Answers
EXPLANATION:
Given;
We are given the quadratic equation as shown below;
[tex]x^2-8x+13=0[/tex]Required;
We are required to solve for x by completing the square method.
Step-by-step solution;
We start with the constant 13.
Subtract 13 from both sides of the equation;
[tex]x^2-8x+13-13=0-13[/tex][tex]x^2-8x=-13[/tex]Next we take the coefficient of x (that is -8). We half it, and then square the result. After that we add it to both sides of the equation;
[tex]\begin{gathered} \frac{1}{2}\times-8=-\frac{8}{2} \\ Next: \\ (-\frac{8}{2})^2 \end{gathered}[/tex]We now have;
[tex]x^2-8x+(-\frac{8}{2})^2=-13+(-\frac{8}{2})^2[/tex]We can now simplify this;
[tex]x^2-8x+(-4)^2=-13+(-4)^2[/tex][tex]x^2-8x+16=-13+16[/tex][tex]x^2-8x+16=3[/tex]We now factorize the left side of the equation;
[tex]\begin{gathered} x^2-4x-4x+16 \\ (x^2-4x)-(4x-16) \\ x(x-4)-4(x-4) \\ (x-4)(x-4) \\ Therefore: \\ (x-4)^2 \end{gathered}[/tex]we can now refine our equation to become;
[tex](x-4)^2=3[/tex]We can now solve for x as follows;
Take the square root of both sides;
[tex]x-4=\pm\sqrt{3}[/tex]Therefore;
[tex]\begin{gathered} x-4=\sqrt{3} \\ x=\sqrt{3}+4 \\ Also: \\ x-4=-\sqrt{3} \\ x=-\sqrt{3}+4 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x_1=4+\sqrt{3} \\ x_2=4-\sqrt{3} \end{gathered}[/tex]Related Questions
Which of the following is equivalent to 10^4 x 10^3? A 10^7 B 20^12 C 20^7 D 10^12
Answers
Explanation
Let's remember some properties for the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]hence
let's calculate the product
[tex]\begin{gathered} 10^4\cdot10^3 \\ 10^4\cdot10^3=10^{4+3}=10^7 \\ 10^4\cdot10^3=10^7 \end{gathered}[/tex]therefore, the answer is
[tex]A)10^7[/tex]I hope this helps you
What is the volume of the cone when the radius is 10 and the height is 18
Answers
The volume of the cone is given by the formula:
Solve the equation. |k + 6| = 3
Question 7 options:
{–3, 9}
{–3, 3}
{–9, –3}
{all real numbers greater than or equal to –9 and less than or equal to –3}
Answers
Step-by-step explanation:
k= {-3,-9}
Because || always gets positive numbers.
For example |-5|=5, and |5|=5.
so |-9+6|=|-3| which is |-3|=3
and |-3+6|=|3| which is equal to 3.
Answer:
c) k = {-9,-3}
Step-by-step explanation:
Given equation,
→ |k + 6| = 3
Now the value of k will be,
→ |k + 6| = 3
→ k + 6 = 3 || → -(k + 6) = 3
→ k = 3 - 6 || → -k = 3 + 6
→ [ k = -3 ] || → [ k = -9 ]
Hence, value of k is -3 & -9.
12.The graph of y=x + 3 is a vertical translation ofthe graph of y = x + 1, 2 units upward. Examine the intercepts of both linesand state another way that the geometric relationship between the two graphscan be described.
Answers
The graph of y=x + 3 is a vertical translation of
the graph of y = x + 1, 2 units upward. Examine the intercepts of both lines
and state another way that the geometric relationship between the two graphs
can be described.
we have
step 1
y=x+3
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+3
solve for x
x=-3
step 2
y=x+1
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+1
x=-1
step 3
The graph of y=x+3 is a horizontal translation 2 units at left of the graph of y=x+1
The rule is
(x,y) -------> (x-2,y)
D. 62B. 1811. Madison bought a sweater and a pair of jeans at the mall for $47. Thesweater cost $7 less than twice the cost of the jeans. How much did thesweater cost?c. $20A $29D. $13B. $27
Answers
Answer:
$29
Step-by-step explanation:
The rectangular rug has side lengths of 3 and 4 ft. What is the length of the diagonal? Draw a picture of the problem and solve. Round to the nearest tenth
Answers
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
[tex]\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]Each ticket to a matinee movie costs $8. Part A: Complete this table relating the number of movie tickets bought, m, to the total cost, c, of the tickets. m C 4 6 9 Part B: Write an equation that models this situation, using the variables m and c. Answer: Brandy thinks the number of movie tickets bought depends on the total cost of the movie tickets. Brandy's brother thinks the total cost of the movie tickets depends on the number of movie tickets bought Part C: Whose thinking is correct, Brandy's, her brother's, or both? Explain how you know.
