Since √(3x+1) and √(x-5) is always positive, you can square out both sides.
[tex] \sqrt{3x + 1} > \sqrt{x - 5} \\ {( \sqrt{3x + 1}) }^{2} > {( \sqrt{x - 5} )}^{2} \\ 3x + 1 > x - 5 \\ 2x > - 6 \\ x > - 3[/tex]
Since substituting x = -2, -1 , ... , 4 into √(3x+1) and √(x-5) will result into complex solutions,
Therefore,
[tex]x > 4[/tex]
Answer:
-3<x≤5
Step-by-step explanation:
√(3x+1)>√(x-5)
Square each one of the square roots. Then create 3 different inequality expressions and solve them/
1. 3x+1>x-5= x>-3
2. 3x+1≥0= x≥-1/3
3. x-5≥0= x≥5
From here I'm going to take the values that cover the most of the area in this expression which should be -3<x≤5.
Find the exact value of tan 195°.
[tex]\tan 195^{\circ}\\\\=\tan\left(3 \times 90^{\circ} - 75^{\circ} \right)\\\\=\cot 75^{\circ}\\\\=\left(\tan 75^{\circ} \right)^{-1}\\\\= \textbf{[}\tan \left(30^{\circ} + 45^{\circ}\right) \right \textbf{]}^{-1}\\\\=\left(\dfrac{\tan 30^{\circ} +\tan 45^{\circ}}{1- \tan 45^{\circ} \cdot \tan 30^{\circ}} \right)^{-1}\\\\\\=\left( \dfrac{\dfrac 1{\sqrt 3}+1}{1- \dfrac 1{\sqrt 3}} \right)^{-1}\\\\\\=\left( \dfrac{\sqrt 3+1}{\sqrt 3-1}\right)^{-1}\\\\\\=\dfrac{\sqrt 3-1}{\sqrt 3 +1}\\[/tex]
[tex]=\dfrac{\left( \sqrt 3-1\right)^2}{\left( \sqrt 3+1\right)\left( \sqrt 3-1\right)}\\\\\\=\dfrac{3+1-2\sqrt 3}{3-1}\\\\\\=\dfrac{4-2\sqrt 3}{2}\\\\\\=2-\sqrt 3[/tex]
Which expression is equivalent to |x| < 11?
x > –11 or x < 11
x < –11 and x > 11
x < –11 or x > 11
x > –11 and x < 11
PEMDAS 4+5 x (6-2) what the answer
Answer:4(5x+1)
Step-by-step explanation: you want to subtract the numbers 4+5x(6-2)/4+5x(4) so you'll need to multiply 5 and 4 so 4+5x*4 but i'm goin to make it smaller so it would be 4+20x but you have to rearrange it instead of it being 4+20x it would be 20x+4 .And the common factor would be 4(5x+1).
I hope this helps and makes sense.
What is the measure of the angle?
Answer:
it a 90 degree angle hope this helps:)
Step-by-step explanation:
Vectors r, s, t, u, and v are shown on the graph.
Which of the following vectors is equivalent to 2/3v (Image shown)
Need help with the answer
Answer:
sine(∡DAB) = 0.5
Step-by-step explanation:
∡[tex]ACD=[/tex]∡[tex]ADB[/tex] = 60°
∡[tex]DAB=(180-90-60)^{o} =30^{o}[/tex]
[tex]sin(30^{o})= 0.5[/tex]
Hope this helps
what is 6/4 in its simplst form
Answer:
Fraction form: [tex]\frac{3}{2}[/tex]
Decimal form: 1.5
Mixed number form: 1 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Find the greatest common factor between the two numbers in the fraction, in this case the largest number both can be divided by equally is 2, so,
Take [tex]\frac{6}{4}[/tex] and divide both parts by 2:
6 ÷ 2 = 3
4 ÷ 2 = 2
Which gives you [tex]\frac{3}{2}[/tex]
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received c fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.How many cookies did Cindy receive? Write your answer as an expression.
Answer: 29 cookies.
Step-by-step explanation: 96/8=32 32-3=29 boom. maths.
