Answer:
[tex] \displaystyle{ \frac{x + 4}{x - 4} + \frac{x - 4}{x + 4} = 3 \frac{1}{3} }[/tex]
[tex]\displaystyle{ \frac{ {(x + 4) }^{2} + {(x - 4)}^{2} }{(x + 4)(x - 4)} = \frac{10}{3} }[/tex]
[tex]\displaystyle{ \frac{ {x}^{2} + 8x + {4}^{2} + {x}^{2} - 8x + {4}^{2} }{ {x}^{2} - {4}^{2} } = \frac{10}{3} }[/tex]
[tex]\displaystyle{ \frac{ {2x}^{2} + 16 + 16 }{ {x}^{2} - 16 } = \frac{10}{3} }[/tex]
[tex]\displaystyle{3( {2x}^{2} + 32) = 10( {x}^{2} - 16) }[/tex]
[tex]\displaystyle{ {6x}^{2} + 96 = {10x}^{2} - 160 }[/tex]
[tex]\displaystyle{ {10x}^{2} - 160 = {6x}^{2} + 96 }[/tex]
[tex]\displaystyle{ {10x}^{2} - {6x}^{2} - 160 - 96 = 0 }[/tex]
[tex]\displaystyle{ {4x}^{2} - 256 = 0}[/tex]
[tex]\displaystyle{4( {x}^{2} - 64) = 0}[/tex]
[tex] {x}^{2} - {8}^{2} = \displaystyle{ \frac{0}{4} }[/tex]
[tex]\displaystyle{(x + 8)(x - 8) = 0}[/tex]
[tex]\displaystyle{ \rm{either, \: x + 8 = 0............(1) }}[/tex]
[tex] \rm{or ,\: x - 8 = 0...............(2)}[/tex]
From equation (1)
[tex]x + 8 = 0[/tex]
[tex]x = - 8[/tex]
From equation (2)
[tex]x - 8 = 0[/tex]
[tex]\displaystyle{x = 8}[/tex]
[tex] \therefore{x=±8}[/tex]
I don’t understand this question
Answer:
First pair: -4 and 8
Second pair: -2 and 6
Third pair: -1 and 5
Step-by-step explanation:
-4 + 8 = 4
-2 + 6 = 4
-1 + 5 = 4
Hope this helps
Solve each of the following equations. Show its solution set on a number line. Check your answers. 7m+4=1
PLS HELP WILL GIVE BRAINLIEST
Answer:
x=-3/7;x=-5/7
Step-by-step explanation:
How do you put 2hundreds 9tens 18ones in standard form
Answer:
308
Step-by-step explanation:
200+90+18=200+108=308
three hundred seven
or
307
Step-by-step explanation:
I can't remember which is standard form. But hope it helps.
The zoo has 14 penguins. There are 6 more penguins than lions. How many lions are at the zoo?
Answer:
8 lions
Step-by-step explanation:
We need to subtract!!
14 - 6 = 8
Have an amazing day!!
Please rate and mark brainliest!!
Step-by-step explanation:
let the number of penguins be X and the number of lions be Y. then X=14 and since there are more penguins than lions the equation will be X=Y+6
Substitute 14 instead of X. 14=Y+6
and now shift 6 to the left 14-6=Y
then the answer should be 8lions
Determine whether the following statement is true or false. If false, provide a counterexample. If two events are independent, then the probability of both events is less than 1
Answer:
TRue
Step-by-step explanation:
Pharmaceutical scientists tested the effectiveness of a new drug designed to cure malaria. They randomly
assigned 400 infected lab rats to receive either the new drug or an existing drug and recorded how many
rats were cured at the end of the study. Here are their results:
Cured
Not
Total
New drug
176
24
200
Existing drug
168
32
200
They want to use these results to construct a 99% confidence interval to estimate the difference in the
proportion of these rats that would be cured under each drug (new - existing). Assume that all of the
conditions for inference have been met.
Which of the following is a correct 99% confidence interval based on their data?
Choose 1 answer:
8 +0.068
Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval is (-0.049, 0.129).
What is the mean and the standard error for the distribution of differences?For each sample, we have that:
[tex]p_N = \frac{176}{200} = 0.88, s_N = \sqrt{\frac{0.88(0.12)}{200}} = 0.023[/tex]
[tex]p_E = \frac{168}{200} = 0.84, s_E = \sqrt{\frac{0.84(0.16)}{200}} = 0.0259[/tex]
Hence, for the distribution of differences, the mean and the standard error are given as follows:
[tex]p = p_N - p_E = 0.88 - 0.84 = 0.04[/tex]
[tex]s = \sqrt{s_N^2 + s_E^2} = \sqrt{0.023^2 + 0.0259^2} = 0.0346[/tex]
What is the confidence interval?It is given by:
[tex]p \pm zs[/tex]
99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
Then:
[tex]p - zs = 0.04 - 2.575(0.0346) = -0.049[/tex]
[tex]p + zs = 0.04 + 2.575(0.0346) = 0.129[/tex]
The 99% confidence interval is (-0.049, 0.129).
