Extended Problems, Extraneous Solutions
I need help asap please, this is due in 1 day!
100 POINTS
Answers
Answer:
1a. 2 is the solution
1b. -3 is because square root of 1 doesn't equal -1.
1c.-3
Step-by-step explanation:
1.
[tex](x + 2 = \sqrt{3x + 10} [/tex]
Square both sides
[tex](x + 2) {}^{2} = 3x + 10[/tex]
Remeber perfect square Rule
[tex](x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]
So now we got
[tex]x {}^{2} + 4x + 4 = 3x + 10[/tex]
[tex] {x}^{2} + x + 4 = 10[/tex]
[tex] {x}^{2} + x - 6 = 0[/tex]
Factor into binomial.
[tex](x + 3)(x - 2) = 0[/tex]
So our solution is 3 or 2. However, let's check our work.
[tex] - 3 + 2 = \sqrt{3( - 3) + 10} [/tex]
[tex] - 1 = \sqrt{1} [/tex]
However square root of 1 is 1. It could be 1 but in Math, We only take the principal square root which is positive always. So -3 isn't a solution.
So let try 2.
[tex]2 + 2 = \sqrt{3(2) + 10} = 4 = \sqrt{16} = 4 = 4[/tex]
So this is indeed the solution.
Make up equation for 2 and 3. Ask me if you need help.
Related Questions
PLEASE Help!!:
Check for understanding:
Answers
1) Circumference: C = D × π = 40 × 3.14 = 125.6
Area: [tex]S=r^2.\pi =(\frac{D}{2} )^2.\pi = (\frac{40}{2})^2.3,14=1256\\[/tex]
2) Perimeter: P = 10.82 +10.82 + 12 + ( 12 . 3,14 )/2 = 52.48 mm
Area: [tex]S=\frac{9.12}{2}+(\frac{12}{2} )^2.\pi = 167.04<mm^2>[/tex]
ok done. Thank to me :>
Please answer this mathematical problem.
Answers
x = total amount of gumballs
let's start subtracting the balls she's giving away
[tex]\stackrel{total}{x}-\stackrel{\textit{to jaysen}}{\cfrac{x}{2}}\implies \stackrel{\textit{what's left}}{\cfrac{x}{2}}~\hfill \stackrel{\textit{half of what's left to Marinda}}{\cfrac{~~ \frac{x}{2}~~}{2}\implies \cfrac{x}{4}} \\\\\\ \stackrel{\textit{what was left minus Marinda's}}{\cfrac{x}{2}-\cfrac{x}{4}\implies \stackrel{\textit{what's left}}{\cfrac{x}{4}}}~\hfill ~\hfill \stackrel{\textit{a third of what's left to Zack}}{\cfrac{~~ \frac{x}{4}~~}{3}\implies \cfrac{x}{12}}[/tex]
[tex]\stackrel{\textit{what was left minus Zack's}}{\cfrac{x}{4}-\cfrac{x}{12}\implies \stackrel{\textit{what's left}}{\cfrac{x}{6}}}~\hfill \stackrel{\textit{her sister gets 5 balls of what's left}}{ \cfrac{x}{6}-5 }[/tex]
and we also know that after all that has been subtracted, she's only left with 5, so we can say that
[tex]\stackrel{\textit{what's finally left}}{\cfrac{x}{6}-5}~~ = ~~\stackrel{\textit{what's finally left}}{5}\implies \cfrac{x}{6}=10\implies \boxed{x = 60}[/tex]
triangle abc was dilated from the orgin by a scale factor of 2 to create triangle A’B’C’ which statement explains why the triangles are similar ?
Answers
Answer:ABC was dilated from the origin by a scale factor of 2 to create Delta A'B'C' . Which statement explains why the triangles are similar? Dilations preserve side length; therefore, the corresponding sides of Delta ABC and Delta A'B'C' are congruent.
Step-by-step explanation:Googel
Caleb sketched the following diagram on graph paper. He dilated points B and C from center o. B a. What is the scale factor r? Show your work. b. Verify the scale factor with a different set of segments. C.) Which segments are parallel? How do you know? d. Which angles are equal in measure? How do you know?
Answers
g(-2) mathematics what’s the answer I’m on a time limit this is due tomorrow omggggg
Answers
Answer:
-2g
Step-by-step explanation:
Distribute G to -2
In simple words multiply G and -2
Identify the x-intercept and y-intercept of the line 3x - 6y = – 12.
Answers
Answer: (solve x) x= -4+2y (solve y) y=2+1/2
Answer:
x=32
Step-by-step explanation:
how to write into fractional expanded form 65.43
Answers
Answer:
6543/100
Step-by-step explanation:
Multiply both numerator and denominator by 10 for every number after the decimal point
65.43 × 100
1 × 100
=
6543
100
What is the 7th term in the sequence below?
-19, -7, 5, 17, .....
Select one:
a.65
b.29
c.101
d.53
Answers
Answer:
53
Step-by-step explanation:
—19 + 12 = —7
—7 + 12 = 5
5 + 12 = 17
.
