Answer:
See below.
Step-by-step explanation:
First check that f(x) has a real value at x = 3:
f(3) = 3^2 + 5(3 - 2)^7
= 9 + 5 * 1^7
= 14,
So the first condition is met.
Now we check if limit as x approaches 3 exists.
As x approaches 3 from below f(x) approaches 14 and at x = 3 = 14.
As x approaches 3 from above f(x) approaches 14 and at x = 3 = 14.
These 3 conditions shows that f(x) is continuous at x = 3.
The function f(x) = x^2 + 5(x - 2)^7 is continuous at x = 3 because it meets all the conditions of continuity: it is defined at x = 3, the limit of the function as x approaches 3 exists, and the limit equals the function's value at x = 3.
Explanation:The function f(x) = x^2 + 5(x - 2)^7 is continuous at x = 3 if it satisfies the following three properties: the function is defined at x = 3, the limit of the function as x approaches 3 exists, and the function value at x = 3 is equal to the limit as x approaches 3.
Step 1
The function is defined at x = 3. When we substitute x = 3, we get f(x) = 3^2 + 5(3 - 2)^7= 9 + 5*1^7 = 14.
Step 2
The limit of the function as x approaches 3 exists. As x approaches 3 from both the left and right sides, the function takes the value 14.
Step 3
Finally, the limit as x approaches 3 is equal to the function's value at x = 3. In other words, the limit is 14, which is equal to the function's value when x = 3 (which is also 14).
Since the function satisfies all these conditions, we can say that the function f(x) = x^2 + 5(x - 2)^7 is continuous at x = 3.
Learn more about Continuity of Functions here:https://brainly.com/question/32522941
#SPJ2
PLEASE HELP!! DUE TODAY! I GIVE BRAINLIEST
Answer:
.54
Step-by-step explanation:
The probability of a non-glove item is: (# of non-glove items)/(total # of items)
There are 27 non-glove items and 23 gloves. That makes the probability of choosing a non-glove item:
27/(23+27)=
27/50 =
.54
Please help me please!!!!
Answer:
1 F
2 C
3 G
4 D
5 A
6 E
7 B
Step-by-step explanation:
p implies q (conditional)
Which is G
It's converse would be
q implies p
Which is G
F and G together become bi-conditional
Which is B
Contraposition is
not q implies not p
Inverse of p implies q is
not p implies not q
Which is D
Conjunction is p and q,
Which is F
Disjunction is p or q,
Which is C
x2 - 14x + 40
O A.
(x + 3)(x + 5)
OB. (x - 10)(x-4)
O C. (x-8)(x - 5)
O D. (x+ 10)(x+4)
Answer:
B
Step-by-step explanation:
(x-4) x (x-10)
Answer:
B
Step-by-step explanation:
Given
x² - 14x + 40
Consider the factors of the constant term (+ 40) which sum to give the coefficient of the x- term (- 14)
The factors are - 10 and - 4, since
- 10 × - 4 = + 40 and - 10 - 4 = - 14, thus
x² - 14x + 40 = (x - 10)(x - 4) → B
HELP PLEASE ASAP 30 PTS I’ll MARK YOU BRAINLIEST
Answer:
x=50 ∠BCX=65
Step-by-step explanation:
The angles is a triangle add up to 180 so
70+45+∠BCX=180 so
115+∠BCX=180 (subtract 115 from both sides)
∠BCX=65
A line adds up to 180
so 2x+15+65=180
so 2x+80=180 (subtract 80 from both sides)
2x=100 (divide by 2)
x=50
If the ratio of red socks to blue socks is 1:6, how many red socks would I have if I had 24 blue socks?
Answer:4
Step-by-step explanation:
1:6
Divide 6 by 24
you will get 4
Times your answer by 1 and then u will get your final answer
Volume of a rectangular prism is 275 cubic Inches. The base is a square with the
side length of 5 inches. Find the height of this prism. Write the formula, and solve
as an equation. V=s?h
Answer:
11 in
Step-by-step explanation:
Starting with the base, we know the side length is 5 inches. So with that in mind, we can do 5 x 5 to get the area of the base, 25. We also know the volume of the whole rectangular prism is 275, so we can do 275 ÷ 25. The quotient of that is 11.