Answers
Part A
Since each ticket costs $8, we need to add $8 for each plus ticket one buys:
[tex]\begin{gathered} 1\text{ ticket: \$}8 \\ 2\text{ tickets: \$}8+\text{ \$}8=\text{ \$}16 \\ 3\text{ tickets: \$}16+\text{ \$}8=\text{ \$}24 \\ 4\text{ tickets: \$}24+\text{ \$}8=\text{ \$}32 \\ 6\text{ tickets: \$}32+\text{ \$}16=\text{ \$}48 \\ 9\text{ tickets: \$}48+\text{ \$}24=\text{ \$}72 \end{gathered}[/tex]Therefore, we have:
Part B
Notice that, instead of summing (8+8+8+...) we can multiply $8 by the number of tickets bought m to obtain the total cost c.
Thus, we have:
[tex]c=m\times\text{ \$}8[/tex]Part C
The equation above (c = m x $8) shows that the total cost c depends on the number of tickets bought.
However, we write that relation in another way:
[tex]m=c\div\text{ \$}8[/tex]Thus, if we know the total cost, we can divide it by $8 to find the number of tickets bought. Then, we can say that the number of tickets boght m depends on the total cost c.
Therefore, both thoughts are correct.
Based on the end behavior, what is the graph of function R?
Answers
As given by the question
There are given that the function
[tex]f(x)=-x^3+3x^2+x-3[/tex]Now,
The graph of the given function is shown below:
Hence, the correct option is C.
Answer:
C
Step-by-step explanation:
Trust
Jeremy is given the choice between two chocoletes,chocolates, and Y. Which..........
Answers
To determine which option is correct, we first need to find the volume of both chocolate.
The volume of X:
The shape is a square-based pyramid. The volume is given by
[tex]\begin{gathered} V_x=\frac{1}{3}\times base\text{ area }\times height \\ V_x=\frac{1}{3}\times l\times b\times h \end{gathered}[/tex]From the diagram,
l = 5 cm
b = 6 cm
h = 10 cm
Substituting,
[tex]\begin{gathered} V_x=\frac{1}{3}\times5\times6\times10 \\ V_x=100\operatorname{cm}^3 \end{gathered}[/tex]The volume of Y:
The shape is a triangular-based pyramid. The volume is given by
[tex]\begin{gathered} V_y=\frac{1}{3}\times base\text{ area }\times height \\ V_y=\frac{1}{3}\times\frac{1}{2}\times b\times l\times h \end{gathered}[/tex]From the diagram,
l = 8 cm
b = 7.5 cm
h = 10 cm
[tex]\begin{gathered} V_y=\frac{1}{3}\times\frac{1}{2}\times7.5\times8\times10 \\ V_y=100\operatorname{cm}^3 \end{gathered}[/tex]From here, the volumes of both chocolates are the same.
Therefore, the chocolate he picks does not matter as both volumes are equivalent.
The SECOND OPTION is correct.
Use the distributive property of multiplication to find 6x14.
Answers
Answer
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Explanation
Distributive property is used to open brackets. For example, the expression
a (b + c) can be solved using the distributive property to multiply into the bracket.
a (b + c) = ab + ac
So,
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Hope this Helps!!!
