Solve the rational equation x over 4 equals x squared over quantity 3 times x plus 3 and check for extraneous solutions.
x = 1; x = 0 is an extraneous solution
x = 0; x = −1 is an extraneous solution
x = 0 and x = 1
x = 0 and x = −1
Answer:
x is -9 is an extraneous solution
Step-by-step explanation:
Given the expression
x/4 = x²/3(x+3)
We are to find the value of x
Cross multiply
3x(x+3) = 4x²
3x²+9x = 4x²
3x²-4x² = 9x
-x² = 9x
-x = 9
x = -9
Hence the value of x is -9 is an extraneous solution
Extra points and brainliest
Caroline spent $56.32 on groceries after using coupons and store discounts. Without the coupons and store discounts, the groceries would have cost $64.00. What is the total discount Caroline received at the grocery store?
A. 8%
B. 14%
C. 9%
D. 12%
Answer:
D. 12%
Step-by-step explanation:
64-56.32= 7.68
(7.68÷64)×100= 12%
hope this helps! please mark me brainliest..
have a good day ahead
Answer:
D. 12%
Step-by-step explanation:
1. Find the amount of money Caroline saved
Original - spent
Subsitute in the given values,
64 - 56.32 = 7.68
2. Set up a proportion
A proportion is
[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]
Substitute in the values;
[tex]\frac{7.68}{64}=\frac{percent}{100}[/tex]
Cross products;
(7.68)(100) = (64)(percent)
768 = 64 * percent
Inverse operations;
768 = 64 percent
/64 /64
12 = percent
Caroline had a 12% discount.
There are eight nickels and five dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. Both times the coin is a nickel.
In the right triangle shown in the diagram below, what is the value of x to the nearest whole number?
Answer:
[tex]x=21[/tex]
Step-by-step explanation:
See attachment for triangle
The relationship between length x, length 24 and angle 30 is as follows:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
In this question;
[tex]Adjacent = x[/tex]
[tex]Hypotenuse= 24[/tex]
[tex]\theta = 30[/tex]
Substitute these values in the above expression,
[tex]\cos(30) = \frac{x}{24}[/tex]
Multiply through by 24
[tex]24 * \cos(30) = \frac{x}{24} * 24[/tex]
[tex]24 * \cos(30) = x[/tex]
Reorder:
[tex]x = 24 * \cos(30)[/tex]
[tex]x = 24 * 0.8660[/tex]
[tex]x = 20.784[/tex]
[tex]x=21[/tex] --- approximated
What two points are contained in the graph of y = log9 (x)?
O (1,0) and (9, 1)
O(0,1) and (1, 9)
O (1,0) and (9, 0)
O (1,0) and (9, 9)
Answer:
the first choice
Step-by-step explanation:
(1,0) and (9,1)
The graph of a function f is the set of all points (x,f(x)). Any point on the graph satisfy the equation of the graph. To check whether a point lie on a graph we need to put the x value and y value of the point to the equation of the graph and check the LHS and RHS . If LHS is equal to RHS , then this point lie on the graph.
The given equation of graph is y=log₉(x) ...........(i)
Now we check whether the points (1,0) and (9, 1) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0) , LHS = 0 and RHS = log₉(1)=0
Therefore LHS=RHS for the point (1,0).
For point (9,1), LHS= 1 and RHS= log₉(9)=1
Therefore LHS=RHS for the point (9,1).
Therefore (1,0) and (9,1) lie on graph of equation (i).
Check whether the points (0,1) and (1, 9) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (0,1), LHS=1 and RHS=log₉(0) is undefined
Therefore LHS≠RHS for the point (0,1).
For point (1,9), LHS= 9 and RHS= log₉(1)=0.
Therefore LHS≠RHS for the point (1,9).
Therefore (0,1) and (1,9) does not lie on graph of equation (i).
Check whether the points (1,0) and (9,0) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0), LHS=0 and RHS=log₉(1)=0.
Therefore LHS=RHS for the point (1,0).
For point (9,0), LHS= 0 and RHS= log₉(9)=1.
Therefore LHS≠RHS for the point (9,0).
Therefore (1,0) lie on (i) but 9,0) does not lie on graph of equation (i).
Check whether the points (1,0) and (9,9) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0), LHS=0 and RHS=log₉(1)=0
Therefore LHS=RHS for the point (1,0).
For point (9,9), LHS= 9 and RHS= log₉(9)=1.
Therefore, LHS≠RHS for point(9,9).