The number of cookies baked by Grandma= 96
If she divides them evenly amount 8 children, then by division operation the number of cookies received by each child = (number of cookies) ÷ (number of children)
= (96) ÷ (8) = 12
Since, Cindy, received c fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.
Hence, the number of cookies received by Cindy = 12-c
how long does it last for Fanger print
Answer:
A fingerprint can last on a surface from 2 hours to 40 years on average.
Step-by-step explanation:
Most fingerprints will get erased due to impact from humidity and heat.
1. which expression is equivalent to 4(9+3).
Multiple Select three expressions
A. 4(12)
B. 36+3
C. 36+12
D. 4+(9+3)
E. (9+3) +(9+3) +(9+3) +(9+3)
Answer:
A. 4(12)
C. 36+12
E. (9+3) +(9+3) +(9+3) +(9+3)
Step-by-step explanation:
[tex]4(9+3)=48[/tex]
[tex]4*9=36\\4*3=12[/tex]
[tex]48[/tex]
[tex]4*12=48[/tex]
[tex]36+12=48[/tex]
[tex](9+3) +(9+3) +(9+3) +(9+3)\\12+12+12+12[/tex]
=48
what is this sphere’s volume? radius is given, please round to nearest tenth
Answer:
179.59438
rounded to the nearest tenth would be 179.6
Step-by-step explanation:
use this formula
volume = (4/3) · π · r3
Help please! I have to turn this in today.
:)
Answer:
Integer: 9
Nearest 10th: 9.5
Step-by-step explanation:
If r = 11, t = 3, s = 9, then 8r - 10s =
Answer:
-2
Step-by-step explanation:
plug values for r and s into the equation 8r - 10s.
so, 8(11) - 10(9)
88 - 90 = -2
hope this helps!
how many inches are in 12 ft
Answer:
the answer is 144
Answer:
144 inches
Step-by-step explanation:
There are 12 inches in 1 foot,
So 12 times 12 is 144 inches.
Calculate the value of X
I neeed hellppppp plissss
Answer:
I believe C is the closest equation to the graph
Step-by-step explanation:
For the equation z – 14 = 29. Jaun says that the solution is 33.Check solution work by substitutions it into the equation .Is his solution correct. Explain
Answer:
Jaun's solution is incorrect.
Step-by-step explanation:
If Jaun's solution to the equation is 33, we can check this by substituting z=33 and solving 33 - 14 = 29. Since 33-14=19 and 19 does not equal 29, Jaun's answer is incorrect.
Hope this helps! :)
A recipe uses brown sugar and caster sugar in the ratio 3:2. What fraction of the sugar is caster?
Answer:
2/5 of the sugar is caster sugar
4 1/2 x 2 1/2 x 8 1/2 =
Answer:
[tex]95\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]4\frac{1}{2} * 2\frac{1}{2} * 8\frac{1}{2}[/tex] = 9/2 * 5/2 * 17/2
765/8 = [tex]95\frac{5}{8}[/tex]
Solve the following:
four and seven twelfths plus six and nine twelfths
Ans:
11 and four twelfths
Step-by-step explanation:
Please help! I really need it
To find the volume of a triangular prism:
⇒ necessary to know the formula
[tex]Volume = (Area-of-Triangular- base)*(length)[/tex]
Let's first find the area of the triangular base:
⇒the formula for the finding the area of a triangle is ⇒ [tex]\frac{1}{2}bh[/tex]
b: length of base --> 3mmh: length of height: 6mmArea of the triangle is [tex]\frac{1}{2}*3*6=3*3=9[/tex]
Since the area of the triangular base is 9 and the length is 5.22
⇒ the volume is:
[tex]Volume = 9 * 5.22=46.98mm^3[/tex]
When the volume is rounded to the nearest tenth, the volume is 47.0 [tex]mm^3[/tex]
Hope that helps!
Please help! I wish you a good day :)
Answer:
A=p2-2p-3
Step-by-step explanation:
The area for a triangle is given by:
A=1/2bh
The base is p + 1 and the height is 2p - 6. Therefore:
A=1/2(p+1)(2p-6)
Simplify the second term:
A=(p+1)(1/2)(2p-6)=(p+1)(p-3)
Distribute:
A=p(p-3)+1(p-3)
Distribute:
A=p2-3p+p-3
Combine like terms:
A=p2-2p-3
Which of the following will form the composite function G(F(x)) shown
below?
