log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)
I assume you're referring to the product,
[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]
Recall the change-of-base identity:
[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
where c > 0 and c ≠ 1. This means the product is equivalent to
[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]
and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to
[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]
Theresa finds a shirt on sale at the store. The regular price of the shirt is $32.00. But there is a 20% off sale today. Theresa remembered that there is 8.1% tax on the sale price of the shirt. What is her final cost?
Question 10 options:
$28.92
$27.67
$29.31
$31.00
Answer:
Step-by-step explanation:
Given tgat:
Regular price = $32
Discount = 20%
Sale tax = 8.1%
What is the slope of a line parallel to the line whose equation is 2x+y=6.
Answer:
-2 is the slope...
So Basically -2/1
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
First, you solve for y by subtracting 2x from both sides of the equation and so now we have a y= -2x+6. The slope is going to be the number that is with x.
A sphere has a radius of 4 in. Which equation finds the volune of the sphere?
Answers above on the picture^ thank you:)
Answer:
The first answer
Step-by-step explanation:
The vertices of a triangle are P(-2, -4), Q(2, -5), and R(-1,-8). Name the vértices of the triangle after reflecting over the x-axis
Answer:
P(-2,4)
Q(2,5)
R(-1,8)
Step-by-step explanation:
The rule for reflecting points across the x-axis is to keep the x-value the same but "negate" the y-value. So, the points above are your answers.
Nineteen and four hundred fifteen thousand in word form
Answer: 19,415,000
I think
Step-by-step explanation:
Hope this helps!! :)
Answer:
If I understand what your trying to do, id think it would be 19,415? (IF IT IS IN THE MILLIONS, IT MAYBE 19,415,000 ALSO!)
I may be wrong, but I hope I helped!
1. Explain and give the formula for the formula for the following properties for segments in a circle.
a. Segments from Chords:
b. Segments from Secants:
c. Segments from a Secant and Tangent line:
2. Explain what a radian is and how it relates to a degree.
3. Define the following terms.
a. Inscribed Circle of a Triangle:
b. Incenter:
c. Circumscribed Circle of a Triangle:
d. Circumcenter:
Answer:
see explanation
Step-by-step explanation:
1
(a)
If 2 chords of a circle intersect then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.
(b)
If 2 secants are drawn from an external point to a circle then the product of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant.
(c)
If a tangent and a secant are drawn from an external point to a circle , then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.
2
A radian is defined as the angle subtended at the centre of a circle by an arc equal to the radius of the circle.
1 revolution = 360° = 2π radians
1 radian = [tex]\frac{360}{2\pi }[/tex] ≈ 57°
3
(a)
An inscribed circle of a triangle is a circle drawn inside a circle so the circle barely touches the sides of the triangle.
(b)
The incentre is at the point of intersection of the triangle's 3 angle bisectors.
(c)
A circumscribed circle of a triangle ( circles drawn around the triangle so that the circle passes through each of the triangles's vertices.
(d)
The circumcentre is at the intersection of the perpendicular bisectors of the triangle's sides.
'
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased
Answer: B
Step-by-step explanation:
It is $29.35 for each of the tickets that they buy for adults, so to figure out how much it is for all the adult tickets, it would be $29.35 times x. Same for the children tickets except it is times y and the amount of money is different.
An employer's accountant has announced that
the budget for the next year must be cut by 1/3 How much must be cut from the
budget if last year's budget was
$166,245?
A. $11,830
B. $55,415
C. $166,245
D. $498,735
What is the point-slope form of the equation of the line that passes through the point (-3,-4) and has a slope
of 2?
Answer:
y=2x+6
Step-by-step explanation:
Answer:
y=2x+2
Step-by-step explanation:
To find the point-slope form of the equation we need to get the slope-intercept form of (-3,-4) and 2
(Slope intercept form formula is y=mx+b) (m is slope) (b is y-intercept)
So we know that the slope of this equation is 2 so we can replace m with 2 since the slope is 2 and m is slope.
Equation will look like this:
y=2x+b
Now we need to find the b or y-intercept of the equation to do this the (-3,-4) come into play: replace x with -3 and replace y with -4
(x,y) -3 is x since it is the same spot in (-3,-4) and -4 is y since it is in the same spot in (-3,-4)
Replace:
-4=2(-3)+b
Multiply 2 and -3:
-4=-6+b
Move 6 to the other side by adding 6 on both side:
6-4=-6+6+b
Simplify
2=b
Now the equation looks like this: (If you replace b with 2 in y=2x+b)
y=2x+2
Answer: y=2x+2 (Point-slope form is the same thing as slope-intercept form)
How do solve this problem?
find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form. line 2x + 5y= -10 point (10, 4)
Answer:
y=-2/5x+8
Step-by-step explanation:
Step 1: Begin by changing the equation into slope-intercept form. Subtract 2x to both sides to get 5y=-10-2x. Divide 5 to both sides to isolate the variable, y. You should get y=-2/5x-2.
Step 2: Because we are looking for a line parallel to the given line, the slope should be the same, but the y-intercept should be different. Remove -2 to replace it with b, so it's unknown. The equation should be y=-2/5x+b. Plug in the ordered pair, (10, 4), into the equation to get 4=-2/5(10)+b. Multiply -2/5 and 10 to get -4. Add -4 to both sides and b=8. Plug in 8 and your final equation should be y=-2/5x+8.
- A beaker is filled with 0.23 liter of water. Leon
fills another beaker with 3 times as much
water. How much water is in Leon's beaker?
A 0.96 liter
B 0.84 liter
C 0.69 liter
D 0.47 liter
Answer:c
Step-by-step explanation:
What is the recursive formula for this sequence? 12, 16, 20, 24, 28, ...
Answer:
A
Step-by-step explanation:
first term is 12, and following terms are obtained adding 4 to previous term.
Doe has 2 3/8 pounds of hamburger meat. He is making 1/4 pound hamburgers .Does doe have enough meat to make 10 hamburgers
hey ms or mr could you help me out with this problem please?
Answer:
3
Step-by-step explanation:
We can approximate that triangle B is half the size of triangle A. We know this because the base for triangle A is six, meanwhile, for trinagle B it's 3. With this info we can then assume that in triangle A it's 10 for one side so, for triangle B it must be 5. However, there is n+2 instead. We can use the algebretic equation: 5=n+2. Once this equation is solved the answer is 3. Thus, n = 3.
Using the function h(x) = 2x – 3, what would the input need to be for an output of 7?
Therefore, the input needed for an output of 7 using the function h(x) = 2x - 3 is x = 5.
What is function?In mathematics, a function is a rule that assigns a unique output or value to each input of a given set. In other words, a function is a relationship between two sets, called the domain and the range, such that for each input value in the domain, there is exactly one output value in the range. A function can be represented by a mathematical expression or formula, a graph, a table, or a set of ordered pairs. Functions are used to model various phenomena and solve problems in many fields, including science, engineering, economics, and finance.
Here,
To find the input (x) that corresponds to an output of 7, we can set h(x) equal to 7 and solve for x as follows:
h(x) = 2x - 3
Setting h(x) = 7, we get:
7 = 2x - 3
Adding 3 to both sides, we get:
10 = 2x
Dividing both sides by 2, we get:
x = 5
To know more about function,
https://brainly.com/question/28193994
#SPJ1
A computer manufacturer has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by where x is the number of days since the start of the job. Find the expenditure if the job takes 8 days.