To learn more about the z-distribution, you can check https://brainly.com/question/25890103
Answer: 0.04, 0.089
Step-by-step explanation:
Gizmo eats 3 crickets per day. If there are 15 crickets in a container, what is the maximum number of days Ms. Evans can go before buying replacement crickets.
An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant
rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and
then decelerates at a constant rate for 5 seconds until he stops.
a) What is the total distance that he ran?
[5]
Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She
however only accelerates for 10 seconds before running at a constant speed.
Answer:
probably 200
Step-by-step explanation:
or something like that
Solve for x 5x + 14 >54
Answer:
x > 8
Step-by-step explanation:
5x > 40
40/5 = 8
x> 8
subtract 14
divide by 5
In a survey of 1,372 office workers, 4.2% said that they do not make personal phone calls. Find the actual number of respondents corresponding to the given percentage.
The actual number of respondents corresponding to the given percentage is 57.
What do percentages mean?Percentage is the fraction of an amount expressed as a number out of 100. The sign used to rerepresnt percentages is %. Percentages are a measure of frequency.
What is the number of respondents?4.2% x 1372 = 57
To learn more about percentages, please check: https://brainly.com/question/25764815
Q. 1. Solve for x using determinants, x + y = 9, x - y + 3z = 2 and 4y - 32 - 5 = 0.
Hello!
x + y = 9,
x= 9-y
x - y + 3z = 2
x= 2+y -3z
4y - 32 - 5 = 0.
4y = 32+5
4y = 37
y = 37/4
At a point on the ground 50 feet from the foot of a tree, the angle of elevation to the top of the tree is 58 degrees. Find the height of the tree.
Answer:
height of tree is 80 feet.
Step-by-step explanation:
Given:-
Distance of point from tree's foot:- 50 feetAngle of elevation:- 58 degreesTo find :-
Height of treeSolution:-
In the given figure we can see that AB is perpendicular , BC is base and AC is hypotenuse.
We know ,
tan 58° = AB/BC
1.6 = AB/50 feet
(Cross Multiplication)
80 feet :- AB
Note:- Figure is in attachment and is a rough work.
Arun and Benny started saving at the same time. Each day, Arun
saved $1.20 and Benny saved $0.30 more than Arun. How much would
Arun have saved if Benny saved $11.40 more than Arun?
Answer:
$45.60 would be what Arun would have saved.
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answer:
Step-by-step explanation:
Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.
Bottles of water are packaged with
24 bottles per case. A store has
365 cases to sell. How many bottles
of water does the store have to sell?
Step-by-step explanation:
1 case = 24 bottles
365 cases = 365×24 = 8,760 bottles
Choose an appropriate metric unit for the mass of bowling ball
A)
kilogram
B)
milligram
C)
meter
D)
gram
Answer:
i think that the correct answer would A
Step-by-step explanation:
hope this helps
Jerry poured water to a height of 1 feet into a
new aquarium with dimensions shown below.
2 ft.
1 ft.
Water
2
3 ft.
One cubic foot of water weighs approximately
62 pounds. What is the weight of the water that
Jerry put in the aquarium?
B. 465 pounds
A. 403 pounds
C. 558 pounds
D. 744 pounds
Since 1 cubic feet = 62 pounds, the weight of the water that Jerry put in the aquarium is 558 pounds
How to calculate the volume/weight of waterWe have to find the volume of water in the aquarium.
Recall the shape of the aquarium is a rectangular prism. Therefore,
volume = lwh
where
l = lengthw = widthh = heightTherefore,
l = 3 ft
w = 2 ft
h = 1.5 ft
volume = 3 × 2 × 1.5
volume of water = 9 ft³
Therefore,
1 ft³= 62 pounds
9 ft³ = ?
cross multiply
weight of water = 9 × 62
weight of water = 558 pounds
learn more on volume here:https://brainly.com/question/24357711
= 1 2 + (2 + tan 1 2 ) where and are constants. Show that (1 + ) ²y/dy²=y
Answer:
Step-by-step explanation:
A shop sells pairs of trainers for £68 each. They make a percentage profit of 70% on each pair.
What was the cost of each pair of trainers to the shop?
Answer:
70% of £68 gives £47.6 for each trainer
Answer:
100-70/100 *£68
Step-by-step explanation:
£40.8
therefore, each pair of trainers cost£40.8
Quite urgent lol but should probably be quick I guess :(
Answer:
(a) [tex]y=x^2-2x-8[/tex]
(b) [tex]y= -\dfrac12x^2+4x-6[/tex]
Step-by-step explanation:
(a) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = -2[/tex] and [tex]x =4[/tex].
Therefore [tex]y = a(x + 2)(x - 4)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -8)
Expanding the equation:
[tex]y = a(x + 2)(x - 4)[/tex]
[tex]\implies y = a(x^2-4x+2x-8)[/tex]
[tex]\implies y= ax^2-2ax-8a[/tex]
Therefore, -8a is the y-intercept
Comparing y-intercepts: -8 = -8a ⇒ a = 1
Substituting a = 1, the final equation in standard form is:
[tex]y=x^2-2x-8[/tex]
--------------------------------------------------------------------------------------------------
(b) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = 2[/tex] and [tex]x =6[/tex].