Simplify: 2x^2 + 19x + 35/2x^2 +11x +15 a) 7/3b) 19x + 35/11x + 15c) 2x + 7/2x + 3d) x + 7/x + 3
Answers
SOLUTION
We want to simplify
[tex]\frac{2x^2+19x+35}{2x^2+11x+15\text{ }}[/tex]Factorising the numerator and denominator, we have
[tex]\begin{gathered} \frac{2x^2+19x+35}{2x^2+11x+15\text{ }} \\ \frac{2x^2+14x+5x+35}{2x^2+6x+5x+15\text{ }} \\ \frac{2x(x+7)+5(x+7)}{2x(x+3)+5(x+3)} \\ \frac{(2x+5)(x+7)}{(2x+5)(x+3)} \end{gathered}[/tex]Canceling out the common factor which is
[tex]2x+5[/tex]We have our answer as
[tex]\frac{x+7}{x+3}[/tex]Hence the answer is option D
Please be clear with the answer thank you bye-bye bye-bye
Answers
Solve the system of equations:
3x + 3y = 3
5x + y = 13
Solving the second equation for y:
y = 13 - 5x
Substituting in the first equation:
3x + 3(13 - 5x) = 3
Opeating:
3x + 39 - 15x = 3
Simplifying:
-12x + 39 = 3
Subtracting 39:
-12x = -36
Dividing by -12:
x = -36 / (-12)
x =3
Substituting in the equation for y:
y = 13 - 5(3)
y = -2
Answer: x = 3, y = -2
Answer: x = 3, y = -2
Step-by-step explanation:
12 1 point Which trig function should Sharlot use to find the measure of angle A ? C 1 B cosine 3 tangent 4 pythagorean theorem sine 6
Answers
using trigonometric ratio
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}} \\ \cos A=\frac{5}{12} \end{gathered}[/tex]We have to use cosine to find angle A
Select all nat apply.Which steps are involved in multiplying fractions?Multip, the denominators togetherMultiply the numerators togetherCheck to see if the product can be simplifiedFind a common denominatorConvert the problem to a division problem
Answers
We want to list the steps involved in multiplying fractions;
Taking an example;
[tex]\frac{2}{3}\times\frac{3}{4}[/tex]First steps are;
- Multiply the numerators together
- Multiply the Denominators together
[tex]\begin{gathered} =\frac{2\times3}{3\times4} \\ =\frac{6}{12} \end{gathered}[/tex]Next is to;
Check to see if the product can be simplified;
[tex]\frac{6}{12}=\frac{1}{2}[/tex]So, we get the product to be;
[tex]\frac{1}{2}[/tex]I'm terrible at explaining answers and this is one of them...
Answers
We see that the sign is a triangle and the area of a triangle is given by the expression:
[tex]A=\frac{1}{2}\text{base}\times height[/tex]base=36
height=32
Then,
[tex]\begin{gathered} A=\frac{1}{2}36\times32 \\ A=\frac{1152}{2}=576\text{ square inches} \end{gathered}[/tex]What expression represents the sum of ages of Hugo and his two siblings?
Answers
The correct option is D
The sum of their ages is 3x + 8
Explanation:Given that Hugo's age = x
Jasmine's age = x + 3
Manny's age = (x + 3) + 2 = x + 5
The sum of their ages is:
x + (x + 3) + (x + 5)
= x + x + x + 3 + 5
= 3x + 8
Solve 2(x-6)+7x = 5-3(x-2)
Answers
To solve x, let's eliminate the parenthesis first by multiplying 2 and -3 to it.
[tex]2x-12+7x=5-3x+6[/tex]Next, let's combine all like terms on either side. We will move -3x to the left side of the equation and -12 to the right side of the equation. Note that when a term crosses the equal symbol, the sign reverses. From -3x to +3x and from -12 to +12.
[tex]2x+7x+3x=5+6+12[/tex]Next, add the terms on both sides.
[tex]12x=23[/tex]Lastly, divide both sides by 12 to isolate x.
[tex]\begin{gathered} \frac{12x}{12}=\frac{23}{12} \\ x=\frac{23}{12} \end{gathered}[/tex]The value of x is 23/12.
Let's check if this is right by substituting the value of x to the equation.
[tex]\begin{gathered} 2(\frac{23}{12}-6)+7(\frac{23}{12})=5-3(\frac{23}{12}-2) \\ 2(-\frac{49}{12})+\frac{161}{12}=5-3(-\frac{1}{12}) \\ -\frac{98}{12}+\frac{161}{12}=5+\frac{3}{12} \\ \frac{63}{12}=\frac{63}{12} \\ \frac{21}{4}=\frac{21}{4} \end{gathered}[/tex]Since we got the same 21/4 on both sides of the equation, our x value 23/12 is correct.
