Isolate one radical on one side of the equation.Raise each side of the equation to a power equal to the index of the radical and simplify. Check all proposed solutions in the original equation.
Answers
The given equation is
[tex]\sqrt[]{3\text{ - 2x}}\text{ - 4x = 0}[/tex]The first step is to add 4x to both sides of the equation. We have
[tex]\begin{gathered} \sqrt[]{3\text{ - 2x}}\text{ - 4x + 4x = 0 + 4x} \\ \sqrt[]{3\text{ - 2x}}\text{ = 4x} \\ \text{Squaring both sides of the equation, we have} \\ (\sqrt[]{3-2x)}^2=(4x)^2 \\ 3-2x=16x^2 \end{gathered}[/tex]3 - 2x = 16x^2
Adding 2x to both sides of the equation, we have
3 - 2x + 2x = 16x^2 + 2x
3 = 16x^2 + 2x
Subtracting 3 from both sides of the equation, we have
3 - 3 = 16x^2 + 2x - 3
0 = 16x^2 + 2x - 3
16x^2 + 2x - 3 = 0
This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have
16x^2 + 8x - 6x - 3 = 0
By factorising, we have
8x(2x + 1) - 3(2x + 1) = 0
Since 2x + 1 is common, we have
(2x + 1)(8x - 3) = 0
2x + 1 = 0 or 8x - 3 = 0
2x = - 1 or 8x = 3
x = - 1/2 or x = 3/8
We would substitute these values in the original equation to check. We have
[tex]\begin{gathered} For\text{ x = }-\text{ }\frac{1}{2} \\ \sqrt[]{3\text{ - 2}\times-\frac{1}{2}}\text{ - 4}\times-\text{ }\frac{1}{2}\text{ = 0} \\ \sqrt[]{3\text{ - - 1}}\text{ + 2 = 0} \\ \sqrt[]{4}\text{ + 2 = 0} \\ 2\text{ + 2 }\ne0 \end{gathered}[/tex][tex]\begin{gathered} \text{For x = }\frac{3}{8} \\ \sqrt[]{3\text{ - 2}\times\frac{3}{8}}\text{ - 4}\times\frac{3}{8}\text{ = 0} \\ \sqrt[]{3\text{ - }\frac{3}{4}}\text{ - }\frac{3}{2}=\text{ 0} \\ \sqrt[]{\frac{9}{4}}\text{ - }\frac{3}{2}\text{ = 0} \\ \frac{3}{2}\text{ - }\frac{3}{2}\text{ = 0} \end{gathered}[/tex]The solution is x = 3/8
Related Questions
Please help I'm not sure what should I substitute the variable (x) by
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From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
Which number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
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∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
The vertex of the parabola below is at the point
Answers
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
How does g(t) = 4t change over the interval t = 3 to t = 4?
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Over the interval t = 3 to t = 4, g(t) increases.
The increasing factor (f) is computed as follows:
[tex]f=\frac{g(4)}{g(3)}[/tex]where g(4) is g(x) at t = 4, and g(3) is g(x) at t = 3. Substituting with the formula of g(t) and evaluating each expression, we get:
[tex]\begin{gathered} f=\frac{4^4}{4^3} \\ f=\frac{4\cdot4^3}{4^3} \\ f=4 \end{gathered}[/tex]Then, g(t) increases by a factor of 4
The volume of a square-based rectangular cardboard box needs to be at least 1000cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces. Assume that there will be no waste material. The Machinery available cannot fabricate material smaller than 2 cm in length.
Answers
We have to find the dimensions of a box with a volume that is at least 1000 cm³.
We have to find the dimensions that require the minimum amount of material.
We can draw the box as:
The volume can be expressed as:
[tex]V=L\cdot W\cdot H\ge1000cm^3[/tex]The material will be the sum of the areas:
[tex]A=2LW+2LH+2WH[/tex]Since the box is square-based, the width and length are equal and we can write:
[tex]L=W[/tex]Then, we can re-write the area as:
[tex]\begin{gathered} A=2L^2+2LH+2LH \\ A=2L^2+4LH \end{gathered}[/tex]Now, we have the area expressed in function of L and H.
We can use the volume equation to express the height H in function of L:
[tex]\begin{gathered} V=1000 \\ L\cdot W\cdot H=1000 \\ L^2\cdot H=1000 \\ H=\frac{1000}{L^2} \end{gathered}[/tex]We replace H in the expression for the area:
[tex]\begin{gathered} A=2L^2+4LH \\ A=2L^2+4L\cdot\frac{1000}{L^2} \\ A=2L^2+\frac{4000}{L} \end{gathered}[/tex]We can now optimize the area by differentiating A and then equal the result to 0:
[tex]\begin{gathered} \frac{dA}{dL}=2\frac{d(L^2)}{dL}+4000\cdot\frac{d(L^{-1})}{dL} \\ \frac{dA}{dL}=4L+4000(-1)L^{-2} \\ \frac{dA}{dL}=4L-\frac{4000}{L^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{dA}{dL}=0 \\ 4L-\frac{4000}{L^2}=0 \\ 4L=\frac{4000}{L^2} \\ L\cdot L^2=\frac{4000}{4} \\ L^3=1000 \\ L=\sqrt[3]{1000} \\ L=10 \end{gathered}[/tex]We now can calculate the other dimensions as:
[tex]W=L=10[/tex][tex]H=\frac{1000}{L^2}=\frac{1000}{10^2}=\frac{1000}{100}=10[/tex]Then, the dimensions that minimize the surface area for a fixed volume of 1000 cm³ is the length, width and height of 10 cm, which correspond to a cube (all 3 dimensions are the same).