G(Fx)) = 3(/* +1)
A. Fx) = x + 1 and G(x) = 13x
B. Fx) = 3x and G(x) = 5x + 1
C. F(x) = 3x and G(x) = 1
D. F(x) = 5x + 1 and G(X) = 3x
Answer:
Step-by-step explanation:
A
The given composition function is combination is F(x)=√x+1 and G(x)=3x. Therefore, option D is the correct answer.
The given function is G(F(x))=3(√x+1).
F(x)=√x+1 and G(x)=3x
The composite function is G(F(x))
Replace x by √x+1 in 3x, we get
3(√x+1)
Therefore, option D is the correct answer.
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You buy tomatoes in 25 lb cases one portion of salad requires. 75 oz of tomatoes how many portions can be made with one case
Find the slope and the y intercept of the line -7x-2y=10
Answer:
Gradient = -3.5, y - intercept = ( 0 , -5 )
Step-by-step explanation:
→ Rewrite into y = mx+ c format
-2y = 7x + 10
→ Divide everything by 2
-y = 3.5x + 5
→ Multiply everything by -1
y = -3.5x - 5
Kevin has a part time job. he earns £9 an hour. he wants to buy a new bike costing £306. how many hours does Kevin have to work to earn enough to buy it?
Answer:
34
Step-by-step explanation:
306/9=34
When should you suggest that a peer rearrange some of the paragraphs in her report?
when you’re having trouble understanding how the sentences are related to each other
when the most convincing or persuasive evidence appears first in the report, followed by background information
when you find a section that seems unrelated to the rest of the report
The main answer:
D: when you find a section that seems unrelated to the rest of the report
Step-by-step explanation:
I don't have an explanation for this, sorry!)
Hope it helps!
F r o g
Answer:
D: when you find a section that seems unrelated to the rest of the report
Step-by-step explanation:
For $1.80 a grocer buys a case of fruit which contains 12 dozen. He knows that 2 dozen will spoil before he sells them. At what price per dozen must he sell the good ones to gain 1/3 of the whole cost?
Answer:
i didnt understand the awnser fully but if i did the awnser is 5 cents a donut
Step-by-step explanation:
Use rounding to estimate the product of 296 and 2, 423. Round both
numbers to the nearest hundred to find your answer.
The solution is
Answer:
Step-by-step explanation:
no problem
296 rounded to the nearest hundred would be 300 and 2423 would be 2400 there hope it helps
The product of 296 and 2.423 rounded to the nearest hundred would be 717.20
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of trimmed from the right in terms of exact digits.
We need to find the product of 296 and 2.423
296 x 2.423 = 717.20
Thus, 717.20 rounded to the nearest hundred .
Learn more about rounding numbers here:
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Victoria is at an elevation of 150 feet. She hikes down to an elevation of 120 feet in 40 minutes.
Then she hikes down to an
elevation of 100 feet in 30 minutes.
What is her average rate of descent, in feet per minute, from 150 feet to 120 feet?
The Victoria's average rate of descent by hiking down from an elevation of 150 feet to an elevation of 120 feet in 40 minutes is equal to 0.75 feet per minute.
How to determine the average rate of descent of a hiker
Geometrically speaking, the average rate of descent (r), in feet per minute, is represented by a secant line, which represents in this case the change in elevation (Δz), in feet, divided by the change in time (Δt). A mathematical description of the formula is shown below:
r = Δz/Δt (1)
If we know that Δz = 30 ft and Δt = 40 min, then the average rate of descent is:
r = 30 ft/40 min = 0.75 ft/min
The Victoria's average rate of descent by hiking down from an elevation of 150 feet to an elevation of 120 feet in 40 minutes is equal to 0.75 feet per minute. [tex]\blacksquare[/tex]
To learn more on average rates, we kindly invite to check this verified question: https://brainly.com/question/14712970