Answer:
x = 4Step-by-step explanation:
[tex]Domain:\\\\x>0\ \wedge\ x-2>0\\\\x>0\ \wedge\ x>2\\\\\boxed{D:\ x>2}\\\\=============================[/tex]
[tex]2\log_9x=\log_98+\log_9(x-2)\\\\\text{use}\ n\log_ab=\log_ab^n\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_9x^2=\log_9\bigg(8(x-2)\bigg)\iff x^2=8(x-2)\qquad\text{use the distributive property}\\\\x^2=8x-16\qquad\text{subtract 8x from both sides}\\\\x^2-8x=-16\qquad\text{add 16 to both sides}\\\\x^2-8x+16=0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)(x-4)=0\\\\(x-4)^2=0\iff x-4=0\qquad\text{add 4 to both sides}\\\\x=4\in D[/tex]
What's the elapsed time between 2:16 am and 8:10 PM
For this case we have that from 2:16 am until 2:16 pm exactly 12 hours have passed. On the other hand, from 2:16 p.m. until 8:16 p.m., exactly 6 hours have elapsed.
If we add, we have that from 2:16 am to 8:16 pm have elapsed: 12 + 6 = 18 hours.
As we ask for the time elapsed between 2:16 am until 8:10 pm we must subtract 6 minutes. So, we have:
18 hours with 54 minutes
Answer:
18 hours with 54 minutes
what is the equation for the line that passes through the points (4,2) and (0,6)?
Answer:
The equation is y=-x+6.
Step-by-step explanation:
To find the slope of this equation, we use the equation m=y2-y1/x2-x1, where m is the slope. Take one y coordinate and subtract it from the other and do the same with the x coordinates. Then, divide the difference of the y coordinates by the difference of the x coordinates. For example, 6-2/0-4. This gets us 4/-4. You can also do 2-6/4-0 which gets us -4/4. No matter what, we get -1 for each (we don't include the 1 in front of the x). To find the y-intercept, plug in the coordinates. For example, do 6=0(-1)+b or 2=4(-1)+b. No matter which you use, you get an answer of b=6. This gives you an equation of y=-x+6. Hope this helps :)
The equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x
To determine the equation for the line that passes through the points (4,2) and (0,6),
We will use the formula for the determining the equation of a line with two given points
The formula for the determining the equation of a line with two given points is
[tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
The given points are (4,2) and (0,6)
Therefore,
x₁ = 4
y₁ = 2
x₂ = 0
y₂ = 6
Now, putting these into the formula,
We get
[tex]\frac{y-2}{x-4}=\frac{6-2}{0-4}[/tex]
This becomes
[tex]\frac{y-2}{x-4}=\frac{4}{-4}[/tex]
[tex]\frac{y-2}{x-4}=-1[/tex]
Then, the equation becomes
[tex]y-2 = -1(x-4)[/tex]
[tex]y-2 = -x +4[/tex]
[tex]y = 4+2-x[/tex]
[tex]y = 6-x[/tex]
Hence, the equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x
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Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt, to solve for Brian's time in minutes.
A.1 minute
B.7 minutes
C.60 minutes
D.420 minutes
To cover the distance of 14 miles at a speed of 14 miles per hour Brian will take 1 hour means 60 minutes.
What is speed?The speed is the rate of distance covered by a person or a vehicle in a particular time.
How to calculate time?We have been given the distance=14 miles
Speed=14 miles per hour
We have also been given the formula of distance which is
d=rt
we have to rearrange it to calculate time
t=d/r
so the time will be calculated as t=14/14
t=1 hour because the speed is of per hour.
Hence Brian will take 60 minutes to cover the required distance.
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If f(x) =x^2 -2x and g(x) = 6x+4 for which value of c does (f+g)(x)=0
Answer:
c = -2
Step-by-step explanation:
The two functions are given as:
f(x) = x^2 - 2x
g(x) = 6x + 4
To find:
(f+g)(x) = 0
We can evaluate (f+g)(x) using the given functions.
We know that:
(f+g)(x) = f(x) + g(x)
= x²- 2x + 6x + 4
= x² + 4x + 4
Now, we have for x = c:
c² + 4c + 4 = 0
x² + 2c + 2c + 4 = 0
c(c+2) + 2(c+2) = 0
(c+2)² = 0
c+2 = 0
c = -2
write the english sentence in 2 variables and then graph,
the y value is 4 less than 5 times the x value
Answer:
y = 5x - 4
see attached for graph
What equation results from completing the square and then factoring? X^2+22x=31
A) (x+11)^2 = 152
B) (x+22)^2 = 152
C) (x+11)^2 = 53
D) (x+22)^2 = 53
Answer:
Step-by-step explanation:
Rewrite X^2+22x=31, leaving space after the "22x:"
X^2+22x = 31
The coefficient of x is 22. Take half of that, obtaining 11.