We can check our answer by doing 11 x 25. This gives us 275, proving that it is correct.
Hope this helped! :)
The width of a human hair is about 0.002 inches, which can be written as
2 x 10" inches. What is n?
Answer:
-3
Step-by-step explanation:
[tex]2*10^{-3}[/tex], n= -3.
What is fraction?A fraction is a number which represents the part of a whole or collection of objects. It is in the from of a/b where a represents the numerator part and the b represents the denominator parts.
The width of a human hair is about 0.002 inches,
It can be written in fraction form as,
[tex]\frac{2}{1000}[/tex]⇒ [tex]\frac{2}{10^{3} }[/tex]
By writing [tex]10^{3}[/tex] in reciprocal from we get,
[tex]2*10^{-3}[/tex], then n= -3.
Hence, [tex]2*10^{-3}[/tex], n= -3.
Learn more about fractions here:
https://brainly.com/question/8482939
#SPJ5
If the diameter of a circle is 15 inches, what is the radius?
Answer:
7.5
Step-by-step explanation:
R= d/2
Divide 15 by 2
Answer:
7.5
Step-by-step explanation:
So the formula is:
[tex]\frac{d}{2}[/tex]=r
So Divide 15 by 2. Which is 7.5
14 divided by 2 is 7, and the 1 left over would be a .5
Hope this helped!
The length of the hypotenuse of a right triangle is 15 in. and one leg has length of 6 in. Find the length of the other leg.
Answer:
C. square root 189 in.
Step-by-step explanation:
60% of x is equal to 87. Write an equation that expresses the relationship between 60%, x, and 87.
Answer: 0.6x = 87
Step-by-step explanation:
Hi, to answer this question we have to write en equation:
We have to multiply the variable x by the percentage given (60%) in decimal form (divided by 100). That expression must be equal to 87.
Mathematically speaking:
x (60/100) = 87
0.6x = 87
Feel free to ask for more if needed or if you did not understand something.
This equation states that 60% (or 0.60) of x is equal to 87.
To express the relationship between 60% of x and 87, we can set up an equation. Since 60% can be written as 0.60, we can write:
0.60x = 87
To solve for x, we divide both sides of the equation by 0.60:
x = 87 ÷ 0.60
So, x will be:
x = 145
This shows that 60% of 145 is equal to 87.
5c + cd, c = 1.5 d = 15
Answer:5(1.5) + 1.5(15)
=7.5 +22.5
=30
Answer:
5(1/5)+ 1/5(15) = 1 + 3 =4
Which expression represents the total surface area, in square centimeters, of the square pyramid?
(8.2) (8.2) + 4 (one-half (8.2) (10.3))
(8.2) (8.2) + 4 (one-half (8.2) (11.1))
(8.2) (10.3) + 2 (one-half (10.3) (10.3)) + 2 (one-half (8.2) (10.3))
(8.2) (10.3) + 2 (one-half (10.3) (11.1)) + 2 (one-half (8.2) (11.1))
Answer:
(8.2) (8.2) + 4 (one-half (8.2) (11.1))
Step-by-step explanation:
Formula for calculating the surface area of a square based pyramid is expressed as:
Surface area = A + 1/2ps
A is the base area
P is the perimeter of base
S is the slant side.
Since the base of the pyramid is a square, then
Base Area A = L²
A = 8.2²
A = 67.24cm²
Perimeter of square = 4L = 4(8.2)
= 32.8cm
Slant Height = 11.1cm
On substituting the gotten value:
Surface area = 8.2(8.2) + 1/2 [4(8.2 (11.1)]
Based on the solution above, the expression below is correct.
S =(8.2) (8.2) + 4 (one-half (8.2) (11.1))
sergio runs 6 miles in three days. At this rate, how many miles will he run in 20 dayshelp
Answer:
40 miles
Step-by-step explanation:
We have to find how many miles he runs per day. So if we divide 3 days by 3 to get 1 day, that means he would run 2 miles per day. So if we are trying to figure out how many miles he runs in 20 days, we do 20*2 which equals 40. Hope this helps.
