Which graph would help solve the equation 5log(x+3)=5
Answers
The value of x is 7 for the given equation.
What is logarithm?Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.
For the given situation,
The equation is 5log(x+3)=5.
On solving this equation, we can get value of x.
⇒ [tex]5log(x+3)=5[/tex]
⇒ [tex]log(x+3)=1[/tex]
We know that, log 10 = 1
Then,
⇒ [tex]log(x+3)=log10[/tex]
⇒ [tex]x+3=10[/tex]
⇒ [tex]x=7[/tex]
Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.
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Related Questions
The perimeter of a rectangular floor is 50 feet. find the dimensions of the floor if the length is four times the width.
Answers
width is 5
let me know if you need more details
The dimensions of the rectangle are width = 5 feet and length = 20 feet.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the length and width.
The perimeter of a rectangle = 2(L + W)
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the perimeter of a rectangular floor is 50 feet.
The length is four times the width.
Let the width of the rectangle is x
So the length of the rectangle = 4x
The perimeter of a rectangle = 2(L + W)
50 = 2(4x + x)
50 = 2(5x)
50 = 10x
10x = 50
x = 50 /10
Apply the division operation,
x = 5
So the length of the rectangle = 4(5) = 20 feet
Therefore, the dimensions of the rectangle are width = 5 feet and length = 20 feet.
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For Jack's birthday, his mom is taking him and 12 friends to the zoo. If she pays $11 for each ticket using her credit card, what impact will it have on the available credit left on her credit card?
Answers
The impact on Jack's mom's available credit after purchasing zoo tickets for Jack and 12 friends at $11 each will be a reduction of $143.
When Jack's mom pays $11 for each zoo ticket for him and his 12 friends, she will be purchasing a total of 13 tickets (one for Jack plus 12 for his friends). To calculate the total cost, multiply the number of tickets by the price per ticket:
Number of tickets: 13 (Jack + 12 friends)Price per ticket: $11Total cost: 13 tickets × $11 per ticket = $143The total impact on her credit card's available credit will be a reduction of $143. If she had some available credit limit before this purchase, we just subtract this amount from her available credit to determine the new available credit.
Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.
Use a two-way table to organize the information and answer the following question:
Approximately what percentage of students signed up for neither canoeing nor trekking?
72%
40%
54%
98%
Answers
Use the following equation to find the amount of people that signed up for an activity:
[tex]72 + 23 - 13 = 82[/tex]
82 students signed up for canoeing or trekking.
Subtract this total from the total amount of students to find the total that did not sign up for an activity:
[tex]180 - 82 = 98[/tex]
Divide this number by the total amount of students in the camp:
[tex]98 \div 180 = 0.54[/tex]
Multiply this decimal by 100 to convert into a percentage:
[tex]0.54 * 100 = 54[/tex]
54% of students did not sign up for neither canoeing nor trekking.
Find the surface area of the following triangular prism
Answers
The surface area of the triangular prism is 144 ft³
How to find the surface area
The surface area of the prism is solved using the formula
= 2 * area of the base + Lateral surface area
Area of the base
= 2 * 1/2 * 6 * 8
= 48
Lateral surface area
= (10 + 6 + 8) * 4
= 24 * 4
= 96
Total surface area
= 48 + 96
= 144 ft³
Simplify the expression 9xy + 6xy − 2xy. What is the coefficient of the simplified expression?
Answers
To find our answer we need to collect the terms of the expression.
[tex]9xy + 6xy - 2xy = \\ 15xy - 2xy = \\ 13xy[/tex]
The coefficient (which is the number just before the variable) of the simplified expression is 13.
13xy is the answer. THey are all like terms so just add then subtract.
A painter places an 8.5 ft ladder against a wall. the bottom of the ladder is 4 ft from the base of the wall. how high up the wall does the ladder reach?
Answers
a² + b² = c²
4² + b² = 8.5²
16 + b² = 72.25
b² = 56.25
b = 7.5
The ladder reaches a height of 7.5 ft on the wall
What’s the quadratic expression for this one
Answers
(2x + 5) * (7-4x)
Rewriting we have:
14x - 8x ^ 2 + 35 - 20x
Grouping terms with the same exponent:
-8x ^ 2 + x (14-20) + 35
Rewriting:
-8x ^ 2 - 6x + 35
Answer:
the quadratic expression for this is:
-8x ^ 2 - 6x + 35
What is the equation, in slope-intercept form, of the line that passes through (0, 3) and has a slope of −6?
y = 3x + 6
y = 3x − 6
y = −6x − 3
y = −6x + 3
Answers
Answer:
y=-6x+3
Step-by-step explanation:
Using the formula,
[tex](y-y_{1})=m(x-x_{1})\\(y-3)=(-6)(x-0)\\y-3=-6x\\y=-6x+3[/tex]
Where does Pythagorean identity come from and how does it relate to right triangles
Answers
each of the circles below has an area of 196 pi square units find the perimeter of the rectangle
Answers
Answer:
Step-by-step explanation:
Alright lets get started.