Square this result: 11^2 = 121.
Write in "+121 -121" after the x term:
X^2+22x + 121 - 121 = 31
Rewrite X^2+22x + 121 as
(x + 11)^2 -121 = 31
Add 121 to both sides:
(x + 11)^2 = 152
Take the square root of both sides:
x + 11 = ±√152 = ±2√38
Finally, x = -11 ±2√38.
This is "solution by completing the square"
Answer: OPTION A
Step-by-step explanation:
We have this quadratic equation: [tex]x^2+22x=31[/tex]
In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:
[tex](\frac{22}{2})^2=11^2[/tex]
Now we must add 11² to both sides of the equation:
[tex]x^2+22x+11^2=31+11^2[/tex]
Therefore, after complete the square and factor, we get:
[tex](x+11)^2=152[/tex]
This matches with the option A.
I need help!! It is possible to trisect a line segment using only a straightedge and a compass. True or fasle
Answer with explanation:
→Draw a Line segment of any length on a piece of paper.Measure the length of segment with the help of Straightedge.
→Now if it is a number divisible by 3,with the help of compass divide the length of segment by 3 and by placing the compass on the straightedge open the compass starting from 0 up to that length.
→If the number is not divisible by 3, round the number to nearest rational number.
→And then Mark arc with the help of Compass from starting of line segment the length being equal to the number obtained after dividing by 3,and after obtaining the first point taking the same width mark second arc from the point obtained.
This is required trisected line segment.
⇒The Statement is True which is we can trisect a line segment using only a straightedge and a compass.
Answer:
True
Step-by-step explanation:
Just did the test :)
In a school 315 girls play at least one sport. 100 play a fall sport, 150 play a winter sport, and 200 play a spring sport. If 75 girls play exactly 2 sports, how many play three?
Answer:
40 students play all three games .
Step-by-step explanation:
You have universal and it says everyone likes all three games so your union is same as universal and there is no complement or any one who didn't like any games so use formule of universal = n A + n B + n C - n only interaction or who likes any two .Solve it and you will get your answer
Multiply or divide as indicated. X^-3•x^7
Answer: X^4 you just subtract or add with exponents
Step-by-step explanation:
In mathematics, when you multiply variables that have the same base, you add their exponents. The solution to the problem X^-3•x^7 is x^4.
Explanation:To multiply the variables with the same base, you need to add their exponents. In this case, x-3 multiplied by x7 would be equal to x-3+7 or x4. Therefore, the answer is x4.
The problem given is X^-3•x^7. This problem involves the multiplication of two variables with exponents. In mathematics, when you multiply variables with the same base, you keep the base and add the exponents. This is called the 'Laws of Exponents'. Therefore, for X^-3•x^7, our base is X, so we add the exponents -3 and 7 to get 4. Hence, the result is x^4.
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simplify 8BC - 9BC + 10BC - 6BC
Answer:
3BC
Step-by-step explanation:
8BC - 9BC + 10BC - 6BC = BC(8 - 9 + 10 - 6) = BC(3) = 3BC
There you go in the attached.
Mathieu is finding the x-intercepts of the function f(x) = x2 + 4x + 3. His work is shown below
. Which error did Mathieu make?
Answer:
I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.
f(x)=x^2+4x+3
f(x)=(x+3)(x+1) Since 3*1=3 and 3+1=4
The x-intercepts can be found by setting y to 0 and solving for x
(in other words replace that f(x) thing with 0 and solve for x)
0=(x+3)(x+1)
Now set both factors equal to 0
x+3=0 or x+1=0
x =-3 x=-1
The x-intercepts are at (-3,0) and (-1,0)
A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The x-intercepts of the function f(x) = x² + 4x + 3 can be found as shown below.
f(x) = x² + 4x + 3
0 = x² + 4x + 3
0 = (x+3)(x+1)
x = -3, -1
Now, it can be seen that Mathieu has actually set the factored expressions equal to each other, which was wrong.
Hence, the correct option is C.
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A total of 505 tickets were sold for a school play they were either adult tickets or student tickets they were 55 more student tickets so than adult tickets how many adult tickets were sold ?
Hello There!
