Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
Answers
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Related Questions
(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
Answers
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
Subtract and simplify the answer. 8/9 - 1/3
Answers
Solution
We want to simplify
[tex]\frac{8}{9}-\frac{1}{3}[/tex]Now
[tex]\begin{gathered} \frac{8}{9}-\frac{1}{3}=\frac{8}{9}-\frac{1\times3}{3\times3} \\ \frac{8}{9}-\frac{1}{3}=\frac{8}{9}-\frac{3}{9} \\ \frac{8}{9}-\frac{1}{3}=\frac{8-3}{9} \\ \frac{8}{9}-\frac{1}{3}=\frac{5}{9} \end{gathered}[/tex]Therefore, the answer is
[tex]\frac{5}{9}[/tex]Solve radical∛x²-8=4
Answers
Let's determine the value of x on the given radical expression:
[tex]\text{ }\sqrt[3]{x^2-8}\text{ = 4}[/tex]use a sum or difference identity to find the exact value of :
Answers
Using the rule
[tex]\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex][tex]\begin{gathered} \sin (225+60)=\sin 225\cos 60+\cos 225\sin 60 \\ \end{gathered}[/tex]Sine is negative in the third quadrant therefore,
[tex]\begin{gathered} -(\sin 45)\cos 60+\cos 225\sin 60 \\ \sin \text{ 45=}\frac{\sqrt[]{2}}{2}\text{ then the negative sign} \\ -\frac{\sqrt[]{2}}{2} \\ -\frac{\sqrt[]{2}}{2}\cos 60+\cos 225\sin 60 \\ \cos \text{ 60=}\frac{1}{2} \\ -\frac{\sqrt[]{2}}{2}(\frac{1}{2})+\cos 225\sin 60 \end{gathered}[/tex]Let us find the other side
[tex]\begin{gathered} \cos \text{ 45=}\frac{\sqrt[]{2}}{2} \\ cos\text{ is negative in the third quadrant } \\ -\frac{\sqrt[]{2}}{2} \\ \sin \text{ 60=}\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Bring everything together
[tex]\begin{gathered} -\frac{\sqrt[]{2}}{2}(\frac{1}{2})-\frac{\sqrt[]{2}}{2}(\frac{\sqrt[]{3}}{2}) \\ -\frac{\sqrt[]{2}}{4}-\frac{\sqrt[]{6}}{4}=\frac{-\sqrt[]{2}-\sqrt[]{6}}{4}=-0.965925826\ldots... \end{gathered}[/tex]You are trying to help a friend calculate their utilization rate for their study time. They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems. What is their utilization rate (in %)? Calculate as a percentage (thus .05 would be entered as 5)
Answers
The utilization rate of friends' study time is 33%
In this question, we need to find the utilization rate for friends' study time.
They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems.
We know that the formula for the utilization rate:
Utilization % = Actual Number of Hours Worked / the Total Available Hours.
So the utilization rate would be,
r = 20/60
r = 0.33
r = 0.33 × 100
r = 33%
Therefore, the utilization rate of friends' study time is 33%
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find the function domain and range and the slope of the graph
Answers
The line end points are (4,3) and (-5,-2).
The value of x coordinates give the domain and values of y coordinates give the range.
Since point (4,3) lies on the line and point (-5,-2) does not lie on ther line.
Domain is,
[tex](-5,4\rbrack[/tex]Range is,
[tex](-2,3\rbrack[/tex]Determine the slope of line.
[tex]\begin{gathered} m=\frac{3-(-2)}{4-(-5)} \\ =\frac{5}{9} \end{gathered}[/tex]So slope is 5/9.
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answers
The derivative of the function f(x) = -5x²+3x-2 is -10x+3.