Answer: the dimensions are length = 10 cm, width = 10 cm and height = 10 cm.
a rectangular prisim has a volume of 80cm cubed it has a length of 2cm and a width of 5cm. What is the prisms height?
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rectangular prism volume is ,
[tex]\begin{gathered} V=l\times b\times h \\ 80=2\times5\times h \\ h=\frac{80}{10} \\ h=8\text{ cm } \end{gathered}[/tex]The marching band director is standing on a platformoverlooking the band practice. The pit section is located 8feet from the base of the platform. If the angle ofdepression from the band director to the pit section is 67°find the height of the platform.
Answers
Through trigonometry, we calculated that the height of the platform is 18.8 feet.
The director of the marching band is observing the band practice from a platform. 8 feet separate the base of the platform from the pit area. If the pit section's angle of depression is 67 degrees from the band director,
The angle formed by the horizontal line and the item as seen from the horizontal line is known as the angle of depression. When the angles and the separation of an object from the ground are known, it is mostly used to calculate the distance between the two objects.
We have,
So, the Angle of Depression = [tex]\alpha[/tex] = 67
Let x be the height of the platform,
Tan [tex]\alpha = \frac{x}{8}[/tex]
[tex]Tan 67 = \frac{x}{8} \\\\2.35 =\frac{x}{8} \\x = 2.35 *8 = 18.8[/tex]
Hence, The height of the platform is 18.8 feet.
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Find x when the f(x) = 350 - 125x ; when f(x) = 0.
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ANSWER
x = 2.8
EXPLANATION
The function given is:
f(x) = 350 - 125x
We want to find the value of x when f(x) = 0.
This means that:
[tex]\begin{gathered} f(x)\text{ = 350 - 125x} \\ \Rightarrow\text{ 0 = 350 - 125x} \\ \Rightarrow\text{ 125x = 350} \\ \frac{125x}{125}\text{ = }\frac{350}{125} \\ x\text{ = 2.8} \end{gathered}[/tex]That is the value of x
RecoverySolve for x usingcross multiplication.2x + 132x11 -=x + 22x = [?]Enter
Answers
Answer:
x = 4
Step-by-step explanation:
Cross-multiplying means multiplying the numerator of one side by the denominator of the other side.
So, let's multiply the sides:
[tex]\begin{gathered} \frac{2x+1}{3}=\frac{x+2}{2} \\ 2\cdot(2x+1)=3\cdot(x+2) \end{gathered}[/tex]Now, we can solve each side:
[tex]\begin{gathered} 4x+2=3x+6 \\ 4x-3x=6-2 \\ 1x=4 \\ x=4 \end{gathered}[/tex]So, x = 4.
How are the strategies the same and how are they different
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Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
I need help answering the questions for person 2 on my group assignment
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The equation for the relation of sides of triangle can be obtained by similar triangle property.
Consider triangle ABC and triangle DBE.
[tex]\begin{gathered} \angle CAB=\angle EDA\text{ (Each angle is right angle)} \\ \angle CBA=\angle EBD\text{ (common angle)} \\ \Delta CBA\cong\Delta EBD\text{ (By AA similarity condition)} \end{gathered}[/tex]Determine the ratio of corresponding sides of simillar triangle.
[tex]\frac{CB}{EB}=\frac{BA}{BD}=\frac{CA}{ED}[/tex]Thus similar triangle property is used to set up the equation.
use the half angle identity to find the exact value of the trigonomic expression. given 0
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Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
For what values of a are the following expressions true?/a+5/=-5-a
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Explanation:
The expression is given below as
[tex]|a+5|=-5-a[/tex]Concept:
We will apply the bsolute rule below
[tex]\begin{gathered} if|u|=a,a>0 \\ then,u=a,u=-a \end{gathered}[/tex]By applying the concept, we will have
[tex]\begin{gathered} \lvert a+5\rvert=-5-a \\ a+5=-5-a,a+5=5+a \\ a+a=-5-5,a-a=5-5 \\ 2a=-10,0=0 \\ \frac{2a}{2}=\frac{-10}{2},0=0 \\ a=-5,0=0 \end{gathered}[/tex]Hence,
The final answer is
[tex]a\leq-5[/tex]In boot camp, a cadet must use a rope swing to cross an obstacle withoutfalling into the water hazard below. Unfortunately, they miss the platform onthe other side and swing back to where they started. If it takes the cadet 3.5seconds to swing from one side of the obstacle to the other and back, howlong is the rope swing? Use the formula:
Answers
Answer:
Choice C: 3.0 m
Explanation:
We are basically asked to solve for L using
help me solve the volume of the cylinder? 20 ft x 17 ft
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Remember that the formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
• r, is the ,radius, of the base
,• h ,is the height of the cylinder
Notice that the base has a diameter of 20 ft. Therefore, the radius is 10 ft.
Using this data and the formula, we get that:
[tex]\begin{gathered} V=\pi(10^2)(17) \\ \rightarrow V=5340.71 \end{gathered}[/tex]The volume of the cylinder is:
[tex]2540.71ft^3[/tex]find the percent notation 7/10
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A notation is a way of communicating through symbols or signs, or it might be a brief written message. A chemist notating AuBr for gold bromide is an illustration of a notation. A quick list of things to accomplish is an illustration of a notation.
Explain about the percent notation?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
When expressing a fraction as a percentage, we multiply the provided fraction by 100.7/10, which is 70%.
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Rierda Elwynn Garvey takes home $1250 each month. In addition to other expenses, she also makepayments to her debt of $230 per month. What is her Debt Payments to Income Ratio?
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The debt payments to income ratio is the amount that Rierda spend paying her debt each mount divided by her monthly income:
[tex]\text{Ratio}=\frac{230}{1250}=\frac{23}{125}=0.184[/tex]Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
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Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these
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Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.
Given the triangles ADH and ECK,
We know that
[tex]\angle ADH\cong\angle ECK[/tex]That is, the angle at D is congruent to the angle at C in the respective triangles.
In this case, we can think of the congruency between the triangles in the following diagram:
Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.
This means that opposite sides are parallel and have the same measure (length).
The opposite sides are AD and CB and DC and AB.
In this case, we find that only AD and CB are an option to this question, therefore the correct answer.
In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.
AE isn't a segment drawn and hence not parallel to any other segment.
The correct answer is the option A).
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
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From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
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The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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how would u decide if 3/5 or 59% is greater?
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SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]if a ray QT bisects
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EXPLANATION
If a ray QT bisects
(3x - 5) + (x+1) = 180 [By the Linear Pair Theorem]
Removing the parentheses:
3x - 5 + x + 1 = 180
Grouping like terms:
3x + x + 1 - 5 = 180
Adding like terms:
4x -4 = 180
Adding +4 to both sides:
4x = 180 + 4
Adding numbers:
4x = 184
Dividing both sides by 4:
x = 184/4
Simplifying:
x=46
Now, we need to compute the resulting angles:
m m
As QT bisects
47/2 = 23.5 degrees
The answer is 23.5°
Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
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The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Answers
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
0.0032% in fraction
Answers
Recall that the x% in fraction form is:
[tex]\frac{x}{100}\text{.}[/tex]Therefore 0.0032% as a fraction is:
[tex]\frac{0.0032}{100}=\frac{\frac{32}{10000}}{100}\text{.}[/tex]Simplifying the above result we get:
[tex]\frac{\frac{32}{10000}}{100}=\frac{32}{100\times10000}=\frac{1}{31250}\text{.}[/tex]Answer:
[tex]\frac{1}{31250}[/tex]A tree casts you say shadow that is 9 feet long at the same time a person standing nearby casts a shadow that is 3 feet long if the person is five point feet tall how tall is the tree
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we have that
Applying proportion
x/9=5.5/3
solve for x
x=9*(5.5/3)
x=16.5 ft
therefore
the answer is 16.5 ftwhat is the value of the q that makes the equation true? 3(q+4)-10q=2q+3
Answers
Distribute:
3q + 12 - 10q = 2q + 3
Combine like terms:
-7q + 12 = 2q + 3
Inverse operation (subtract 3 on both sides):
-7q + 9 = 2q
Inverse operation; Add -7q on both sides:
9 = 9q
Solve: Divide 9 on both sides to single out the variable
[ q=1 ]
slope= 2; point on the line (-2,1) in slope intercept form I know y=m*x+b but all I know is 2 would be m
Answers
y=2x+5
1) Since we were told the slope is m=2, one point on the line (-2,1), and the slope-intercept form is:
[tex]y=mx+b[/tex]2) The next step is to find the value of "b", the y-intercept. So, let's pick that point, the slope, and plug them into the Slope-Intercept form:
[tex]\begin{gathered} y=mx+b,m=2,(-2,1) \\ 1=2(-2)+b \\ 1=-4+b \\ 1+4=b \\ b=5 \end{gathered}[/tex]3) Now that we know the y-intercept (b), we can write the function's rule as
[tex]y=2x+5[/tex]Determine the vertex and the axis of symmetry based on the equation, y =-12 -8x - 36
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Solution
Determine the vertex and the axis of symmetry based on the equation:
[tex]y=-x^2-8x-36[/tex]Therefore the correct answer is Option A