The number of adult tickets sold in the school play = 225
Total Number Of Tickets = 505
Number Of Student Tickets = x + 55
Number of adult tickets sold can be represented by X
Number of student tickets = X + 55
X+X+55=505
2x+55=505
2x=505-55
2x=450
X=225
Answer:
225
Step-by-step explanation:
x+x+55 = 505
2x + 55 = 505
2x = 505-55
2x = 450
x = 225
GOOD LUCK ! ;)
Which equation could be used to find the distance, x, from the foot of the ladder to the base of the house?
Answer:
4,444097208657794
Step-by-step explanation:
c = 20ft
b = 19.5ft
just use the pythagorean theeorem
How to did a volume of a cylinder
Base x height
To find the base, do pi r squared.
What is the simplified form of square root of 400 to the 100th power ?
Answer:
1.267650600228229401496703205376e+130
Step-by-step explanation:
√400 =20
20¹⁰⁰ = 1.267650600228229401496703205376e+130
Hope this helps!
(5/x)+(3x-2)=4 what is the first step
Answer:
Step-by-step explanation:
get rid of the denominator by multiplying by x
the number of wheel on a group of buses
The number of wheels on a group of buses involves mathematical calculations and can be analyzed using multiplication, probability, and physics, particularly when combined with other factors such as passenger capacities or mechanical variables like angular velocity of a flywheel within the bus.
Explanation:The question about the number of wheels on a group of buses relates to mathematical calculations, specifically pertaining to multiplication and potentially to probability and combinatorics if one were analyzing how to most efficiently deploy a fleet of buses for transportation or which bus to take based on passenger load and capability.
A practical example of a bus-related math problem would be: if a bus has 6 wheels, then a fleet of 10 buses would have a total of 60 wheels. This is a straightforward multiplication problem (10 buses x 6 wheels per bus = 60 wheels).
In the context of probabilistic analysis, considering a situation where buses have different passenger capacities, we might use the expected value formula E(X) = Σx₁p(x₁) to calculate the best option for transportation based on various factors, including the number of passengers each bus can transport.
Moreover, buses also have a place in physics problems. For instance, calculating the angular velocity a bus's flywheel must have to achieve a certain speed involves understanding the concepts of rotational kinetic energy and its transformation into translational energy. This more complex application lies within the realm of physics but has roots in mathematical computation.
a state charges 4% sales tax on all purchases and there is a federal tax of 10% on jewelry what will be the cost to the purchase of a $15 bracelet
Answer:
$17.10
Step-by-step explanation:
Bracelet cost $15
4% sales tax: 0.04($15) = $0.60
10% Fed tax: 0.10($15) = $1.50
Summing these three amounts, we get a total cost of $17.10.
(Score for Question : __of 5 points)
1. 15% of the toddlers in a preschool class drink water with their lunch. How many toddlers are in the class if3 drink water with their lunch?
(a) Write a proportion for the situation
[b] Solve the problem. Show your work
Answer:
Answer:
(a) 15/3 = 100/x
(b) There are 20 toddlers in the class.
Step-by-step explanation:
(a)
The total number of students is 100% of the students.
Let the total number of students be x.
15% of students is to 3 as 100% of students is to x.
15/3 = 100/x
(b)
15/3 = 100/x
Cross multiply the equation.
15x = 3 * 100
15x = 300
Divide both sides by 15.
x = 20
Answer: There are 20 toddlers in the class.
Find the digit in the tenths place of 25.391
Answer:
3
Step-by-step explanation:
The digit in the tenths place of 25.391 is 3.
Answer: [tex]3[/tex]
Step-by-step explanation:
It is important to know that, in order to find the digit in the tenth place of a decimal number, you need to indentify the first digit located to the right of the decimal point.
Therefore, knowing this and having the decimal number provided in the exercise:
[tex]25.391[/tex]
You can observe that the first digit to the right of the decimal point is 3.
Therefore, the digit in the tenths place of ths decimal number is: [tex]3[/tex]
Which figure repeats in the tessellation shown below?
Answer:
B???
Step-by-step explanation:
Answer:
The correct option is A. Figure B repeats in the tessellation shown below.
Step-by-step explanation:
Tessellation can be defined as the arrangement of geographical patterns that are closely attached together to form a particular pattern.
The given figure is formed by the arrangement off figure B.
This large pattern is formed by the repetition of this smaller pattern,
Figure B repeats in the tessellation shown below. Therefore, the correct option is A.
Evaluate: (36/49)^1/2
Answer:
6/7
Step-by-step explanation:
One way of doing this problem is to find the square root of numerator separately (it is 6) and the square root of the denominator likewise (it is 7). Then the value of the given expression is 6/7.