Therefore (1,0) lie on (i) but 9,9) does not lie on graph of equation (i)
Hence, the points (1,0) and (9,1) lie on the graph of y=log₉(x).
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2. The Youngs decided to book the room at the price that Mrs. Young was given, $1879, because it included breakfast for both of them for the entire stay. The travel agent could not match that price. At the end of the trip, Mr. Young received a bill showing a pre-tax amount of $1879. The tax is 8.5%. When the Youngs went to check out, they told the front desk that the refrigerator in the room had not worked during the majority of their time there. The hotel decided to give them a 5% discount off the pre-tax amount. Mr. Young says the new total will be $1944.77. He shows Mrs. Young how he found the new total.
Since we have to add 8.5% tax and subtract 5% for the discount, this means we will add 3.5% in the end.
8.5 − 5 = 3.5
Therefore, we just need to multiply the cost of the room by 3.5% and add this number to the cost of the room to determine what we owe.
3.5% x 1879= 0.035 x 1879= 65.765, which rounds to $65.77.
Add $65.77 to the total $1879 to get $1944.77.
Explain why Mr. Young’s calculations are incorrect. What is the correct total? Show your work. Round your answers to the nearest cent.
Answer:
yes
Step-by-step explanation:
Which theorem shows QMP=RNP?
A. ASA
B. AAS
C. SAS
D.none of the above
Answer: i believe it’s A
Step-by-step explanation:
By ASA criteria, ΔQMP is congruent to ΔRNP.
What is triangle?A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a figure as shown in the image.
In ΔQMP and ΔRNP -
∠QPM = ∠NPR {Vertically opposite angles}
QM = NR {Given}
∠MQP = ∠NRP {Alternate interior angles}
So, by ASA criteria, ΔQMP is congruent to ΔRNP.
Therefore, by ASA criteria, ΔQMP is congruent to ΔRNP.
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F(x)=3x^2-10x+4, find f(-4)
Answer:
substitute -4 for x
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.
Therefore, the value of the function when the value of x is -4 can be calculated as shown below,
F(x) = 3x² - 10x + 4
F(-4) = 3(-4)² - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Hence, the value of the function when the value of x is -4 is 92.
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Simplify the expression.
4(-8x + 5) – (-33x – 26) = ______
Answer:
14+33x
Step-by-step explanation:
you have to break it up
4x(-3)+33x+26 MILTIPLY
-12+33x+26 CALCULATE
Solution is 14+33x
I HOPE THIS HELPS YOU
Two pounds of dried cranberries cost $5.04, 3 pounds of dried cranberries cost $7.56, and 7 pounds of dried cranberries cost $17.64. What equation gives the total cost y of x pounds of dried cranberries?
Answer:
y = 2.52x
y = cost, x = pounds of cranberries.
each pound costs 2.52
Step-by-step explanation:
5.04/2 = 2.52
If the total value of the coins is 30¢, what is the missing coin?
Answer:
$70
Step-by-step explanation:
Find the measure of the missing angle.
Answer:
you have a 90 degree angle and to find your answer subtract 90-63=27.
Step-by-step explanation:
The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)
and Q(c,-7,4)
Find the values of:
a=
b=
C=
Answer:
The values are:
[tex]a = -5/2[/tex][tex]b = -6[/tex][tex]c = -7[/tex]Step-by-step explanation:
Given:
P = (x₁, y₁, z₁) = (1, 2, b) Q = (x₂, y₂, z₂) = (c, -7, 4) m = R = (x, y, z) = (-3, a, -1)To Determine:
a = ?
b = ?
c = ?
Determining the values of a, b, and c
Using the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), som = R = (x, y, z) = (-3, a, -1)
Using the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
given
(x₁, y₁, z₁) = (1, 2, b) = P
(x₂, y₂, z₂) = (c, -7, 4) = Q
m = (x, y, z) = (-3, a, -1) = R
substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P, (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
as (x, y, z) = (-3, a, -1), so
[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
Determining 'c'
-3 = (1+c) / (2)
-3 × 2 = 1+c
[tex]1+c = -6[/tex]
[tex]c = -6 - 1[/tex]
[tex]c = -7[/tex]
Determining 'a'
a = (2+(-7)) / 2
[tex]2a = 2-7[/tex]
[tex]2a = -5[/tex]
[tex]a = -5/2[/tex]
Determining 'b'
-1 = (b+4) / 2
[tex]-2 = b+4[/tex]
[tex]b = -2-4[/tex]
[tex]b = -6[/tex]
Therefore, the values are:
[tex]a = -5/2[/tex][tex]b = -6[/tex][tex]c = -7[/tex]Shelly biked 21 miles in 4 hours what is shellys average speed per hour?
