[tex]Domain:\\\\x+3\geq0\ \wedge\ 2x-1\geq0\\\\x\geq-3\ \wedge\ x\geq0.5\\\\D:x\in[0.5;\ \infty)[/tex]
[tex]\sqrt{x+3}-\sqrt{2x-1}=-2\qquad\text{square of both sides}\\\\(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(\sqrt{x+3})^2-2(\sqrt{x+3})(\sqrt{2x-1})+(\sqrt{2x-1})^2=4\qquad\text{use}\ (\sqrt{a})^2=a\\\\x+3-2\sqrt{(x+3)(2x-1)}+2x-1=4\qquad\text{combine like terms}\\\\3x+2-2\sqrt{(x+3)(2x-1)}=4\qquad\text{subtract 3x + 2 from both sides}\\\\-2\sqrt{(x+3)(2x-1)}=2-3x\qquad\text{square of both sides}\\\\\left(-2\sqrt{(x+3)(2x-1)}\right)^2=(2-3x)^2[/tex]
[tex]4(x+3)(2x-1)=2^2-2(2)(3x)+(3x)^2\qquad\text{use distributive property}\\\\(4x+12)(2x-1)=4-12x+9x^2\\\\(4x)(2x)+(4x)(-1)+(12)(2x)+(12)(-1)=4-12x+9x^2\\\\8x^2-4x+24x-12=4-12x+9x^2\\\\8x^2+20x-12=4-12x+9x^2\qquad\text{subtract }\ 9x^2\ \text{from both sides}\\\\-x^2+20x-12=4-12x\qquad\text{add 12 and}\ 12x\ \text{from both sides}\\\\-x^2+36x=16\qquad\text{change the signs}\\\\x^2-36x=-16\\\\x^2-2(x)(16)=-16\qquad\text{add}\ 16^2\ \text{to both sides}[/tex]
[tex]\underbrace{x^2-2(x)(16)+16^2}_{(a-b)^2=a^2-2ab+b^2}=16^2-16\\\\(x-16)^2=256-16\\\\(x-16)^2=240\iff x-16=\pm\sqrt{240}\\\\x-16=\pm\sqrt{16\cdot15}\\\\x-16=-\sqrt{16}\cdot\sqrt{15}\ \vee\ x-16=\sqrt{16}\cdot\sqrt{15}\\\\x-16=-4\sqrt{15}\ \vee\ x-16=4\sqrt{15}\qquad\text{add 16 to both sides}\\\\x=16-4\sqrt{15}\notin D\ \vee\ x=16+4\sqrt{15}\\\\\boxed{x=4(4+\sqrt{15})}[/tex]
Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.
recall that the slope, namely the average unit rate of change, is rise/run.
so, what's the slope for the function in the table? well, we can simply pick any two points and get it, or just use the first point rise of 8 and a run of 7, gives us a slope of 8/7 or 1⅐.
now, let's take a peek at the lines, they all have a "rise" of 6, notice they're all lying on the y = 6 line horizontally.
1)
rise = 6, run = 2, slope 6/2 = 3.
well, 3 is more than 2, so no that one.
2)
rise = 6, run = 3, slope = 6/3 = 2.
well 2 = 2, so no that one either.
3)
rise = 6, run = 4, slope 6/4 = 3/2.
3/2 is actually larger than 8/7 and less than 2, you can check. so ✔
4)
rise = 6, run = 5, slope = 6/5.
6/5 or 1⅕ is more than 8/7, and is clearly less than 2, so ✔
5)
rise = 6, run = 6, slope = 6/6 = 1.
well, needless to say 1 is less than 2 but is less than 8/7, recall 8/7 is actually 1⅐.
Answer:
View the picture for your answer!
Have a wonderful day:))
Michelle multiple 3.4×52. she incorrectly wrote 1,768 as her product.
