The solution -1 is an extraneous solution
Neither -1 nor -6 is a true solution to the equation.
Option D is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the equation x + 4 = √(x + 10), we need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical.
Here are the steps:
x + 4 = √(x + 10)
Subtract 4 from both sides:
x = √(x + 10) - 4
Square both sides:
x² = (√(x + 10) - 4)²
Expand the right side using the formula (a - b)^2 = a^2 - 2ab + b^2:
x² = x + 6 - 8√(x + 10)
Move all terms to the left side:
x² - x - 6 + 8√(x + 10) = 0
To solve this equation, we can use a substitution u = √(x + 10):
u = √(x + 10)
Square both sides:
u² = x + 10
Substitute into the original equation:
(u² - 10) + 4 = u
Simplify:
u² - u - 6 = 0
Factor:
(u - 3)(u + 2) = 0
So u = 3 or u = -2.
But u = -2 leads to a negative value under the square root in the substitution u = √(x + 10), which is not allowed.
Therefore, we only consider u = 3, which gives:
√(x + 10) = 3
Square both sides:
x + 10 = 9
Subtract 10 from both sides:
x = -1
So the solution to the original equation is x = -1.
To check if it is extraneous, we need to substitute it back into the original equation:
x + 4 = √(x + 10)
-1 + 4 = √(-1 + 10)
3 = √9
3 = 3
The equation is true, so x = -1 is a valid solution and not extraneous.
Therefore,
Neither -1 nor -6 is a true solution to the equation.
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Solve (x+7)^2=49 algebra
Answer: x = 0
Step-by-step explanation:
Given:
(x + 7)² = 49
Distribute:
x² + 7² = 49
Square:
x² + 49 = 49
Subtract 49 from both sides of the equation:
x² = 0
x = 0
The only solution to this equation is 0.
-> We can also see this with graphing. See attached.
answer:
x=0
Step-by-step explanation:
(x+7)^2=49
take the square root of both sides
√(x+7)^2=√49
x+7=7
x=0
Can someone help. I literally forgot this how
Answer:
Below.
Step-by-step explanation:
The 2 triangles are congruent ( By 2 angles and corresponding side).
The 2 marked angle are congruent so
5y - 30 = 2y + 6
3y = 36
y - 12.
So m < O = 5(12) - 30 = 30 degrees.
and m <N = 180 - 30 - 90 = 60 degrees, (as there are 180degrees in triangle)
EN = IV = 14.
It is possible to find the measure of OE and ON by using trigonometry of a right triangle.
tan 30 = EN / OE
OE = EN / tan30
= 14/tan30
= 24.3.
sin 30 = 14/ON
ON = 14 / sin 30
= 28.
how do you write 10^3 / 10^7 in standard form for properties of exponents
Answer:
1 / 10000
Step-by-step explanation:
10^3 / 10^7
apply exponent rule: x^a / x^b = x^(a-b)
10^3 / 10^7 where a = 3 and b = 7
10^(3 - 7) = 10^(-4)
apply exponent rule: a^-b = 1 / a^b
1 / 10^(4)
10^4 = 10000
1 / 10000
Let me know if you have any questions !
AND WELCOME TO BRAINLY :)
Answer:
10^-4
Step-by-step explanation:
In division of powers (when the numbers are the same), you subtract both the powers. In this case, it would be 3 - 7 = -4, resulting in a power of -4
What are practical situations of geometric series.
Answer:
One of the practical situation of geometric series is : A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it’s height gets cut down by half. If the ball’s first height is 4 feet, the next time it bounces it’s highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing
Answer:
Geometric series are seen in practical situations, most notably in those involving geometric growth or decay. If a series of numbers are formed by percentages, then it can result in a geometric sequence. Ex. compound interest (see below).
Step-by-step explanation:
A geometric series is the result of adding the terms of a geometric sequence. These sequences have a common ratio, r, which is used to find missing terms. The common ratio is found with [tex]r=\frac{a_n}{a_{n-1}}[/tex]. For example, [tex]a_1(r)=a_2, \mbox{ and } a_2(r)=a_3... \mbox{ etc.}[/tex]
Geometric sequences can be used to model practical situations, and such situation could involve geometric growth or decay.
A geometric sequence can be used to model compound interest. An example of this is [tex]A = P (1 + \frac{r}{100})^n[/tex] where the common ratio, r, of the series is equal to 1 + r/100 in the compound interest formula above.
PLEASE I NEED THIS
determine the value of θ to the nearest degree
csc θ = 1.2711
the answer in my textbook is 52 degrees, but i've no idea how they got that.
p.s i need this asap - will give brainliest!!! thank u!!