We have given the area of each circle as 196 pi square units.
since the area of the circle =[tex]\pi*radius^2[/tex]
so,the radius of the circle :
[tex]196\pi =\pi r^2[/tex]
[tex]r^2=196[/tex]
[tex]r=14[/tex]
therefore the diameter of the circle will be [tex]2*radius=2*14=28[/tex]
the perimeter of the rectangle=[tex]2*(length+ width)[/tex]
the length of the rectangle will be addition of diameters of the circle=[tex]28+28=56[/tex]
breadth of the rectangle is equal of the diameter =28
Perimeter of the rectangle =[tex]2*(56+28)=168[/tex]
Answer 168 units.
The perimeter of the given rectangle is 168 units
Given that area of each of the circles are [tex] 196 \pi [/tex] sq units and we know that the area of circle [tex]=\pi r^{2}[/tex] using this radius of the circle will be
[tex]\pi r^{2} =196\pi\\ r^{2} = 196\\ \\ r=14[/tex]
So, the diameter of the circle is twice the radius which is
[tex]2\times r\\ 2\times 14 =28 [/tex]
Here we can see that length of rectangle is equal to twice the diameter of the circle and breadth is equals to twice the radius
[tex]length= 28+28=56[/tex]
[tex]breadth = 2\cdot14=28[/tex]
How to find the perimeter of the given rectangle ?
To find the perimeter we use the formula
Perimeter of rectangle = [tex]2\cdot(length + breadth)[/tex]
On solving we get ,
[tex]2\cdot(56 +28)\\ 168 units[/tex]
Therefore, The perimeter of the given rectangle is 168 units
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A bag contains 12 red marbles and 6 blue marbles. two marbles are drawn with replacement. find the probability.
Answers
Eric plans to rent a car for a day from Easy Car Rental. He has a coupon for 25% off the daily base rate of $40. He will also have to pay an additional $0.15 for each mile he drives. Which expression represents the situation?
Answers
Base rate: 40 - (40 · 0.25) plus mileage: 0.15 · x
Total cost = 30 + 0.15x
At 7 a.m. Gene left Austin and headed south at 10 miles per hour. At 8 a.m. Anne left from the same place and headed south on the same road. If Anne was 60 miles ahead by 3 p.m. on the same day, what was her speed?
Answers
Anne's speed is 20 miles per hour. If she returned home by the same path 7 hours and 30 minutes after she left, her average speed for the entire trip is 18.67 miles per hour while her average velocity is zero.
To answer this question, we need to calculate Anne's speed based on the information given. Gene started at 7 a.m. traveling at 10 miles per hour. By the time Anne starts at 8 a.m., Gene has already covered 10 miles (since he travels for 1 hour). The time from 8 a.m. to 3 p.m. is 7 hours. Both Anne and Gene travel the same path for these 7 hours, but Anne is 60 miles ahead of Gene by 3 p.m. Therefore, we need to calculate the total distance Gene traveled in 8 hours, add 60 miles to that distance, and then divide by 7 to find Anne's speed.
First, we determine Gene's total travel distance by 3 p.m., which is 10 miles/hour * 8 hours = 80 miles. Anne is 60 miles ahead, meaning she traveled 80 miles + 60 miles = 140 miles in 7 hours. Thus, Anne's speed is 140 miles \/ 7 hours = 20 miles per hour.
For part (c), if Anne returned home by the same path 7 hours and 30 minutes after she left, the total trip time would be 15 hours (7 hours to 3 p.m. and another 7 hours and 30 minutes back). Since the round trip distance is 140 miles out and 140 miles back, the total distance is 280 miles. Her average speed is total distance divided by total time, hence 280 miles / 15 hours = 18.67 miles per hour. The average velocity for the round trip is zero because she ends up at the starting point, so the overall displacement is zero.
Please give an explanation with you answer, thank you :)
Answers
Here 2 on left most side is the coefficient, 2x is the exponent and the of the function is cube root of 27.