Therefore [tex]y = a(x -2)(x - 6)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -6)
Expanding the equation:
[tex]y = a(x -2)(x - 6)[/tex]
[tex]\implies y = a(x^2-6x-2x+12)[/tex]
[tex]\implies y= ax^2-8ax+12a[/tex]
Therefore, 12a is the y-intercept
Comparing y-intercepts:
[tex]-6 = 12a \implies a = -\dfrac12[/tex]
Substituting found value of a into the equation:
[tex]\implies y= (-\dfrac12)x^2-8(-\dfrac12)x+12(-\dfrac12)[/tex]
[tex]\implies y= -\dfrac12x^2+4x-6[/tex]
y = a(x-h)²+k where (h,k) denotes the vertex
Q.1)
vertex: (1, -9) where h=1, k = -9
coordinates: (0, -8) where x = 0, y = -8
find for a:
y = a(x-h)²+k
-8 = a(0-1)²-9
-8 = a -9
a = 1
============
equation: y = (x-1)²-9
Q.2)
vertex: (4, 2) where h=4, k = 2
coordinates: (2, 0) where x = 2, y = 0
find for a:
y = a(x-h)²+k
0 = a(2-4)²+2
-2 = 4(a)
a = -1/2
============
equation: y = -1/2(x-4)²+2
Which function should be used when evaluating the function at x = -1?
S -x2 + 8x if x < -1
p(x) =
*x? - 4 if x 2-1
O p (x) = {x? - 4
O p(x) = -x2 + 8x
Point G is on line segment FH. Given FG = 7 and GH = 2, determine the length
FH.
Point G is on line segment FH. Given FG = 7 and GH = 2, the length of line segment FH is 9 units.
The length of line segment FH can be determined by adding the lengths of its two parts, FG and GH.
This is based on the property that the whole length of a line segment is equal to the sum of its parts.
Given that FG = 7 and GH = 2,
we can find the length of FH as follows:
FH = FG + GH
FH = 7 + 2
FH = 9
So, the length of line segment FH is 9 units.
This is a basic principle in geometry where the total length of a segment can be calculated by adding the lengths of its individual parts.
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#SPJ3
Help picture below problem 11
The sum of all the angles of any triangle is 180 degrees
--> Therefore the missing angle is:
x = 180 - 60 - 75 = 45
Hope that helps!
The sum of the angles of a triangle is 180 degrees
--> to put that into mathematical terms
Angle O + Angle K + Angle C = 180
60 + 75 + Angle C = 180
Angle C = 45 degrees
Therefore the missing angles' measure is 45 degrees
Hope that helps!
find the equation (in the terms of x) of the line through the points (-2,-5) and (5,0)
Answer:
-5x+7y+25=0
Step-by-step explanation:
vecto AB= (7;5)
vecto n = (-5;7)
line through the points (-2;5) and (5;0) :
-5*(x+2)+7*(y+5)=0
-5x+7y+25=0
Which statements are true of continuous data?
It is used in pictographs.
It is used in line graphs.
It can be any value within a range.
It can only have certain values.
Answer:
It is used in line graphs.
It can be any value within a range.
Step-by-step explanation:
Line graphs use :
Track numerical data over time within any value range therefore it is considered continuous data.
A line graph is a way to display data (information) that changes over time using a series of points joined with a straight line.
The line along the bottom is called the horizontal or (x-axis). Use this line to show time, days, weeks, months , or years.
The line up the side is called the vertical or (y-axis) is the value being measured, it starts at 0 and number it in even increments ; separated by twos, fives, tens, or hundreds.
Enter the number of rows needed and the number of seats that will be left over.
Answer: 6.
Step-by-step explanation: The total number of seats is 328. There are 14 rows with 23 seats in each row. To solve this, we need to multiply the amount of rows with the amount of seats in each row, which would look like this:
14 x 23 = 322.
As you can see, there are only 322 seats. However, there are 328 seats in total, so there are 6 extra seats that aren't in a specific row. Therefore, there are 6 extra seats.
Hope this helps! :)
The number 2 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
the number 2 is a factor of all even numbers (b)
2 is a factor of all even numbers (numbers that end with 2, 4, 6, 8, 0)
Option A) is wrong because 1, 3, 5, 7, 9 & numbers that end with the digits listed above are not evenly divisible by 2; this is the reason why Option C) is wrong.
In order for a digit/number to be a factor of a number, it should be evenly divisible by that number.
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)
Find the volume of the
following triangular prism.
height: 2cm
length: 5cm
width: 3.5cm
A. 17.5cm3
B. 35cm3
C. 42.5cm3
D. 45cm3
Choose the set of numbers with an average of 9.
A) 3, 5, 7, 8, 12
B) 2, 3, 6, 13, 16
C) 2, 4, 8, 11, 20
Answer:
C. 2, 4, 8, 11, 20.
Step-by-step explanation:
Solution,
Add all the number by numbers together = 45 . Dividing the sum with the total number added together = 45/5 = 9.Answer:
Step-by-step explanation:
c
!!20 POINTS!!
Find the value of X. Round to the nearest tenth