Answer:
Wrong Answer 176.8
Step-by-step explanation:
Multiply 3.4 * 52 = 176.8
please help me Find the legth of x
Answer: 6
=====================================
Explanation:
The triangles are similar triangles (we can use the AA similarity theorem to prove this). So the vertical sides pair up, and the horizontal sides pair up, to form the proportion below
x/4.5 = 8/6
Note the order of the terms. I'm dividing the upper triangle's sides by the corresponding lower triangle's sides. Cross multiply and solve for x
x/4.5 = 8/6
6x = 4.5*8
6x = 36
x = 36/6
x = 6
Divide. 413÷129 Enter your answer, as a mixed number in simplest form, in the box.
For this case we must divide the following expression:
[tex]\frac {413} {129}[/tex]
The expression can not be simplified. When dividing we have that its decimal form is given by:
3,201550
If we convert to a mixed number we have:
[tex]3 \frac {26} {129}[/tex]
Verifying:
[tex]3 \frac {26} {129} = \frac {129 * 3 + 26} {129} = \frac {413} {129}[/tex]
Answer:
[tex]3 \frac {26} {129}[/tex]
You can buy 5 pounds of grapes for $9.95 .what is a proportion that gives the cost c if you buy 4 pounds of grapes
9.95 / 5 = 1.99
4 x 1.99 = 7.96
$7.96
What is the value of (-14⁰)-2
a -1/196
b 1/196
c 0
d 1
The value of (-14°)-2 is the reciprocal of 196 since the negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent. The correct answer is 1/196.
The question asks for the value of (-14°)-2, which represents a mathematical expression that requires simplification using exponent rules. The notation a-n means that you should take the reciprocal of an, which in this case is the reciprocal of (-14°) squared. When squaring a negative degree value, the square of a negative number is positive, so (-14°)2 = 196°. Therefore, taking the reciprocal of 196° gives us 1/196.
The value of (-14°)-2 is 1/196.
Help!
If I were to Buy a bright bomer from the item shop and buy the glider. The Bright bomer is Rare and so is the glider. How much?
Answer: 2000 v-bucks
Step-by-step explanation: The bright bomber costs 1,200 and the glider costs 800
use the law of sines to find the length of side c
Look at the picture.
The law os sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
We have
[tex]m\angle A=46.7^o\\\\m\angle C=48^o\\\\a=44\\\\c=?[/tex]
Substitute:
[tex]\dfrac{c}{\sin48^o}=\dfrac{44}{\sin46.7^o}\\\\\boxed{c=44.93}\to\boxed{A.}[/tex]
Answer:
A!
Step-by-step explanation:
47 POINTS!
PLEASE HELP! (SHOW YOUR WORK)
Answer:
2. No it is not direction variation
3. This is direct variation with the constant being 2
Step-by-step explanation:
The equation for direct variation is y=kx
2. 8y = 3x+1
Divide each side by 8
8y/8 = 3x/8 + 1/8
y = 3/8 x + 1/8
We are adding 1/8 to each time so it is not direct variation
3. 12y = 24x
Divide each side by 12
12y/12 = 24x/12
y = 2x
This matches y= kx, where k=2
This is direct variation with the constant being 2
Two factory plants are making TV panels. Yesterday, Plant A produced 6000 panels. Seven percent of the panels from Plant A and 2 % of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 4 % ?
Answer:
1% of 4000 + 4% of B = 2% of (4000 + B)
40 + 0.04*B = 0.02( 4000 + B)
40 + 0.04* B = 80 + 0.02*B
40 + 0.04*B - 80 - 0.02B = 0
0.02*B - 40 = 0
0.02*B = 40
2B = 4000
B = 2000
Step-by-step explanation:
Plant B produced 1000 panels.
The total number of defective panels from Plant A is 7% of 6000,
= (7/100) x 6000
= 420 panels.
and, total number of defective panels from Plant B is 2% of x,
= (2/100) x
= (1/50) x.
The overall number of defective panels from both plants is 4% of the total number of panels
= (4/100)(6000 + x)
= (1/25) (6000 + x).
Now, set up the equation:
420 + (1/50) x = (1/25) (6000 + x)
To solve for x, we can multiply both sides of the equation by 50 * 25 to eliminate the fractions:
50 . 25 . 420 + 50 x = 25 (6000 + x)
125000 + 50x = 150000 + 25x
50x - 25x = 150000 - 125000
25x = 25000
x = 25000 / 25
x = 1000
Therefore, Plant B produced 1000 panels.