.
.
so the n term of the sequence will be: 12n — 31
so 7th term will be: 12 × 7 — 31 = 53
Answer:
d. 53
Step-by-step explanation:
increases 12 units at each step:
17 + 12 = 29
29 +12 = 41
41 + 12 = 53 (7th term)
Hope this helps
4. Tomas uses 12 gallons of water to prepare lemonade for a party. The lemonade recipe states that for every 2 quarts of water, he should add cup of lemon juice and cup 1 of sugar. How much lemon juice does Tomas need?
Answers
Answer:
Thomas will need 24 cups of lemon juice.
Step-by-step explanation:
There are 4 quarts in every gallon.
12 x 4 = 48
2 cups of lemon juice for every 2 quarts of water.
48 / 2 = 24
Hope This Helps!
patsy can decorate 3 1/2 cupcakes in 1/4 hour at this rate how many cupcakes can patsy decorate in 1 hour
Answers
Answer:
14
Step-by-step explanation:
3.5 cupcakes can be done by 15 mn
X cupcakes can be done by 1 hour
35 ×60mn =15X
210 /15=X
X= 14
so 14 cupcakes will be done by an hour
What is the average rate of change on the interval from 3 to 9?
Enter your answer in the grid below. Make sure your answer contain
Answers
Answer:
5
Step-by-step explanation:
what is 5y² if y= -1
Answers
Answer:
5
Step-by-step explanation:
Input all of the numbers and solve:
5×-1×-1
Start by solving -1*-1=1
5*1=5
Answer:
the answer for this question is 5
please help ill mark brainliest
Answers
Answer:
I think it is 8
Step-by-step explanation:
sorry If I'm wrong
Convert 8 fluid ounces into milliliters. Round your answer to the nearest whole number.
Answers
Answer:
236.588 milliliters so the answer is 240
Step-by-step explanation:
for an approximate result, multiply the volume value by 29.574
A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262. .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
A) .18
B) .622
C) .262
D) .442
Answers
===================================================
Explanation:
To get the point estimate, we average the endpoints of the given confidence interval. Add up the endpoints and divide by 2
(low+high)/2 = (0.262+0.622)/2 = 0.442
The value 0.442 is right in the middle of the confidence interval, so it's a natural point estimate for the population proportion.
--------------
Alternative Method:
Subtract the endpoints to find the confidence interval width
width = high - low = 0.622 - 0.262 = 0.36
Cut this in half to get the margin of error (MoE)
MoE = width/2 = 0.36/2 = 0.18
Then we can either add on the MoE to the low endpoint, or subtract it from the high endpoint, to land on the center
center = low + MoE = 0.262 + 0.18 = 0.442center = high - MoE = 0.622 - 0.18 = 0.442
Golf Club Distance (yards) Distance (feet)
9 iron
99
7 iron
120
5 iron
144
3 iron
162
3 wood
174
Driver
192
Answers
Answer:
7 Iron
Step-by-step explanation:
Just smort
HELP!! I'm not sure what goes in the blank.
Answers
Answer:
10[tex]sin^{2} ([/tex]β[tex])[/tex]
Step-by-step explanation:
We can find this two ways, first by seeing in the step after it, cosines are canceled out. Since you already have 10[tex]sin^{2} ([/tex]β[tex])[/tex] on the next step, you can assume that (since only the cosines changed and the cosine next ot the blank was removed), the value is 10[tex]sin^{2} ([/tex]β[tex])[/tex].
You can also use double angle formulas from the previous step:
(sin(2β) = 2 sin(β) cos(β))and find that:
5 sin (2β) sin(β) = 5 * (2 sin(β) cos(β)) sin(β)) = (10 sin(β) sin(β)) cos(β) =
10[tex]sin^{2} ([/tex]β[tex])[/tex] cos(β)
But since cos(β) is already present, we can see that the answer is 10[tex]sin^{2} ([/tex]β[tex])[/tex]
Your current salary is $30,900 per year. You’ve just accepted a new position at a company that’s to pay you $32,500 per year. How much more will you get per month at the new job? (Round your answer to the nearest dollar.)
Answers
Answer: $133
Explanation:
\cfrac{32\ 500 - 30\ 900}{12} = \$133
12
32 500−30 900
=$133
2x2 is what its due in 1 minute
Answers
Answer: 4
Step-by-step explanation: You multiplied 2 and 2 which equals to 4
Answer:
9
Step-by-step explanation:
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
Is the inequality 5-x^2<4 true for x=1?
Answers
5 - x² < 4
- x² < 4 - 5
- x² < - 1
=》x² < 1
Now, let's check with x = 1
x² < 1
(1)² < 1
1 < 1
1 is not less than or greater than 1. They are equals. So, the inequality 5 - x² < 4 is NOT true for x = 1.
_____
Hope it helps ⚜
What is the answer to the question?? Is the answer even on there?