Answer:
See below
Step-by-step explanation:
[tex]\csc\theta=1.2711\\\\\frac{1}{\csc\theta}=\frac{1}{1.2711}\\ \\\sin\theta=\frac{1}{1.2711}\\ \\\theta=\sin^{-1}(\frac{1}{1.2711})\\\\\theta\approx51.88^\circ\approx52^\circ[/tex]
Remember the identity [tex]\csc\theta=\frac{1}{\sin\theta}[/tex], so [tex]\sin\theta=\frac{1}{\csc\theta}[/tex] and it makes the problem easier. Just remember to take the inverse sine (let me know if you are not sure what that means).
The value of the θ in csc θ = 1.2711 is 51.88°.
What is trigonometric ratio?A trigonometric ratio is a ratio of the length of sides of a right-angle triangle. It relates the ratio of sides to the respective angle. The most common trigonometric ratios are sine, cosine, and tangent.
Given csc θ = 1.2711, we need to find the value of θ,
So, csc θ = 1.2711
θ = csc⁻¹(1.2711)
θ = 51.88°
Hence, the value of the θ in csc θ = 1.2711 is 51.88°.
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I NEED HELP ON THE ONES THAT AREN'T CROSSED OFF!!!!!!!!!!!!!!!!!!!!! PLEASEEEEEEEEEEEEEEEEEEEEE ( i already did 8)
The computation of the word problem shows that the oranges will John have in 12 weeks will be 70 oranges.
How to solve the word problem?The word problem will be that John has 10 oranges and buys 5 more oranges every week. How many oranges will John have in 12 weeks.
The computation will be:
= 10 + 5x
where x= number of weeks.
= 10 + 5x
= 10 + 5(12)
= 10 + 60
= 70 oranges
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Solve the system of equations graphically. Then classify
the system as consistent or inconsistent and the
equations as dependent or independent.
5x - y = 7
5x+6y= -7
Answer:
They are consistent and independent
Step-by-step explanation:
Consistency
If two lines have an intersection point, they are said to be consistent. For example, two parallel lines do not have an intersection and therefore they are inconsistent.
In the problem, the two lines intersect at (1, -2) so they have a unique solution and therefore consistent.
Dependency
Two lines are said to be independent if one of them cannot be written as an integer multiple of the other. Or, in other words, if the slope-intercept form of both equations have different slope and y intercept
Note: slope-intercept form of an equation is y = mx + c where m is the slope and c the y intercept
Line 1: 5x - y = 7 can be written as y = 5x - 7 which has slope +5 and y intercept -7
Line2 : 5x + 6y = -7 can be re-written as y = (-5/6)x - (7/6). This has slope -5/6 and y intercept -7/6
Since slope and intercepts of both lines are different they form a system of independent equations
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answer:
The number of walnut pounds we need to add is 10
Step-by-step explanation:
We need to make a mixture that costs $1 per pound.
That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.
[tex]\frac{MixtureCost}{NumberOfPounds} = 1[/tex]
Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.
[tex]MixtureCost = CashewsCost + WalnutsCost[/tex]
We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.
Knowing all of that, we can write this:
[tex]MixtureCost=8*1.25 + x*0.8[/tex]
If we make that multiplication, we have that
[tex]MixtureCost=10+x*0.8[/tex]
Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?
We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:
[tex]NumberOfPounds=8+x[/tex]
Now, if we plug in the values we found in the first equation, here's what we have:
[tex]\frac{10+x*0.8}{8+x}=1[/tex]
The 8+x is dividing, so i'll pass it to the other side multiplying:
[tex]10+0.8*x=x+8[/tex]
The 10 in the left side will go to the right side with a negative sign:
[tex]0.8x=x-2[/tex]
Now, if I pass the x from the right side to the left one changing signs:
[tex]0.8x-x=-2\\\\-0.2x=-2[/tex]
By changing signs from both sides, we have that:
[tex]0.2x = 2\\\\x = 10[/tex]
Therefore, the number of walnut pounds we need to add is 10
please help me with math i’d really appreciate it thank you
Answer:
Step-by-step explanation:
[tex]f(x) = \dfrac{2}{3}x-4\\[/tex]
When x = 0 ; f(x) = 0-4 = -4
When x = 3 ;
[tex]\sf f(3) =\dfrac{2}{3}*3-4\\\\ = 2-4\\\\ f(3) = -2[/tex]
When x = 6,
[tex]\sf f(6) = \dfrac{2}{3}*6-4\\\\ f(6) =2*2-4 = 4-4\\\\ f(6)= 0[/tex]
When x = -6;
[tex]\sf f(-6) =\dfrac{2}{3}*(-6)-4\\\\[/tex]
= 2*(-2)-4
= -4 - 4
f(-6) = -8
NEED HELP ASAP!!!!!!