Answer:
The average speed per hour of Shelly is 5.25 minutes.
Step-by-step explanation:
We can do proportion to solve this.
[tex] \frac{21 \: miles}{4 \: hours} = \frac{x}{1 \: hour} \\ \frac{4x}{4} = \frac{21}{4} \\ x = 5.25[/tex]
A sample of 11 students using a Ti-89 calculator averaged 31.5 items identified, with a standard deviation of 8.35. A sample of 12 students using a Ti-84 calculator averaged 46.2 items identified, with a standard deviation of 9.99. Can we conclude that the mean number of times identified with the Ti-84 calculator exceeds that of the Ti-89 calculator by more than 1.80
Answer:
We reject H₀, with CI = 90 % we can conclude that the mean numbers of times identified with Ti-84 does not exceed that of the Ti-89 by more than 1,80
Step-by-step explanation:
Ti-89 Calculator
Sample mean x = 31,5
Sample standard deviation s₂ = 8,35
Sample size n₂ = 11
Ti-84 Calculator
Sample mean y = 46,2
Sample standard deviation s₁ = 9,99
Sample size n₁ = 12
t(s) = ( y - x - d ) / √s₁²/n₁ + s₂²/n₂
t(s) = 12,9 / √(99,8/12) + (69,72/11)
t(s) = 12,9 / √8,32 + 6,34
t(s) = 12,9 / 3,83
t(s) = 3,37
Test Hypothesis
Null Hypothesis H₀ y - x > 1,80
Altenative Hypothesis Hₐ y - x ≤ 1,80
We have a t(s) = 3,37
We need to compare with t(c) critical value for
t(c) α; n₁ +n₂-2 df = 12 +11 -2 df = 21
If we choose CI = 95 % then α = 5 % α = 0,05
From t-student table
t(c) = 1,72
t(s) = 3,37
t(s) >t(c)
t(s) is in the rejection region therefore we accept Hₐ with CI = 95 %
simplify: √(4√3-√15)^2
I WILL AWARD BRAINLIEST TO THE CORRECT ANSWER!
Answer:
3.05521988407
Step-by-step explanation:
used a calculator lol
The area of a rectangle is 216 inches squared. The ratio of the length to width is 3:2. Find the length and the width
Answer:
Length = 18 inches
Width = 12 inches
Step-by-step explanation:
Let the Length be 3x and width be 2x
Area= Length*Width=216 inches squared
216=3x*2x
216=6x²
x²=216/6
x²=36
x=√36
x=6 inches
Therefore
Length = 3x = 3*6 = 18 inches
Width = 2x = 2*6 = 12 inches
How many 3/2 are in 10
Answer:
not sure,but i will tell you when i figure it out
Step-by-step explanation:
Will give brainly. question in picture below
Answer:
Its the letter F
Step-by-step explanation:
25/18 as a mixed number
Plsss help me
Step-by-step explanation:
7
1 ---
18
hope it helps !
Rachel wants to save money for a foreign exchange student program. She
needs $950 to belong to the program. She has $200. She earns $40 per
week. How can she figure out the number of weeks that she will take to
save enough money for her program?
O A. Add 200 plus 950 and then divide by 40.
O B. Subtract 40 from 950 and then divide by 200.
O C. Add 200 plus 40 and then divide by 950.
O D. Subtract 200 from 950 and then divide by 40.
9hr. 8min+ 6hr. 42min.+ 8hr. 39min.
Step-by-step explanation:
24 hours and 29 minutes
please help
/ The Hotel is 163 miles from your house.your car travels 10.5 miles for every litre of petrol. Work out approximately how many litres of petrol the journey will use.
2/The price of petrol is 138.9 pence per litre Work out the approximate cost for the petrol to the hotel .
3/ you expect to travel 50 miles in each hour of a jurney how long the whole journey should take
Answer:
The answers are:
15.523 liters of petrol will be used.The cost of petrol will be: 2156.2 penceThe journey will take 3 hours and 16 minutes approximatelyStep-by-step explanation:
Given:
Distance of Hotel and car = 163 miles
Distance travelled by car per liter = 10.5 miles
The number of liters will be obtained by dividing the total distance by distance travelled in one liter.