Given the function is f(x) = -5x²+3x-2
Differentiate with respect to x.
d/dx -5x²+3x-2 = d/dx (-5x²) + d/dx(3x) - d/dx(2)
using the power rule d/dx [xⁿ] = nxⁿ⁻¹
⇒ d/dx -5x²+3x-2 = -5(2)x²⁻¹ + 3(1) - 0
⇒ d/dx -5x²+3x-2 = -10x+3
The power rule states that the derivative of xn is nx(n-1) for every x if n is a positive integer, regardless of whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).
Hence we get the derivative as -10x+3.
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Based on the two data sets represented below, complete the following sentences.Options: "greater" or "less"
Answers
We can check that the median of the dataset T is 14, and its mean is also close to 14, while the median of the dataset U is 17 and its mean is close also close to 17. We can also check that the range of the dataset T is 14 and the data is more concentrated at its center, while the range of the dataset U is 20 and the data is more dispersed.
Therefore, we can state that The center of Data Set T is less than the center of Data Set U, and the spread of Data Set T is less than the spread of Data Set U.
Find the rate of change of the line represented by the table.
Answers
Slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replacing:
[tex]m=\text{ }\frac{4-6}{3-3}=-\frac{2}{0}=\text{ undefined}[/tex]since x is constant , it is a vertical line, with an undefined slope.
Arc Length Formula:: Cx = degree measure of arcC-circumferenceDirections: Find each arc length. Round to the nearest hundredth.10. If EB = 15 cm, find the length of CD. 11. IF NR = 8 ft, find the length of NMP.DC12. IF VS = 12 m, find the length of UT.13. If JH = 21 in, fnd the length of KJG.12759DBS14. If FG = 27 yd, find the length of FED.15. If WS = 4.5 mm, find the length of TS.4780128317.62
Answers
Arc length formula:
[tex]\begin{gathered} \text{Arc length=}\frac{x}{360}\cdot C \\ \\ C=2\pi r \\ r=\text{radius} \end{gathered}[/tex]____________________________
10. r= 15cm
Angle CED is supplementary with angle BEC (add up to 180°)
[tex]\begin{gathered} m\angle\text{CED}+m\angle\text{BEC}=180 \\ \\ m\angle CED=180-m\angle BEC \\ m\angle CED=180-68 \\ m\angle CED=112 \end{gathered}[/tex]Then, arc CD is:
[tex]\begin{gathered} CD=\frac{112}{360}\cdot2\pi(15\operatorname{cm}) \\ \\ CD\approx29.32\operatorname{cm} \end{gathered}[/tex]___________________________________________________
11. r=8ft
The measure of central angle MRQ is equal to the measure of the given arc MQ (162°) and this angle and angle NRP are vertical angles (have the same measure) then, angle MRN and QRP (also vertical angles) need to add up 360° with the other angles, use it to find the measure of angle MRN:
[tex]\begin{gathered} m\angle NRP+m\angle NRP+m\angle MRN+m\angle QRP=360 \\ \\ 2m\angle NRP+2m\angle MRN=360 \\ 2(162)+2m\angle MRN=360 \\ 324+2m\angle MRN=360 \\ 2m\angle MRN=360-324 \\ m\angle MRN=\frac{36}{2} \\ \\ m\angle MRN=18 \end{gathered}[/tex]The angle for arc NMP is equal to the sum of angle MRP (180°) and angle MRN (18°).
Then, the length of arc NMP is:
[tex]\begin{gathered} \text{NMP}=\frac{180+18}{360}\cdot2\pi(8ft) \\ \\ \text{NMP}=27.65ft \end{gathered}[/tex]___________________________
evaluate each limit. this is in the topic of jump discontinuities.
Answers
we have
[tex]\begin{gathered} \lim _{x\to-2}-x^2-4x-5 \\ \lim _{x\to-2}-(-2)^2-4(-2)-5 \\ \lim _{x\to-2}-4^{}+8-5 \\ \lim _{x\to-2}--1 \end{gathered}[/tex][tex]\lim _{x\to-2}-1=-1[/tex]therefore
the answer is -1hey there ms or mr could you help me out with this problem please?