You would like to estimate the proportion of all students in your school who have traveled to a foreign country. You poll a random sample of students and get a sample proportion of 0.18. Explain why the standard error of the sampling distribution of the sample proportion helps you gauge how close this sample proportion is to the unknown population proportion.
Answer:
I do not know. sorry I couldn't help
The class was divided into 4 teams. Each team had 5 players. The
remaining class members- Ty, Keesha, and Sam- served as score keepers.
How many students were in the class?
EASY QUESTIONS EASY POINTS!!
Answer:
23 players.
Step-by-step explanation:
5 x 4 + 3 = 23
What are the values of x and y?
Step-by-step explanation:
In figure:
∠PRT+∠RTP+∠TPR=180
O
(angle sum property of triangle)
⇒x+(180
O
−∠RTQ)+60
O
=180
O
(linear pair)
⇒x+(180
O
−97
0
)+60
o
=180
O
⇒x=31
o
Now, ∠PRT+∠TRQ+∠QRS=180
O
(angle of straight line)
⇒x+48
o
+y=180
O
⇒31
o
+48
o
+y=180
O
⇒y=101
0
Consider figures 1 through 4 on the coordinate plane.
The true statement about the coordinate plane is C. Figures 1 and 2 are not congruent because figure 1 cannot be mapped into figure 2.
What is a coordinate plane?A coordinate plane simply means a two dimensional plane that's is formed by the intersection of a vertical line.
In this case, the true statement about the coordinate plane is that Figures 1 and 2 are not congruent because figure 1 cannot be mapped into figure 2 using a sequence of rigid transformation.
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Gertrude climbs a 8-meter tower to ride a straight water slide. The
slide is 33 meters. After landing in the splash pool, how far does she
walk to get back to the base of the tower? Provide an answer accurate
to the nearest tenth.
33 m
8 m
walk
label required
Answer:
Hello,
11.2 is your answer!
Let's Beginnn.... READ EXPLANATION!!! ITS ALWAYS HELPS... TRUST MEEEEEEEEEEE!!!!
Step-by-step explanation:
Okay so this is clearly a pythagorean theorem question....
Imagine a ladder on a wall..... its kinda like a triangle.....
with that said... lets begin the math... A^2 + B^2 = C^2
The problem itself gives us c and a.
We have to solve for b.
33^2 - 8^2= b^2
1089 - 64 = 1025 = b^2
notice that we found b^2 but we are looking for b
so we have to take the square root....
√1025= 11.18
it says round to nearest tenth.... sooooo
11.2 is your answer!
Which function has zeros of -8, 1, and 3?
Answer:
A?
Step-by-step explanation:
(x-3) (x+8)(x-1) would be the solution
HELP PLS
The function of F is defined by f(x)=x+2
find F(n-4)
Answer:
Step-by-step explanation:
f(n - 4)= n - 4 + 2 = n - 2
Find the area of the figure. Round to the nearest hundredth where necessary.
24 m
28 m
Which is true about the line whose equation is y + 3 = 0?
The slope is 3.
The y-intercept is 3.
The slope is zero.
The value of x always equals the value of y.
Answer:
The slope is 0
Step-by-step explanation:
Solve the equation for y
y+3=0
y = -3
The slope intercept form is
y = mx+b
where m is the slope and b is the y intercept
y = 0x-3
The slope is 0 and the y intercept is -3
Answer: The Slope Is 3
Step-by-step explanation:
You are missing the x after the 3.
considering the linear equation y=mx+b, the coefficient of x is ALWAYS the slope (rate of change)
Work out 2/15 of 5 Give your answer as a fraction in its simplest form.
Answer:
2/3
Step-by-step explanation:
2/15 of 5
Of means multiply
2/15 * 5
Multiply the numerators
2*5 = 10
Put over the denominator
10/15
We can divide the top and bottom by 5
10/5 =2
15/5 =3
2/3
Answer:
Step-by-step explanation:
whats the mean and median of 13, 1, 17, 6, 2, 111, 3?
Answer:
111
Step-by-step explanation:
Martin has a bag of marbles. He removed 1 marble at random, recorded the color and then placed it back in the bag. He repeated this process several times and recorded his results in a table. Find the experimental probability of drawing green color.