Learn more about Equation here:
https://brainly.com/question/29657983
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The cost of a candy bar in a vending machine is $0.95. The cost of a bottle of water in the same machine is $1.25. Jamie has $25.00 to spend on candy bars and bottles of water for her friends. She must buy nine candy bars. If b represents the number of bottles of water, which inequality represents all the possible values of b?
Final answer:
The inequality representing all possible values of b, the number of bottles of water Jamie can buy, is b ≤ 13, as Jamie has $16.45 left to spend after buying nine candy bars and each bottle costs $1.25.
Explanation:
The student must buy nine candy bars, which cost $0.95 each. The total cost for the candy bars is 9 * $0.95 = $8.55. Jamie has $25.00 to spend, so after buying the candy bars, she will have $25.00 - $8.55 = $16.45 left for bottles of water. Each bottle of water costs $1.25, so the number of bottles she can buy is represented by the inequality $1.25b ≤ $16.45, where b is the number of bottles of water Jamie can purchase.
Now, let's solve this inequality for b. Dividing both sides of the inequality by $1.25 gives us b ≤ 13.16. Since Jamie can't buy a fraction of a bottle, she must buy at most 13 bottles of water.
Therefore, the inequality representing all possible values of b (i.e., the number of bottles of water Jamie can buy) is b ≤ 13.
what is the ratio of triangles to circle 3 trangle 2 circle
Answer:
3:2
Step-by-step explanation:
Triangle:circle
3 triangle:2 circle
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
There are 3 calories in 1 gram of protein.
There are 3 calories in 12 grams of protein.
There are 12 calories in 3 grams of protein.
There is 1 calorie in 4 grams of protein.
Hello :3
Your answer would be C. (or "There are 12 calories in 3 grams of protein).
Hope This Helps (Hope i am not to late sorry if i am)
Cupkake~
Which expression is equivalent to -9( -2x - 3)
Answer:
-18x+ 27
Step-by-step explanation:
HELP RIGHT AWAY PLEASE!!!!
The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 0 and the ordered pair 0, 4. Another straight line labeled B joins the ordered pair 0, 1 and the ordered pair 5, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(1, 2) is the solution to line A but not to line B.
(1, 2) is the solution to both lines A and B.
(0, 1) is the solution to both lines A and B.
(0, 1) is the solution to line A but not to line B.
Answer:
(1,2) is the solution to both lines a and b
Step-by-step explanation:
You find the slope using 2 point and do y2-y1/x2-x1 . To create the equations for the two lines you do y=mx+b where m=slope and b=y-intercept.
I need to know where did kellys collection go the most?
Answer:
What options are there
Step-by-step explanation:
Answer:
Step-by-step explanation:
Between the third and fourth months, the size of K's collection grew by 3. This is the steepest slope / greatest rate of change.
The Carson’s are on a road trip they paid $62.70 for 16 1/2 gallons of gasoline
Part 1-Find the price of gasoline per gallon show your work
Part 2-Give an example of a cost and amount that would make the gasoline have a rate of $3.49 per gallon
Answer:
$3.92 per gallon
10 gallons of gas at $3.49 a gallon will cost $34.90
Step-by-step explanation:
To find the price per gallon, we take the total cost, and divide by the number of gallons. I will change 16 1/2 to a decimal for ease of math calculations.
16 1/2 = 16.5
cost/gallons
$62.70/16.5
3.91875
Since we are working with money, we round to the nearest cent
$3.92 per gallon
To find the total cost, we multiply the cost per gallon times the number of gallons. We have a cost per gallon of $3.49. If we multiply by 10 gallons
cost = $3.49 * 10
$34.90
10 gallons of gas at $3.49 a gallon will cost $34.90
Travis is sewing a pillow for his Home Arts class. The pillow will be made from 2 identical rectangles. Each rectangle is 1 1/2 feet wide and 1 3/4 feet long. How many square feet of material is used in the sewing of the pillow?