The value of the given expression is [tex]\frac{6}{7}[/tex].
What is a mathematical expression?
"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."
The given mathematical expression is
[tex](\frac{36}{49})^{\frac{1}{2}} \\= (\frac{6^{2} }{7^{2} })^{\frac{1}{2}}\\= [(\frac{6}{7})^{2}]^{\frac{1}{2}}\\= \frac{6}{7}[/tex]
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In its first year of operation, Big Lake Camp had 40 campers. This year’s attendance was 180% of the first year’s. How many campers participated this year?
Answer:
72 campers.
Step-by-step explanation:
You can do this with a simple equation. 180% = 1.8 as a decimal fraction. Let x be this year's attendance. Then:
x = 1.8* 40
x = 72 campers.
Answer:
72 Campers
Step-by-step explanation:
Hope this helps:)
The zeros of the function p(x) = x2 – 2x – 24 are
Answer: x = 6, x = -4
Step-by-step explanation:
Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):
0 = x² - 2x - 24
∧
1 -24
2 -12
3 -8
4 -6 = -2 This works!
0 = (x + 4)(x - 6)
Apply the Zero-Product Property (set each factor equal to zero and solve)
0 = x + 4 0 = x - 6
-4 = x 6 = x
The solutions are x = 6 and x = -4. Therefore, the zeros of the function are 6 and -4.
Finding the Zeros of the Function p(x) = x^2 – 2x – 24
To find the zeros of the function p(x) = x^2 – 2x – 24, we need to determine the values of x that make the function equal to zero. This means we solve the equation:
x^2 – 2x – 24 = 0
This is a quadratic equation and can be solved using factoring. We look for two numbers that multiply to -24 and add to -2. These numbers are 4 and -6:
(x - 6)(x + 4) = 0
Setting each factor equal to zero gives us the solutions:
x - 6 = 0 → x = 6x + 4 = 0 → x = -4So, the zeros of the function p(x) = x^2 – 2x – 24 are 6 and -4.
Jacob bought a magazine for $2.80 and three candy bars. If the candy bars cost $5 each how much did he pay?
Answer: $17.80
Step-by-step explanation:
2.80 + 3(5) = x
2.80 + 15 = x
17.80 = x
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The total amount paid by Jacob is $17.8.
What is multiplication?
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Jacob bought a magazine for $2.80. Also, three candy bars for $5 each. Therefore, the amount paid by Jacob is,
Amount paid by Jacob = $2.80 + (3 × $5)
= $17.8
Hence, the total amount paid by Jacob is $17.8.
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(X+2)(x+6) simplified
Answer:
x^2 +8x+12
Step-by-step explanation:
(X+2)(x+6)
Foil
first: x*x = x^2
outer: x*6 = 6x
inner : 2*x = 2x
last: 2*6 = 12
Add them together: x^2 +6x+2x+12 = x^2 +8x+12
I don't understand?
Answer:
see explanation
Step-by-step explanation:
The perimeter (P) is the length of all 3 sides of the triangle
The triangle is isosceles with 2 equal sides 20 - 7xy
P = 20 - 7xy + 20 - 7xy + 12 = 52 - 14xy
When x = 2, y = 1, then
P = 52 - 14(2)(1) = 52 - 28 = 24
Write the rule for finding a point translated vertically k units up. 2. Use this rule to find the coordinates for (−3, −6) when translated 5 units up.
Answer:
Rule is (x, y+k)
New point is (-3,9)
Step-by-step explanation:
A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units
This can be represented mathematically as;
Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under a vertical translation k units up you add k to the y coordinate value.
Given ;
[tex]A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)[/tex]
where T is the translation
In the question
Given (-3,-6) and T is (0,5) the new coordinate will be
[tex]=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)[/tex]
What is the slope of the line that contains the points (-1,2) and (4,3)
Answer:
slope = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, 3)
m = [tex]\frac{3-2}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]
Answer:
1/5
Step-by-step explanation:
Drag the values to order them from least to greatest, with the least at the top.
A. [tex]\sqrt{17}[/tex]
B. [tex]\frac{\pi +7 }{5}[/tex]
C. [tex]\sqrt{5}[/tex]
Answer:
Step-by-step explanation:
You use latex very well. Nice work.
sqrt(17) = 4.123
sqrt(5) = 2.236
==============
pi + 7
=====
5
3.14 + 7
======
5
10.14/5 = 2.028
Answer
B. \frac{\pi +7 }{5} 2.028
C. \sqrt{5} 2.236
A. \sqrt{17} 4.123