Answers
Similar figures have corresponding sides that are proportional.
We can set up a ratio where we are putting corresponding sides of each triangle, cross mutliply, and solve for the unknow.
Looking at answer choices:
A)
if we have x and 24 to one side, we need corresponding pair from right hand side triangle, which should be 15 and 9. But the ratio is 9 over 15. So, this isn't right.
B)
If 24 is paired with 9 [corresponding side of each triangle], then we need same correspondence.
But we have 15 and x, which is opposite of what we want. So, this isn't right.
C)
32 goes with x and 12 goes with 15. They are indeed in correspondence to each other.
This ratio is correct.
We can say Option C is the correct answwer.
Aaron took out a 30-year mortgage for $70,000. His monthly mortgage payment is $466. How much will he pay over 30 years? Interest rate = 7%
Answers
Answer:
[tex]\text{ \$167,760}[/tex]Explanation:
Here, we want to get how much will be ppaid over the course of 30 years
From the question, we have it that he pays $466 monthly
Now, to get the amount he will pay over the course of the years, we have to understand that there are 12 months in a year
The total number of months for which he will be paying will be:
[tex]30\times\text{ 12 = 360}[/tex]He will be paying $466 per month for a total of 360 months
So, the total amount he is to pay is the product of this two
Mathematically, that would be:
[tex]360\times466\text{ = 167,760}[/tex]5. Infer from the problem: What is the y-intercept of the line y=3x-5 ?
Answers
the given expression is
y = 3x - 5
y +5 = 3x
y - (-5) = 3(x - 0)
so the y-intercept is -5.
PLEASE HURRY!!!!!
Here is a hanger diagram. With a hanger diagram, when the diagram is balanced, there is equal weight on each side. Write an equation to represent the hanger. (Do NOT put spaces in your answer.)
Answers
Answer:
x = 8
x = 3
x = 2
x = 1
x = 1
x = 2
x + x+ x+ x+ x+ 2 = 17
try any number
what kind of triangle congruence would i put for the last reason?
Answers
Looking at the diagram, The last statement means that trangle PQS is congruent to triangle RSQ. This means that
line PQ is equal to line RS
line QS is equal to line SQ
angle Q is equal to angle S
Thus, the reason would be
Side Angle Side(SAS)
Two sides and one angle are equal or congruent
INT ALGEBRAL: 1. Write an equation that passes through (0,5) and is parallel to 3x+5y=6
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
Answers
The equation of the parallel line is y = -3/5x + 5
How to determine the line equation?The equation is given as
3x + 5y = 6
The point is also given as
Point = (0, 5)
The equation of a line can be represented as
y = mx + c
Where
Slope = m and c represents the y-intercept
So, we have
3x + 5y = 6
This gives
5y = -3x + 6
Divide
y = -3/5x + 6/5
By comparing the equations y = mx + c and y = -3/5x + 6/5, we have the following
m = -3/5
This means that the slope of y = -3/5x + 6/5 is -3/5
So, we have
m = -3/5
The slopes of parallel lines are equal
This means that the slope of the other line is -3/5
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -3/5
(x₁, y₁) = (0, 5)
So, we have
y = -3/5(x + 0) + 5
Open the brackets and evaluate
y = -3/5x + 5
Hence, the parallel line has an equation of y = -3/5x + 5
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I have a question so yall can get points so Whats 1+1
Answers
answer needs at least 20 characters so here's ur answer 2
Step-by-step explanation:
thank u
Answer: 2
1 + 1 = 2
lol thanks for the points
What is the value of an edge length of the larger prism in centimeterMecand vou answer and now in the bubbles on your answer document. Be sure to use thecorect place value
Answers
Ok, we have here two similar prisms, which means that the length of every sides of one prism is proportional to the correspondent side of the other prism.