A.2 3/8 sq. feet
B.2 5/8 sq. feet
C.5 1/4 sq. feet
D.6 1/2 sp. feet
Answer:
The answer is A.
Step-by-step explanation:
If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.
Answer:
[tex]\frac{(L x M)}{6}[/tex]
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.
The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.
We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.
As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.
We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.
[tex]\frac{(L x M)}{6}[/tex]
F(x)=5x-3 what does f(5)=
f(5) means that x=5
Now, we solve 5x-3 because we know what x is.
5(5)-3
25-3
22
F(5)=22
Answer:
F (5)= 22
Step-by-step explanation:
How many 1/2’a are in 7
Answer:
There are 14 halves in seven.
Step-by-step explanation:
7(1/2)=14
7(2)=14
OR, you could just count by halves until you reach 7, but that takes a while. (;
Profit P(x) can be calculated as revenue minus cost. R(x) = 55x - 2x2 C(x) = 21x + 97 P(x) = - 2x2 + 34x - 97 Calculate the x-value that maximizes profit.
8.5
Step-by-step explanation:The vertex of a quadratic ax²+bx+c is located at x = -b/(2a). When the x² coefficient is negative, the vertex represents a maximum.
For P(x), the x-value of the maximum profit is ...
... x = -34/(2(-2))
... x = 8.5
Find the constant of variation for the relationship described in the table.
x f(x)
–2 –60
1 30
4 120
5 150
90
30
f(x)
x
Answer:
i believe the answer is 30
Step-by-step explanation:
Solve for x:
-15x – 3 > 42
Answer: X < -3
Step-by-step explanation:
-15x - 3 > 42
-15x - 3 + 3 > 42 + 3
-15x > 45
-15x/-15 > 45/-15
Since we are dividing by a negative, we flip the >
x < -3
So, let's check
-4 < -3
-15*-4 - 3 > 42
60 - 3 > 42
57 > 42
Now, let's see if -3 will work.
-15*-3 - 3 > 42
45 - 3 > 42
42 > 42 (False)
Okay, now let's try 4
-15*4 - 3 > 42
-60 - 3 > 42
-63 > 42
This is false, so it is x < -3
The correct answer is x < -3
Explanation:
To solve our equation we first need to set out our equation, -15x – 3 > 42. Next, we add 3 to both sides of our equation, -15x - 3 + 3 > 42 + 3 = -15x > 45. Then, we multiply both sides by -1(Or in other words, reverse the inequality), -15x * -1 > 45 * -1 = 15x < -45. And then, we divide both sides by 15, 15x/15 < -45/15 = x < -3. Finally, we have our answer of x < -3.
Hope This Helps!!!
-AnimeDabGirl
what is 6.5 as a fraction
Answer:
13/2 is 6.5 as a fraction
Can someone please help
Answer:
3 Bookmarks
Step-by-step explanation:
1) Find the remaining money which is 0.96
2)Divide 0.96 evenly into 3 people, you should get O.32
3) If each bookmark costs 0.10, and each person gets 0,32 the greatest number of bookmarks they can get is 3.
What algebraic expression is 5+3(2x-7)=5+6x-21
The length of a rectangle is three centimeters more than twice the width. The perimeter is 78 centimeters. Define a variable and write and solve an equation to find out how long and wide the rectangle is?
I need to find the length? how?
Betty can drive her car 400 miles at a steady speed using 20 gallons of gasoline. at this rate how many gallons of gas will she use to travel 1600 miles
Answer:
80 gal
Step-by-step explanation:
20 gal takes her 400 mi
Vol. of gas = 1600 ×20/400
Vol. of gas = 1600 ×1/20
Vol. of gas = 80 gal
Betty will use 80 gal of gas.
Which logarithmic equation is equivalent to the exponential below? e^a= 35
Answer:
[tex]log_{e}[/tex] 35 = a
Step-by-step explanation:
using the law of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
[tex]e^{a}[/tex] = 35 ⇒ [tex]log_{e}[/tex] 35 = a