Heather dropped a water balloon over the side of her school a height of 80 feet. The approximate height of the balloon at any point during it's fall can be represented by the following quadratic equation: h=-16t^2+80. About how long did it take for the balloon to hit the ground.A.1.73B.2.24C.2.45D.2.83
Answers
h = - 16t^ 2 + 80
[tex]h=-16t^2\text{ + 80}[/tex]The balloon will hit the ground when the height = 0
[tex]\begin{gathered} 0=-16t^2\text{ + 80} \\ \text{collect like terms} \\ \\ 16t^2\text{ = 80} \\ \text{Divide both sides by 16} \\ t^2\text{ = }\frac{80}{16} \\ t^2\text{ = 5} \\ t\text{ =}\sqrt[]{5} \\ t\text{ = 2.236} \\ t\text{ = 2.24} \end{gathered}[/tex]The correct option is B = 2.24
Kellen earned $52.92 for waitressing at a burger restaurant on Friday night.if she waitressed for 4.5 hours,on average how much did she earn per hour?
Answers
Given data:
The amount Kellen earned in 4.5 hours is $52.92.
The expression for the given statement is,
[tex]\begin{gathered} 4.5\text{ hours=\$52.92} \\ 1\text{ hour= \$11.76} \end{gathered}[/tex]Thus, Kellen earned $11.76 per hour.
If you randomly select a letter from the phrase "Ichiro Suzuki is at the top of the lineup," what is theprobability that you select a consonant? (Your answer must be in the form of a reduced fraction.)Submit Question
Answers
Given the phrase "Ichiro Suzuki is at the top of the lineup", you can identify that:
- The total number of letters the phrase has is:
[tex]Total=33[/tex]- The number of consonants the phrase has is:
[tex]Consonants=18[/tex]Therefore, you can find the probability that you select a consonant by dividing the number of consonants in the phrase by the total number of letters:
[tex]P=\frac{18}{33}[/tex]You can reduce the fraction by dividing the numerator and the denominator by 3:
[tex]\begin{gathered} P=\frac{18\div3}{33\div3} \\ \\ P=\frac{6}{11} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{6}{11}[/tex]hello. I need help with solving log6 129 on a calculator.
Answers
With the aid of a scientific calculator (most smart phones are equipped with one), you need to look out for the "LOG" button.
The button usually has the inscription shown as;
[tex]\text{Log}_{10}[/tex]Press the Second Function button and this key changes to;
[tex]\text{Log}_y[/tex]This second function button means,
"The log of x base y".
In this case it means, you take the log of 129, base 6.
The steps are;
[tex]\begin{gathered} (1)\text{Press 129} \\ (2)\text{Press Second Function button} \\ (3)\text{Press 6} \\ (4)\text{Press the "equal to" button} \end{gathered}[/tex]What is the greatest common factor of the polynomial: 35y + 5y + 157 "
Answers
The greatest common factor of the expression is:
[tex]5y^3[/tex]This comes from the fact that 5 is the greatest common factor of the constants, whereas y^3 is the greatest common factor of the variable.
consider the equation -4x+3y=7. Assume that y is a function of x. rewrite the equation using function notation F(x)
Answers
y=(7+4x)/3
y=F(x)
Answer: F(x)=(7+4x)/3
6. You deposit $1000 a year into an account. This account earns 8% interest compounded yearly,(20 points)a) how much will you have after 10 years?b) How much total money did you put in the account.c) How much total interest did you earn?