From this, we have the following relation: (7/2.8) = (x/11.2)
Multiplying both sides by 11.2, we got: x = (11.2*7)/2.8 = 28 cm.
f A and B are independent events with P(A)=0.3 and P(B)=0.7, find P(A AND B). Provide your answer below:
Answers
If A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
A and B are independent events
Independent events are events that does not depends on any other events.
Probability is the ratio of number of favorable outcomes to the total number of outcomes
The value of P(A) = 0.3
The value of P(B) = 0.7
If A and B are independent events, then P(A AND B) = P(A) × P(B)
Substitute the values in the equation
P(A AND B) = 0.3 × 0.7
= 0.21
Hence, if A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
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Please help. I've been trying to answer this question but I haven't been successful.
Answers
Equations
It's required to find the value of x that satisfies the conditions of the figure.
We have an equilateral triangle. We know it's equilateral because all of its interior angles have the same measure (look at the tick mark on each angle).
Recall the sum of the interior angles of any triangle is 180°.
If all the interior angles have the same measure, then each angle measures 180/3 = 60°.
One of the angles is assigned an expression of x. We can equate it to 60:
5x - 18 = 60
Adding 18:
5x = 78
Dividing by 5:
x = 78/5
x = 15.6
Answer: I do believe the answer is 15.6. Hope this helps! ^w^
There are 120 teachers. Select a sample of 40 teachers by using the systematic sampling technique.
Answers
Given:
Total number of teachers = 120
To select a number of teachers = 40
Required:
To find a sample of 40 teachers by using the systematic sampling technique.
Explanation:
The probability formula is given as:
[tex]\begin{gathered} P=\frac{number\text{ of favourable outcomes}}{Total\text{ number of outcomes}} \\ P=\frac{40}{120} \\ P=\frac{1}{3} \end{gathered}[/tex]Final Answer:
[tex]undefined[/tex]Which of these shows the result of using the first equation to substitute for y?
Answers
D) 9x=18
Explanationgiven
[tex]\begin{gathered} y=3x\Rightarrow equation(1) \\ 3x+2y=18\Rightarrow equation(2) \end{gathered}[/tex]Step 1
substitute the y value from equation (1) into equation(2)
so
[tex]\begin{gathered} 3x+2y=18\operatorname{\Rightarrow}equat\imaginaryI on(2) \\ replace \\ 3x+2(3x)=18 \\ 3x+6x=18 \\ add\text{ like terms } \\ 9x=18 \end{gathered}[/tex]therefore, the answer is
D) 9x=18
I hope this helps you
A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 9 ft from the side of the house. Find thelength of the ladder. If necessary, round your answer to the nearest tenth.х5?9ExplanationCheck
Answers
Given:
Distance of top of ladder to the ground = 10 ft
Distance of bottom of ladder from the side of the house = 9 ft
Let's find the length of the ladder.
Since the ladder forms a right triangle with the house, to find the length of the ladder apply Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]Where:
a = 10 ft
b = 9 ft
c = length of ladder
Thus, we have:
[tex]\begin{gathered} c^2=10^2+9^2 \\ \\ c^2=100+81 \\ \\ c^2=181 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{181} \\ \\ c=13.5 \end{gathered}[/tex]Therefore, the length of the ladder rounded to the nearest tenth is 13.5 ft
ANSWER:
13.5 ft
simplify 425xy⁴/25xy²
Answers
We have the expression
[tex]\frac{425xy^4}{25xy^2}[/tex]We can already simplify x because it's both on the numerator and denominator
[tex]\frac{425y^4}{25y^2}[/tex]Now we can simplify 425/25 = 17
[tex]\frac{17y^4}{y^2}[/tex]Remember that
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]Then
[tex]17y^{4-2}=17y^2[/tex]The final result is
[tex]17y^2[/tex]Find the equation of the line though the point (-3, -2) and perpendicular to the line y = 2/3x-2.Write your answer in the form y=mx+b.
Answers
For this question we know that we have a point (-3,-2) and we want to find an equation perpendicular to the line
y=2/3x-2.