(please mark me brianliest)
Answer:
40 miles
Step-by-step explanation:
He runs 2 miles per day
6 miles over 3 days is 2 miles per day
6 divided by 3 is 2
8(3x+1) please give me your Brainly answer
Answer:
its 3
Step-by-step explanation:
Simplifying
8 = 3x + -1
Reorder the terms:
8 = -1 + 3x
Solving
8 = -1 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
8 + -3x = -1 + 3x + -3x
Combine like terms: 3x + -3x = 0
8 + -3x = -1 + 0
8 + -3x = -1
Add '-8' to each side of the equation.
8 + -8 + -3x = -1 + -8
Combine like terms: 8 + -8 = 0
0 + -3x = -1 + -8
-3x = -1 + -8
Combine like terms: -1 + -8 = -9
-3x = -9
Divide each side by '-3'.
x = 3
Simplifying
x = 3 this took forever to type hope it helped
It takes 41.7 BTUs to heat a 5 gallon jug of water. What is the density of a gallon of water. Round your answer to the nearest hundredth
Answer: The density is 0.002 lb/cm^3
Step-by-step explanation:
1 BTU is neded to increment the temperature of 1 Lb of water by 1° F
Then if we need 41.7 BTU to increment 1°F of 5 gallons of water, this means that in the 5 gallons we have a mass of 41.7 lbs of water.
And as you know, density = mass/volume
now, 1 gallon = 3.78 liters = 3780 cm^3
then 5 gallons = 5*3780 cm^3 = 18900 cm^3
The density is D = 41.7Lb/18900 cm^3 = 0.002 lb/cm^3
What is the value of a?
Answer:
a = 2
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Sum the exterior angles and equate to 360, that is
66a + 56a + 31a + 27a = 360, that is
180a = 360 ( divide both sides by 180 )
a = 2
What is the value of log8 512
Answer:3
Step-by-step explanation:
Logarithm base 8 of 512 is 3.
Answer:3
Step-by-step explanation:
Rewrite 10^32 x 10^6 using a single exponent
10^38
Step-by-step explanation:
Given that,
10^32 x 10^6
Here the base is same (10) and the powers are 32 and 6.
These 2 bases are in multiplication form so the powers can be added up.
10^32 x 10^6 = 10^(32+6)
= 10^38
How many solutions does this equation have?
4x − 10
2
= 2x − 5
A) no solution
B) exactly one solution
C) exactly two solutions
D) infinitely many solutions
Answer:
The correct answer is infinitely many
Step-by-step explanation:
4x-10/2=2x-5
after that you will multiply the 2 times 2x and 2 times -5
so now it becomes
4x-10=4x-10 that's why it's infinitely many
Answer:
D) infinitely many solutions
Step-by-step explanation:
The equation yields a statement that is always true, −10 = −10.[
So, the equation has infinitely many solutions.
4x − 10 2 = 2x − 5 4x − 10 = 4x − 10 −10 = −10
A photo is printed on a 20-inch by 24-inch piece of paper. The photo covers 320 square inches and has a uniform border. What is the width of the border?
Answer: The width of the border is 4 inches
Step-by-step explanation: The paper frame has its dimensions given as 20 inch by 24 inch. That means the area of the paper frame would be;
Area = L x W
Area = 20 x 24
Area = 480 square inches.
However, the photo itself covers an area of 320 square inches of this total surface area. If the photo has a uniform border, that means the photo and the paper frame are best described as congruent parallelograms (similar rectangles).
The ratio of the area of both paper frame and photo is given as;
Ratio = 480 : 320
Ratio = 3 : 2
When the length of the photo frame is given as 24, the length of the photo would be
3/2 = 24/L
L = (2 x 24)/3
L = 48/3
L = 16
Having calculated one side of the photo as 16 inches and the area has been given as 320 square inches, the other side of the photo is now derived as;
Area = L x W
320 = 16 x W
320/16 = W
20 = W
The dimensions of the paper frame is given as 24 inches and 20 inches, while those of the photo is given as 20 inches by 16 inches. The difference in both dimensions is 4 inches on either side (24 - 20 = 4, and 20 - 16 = 4)
Therefore the width of the border is 4 inches
ok i do not know how to do this please help asap ;-;
Answer:
Look and see >:/
Step-by-step explanation:
1) 13, 34 Rate of change: 3
2) 15, 1 Rate of change: -2
3) 17, 32 Rate of change: 0.75
4) 9, -1 Rate of change: -0.4
what is the length of bc in the triangle below
Answer:
This is how i solve it:
Pythagorean theorem:
a squared + b squared = c squared
12 squared + 16 squared = c squared
144 + 256 = 400
square root of 400 is 20
final answer: 20
15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each
container? Express your answer as a decimal and as a fraction,
Final answer:
Each container will have approximately 3.75 kilograms of rice, which can be expressed as 3.75 kg or 15/4 kg.