Using it's concept, it is found that there is a 0.3 = 30% experimental probability of drawing green color.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that 15 out of 12 + 10 + 15 + 13 = 50 trials resulted in a green marble, hence the probability is given by:
p = 15/50 = 0.3.
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help me help me help me help me help me help me help me help me
Answer:
Hope it help
Step-by-step explanation:
1. B
2. A
3. C
4. C
5. D
Find the approximate values of the five-number summary for the data set represented by this box plot.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Answer:
Minimum: 0
Quartile Q1: 22.5
Median: 50
Quartile Q3: 77.5
Maximum: 100
Step-by-step explanation:
Joe thinks the area to be pantries on wall 2is 84 square feet.
Please put a picture next time :)
What is the perimeter of rhombus ABCD?
10 units
20 units
2√7 units
4√7 units
Answer:
The perimeter of the rhombus is 20 units
Step-by-step explanation:
One important fact about a rhombus is that all four of its sides are equal, so we only need to solve for one side in order to find the perimeter. We can use the Pythagorean Theorem to solve the side length of the rhombus. Using line AD as a reference, we know that the length of AD is the square root of the change in x squared plus the change in y squared, or [tex]\sqrt{3^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex] units. Multiply the length of AD by 4 and you'll get that the perimeter of rhombus ABCD is 5 × 4 = 20 un.
The perimeter of the rhombus ABCD is 20 units.
Option B is the correct answer.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add upto 180 degrees.
We have,
We can use the distance formula to find the length of each side of the rhombus, and then add them up to find the perimeter.
The distance between points A and B is:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\= \sqrt{(-2 - 1)^2 + (-3 - 1)^2}\\ = \sqrt{9 + 16}\\= \sqrt(25) \\= 5[/tex]
The distance between points B and C is:
[tex]BC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\= \sqrt{(-5 - (-2))^2 + (1 - (-3))^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\= 5[/tex]
The distance between points C and D is:
[tex]CD = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(-2 - (-5))^2 + (5 - 1)^2}\\ = \sqrt{9 + 16}\\ = \sqrt{25}\\ = 5[/tex]
The distance between points D and A is:
[tex]DA = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(1 - (-2))^2 + (1 - 5)^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\ = 5[/tex]
Since a rhombus has all sides of equal length, we can add up the lengths of the sides to find the perimeter:
P = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20
Therefore,
The perimeter of the rhombus ABCD is 20 units.
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A PACK OF TOILET PAPER WAS ORIGINALLY $4.50 , IT COST $6.75. DID THE PRICE INCREASE OR DECREASE?
PLEASE HELP ILL MARK BRAINLIEST kellys farm has 8 chickens for every 3 cows and 2 pigs for every 5 cows. if kellys farm has 30 pigs how many chickens are on the farm
Answer:
Step-by-step explanation:
) Evaluate
42+(9 divided by 3 x 2) - 4
Answer:
44
Step-by-step explanation:
Parenthesis
Exponents
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
42 + (9 ÷ 3 x 2) - 4 <== divide first (left to right)
42 + ((9 ÷ 3) x 2) - 4
42 + (3 x 2) - 4 <== multiply
42 + 6 - 4 <== add
48 - 4 <== subtract
44
Final answer: 44
Hope this helps!
i need help with 7th grade math please 30 points need help ASAP
Answer:
Area = 657 ft^2
Step-by-step explanation:
Heron's Formula: [tex]S=\frac{a+b+c}{2}[/tex] ,
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\frac{20+21+29}{2}=\frac{70}{2} =45 ft[/tex]
[tex]Area=\sqrt{45(45-20)(45-21)(45-29)}\\\\=\sqrt{45(25)(24)(16)}\\\\=\sqrt{432000}[/tex]
= 657.267069
Area = 657 ft^2
Answer:
210 ft²
Step-by-step explanation:
Take the base and height of the triangle.
Base = 21 ft.Height = 20 ft.Solving for area :
A = 1/2 x base x heightA = 1/2 x 21 x 20A = 10 x 21A = 210 ft²Having trouble with this, pretty sure the answers i have in there are wrong, please help. especially need help with the last question , thank you
The year in which the two quantities will be equal is 2133.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Here we have the following data.
y=0.221x-368.264 For men
y=0.168x-255.196 for women
So when we will equate these two equation we will get the year in which two quantities will be same.
0.221x-368.264=0.168x-255.196
0.221x-0.168x=368.264-255.196
0.053x = 1123.068
x= 2133 year
Hence the year in which the two quantities will be equal is 2133.
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