Answers
Compound interest formuae :
A = P ( 1+r/100)^ n or A = P( 1+i)^n or A = P ((1 + i )^n -1 )/i
we will use the highlighted formular due to compounded yearly statement on the question:
where A = Accumulated amount;
P = original amount invested/ (borrowed )
n = number of years
r = interest rate as a percentage
i = r/100
Answer to (a )
A = P ((1 + i )^n -1 )/i
where n = 10; i = 8/100 =0.08 ; P = 1000
A = 1000 ( 1 + (8/100))^10 -1)/ 0. 08
A =1000 ( 14.48)
A =$14486.56
b. 1000 X 10 = $12000
c. you earned interest of $14486 - $12000 = $2486
O 9,976 15) An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answers
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
we know that
1 min=60 sec
we have
125 rev/sec
so
1 sec=1/60 min
substitute
125 rev/sec=125/ (1/60)=7,500 rev/min
Multiply by 30 min
7,500*30=225,000 rev
therefore
the answer is225,000 revolutionsIf I have 2 and a 1/2 bags of mortar
or every 100 cement blocks how many bags of water Mason needed for 350 blocks
Answers
The number of bags for 350 blocks is 8.75 bags
How to determine the number of bags for 350 blocks?From the question, we have the following parameters that can be used in our computation:
Bags of mortal = 2 and a 1/2 bags
Number of cements blocks = 100 blocks
The above parameters can be represented using the following ratio
Ratio = Bags of mortal : Number of cements blocks
Substitute the known values in the above equation, so, we have the following representation
Bags of mortal : Number of cements blocks = 2 and a 1/2 bags : 100 blocks
When the number of blocks is 350, we have the following equation
Bags of mortal : 350 = 2 and a 1/2 bags : 100 blocks
Express the ratio as fraction
Bags of mortal/350 = 2.5/100
Multiply both sides by 350
Bags of mortal = 350 * 2.5/100
Evaluate the products
Bags of mortal = 8.75
Hence, the number of bags is 8.75
Read more about ratio at
https://brainly.com/question/2328454
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Data with a correlation coefficient of 0.05 has a _[blank A]_ correlation, and data with a correlation coefficient of −0.80 has a _[blank B]_ correlation.Which answers provide the words that fill in the blanks in the previous sentence, in the correct order, to make it a true statement?Select two answers. Select one answer for the blank labeled "A," and select one answer for the blank labeled "B."
Answers
We have two correlations:
1) One with r = 0.05.
2) Another with r = -0.80.
The absolute value of r tells us how strong or weak is the correlation: strong correlation have values of |r| closer to 1, while weak correlations have values of |r| closer to 0.
The sign of r tells us if the correlation is positive or negative, independently of how strong it is.
Then, for a correlation with r = 0.05 we can conclude that it is a weak positive correlation.
For a correlation r = -0.80 we can conclude that it is a strong negative correlation.
Answer:
The correct options are
B: strong negative [second option]
A: weak positive [seventh option]
is the point (1,3) a solution to the linear equation 5x - 9y = 32?
Answers
We are given the following equation:
[tex]5x-9y=32[/tex]To determine if the point (1, 3) is a solution to this equation we will replace the given values since the point (1, 3) means that when x = 1, y = 3. Replacing in the equation:
[tex]5(1)-9(3)=32[/tex]Solving the operation we should get the same value on both sides of the equation:
[tex]\begin{gathered} 5-27=32 \\ -22\ne32 \end{gathered}[/tex]Since both sides are different this means that the point (1, 3) is not a solution to the equation.
Answer:
89
Step-by-step explanation:
A nurse measured The blood pressure of each person who visit a hair clinic and created a relative frequency histogram for the systolic blood pressure readings approximately what percentage of the people had a systolic blood pressure Reading between 110 and 139 inclusive
Answers
Given a relative frequency histogram for the systolic blood pressure readings.
We will find the percentage of the people who had a systolic blood pressure reading between 110 and 139
As shown:
The percentage of people who had a systolic blood pressure reading between 110 and 119 = 0.35
The percentage of people who had a systolic blood pressure reading between 120 and 129 = 0.25
The percentage of people who had a systolic blood pressure reading between 130 and 139 = 0.15
So, the answer will be = 0.35 + 0.25 + 0.15 = 0.75
So, the answer will be option 3) 75%
The perpendicular bisectors of triangle ABC intersect at point G and are shown in blue. Find BG
Answers
Answer:
9
Explanation:
A perpendicular bisector of a triangle is a line that is perpendicular to the side and passes through the midpoint of the triangle.
So when three perpendicular bisectors of the sides of a triangle meet at a point in a triangle, that point is called a circumcenter.
From the circumcenter theorem, we know that the circumcenter is equidistant from the vertices of a triangle, that is, the circumcenter is the same distance from each of the vertices of the triangle.
Looking at the given triangle, we can see that G is the circumcenter of the triangle because all the perpendicular bisectors DG, EG, and FG meet at this point.
We can see that AG is 9 which is the distance from vertex A to the circumcenter, G, since the circumcenter is equidistant from the vertices of a triangle according to the circumcenter theorem, therefore, BG will also be 9.