 48Adding these values together: 3 - 6 + 12 - 24 + 48 = 33.
So the correct answer to the summation is 33, which corresponds to choice C.
Centered 7 meters above the ground, a Ferris wheel of radius 6 meters is rotating with angular speed 24 degrees per second.
a. Assuming that you begin at time t = 0 seconds at the lowest point on the wheel, find a formula that describes the distance h (in meters) from you to the ground after t seconds of riding.
b. At what times are you 10 meters above the ground? Please explain clearly how you got your solution.
Which explanation justifies how the area of a sector of a circle is derived?
Determine the percent of the sector of the circle divided by the degrees in a circle. Then find the number of triangles within a circle. Divide the two numbers and multiply by the area of the circle.
The sector of a circle is a fractional part of the circle. Determine the fraction of the circle that the sector represents. Multiply this fraction by the area of the entire circle.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle.
Find how many sector pieces fit in a circle. Divide this number by the total degrees in a circle. Then multiply the quotient by the diameter of the circle.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle justifies how the area of a sector of a circle is derived
The explanation that justifies how the area of a sector of a circle is derived is:
"The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle."
This method involves finding the fraction of the circle that the sector represents by dividing the central angle of the sector by 360 degrees. Then, multiply this fraction by the area of the whole circle to get the area of the sector.
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Explain why (√10)^3d is equivalent to (10^d)^3/2