Answers
Answer:
D. $105,750
Step-by-step explanation:
Use the formula I=prt,which stands for "Interest equals principal × rate × time" The clue to use that formula was the phrase "simple interest" The principal is the original amount of the loan, $150,000.
The interest rate is the 3.7% or 4.2% but you MUST change these to a decimal to use them. So we'll be using .037 and .042 for these calculations. The time part of the equation is the 15 years or the 30 years. See image.
I need to know the area of this triangle and I would like to have an explanation because I dont know how to do it I know the formula just not how to get the height
Answers
Answer: 69
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
The x coordinate of vertex J and L are same of x= -2, JL // Y axis
Height is the perpendicular segment (KD) from K to JL, KD // X axis
area = JL * KD /2 = ((1 - -5)* (4 - -2)) / 2 = (6 * 6) / 2 = 18
At the beginning of year 1, Sam invests $700 at an annual compound interest
rate of 5%. He makes no deposits to or withdrawals from the account.
Which explicit formula can be used to find the account's
beginning of year 4? What is the balance?
Answers
at the beginning of year 4, only 3 years have elapsed, the 4th year hasn't started yet, since it's at the beginning, so at the beginning of year 4 we can say only 4-1 years have elapsed.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$700\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=\textit{elapsed years}\dotfill &3 \end{cases}[/tex]
[tex]A=700\left( 1 + \frac{0.05}{1} \right)^{1\cdot 3}\implies A = 700(1+0.05)^3\implies A(4)=700(1+0.05)^{4-1} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A(n)=700(1+0.05)^{n-1}~\hfill[/tex]
Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x
Answers
The equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100
Percentages can be expressed as decimals or fractions.
Given the expression 60% of 25, this can b expressed as:
60% of 25 = xwhere x is the result of the expression.
60/100 * 25 = xExpressing 60% as a decimal will give;
0.6 of 25 = x
0.6 * 25 = x
From the expression 60/100 * 25 = x, this can also be written as:
25 = 100/60 x
25 = 10/6 x
25 = 1.6x
Hence the equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100
Learn more on equation here: https://brainly.com/question/2972832
Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
18 divided by StartFraction 2 Over 9 EndFraction = 81
18 times StartFraction 2 Over 9 EndFraction = 4
StartFraction 2 Over 9 EndFraction divided by 18 = StartFraction 1 Over 81 EndFraction
StartFraction 9 Over 2 EndFraction divided by 18 = one-fourth
Answers
Answer:
18 times StartFraction 2 Over 9 EndFraction = 4
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
Answer:
IT'S B I CAN CONFIRM BC I JUST FINISHED THE TEST
Step-by-step explanation:
Multiply.
(−2/3) x (5/4)
Answers
Answer:
-5/6
Step-by-step explanation:
multiply the top
-10
multiple the bottom
12
you get
-10/12
or simplified
-5/6
Answer:
de 35
Step-by-step explanation:
To increase the volume of a sphere, you
must in crease the radius
decrease the radius
None of the answer choices is correct
decrease the circumference
Answers
The volume of a sphere is directly proportional to the radius cube thus with an increase in the radius it will increase so option (A) is correct.
What is the sphere?A sphere is a 3D geometrical object which has a radius and becomes a point that revolves around a fixed point called the center.
For example, if you have a sphere of radius r then its surface area will be 4πr² and
The volume of a sphere with radius r is given as (4/3)πr³.
V ∝ r³
By increasing the radius r the volume V will rapidly increase.
Hence "Because the volume of a sphere is precisely proportional to the cube of its radius, it will grow as the radius grows".
For more about a sphere,
https://brainly.com/question/9994313
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How many meters are equal to 18 kilometers?
Answers
Answer:
18000
Step-by-step explanation:
The number of meters in 18 kilometers is 18,000 meters(m)
How to convert meters to kilometers1900 meter(m) = 1 kilometer(km)x meters = 18 kilometers
x meters = 18 kilometers × 1000
x = 18,000 meters
Therefore, 18 kilometers is equivalent to 18,000 meters
learn more about conversion:
https://brainly.com/question/9032119
can someone plz help with this FAST
I WILL MARK BRAINLIEST
Answers
Answer:
Maria
Step-by-step explanation:
Sean - 2 minutes (1 mile/minute)
Maria - 4 minutes (0.5 miles/minute)
David - 3 minutes (1 mile/minute)
Carrie - 2 minutes (0.5 miles/minute)
Which equation is correct?
235 × 8 = 200 × 8 + 30 × 8 + 5
235 × 8 = 2,000 × 8 + 300 × 8 + 50 × 8
235 × 8 = 200 + 30 × 8 + 5 × 8
235 × 8 = 200 × 8 + 30 × 8 + 5 × 8
I LOVE YOUUU
Answers
The correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
How to determine the correct expression?The product expression is given as:
235 * 8
Express 235 as place values
235 * 8 = (200 + 30 + 5) * 8
Expand the bracket
235 * 8 = 200 * 8 + 30 * 8 + 5 * 8
Hence, the correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
Read more about place values at:
https://brainly.com/question/12386995