Answer:
The expenditure would be $ 8600
Step-by-step explanation:
If the cost is given by the function
C(x)= 10x + 6 where x is the number of days
The cost for 1 day would be
C(1)= 16 *100 = 1600 $ ( the expenses are in hundreds of dollars)
Then Putting x= 8 in the given equation we get
C(8)= 10(8) + 6
= 86
Multiplying 86 by 100 because expenditure rate per day is in hundreds of dollars
The expenditure would be $ 8600
chose the correct one quality to match the real-world situation. Gabe will spend no more than $100.
the answer choices are
a.x ≥100
b.x≤100
c.x>100
Answer:
B
Step-by-step explanation:
the other too are stating that Gabe will spend more than or more than/equal to $100
look at picture and answer ASAP
Answer:
its B and A
Step-by-step explanation:
Answer:
its in between the fist and second one cuusing what is given thats what i figured out
Step-by-step explanation:
3 x 36= 108 / 3 x 15 = 45
9 x 12 = 108 / 9 x 5 = 45
6 x 18 = 108 / 6 x 7 = 42
i hope this helps :)
Find the value of y,please help
Answer:
4.5255
Step-by-step explanation:
Use the Pythagorean theorem (a²+b²=c²) where A and B are equal to 3.2
a square and rectangle are shown below the width of the rectangle is the same length at a side of the square both represented by x the length of the rectangle is one foot more than twice its width the perimeter of the rectangle is 26 feet more than that of the square write an expression for the length of the rectangle in terms of x label of the drawing
Answer:
The answer for the length of the rectangle in terms of x is 2x+1=26
Step-by-step explanation:
Find the volume and surface area of each prism 3cm by 3cm by 3cm
Answer:
3 x 3 x 3= 18 so 18cm squared
Step-by-step explanation
Answer:
Volume =27cm³
Total surface area=54cm²
Step-by-step explanation:
Formula for finding volume of an object is Volume =length×breadth×height
so V=3cm×3cm×3cm=9cm²×3cm=27cm³ because the cm is three so it will become cube.
Formula for finding the total subject of an object is T.S.A meaning total surface area=2((length ×breadth)+(length×height)+(breadth ×height))
so it will be 2((3cm ×3cm)+(3cm ×3cm)+(3cm ×3cm)) calculate and if you any problem let me know.
Mrs. 1 ran 10 meters in 3.8 seconds. Mrs. 2 ran 10 meters in 3.2 seconds.
Who ran faster?
Answer:
Mrs. 2
Step-by-step explanation:
3.2 seconds is shorter than 3.8 seconds
Answer:
Mrs 2 ran 10 meters in 3.2seconds
compare:
-5/6 is greater than or less than or equal to 2/3
Answer:
less than
Step-by-step explanation:
Answer:
-5/6 is less than to 2/3
Calculate the paychecks of the following people. Select the total hours and paycheck.
Answer:
If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5 Sam-38.75,$8.75,339 Step-by-step explanation:
Just add up the number of hours worked and multiply by the rate.
what is the equation for (4, 9.4) and (-3, -9.5)
Answer: I got an eqaution I hope it is basic
Step-by-step explanation:
4 times 9
9 - (-3 ) times -9 + 5
Please help! I will give brainliest!!!!!!
Answer:
3,10 please give me brainliest i need one more for 5 please please please
Step-by-step explanation:
1. Given: y = -2x2
Domain
Range
Opening of the
parabola
Vertex
Axis of Symmetry
X - intercept
y - intercept
Domain: (-∞,∞) or -∞ < x < ∞ or all real numbers
Range: (-∞,0] or -∞ < y ≤ 0
Opens: Downwards since a is negative
Vertex: ( 0 , 0 )
Axis of Symmetry: x=0
x-intercept: ( 0 , 0 )
y-intercept: ( 0 , 0 )
Please help me out quickly
Answer:
I dont see the stuff I think my internet is slow but I will help you when its up again im using hotspot just remind me
Step-by-step explanation:
Need brief explanation about why false is correct
We are given the equation:
(a + b)! = a! + b!
Testing the given equation
In order to test it, we will let: a = 2 and b = 3
So, we can rewrite the equation as:
(2+3)! = 2! + 3!
5! = 2! + 3!
We know that (5! = 120) , (2! = 2) and (3! = 6):
120 = 2 + 6
We can see that LHS ≠ RHS,
So, we can say that the given equation is incorrect