So,
[tex]Base= \sqrt[3]{27} \\ \\ Base= \sqrt[3]{3^{3} } \\ \\ Base=3 [/tex]
Thus, the simplified base for the function is 3. So correct answer is option B
Evaluate the expression for = −3 and = 5.
r^{-4} s^2
Answers
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81
If r = 5 and s = -3:
(r^-4)(s^2) = (5^-4)(3^2) = (1/625)(9) = 9/625
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81
Which item produces the magnetic field in the electromagnet?
I’m sorry if the picture is blurry but try please! :)
Thank you all
Answers
Image option 2 will produce the magnetic field in the electromagnetism.
What is Magnetic field?The portion of space near a magnetic body or a current-carrying body in which the magnetic forces due to the body or current can be detected.
Given that figures,
In figure option 2 there are wires given and as we know when there is current flowing in a body or wire it will create an electric field as well as magnetic field.
Hence, image option 2 is the correct option.
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ANOTHER FILL IN THE BLANKS QUESTION, MARKING BRAINLIEST FOR CORRECT ANSWER
Answers
First blank: multiplication property of equality
Both sides of the equation were multiplied by (1/2).
Second blank: m<E
Angle E is an inscribed angle intercepting arc FGD, so by the inscribed angle theorem, its measure is half the measure of the arc.
Third blank: m<G
Same explanation as the prior blank
Fourth blank: substitution property of equality
Since angle E is equal to half the measure of arc FGD, we can replace that term. Likewise with angle G.
An empty box weighs 200g the box is filled with birthday party goozy bags and now weighs 6.2kg Each goody bag weighs 150Work out how many goody bags are inside the box
Answers
We have then:
x: number of birthday party goozy bags
y: total weight
We then have the following equation:
y = 150x + 200
For y = 6200 we have:
6200 = 150x + 200
Clearing x:
x = (6200-200) / (150)
x = 40
Answer:
there are 40 goody bags inside the box
Answer:
40
Step-by-step explanation:
(05.07 mc) mandy needs to paint all the faces and the base of a model pyramid she made for her history project. the dimensions of the pyramid are shown here. what is the total surface area of the pyramid? a square pyramid is shown. the side of the square is 10 inches. the height of the triangular faces is 9 inches.
Answers
There are 4 congruent (same size and shape) triangles and a square.
The area of the square is
A = bh
10 in x 10 in
A = 100 square inches.
The area of one triangle is
A = 1/2bh
1/2 x 10 in x 9 in
A = 45 square inches
45 square inches x 4 (for the 4 triangles)
180 square inches of triangles
180 + 100 = 280
The total surface area of the square pyramid is 280 square inches.
Answer:
280
Step-by-step explanation:
i n e e d p o i n t s
46 points for yall, i need math help.
Answers
4x= -9x+6
-5x= 6
x= -(6/5)
Find the dimensions of a rectangle whose width is 6 miles less than its length and whose area is 55 square miles.
Answers
x-----------> the length of a rectangle
y-----------> the width of a rectangle
we know that
area of a rectangle =length*width
area=55 mi²
55=x*y--------> equation 1
y=x-6-------> equation 2
substitute equation 2 in equation 1
55=x*[x-6]------> 55=x²-6x----------> x²-6x-55=0
using a graph tool-----> to resolve the second order equation
see the attached figure
the solution is
x=11 mi
y=x-6-----> y=11-6-----> y=5 mi
the answer is
the length of a rectangle is 11 miles
the width of a rectangle is 5 miles
Assuming that one-pint is equal to 473 ml., how many pints can be found in one liter?
Answers
1 pint is equal to --------> 473 ml
1 liter is equal to--------> 1000 ml
so
1 pint is equal to --------> 473 ml
x pints------------------> 1000 ml
x=1000/473-----> 2.11 pints
the answer is
2.11 pints can be found in one liter
1 pint -------> 473 ml
x -------------> 1000 ml
Clearing x we have:
x = (1000/473) * (1)
x = 2.114164905
Rounding off we have:
x = 2
Answer:
can be found 2 pints in one liter
In the ancient chinese proverb, there are more than how many different ways to breathe
Answers
Answer: 40
What we all know is that there is only one way to breath (inhaling and exhaling) For the ancient Chinese, as cited on ancient proverb there are forty (40) ways. These different ways promote relaxation thru breathing on the lower stomach.
The square of a positive number decreased by twice the number is 48. Find the number
Answers
x^2-2x-48=0
(x-8)(x+6)=0
x=8 x=-6
x must be negative so x=-6
check
36=48+-12
36=36
Let the required positive number is x.