Since both lines are perpendicular we need to satisfy this:
[tex]m_1\cdot m_2=-1[/tex]With m1= 2/3. If we solve for m2 we got:
[tex]m_2=\frac{-1}{m_1}=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}[/tex]And then we can find the intercept for the new line using the point given with x=-3 and y=-2 and we got this:
[tex]-2=-\frac{3}{2}(-3)+b[/tex]And solving for b we got:
[tex]b=-\frac{9}{2}-2=-\frac{13}{2}[/tex]And then our final answer would be:
[tex]y=-\frac{3}{2}x-\frac{13}{2}[/tex]HELP I JUST WANT TO FINISH GET MY CREDIT AND GRADUATE 70 POINTS HELP ASAP What are the values of x and y in the matrix subtraction below? [[- 20, 16], [4, 0], [9, - 6]] - [[- 5, 1], [- 6, 7], [0, 11]] = [[x, y], [10, - 7], [9, - 17]]
Answers
SOLUTION
We want to solve the question below
We can see that a matrix was subtracted from another. In Addition or subtraction of matrix, we just add or subtract the element. So
We have in the first row
[tex]\begin{gathered} -20-(-5)=x \\ -20+5=x_ \\ x=-15 \end{gathered}[/tex]And
[tex]\begin{gathered} 16-1=y \\ 15=y \\ y=15 \end{gathered}[/tex]Hence x = -15 and y = 15, the first option is correct
Select the correct answer.
What is the approximate value of this logarithmic expression?
log5 18
Answers
The logarithms as a sum or difference of logarithms, using the power rule if necessary, to expand them.
The approximate value exists [tex]$\log _5 18 \approx 1.80$[/tex].
What is meant by logarithmic expression?An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Write logarithms as a sum or difference of logarithms, using the power rule if necessary, to expand them. Utilizing the quotient rule, product rule, and power rule in that order is frequently beneficial.
The change of base formula can be used.
[tex]$\log _5(18)=\frac{\log 18}{\log 5} \approx \frac{1.25527}{0.69897} \approx 1.7959$$[/tex]
simplifying the above equation, we get
[tex]$\log _5 18 \approx 1.80$[/tex]
Therefore, the correct answer is option B. 1.80.
The complete question is:
Select the correct answer.
What is the approximate value of this logarithmic expression? [tex]$\log _5 18$[/tex]
A. 1.28
B. 1.80
C. 0.56
D. 2.89
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Rewrite the expression by factoring out (y+4).3(y + 4)+7y(y+4)
Answers
Given-:
Function is:
[tex]3(y+4)+7y(y+4)[/tex]Find-:
Expression by factoring
Explanation-:
Factoring the function is:
[tex]\begin{gathered} =3(y+4)+7y(y+4) \\ \\ =(y+4)(3+7y) \end{gathered}[/tex]Factoring is:
[tex]=(y+4)(3+7y)[/tex]Use the Distributive Property to rewrite each product below. Simplify your answer.
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
Answers
As per the concept of distributive property, the values of
A.) 28 · 63 = 1768
B.) 17 (59) = 1003
C.) 458 (15) = 6870
Distributive property:
Distributive property states that, " multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together."
It can be written as expression like the following,
A( B + C) = AB + AC
Given,
Here we have the expressions,
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
Now, we have to find the solution for this by using the distributive property.
Now, we have to expand the given expressions by using the distributive property then we get,
A) 28. ( 60 + 3) = (28 x 63) + (28 x 3)
=> 1680 + 84
=> 1768
Similarly, we have simplify the next expression as,
B) 17 (59) = 17 x (50 + 9)
As per the distributive property,
17 x (50 + 9) = (17 x 50) + (17 x 9)
=> 850 + 153
=> 1003
Finally, applying the distributive law, we get,
C) 458 (15) = (450 + 8) x 15
=> (450 x 15) + (8 x 15)
=> 6750 + 120
=> 6870
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