Explanation:
To find out how many kilograms of rice are in each container, we need to divide the total weight of the rice by the number of containers. In this case, we have 15 kilograms of rice and 4 containers, so we divide 15 by 4. The result is 3.75 kilograms.
So, each container will have 3.75 kilograms of rice.
As a decimal, this can be expressed as 3.75 kg. As a fraction, it can be written as 15/4 kg.
There are 14 books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
?
a) 8:14
b) 6:8
yeah its telling me I'm short of words
Calculating Factorials
Quick
Check
Evaluate each expression.
6! =
Answer:
6! = 720
Step-by-step explanation:
In evaluating factorial functions, generally
n! = n(n-1)(n-2)(n-3)...× 1
We can see that as we are moving, the value keep decreasing by 1 until it reaches the least value which is 1.
6! = 6(6-1)(6-2)(6-3(6-4)(6-5)
6! = 6×5×4×3×2×1
6! = 720
What is 3=7(4 - 2u)-6u
Answer:
u = 5/4
Step-by-step explanation:
to evaluate for the value of u we would simply open the bracket and then evaluate for the value of u by collecting the like terms together.
solution
3=7(4 - 2u)-6u
3 = 28- 14u - 6u
collect the like terms
3 + 14u + 6u = 28
20u = 28 - 3
20u = 25
divide both sides by the coefficient of u which is 20
20u/20 = 25/20
u = 5/4
Answer:
[tex]u = 5/4[/tex]
Step-by-step explanation:
Step 1: Distribute on the right side
[tex]3 = 7(4 - 2u) - 6u[/tex]
[tex]3 = (7 * 4) + (7 * -2u) - 6u[/tex]
[tex]3 = 28 - 14u - 6u[/tex]
Step 2: Combine like terms
[tex]3 = 28 + (-14u - 6u)[/tex]
[tex]3 = 28 + -20u[/tex]
Step 3: Subtract 28 from both sides
[tex]3 - 28 = 28 - 20u - 28[/tex]
[tex]-25 = -20u[/tex]
Step 4: Divide both sides by -20
[tex]-25 / -20 = -20u / -20[/tex]
[tex]5/4 = u[/tex]
Answer: [tex]u = 5/4[/tex]
List the possible rational zeros.
m(x) = - 4x + 11x² +6x+14
How do I solve this
[tex]m(x)=-4x+11x^2+6x+14\\m(x)=11x^2+2x+14[/tex]
Equating the equation to 0 and solving it
[tex]11x^2+2x+14=0\\D=2^2-4*11*14=-612<0[/tex]
This equation has no solution, so we can't find rational zeros
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
P.S. Hello from Russia
Which expression is equivalent to 5 divided by 2
A. 5•1\2
B. 2/5
C. 10
D. 2•1/5
Answer:
a
Step-by-step explanation:
Answer:
= 5 × 1/2
Step-by-step explanation:
Five divided by 2
= 5 ÷ 2
= 5/2
Which is same as
= 5 × 1/2
I hope this was helpful, please rate as brainliest
IM giving 15 points please help!
a 42 meter lighthouse is observed by a ships officer at a 65 degree anlge to a path of the ship. At the next sighting, the lighthouse is observed at a 42 degree angle. To the nearest meter what is the distance between the 2 sightings?
Answer:
the hhh
Step-by-step explanation:
2A - 5B + 4X = C - 8X
Answer:
(5B+C-2A)/8 = x
Step-by-step explanation:
2A - 5B + 4X = C - 8X
subtract 4x from both sides
2A - 5B + 4X-4x = C - 8X-4x
2A - 5B = C - 12X
subtract C from both sides
2A - 5B -C = C-C - 8X
2A - 5B -C = - 8X
divide both sides by -8
(2A - 5B -C)/-8 = - 8X/-8
(-2A+5B+C)/8 = x
(5B+C-2A)/8 = x