The square of the number is [tex]x^2[/tex]
Now, we have been given that square of a positive number decreased by twice the number. It means we have
[tex]x^2-2x[/tex]
Now, it is equal to 48. Hence, we have
[tex]x^2-2x=48\\ x^2-2x-48=0\\ x^2-8x+6x-48=0\\ x(x-8)+6(x-8)\\ (x-8)(x+6)=0\\ x=8,-6[/tex]
The number is positive, Hence, we have [tex]x=8[/tex]
Therefore, the required number is 8
Karen makes $5 per hour baby-sitting and $12 per hour giving music lessons. one weekend, she worked a total of 18 hours and made $139. how many hours did she spend baby-sitting?
Answers
Let the number of hours she spent in baby- sitting is x
and the number of hours she spent in music lessons is y.
Now, we have been given that she worked a total of 18 hours. Hence, we have
[tex]x+y=18\\ y=18-x...............................(1)[/tex]
And she made $139. Thus, we have
[tex]5x+12y=139..............................(2)[/tex]
Substituting the value of y from equation 1 in 2, we get
[tex]5x+12(18-x)=139\\ 5x+216-12x=139\\ -7x=-77\\ x=11[/tex]
Therefore, she spent 11 hours in baby-sitting.
Karen spent 11 hours baby-sitting and 7 hours giving music lessons.
Explanation:Let x be the number of hours spent baby-sitting, and let y be the number of hours spent giving music lessons.
We are given the following information:
Karen makes $5 per hour baby-sitting, so she earned 5x dollars from baby-sitting.
Karen makes $12 per hour giving music lessons, so she earned 12y dollars from giving music lessons.
She worked a total of 18 hours, so x + y = 18.
She made a total of $139, so 5x + 12y = 139.
We can now set up a system of equations:
x + y = 18
5x + 12y = 139
To solve this system, we can use substitution or elimination method. Let's use the elimination method:
Multiply the first equation by 5 to make the coefficients of x the same: 5x + 5y = 90.
Subtract this new equation from the second equation: (5x + 12y) - (5x + 5y) = 139 - 90.
Simplify both sides of the equation: 7y = 49.
Divide both sides of the equation by 7: y = 7.
Substitute y = 7 into the first equation: x + 7 = 18.
Solve for x: x = 11.
Therefore, Karen spent 11 hours baby-sitting and 7 hours giving music lessons.
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Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
Answers
4y = -2x + 6
y = -1/2x + 3/2
slope = -1/2
y = mx + b
y = -1/2x + b
At point (6, 4)
4 = -1/2(6) + b
4 = -3 + b
b = 7
Equation : y = -1/2x + 7
Solve 4x - 2= 86
thanks
Answers
+2 +2 (-2 and +2 cancel each other out)
_______
4x=88 ( divide 4 on both sides)
x=22
4x-2=86
+2 +2
_______
4x=88
4x/4=x
88/4=22
Use the given information to match the answers.
ABC is a right triangle.
1. 2√13
2. √5
3. 3√3
1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =
Answers
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
1)
[tex] {3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5} [/tex]
2)
[tex] {6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3} [/tex]
3)
[tex] {c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13} [/tex]
Solve them by using
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
1.
[tex] {a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5} [/tex]
2.
[tex] {3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3} [/tex]
3.
[tex] {4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13} [/tex]
Hope this helps. - M
Compare the functions shown below:
f(x) = −3x − 5
g(x)
cosine function with y intercept at 0, negative 3 h(x) = 2 cos(2x − π) + 4
Which function has the greatest y-intercept?
a. f(x)
b. g(x)
c. h(x)
d. all three functions have the same y-intercept
Answers
Find all y-intercepts:
1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).
2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).
3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).
As you can see the greatest y-intercept has function h(x).
Answer: correct choice is C.
Answer:
C
Step-by-step explanation:
I just took the test. :)
Find area of trapezoid using the Pythagorean theorem
Answers
Finding the height:
We need to look at the equation for find the diagonal of a triangle.
a²+b²=c²
We don't have leg one, but we have leg two. If we subtract the longer base by the shorter base, we have leg two.
11-7=4
a²+4²=5²
a²+16=25; let's subtract 16 from both sides.
a²=9
a=3
So, the height is 3.
Finding the area of the trapzoid:
Let's look at the formula for finding the area.
(b1+b2)(h÷2)=A; let's fill the variables in.
(7+11)(3÷2)=A
(18)(1.5)=A
27=A
So, the area of the trapezoid is 27 in²