So,
[tex]number\ of\ liters = \frac{163}{10.5} = 15.523\ liters[/tex]
2. Cost for petrol:
Cost of petrol per liter = 138.9 pence per liter
Then the total cost of petrol will be:
[tex]Total\ cost = 138.9*15.523 = 2156.1447 => 2156.2\ pences[/tex]
3. Time taken for journey
Distance travelled in an hour = speed = 50 miles per hour.
The speed is given by the formula:
[tex]speed = \frac{distance}{time}[/tex]
Putting the values
[tex]50 = \frac{163}{t}\\t = \frac{163}{50}\\t = 3.26\ hours[/tex]
It will take: 3 hours and 0.26*60 = 15.6 minutes => 3 hours 16 minutes
Hence,
The answers are:
15.523 liters of petrol will be used.The cost of petrol will be: 2156.2 penceThe journey will take 3 hours and 16 minutes approximatelyplease help can't figure it out...
Match the term to its definition.
1. every two weeks.
2. a time period in which income is earned.
3. a payment based on a time period.
4. twice a month.
5. a payment based on actual working time or actual production.
biweekly
pay period
wage
salary
semimonthly
Answer:
1. biweekly
2. pay period
3. salary
4. semimonthly
5. wage
Answer:
biweekly- every two weeks
pay period- a time period in which income us earned
wage- a payment based on actual working time or actual production
salary- a payment based on time period
semimonthly- twice a month
Step-by-step explanation:
What is the slope of (-3,-5)
(-6.-11)
Answer:3
Step-by-step explanation:
Use equation for slopes: y1- y2/ x1_ x2=
-11-(-5)/-3-(-6)=3
*****HELP ASAP WILL MARK BRAINLIEST****** Ignore if you don't know!!!! Geometry problem: Point D is the incenter of triangleABC, if DE=x^2 and DF= 20-8x, find each of the following
Answer:
x = 2
DG = 4
Step-by-step explanation:
The thing to know about the incenter of a triangle, is that the segments to each side are equidistant. In other words, they are identical lengths.
This means that ED = FD = GD.
Which means:
DE = DF
x^2 = 20 - 8x
So we need to solve for X. I would solve this using factoring:
Subtract 20 from both sides.
x^2−20=−8x
Add 8x to both sides.
x^2−20+8x=0
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
x^2+8x−20=0
Factor the left hand side by grouping. First, the left hand side needs to be rewritten as x^2+ax+bx−20. To find a and b, set up a system to be solved.
a+b=8 ab=1(−20)=−20
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −20.
(−1,20) (−2,10) (−4,5)
Calculate the sum for each pair.
−1+20=19
−2+10=8
−4+5=1
The solution is the pair that gives sum 8.
a=−2 b=10
Rewrite x^2+8x−20 as (x^2−2x)+(10x−20).
(x^2−2x)+(10x−20)
Factor out x in the first and 10 in the second group.
x(x−2)+10(x−2)
Factor out common term x−2 by using distributive property.
(x−2)(x+10)
To find equation solutions, solve x−2=0 and x+10=0.
x = 2
x = −10
In this case, X is equal to 2 as the solution -10 doesn't make much sense given the context of the problem.
To find DG we just need to plug the solution back into one of the equations and solve:
20 - 8x
20 - 8(2)
20 - 16 = 4
DG = 4
Answer:
x=2
Step-by-step explanation:
p(x)=2x3-3x2+14x÷15 and why?
Answer:
I think you have not written the full question
Which of these is the best source of information about a health product?
Answer:
is there something suggested?
Need Help Math question
The point of intersectiom where the 2 lines cross each other is when it is 14 minutes.
Answer:
14 minutes according to the graph
20 points
Two mountain bikers are riding on a 35-mile trail. Abel started at the beginning of the trail and is riding at a rate of 14
miles per hour. Neal started 6 miles ahead of Abel and is riding at a rate of 11 miles per hour. When will the boys be
at the same point on the trail?
If Abel's journey is represented by the equation d = 14t, where d represents the total distance and t represents time
in hours, what equation represents Neal's journey?
Two mountain bikers are riding on a 35-mile trail. Abel started at the beginning of the trail and is riding at a rate of 14 miles per hour. Neal started 6 miles ahead of Abel and is riding at a rate of 11 miles per hour. When will the boys be at the same point on the trail?
If Abel’s journey is represented by the equation d = 14t, where d represents the total distance and t represents time in hours, what equation represents Neal’s journey?
d = 11t + 6
11 and 6 are your answers
Please mark Brainliest
Answer:
11 and 6 are correct
Step-by-step explanation: