Answers
We must solve the following equation for x:
[tex]x+3=\sqrt{3-x}[/tex]We can square both sides of the equation so we can get rid of the radical:
[tex]\begin{gathered} (x+3)^2=(\sqrt{3-x})^2 \\ (x+3)^2=3-x \end{gathered}[/tex]We expand the squared binomial on the left:
[tex]\begin{gathered} (x+3)^2=x^2+6x+9=3-x \\ x^2+6x+9=3-x \end{gathered}[/tex]Then we substract (3-x) from both sides:
[tex]\begin{gathered} x^2+6x+9-(3-x)=x-3-(3-x) \\ x^2+6x+9+x-3=0 \\ x^2+7x+6=0 \end{gathered}[/tex]Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our case a=1, b=7 and c=6 so we get:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot6}}{2\cdot1}=\frac{-7\pm\sqrt{49-24}}{2}=\frac{-7\pm\sqrt{25}}{2}=\frac{-7\pm5}{2} \\ x=\frac{-7+5}{2}=-1\text{ and }x=\frac{-7-5}{2}=-6 \end{gathered}[/tex]So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:
[tex]\sqrt{3-x}[/tex]Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:
[tex]x+3\ge0\rightarrow x\ge-3[/tex]From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.
AnswerThen the answer is option A.
Related Questions
Write the Distance Formula
Replace c with d to write the distance formula. Use the Distance Formula to Find the Distance Between Two Points
Find the distance, d, between G and H using the distance formula.
The distance between any two points (x1,y₁) and (x2,y2) on a
coordinate plane can be found by using the distance formula. Let (x,y)= (-2,1) and (x2,y2) =(4,-3). Substitute these values into the
distance formula and evaluate.
Answers
The distance between the two points is [tex]2\sqrt{13} units[/tex]
What is distance formula?
Distance formula is the measurement of distance between 2 points. It calculates the straight line distance between the given points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex] Where A(a, b) B(c, d) Are the coordinates.
We are given the coordinates as (-2, 1) and (4, -3)
We substitute the values in the distance formula we get
[tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} } \\distance=\sqrt{(4+2)^{2} +(-3-1)^{2} }\\ distance=\sqrt{36+16 } \\distance=\sqrt{52 } \\distance =2\sqrt{13}[/tex]
Hence the distance between two points is [tex]2\sqrt{13} units[/tex]
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Hello! I need some guidance please. Having trouble with which graph is correct
Answers
Given:
[tex]y\ge3x+3[/tex]Required:
to show which graph is correct for the inequality.
Explanation:
Given graph is correct for the equation.
Required answer:
The given graph is correct.
find the lowest common denominator of - not graded !
Answers
Given:
There are two equation given in the question.
Required:
We have to find the lowest common denominator of both equation.
Explanation:
[tex]\frac{p+3}{p^2+7p+10}and\frac{p+5}{p^2+5p+6}[/tex]are given equations
first of all we need to factorization both denominator
[tex]\begin{gathered} p^2+7p+10and\text{ }p^2+5p+6 \\ (p+5)(p+2)and\text{ \lparen p+3\rparen\lparen p+2\rparen} \end{gathered}[/tex]so here (p+2) is common in both so take (p+2) for one time only
so now the lowest common denominator is
[tex](p+5)(p+2)(p+3)[/tex]Final answer:
The lowest common denominator for given two equations is
[tex](p+5)(p+2)(p+3)[/tex]
Find the lateral area of the cylinder .The lateral area of the given cylinder is _ M2(Round to the nearest whole number as needed .)
Answers
The lateral area of a cylinder is:
[tex]LA=2\pi rh[/tex]r is the radius
h is the height
For the given cylinder:
As the diameter is 4m, the radius is half of the diameter:
[tex]r=\frac{4m}{2}=2m[/tex]h=12m
[tex]\begin{gathered} SA=2\pi(2m)(12m) \\ SA=48\pi m^2 \\ SA\approx151m^2 \end{gathered}[/tex]Then, the lateral area of the given cylinder is 151 square metersPreston drove to his new college and then back home.Round trip he traveled 642 miles. Preston drives aHonda Civic and gets 38 miles for every gallon of gas. IfPreston needs to make 15 round trips a year how muchwill it cost him in gas assuming the price of gas stays at$2.48 a gallon for all his trips?$Round all answers to the nearest hundredthsDo not put a label, just the numeric value
Answers
1) Gathering the data
Preston
642 miles
38 miles/gallon
15 round trips
1 gallon = $2.48
2) Considering that each round trip consists of 642 miles
So Preston in 15 roundtrips is going to make
15 x 642 miles =9,630 miles
His car gets 38 miles per gallon. So we can write a proportion for that:
38 miles ---------1 gallon
9,630 miles ----- x
Cross multiplying it:
38x = 9,630 Divide by 38
x =9630/38
x=253.42 gallons
Finally, let's set another proportion to find out the cost of it
1 gallon -------------- $2.48
253.42 -------------- y
y= 253.42 x 2.48
y=628.4816
3) Rounding off to the nearest hundredth
$628. 48 That's how much Preston will spend.
Write the first six terms of each arithmetic sequence,Please see the photo
Answers
Answer: - 9, - 3, 3, 9, 15, 21
Explanation:
The given formula is
an = a(n - 1) + 6
a1 = - 9
where
n, n - 1 and 1 are subscripts
This is a recursive formula. Each term is defined with respect to the term before it.
From the information given,
first term = a1 = - 9
Second term = a2 = a(2 - 1) + 6 = a1 + 6 = - 9 + 6
a2 = - 3
Third term = a3 = a(3 - 1) + 6 = a2 + 6 = - 3 + 6
a3 = 3
Fourth term = a4 = a(4 - 1) + 6 = a3 + 6 = 3 + 6
a4 = 9
Fifth term = a5 = a(5 - 1) + 6 = a4 + 6 = 9 + 6
a5 = 15
Sixth term = a6 = a(6 - 1) + 6 = a5 + 6 = 15 + 6
a6 = 21
Thus, the first six terms are
- 9, - 3, 3, 9, 15, 21
In solving for the inverse function for y = sqrt(3x + 2) - 1 , which of the following represents the first step?
Answers
we know that
The first step to find out the inverse of the function is to exchange the variables (x for y and y for x)
therefore
the answer is the second optionFind the greatest common factor of the following monomials. 28g^5h^2 12g^6h^5
Answers
The GCF of these monomials i.e, 28g^5h^2 and 12g^6h^5 is 4h^2g^5
What is monomials?
Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.
First take the coefficient ie, 28 and 12 to find the GCF
The GCF of 28 and 12 is 4
Now, find out the GCF of the variables for that you take the lowest exponent from both the variables g and h
for g variable it will be g^5 and,
for h variable it will be h^2
Therefore, the GCF of these monomials is 4h^2g^5
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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment n=10, p=0.2, x=2
Answers
The binomial probability of x successes is 0.302.
How to calculate the probability of x successes?Since we are dealing with a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Given: n=10, p=0.2, x=2
The failures can be calculated using q = 1 - p = 1 - 0.2 = 0.8
P(x = 2) = 10C2 x 0.2² x 0.8¹⁰⁻²
= 10!/(10-2)! 2! x 0.2² x 0.8⁸
= 10!/(8!2!) x 0.2² x 0.8^8
= 10x9x8!/(8!2!) x 0.2² x 0.8⁸
= 45 x 0.2² x 0.8⁸
= 0.302
Therefore, the probability of x successes in 10 trials is 0.302
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vertical anges are always equal to each other
Answers
Given the statement:
Vertical angles are always equal to each other
The answer is: True
Because they are inclosed by the same lines
95-a(b+c) when a= 9, b = 3 and c=7.4 I don’t get how to solve this please put an explanation
Answers
Notice that in the statement of the exercise are the values of a, b and c. Then, to evaluate the given expression, we replace the given values of a, b, and c. So, we have:
[tex]\begin{gathered} a=9 \\ b=3 \\ c=7.4 \\ 95-a\mleft(b+c\mright) \\ \text{ We replace the given values} \\ 95-a(b+c)=95-9(3+7.4) \\ 95-a(b+c)=95-9(10.4) \\ 95-a(b+c)=95-93.6 \\ 95-a(b+c)=\boldsymbol{1.4} \end{gathered}[/tex]Therefore, the result of evaluating the given expression when a = 9, b = 3, and c = 7.4 is 1.4.
What is the value of sinθ given that (3, −7) is a point on the terminal side of θ?
Answers
Solution
[tex]\begin{gathered} \text{ using pythagoras theorem} \\ \\ OB=\sqrt{OA^2+AB^2}=\sqrt{3^2+7^2}=\sqrt{58} \\ \\ \Rightarrow\sin\theta=\frac{AB}{OB}=-\frac{7}{\sqrt{58}}=-\frac{7\sqrt{58}}{58} \end{gathered}[/tex]0> -2x^2+4x+4Solve each inequality by graphing. Sketch it.
Answers
To solve the inequality we need to find the x-values that are the roots of the quadratic equation, let's use the quadratic formula:
[tex]\begin{gathered} \text{For an equation in the form:} \\ ax^2+bx+c=0 \\ The\text{ quadratic formula is:} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Then a=-2, b=4 and c=4} \\ x=\frac{-4\pm\sqrt[]{4^2-4(-2)(4)}}{2(-2)} \\ x=\frac{-4\pm\sqrt[]{16+32}}{-4} \\ x=\frac{-4\pm\sqrt[]{48}}{-4} \\ x=\frac{-4\pm6.93}{-4} \\ \text{Then} \\ x1=\frac{-4+6.93}{-4}=\frac{2.93}{-4}=-0.732 \\ x2=\frac{-4-6.93}{-4}=\frac{-10.93}{-4}=2.732 \end{gathered}[/tex]Now, let's try values less or greater than these roots:
If x=-1:
[tex]\begin{gathered} 0>-2(-1)^2+4(-1)+4 \\ 0>-2\cdot1-4+4 \\ 0>-2\text{ This is right, then number less than -0.732 are solutions of the inequality} \end{gathered}[/tex]Now let's try x=3:
[tex]\begin{gathered} 0>-2(3)^2+4(3)+4 \\ 0>-2\cdot9+12+4 \\ 0>-18+16 \\ 0>-2\text{ This is correct two, then the values greater that 2.732 are solutions to the inequality too} \end{gathered}[/tex]Then, the graph of the inequality is:
The red-shaded area are the solution to the inequality, then in interval notation we have:
[tex](-\infty,-0.732)\cup(2.732,\infty)[/tex]In builder notation it would be:
[tex]x|x<-0.732orx>2.732[/tex]Select from these metric conversions1 kg = 1000 g1 g = 1000mgand use dimensional analysis to convert 4.59 kg to g.4.59 kg X 1
Answers
Since
[tex]1kg=1000g,[/tex]then:
[tex]1=\frac{1000g}{1kg}.[/tex]Then:
[tex]4.59kg=\frac{4.59kg}{1}\times\frac{1000g}{1kg}=4590g.[/tex]Answer:
[tex]\frac{4.59kg}{1}\times\frac{1000g}{1kg}=4590g.[/tex]A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is 40 feet, and the maximum horizontal width is 18 feet. Which of the following equations represents the pool?
Answers
If the maximum vertical length of pool is 40 feet, and the maximum horizontal width of pool is 18 feet , then the equation that represent the pool is x/81 + y/400 = 1 , the correct is option is (B) .
In the question ,
it is given that
the shape of the pool is ellipse .
the maximum vertical length is 40 feet
the maximum horizontal length is 18 feet .
the general equation of the ellipse , is given by x/a + y/b = 1 ,
where a is the length of horizontal axis from origin
and b is the length of the vertical axis from the origin ,
So , the equation that represents the pool is x/81 + y/400 = 1
Therefore , if the pool is in the shape of ellipse , then the equation of the pool is x/81 + y/400 = 1 .
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Create three different proportions that can be used to find BC in the figure above. At least one proportion must include AC as one of the measures.
Answers
We are given two similar triangles which are;
[tex]\begin{gathered} \Delta AEB\text{ and }\Delta ADC \\ \end{gathered}[/tex]Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.
To calculate the length of side BC, we can use any of the following ratios (proportions);
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex][tex]\frac{AB}{AC}=\frac{AE}{AD}[/tex][tex]\frac{AE}{AB}=\frac{AD}{AC}[/tex]Using the first ratio as stated above, we shall have;
[tex]\begin{gathered} \frac{AE}{ED}=\frac{AB}{BC} \\ \frac{8}{5}=\frac{6.5}{BC} \end{gathered}[/tex]Next we cross multiply and we have;
[tex]\begin{gathered} BC=\frac{6.5\times5}{8} \\ BC=4.0625 \end{gathered}[/tex]ANSWER:
[tex]BC=4.0625[/tex]Find the area of the sector interms of pi.2460°Area = [?]
Answers
Answer:
Area= 24π.
Explanation:
The area of a sector is calculated using the formula below:
[tex]A=\frac{\theta}{360\degree}\times\pi r^2[/tex]From the diagram:
• The central angle, θ = 60°
Diameter of the circle = 24
• Therefore, Radius, r = 24/2 = 12
Substitute these values into the formula:
[tex]\begin{gathered} A=\frac{60\degree}{360\degree}\times\pi\times12^2 \\ =24\pi\text{ square units} \end{gathered}[/tex]The area of the sector in terms of pi is 24π square units.
help meeeeeeeeee pleaseee !!!!!
Answers
The composition will be:
(g o h)(x) = 5*√x
By evaluating in x = 0, we get:
(g o h)(0) = 0
How to evaluate the composition?Here we have the two functions:
g(x) = 5x
h(x) = √x
And we want to get the composition:
(g o h)(x) = g( h(x))
So we need to evaluate g(x) in h(x), we will get:
g( h(x)) = 5*h(x) = 5*√x
And now we want to evaluate this in x = 0, we will et:
(g o h)(0) = 5*√0 = 0
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Can anyone help? I’ve asked this same question 6 times!
Answers
Answer: 54080
Since the first number cannot be 0 or 1, there would be only 8 possible numbers for the first number. For the second number, we can now have all 10 numbers.
The number of different combinations of numbers would then be:
[tex]8\times10=80[/tex]Then, for the first letter, we have 26 possible letters, as well as the second letter. The number of different combinations of letters would then be:
[tex]26\times26=676[/tex]So, for a license plate that has 2 numbers and 2 letters, where the first number cannot be 0 or 1, there would be:
[tex]8\times10\times26\times26=54080[/tex]an art teacher makes a batch of green paint by mixing 5/8 cup of yellow paint with 5/8 cup of blue paint if she mixes 29 batches how many cups will she have with green paint
Answers
1 lote = 5/8 cup yellow + 5/8 cup blue
29 lotes = 29(5/8) +29(5/8) cups
29 lotes = 58(5/8)= (58*5)/8=290/8=145/4
145/4 =35.25 cups of paint
12. Suppose you roll a pair of six-sided dice.(a) What is the probability that the sum of the numbers on your dice is exactly 4? (b) What is the probability that the sum of the numbers on your dice is at most 2? (c) What is the probability that the sum of the numbers on your dice is at least 12?
Answers
Probability is computed as follows:
[tex]\text{probability}=\frac{\text{ number of favorable outcomes}}{\text{ total number of outcomes}}[/tex]When rolling a pair of six-sided dice, the total number of outcomes is 36 (= 6x6)
(a) number of favorable outcomes: 3 (dice: 1 and 3, 2 and 2, 3 and 1)
Then, the probability that the sum of the numbers on your dice is exactly 4 is:
[tex]\text{probability }=\frac{3}{36}[/tex](b) number of favorable outcomes: 1 (dice: 1 and 1)
Then, the probability that the sum of the numbers on your dice is at most 2 is:
[tex]\text{probability }=\frac{1}{36}[/tex](c) number of favorable outcomes: 1 (dice: 6 and 6)
Then, the probability that the sum of the numbers on your dice is at least 12 is:
[tex]\text{probability }=\frac{1}{36}[/tex]A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 1 feet from the base of the flagpole, how tall is the flagpole?
Answers
The figure for the height of flagpole, wire and ground is,
Determine height of the pole by using the pythagoras theorem in triangle.
[tex]\begin{gathered} l^2=b^2+h^2 \\ (35)^2=(14)^2+h^2 \\ 1225-196=h^2 \\ h=\sqrt[]{1029} \\ =32.078 \\ \approx32.08 \end{gathered}[/tex]Thus, height of the flagpole is 32.08 feet.
mr dudzic has above ground swimming pool thatbis a circular cylinder. the diameter of the pool is 25 ft. and the height isb4.5 ft. in order to open he needs to shock it with chlorine. if one gallon of liquid chlorin treats 3000 gallons of water, how many full gallons will he need to buy. (1 foot^3=7.48 gallons)
Answers
The volume of the cylinder is
[tex]V=\pi\text{ }\times r^2\times h[/tex]The diameter of the cylinder is 25 feet, then
The radius of it = 1/2 x diameter
[tex]r=\frac{1}{2}\times25=12.5ft[/tex]Since the height is 4.5 ft
Substitute them in the rule above
[tex]\begin{gathered} V=3.14\times(12.5)^2\times4.5 \\ V=2207.8125ft^3 \end{gathered}[/tex]Now we will change the cubic feet to gallons
[tex]\because1ft^3=7.48\text{ gallons}[/tex]Then multiply the volume by 7.48 to find the number of gallons
[tex]7.48\times2207.8125=16514.4375gallons[/tex]Now let us divide the number of gallons by 3000 to find how many gallons of liquid chlorin he needs to buy
[tex]\frac{16514.4375}{3000}=5.5048125[/tex]Then he has to buy 6 full gallons
Calculate Sample Variance for the following data collection: 10, 11, 12, 13, 14,18.
Answers
The Variance of a set of data is defined as the average of the square of the deviation from the mean.
The first step is to calculate the mean of the data.
[tex]\frac{10+11+12+13+14+18}{6}=13[/tex]Now we take the difference from the mean, square it, and then average the result.
[tex]\frac{(10-13)^2+(11-13^2)+(12-13)^2+(13-13)^2+(14-13)^2+(18-13)^2}{6}[/tex][tex]\Rightarrow\frac{9+4+1+0+1+25}{6}[/tex][tex]\Rightarrow6.67[/tex]Hence, the variance of the data is 6.7 (rounded to the nearest tenth)
StatusRecovery8Help ResourcessAABC ~ AXYZFind the missing side length, s.B.3 65А&Х-ZCross multiplySE ][?] = [ ]153s
Answers
Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ} \\ \Rightarrow\frac{3}{5}=\frac{6}{s} \end{gathered}[/tex]Solving for s,
[tex]\begin{gathered} \frac{3}{5}=\frac{6}{s} \\ \Rightarrow\frac{3}{5}\cdot s=\frac{6}{s}\cdot s \\ \Rightarrow\frac{3s}{5}=6 \\ \Rightarrow\frac{3s}{5}\cdot5=6\cdot5 \\ \Rightarrow3s=30 \\ \Rightarrow s=\frac{30}{3} \\ \Rightarrow s=10 \end{gathered}[/tex]Thus, the result of the cross multiplication is 3s=30 and the answer is s=10
If the expression 1/ square root of x was placed in form x^a, then which of the following would be the value of a?
Answers
4) -1/2
1) Rewriting the expression:
[tex]\frac{1}{\sqrt[]{x}}[/tex]2) As a power we can write this way, considering that we can rewrite any radical as a power and that when we have a radical on the denominator we can rewrite it as a negative rational exponent. So we can write it out:
[tex]\frac{1}{\sqrt[]{x}}=\frac{1}{x^{\frac{1}{2}}}=x^{-\frac{1}{2}}[/tex]3) Hence, the answer is 4) -1/2
Write standard form for the equation of the line: y = 1/2x - 5*
Answers
Explanation
the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers
so, we need to write in this form
[tex]Ax+By=C[/tex]Step 1
subtrac 1/2x in both sides
[tex]\begin{gathered} y=\frac{1}{2}x-5 \\ \\ y-\frac{1}{2}x=\frac{1}{2}x-5-\frac{1}{2}x \\ \\ y-\frac{1}{2}x=-5 \\ \text{reorder} \\ -\frac{1}{2}x+y=-5 \end{gathered}[/tex]I hope this helps you
Solve for k 4k – 6/3k – 9 = 1/3
Answers
hello
to solve this simple equation, we need to follow some simple steps.
[tex]4k-\frac{6}{3}k-9=\frac{1}{3}[/tex]step 1
multiply through by 3
we are doing this to eliminate the fraction and it'll help us solve this easily
[tex]\begin{gathered} 4k(3)-\frac{6}{3}k(3)-9(3)=\frac{1}{3}(3) \\ 12k-6k-27=1 \end{gathered}[/tex]notice how the equation haas changed suddenly? well this was done to make the question simpler and faster to solve.
step 2
collect like terms and simplify
[tex]\begin{gathered} 12k-6k-27=1 \\ 12k-6k=1+27 \\ 6k=28 \\ \end{gathered}[/tex]step three
divide both sides by the coefficient of k which is 6
[tex]\begin{gathered} \frac{6k}{6}=\frac{28}{6} \\ k=\frac{14}{3} \end{gathered}[/tex]from the calculations above, the value of k is equal to 14/3
4. Which of the following represent the distance
formula? Select all that apply.
A d = √(x₁-x₂)² + (y₁ − y₂)²
B d = √(x₂− ×₂)² + (⁄₂ − y,}²
C d = √(x₂+x₂)² + (y₂ + y,)²
D d=√√₂-X₁1² + VY₂ − Y₁1²
Answers
A appears to be the only correct answer
a^2+b^2=c^2
you are solving for c when finding distance, so (a^2 + b^2) must be square rooted, as a whole, not separately
and a = (x1-x2)
and b = (y1-y2)
you can flip the 1 and 2 but you have to flip for both x and y
like x1-x2 means you have to do y1-y2
like x2-x1 means you have to do y2-y1
so both above are correct as long as the order of 1 and 2 stays the same for both x and y
need help with image
Answers
Step by step explanation:
sum of co-exterior angle is 180°
(10x-48)+(6x)=180°
4x-48=180°
4x=180-48
4x=132
x=132/4
x=33