Step 1
Given;
[tex]3x^2+18x+15=0[/tex]Required; To solve by completing the square method.
Step 2
Subtract 15 from both sides of the equation.
[tex]\begin{gathered} 3x^2+18x+15-15=0-15 \\ 3x^2+18x=-15 \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ all terms by 3} \\ x^2+6x=-5 \end{gathered}[/tex]Find half of the coefficient of x (i.e 6) and square it
[tex](\frac{6}{2})^2=3^2[/tex]Add it to both sides
[tex]\begin{gathered} x^2+6x+3^2=-5+3^2 \\ Use\text{ perfect square} \\ (x+3)^2=-5+9 \\ (x+3)^2=4 \\ x+3=\pm\sqrt{4} \\ x=\operatorname{\pm}\sqrt{4}-3 \end{gathered}[/tex][tex]\begin{gathered} x=\pm2-3 \\ x=-1\text{ or -5} \end{gathered}[/tex]Answer;
[tex]x=-1,-5[/tex]the graph below shows a rotation ground things that the shape of rotation quadrant one caller ID by the way which
Simplify the following expressions, SHOW UR SOLUTIONS PLS
Answer:
Q1. 3² × 3² × x² = 9 × 9 × x²
= 81x²
Q2. (2x)² × (3x)² = 4x² × 9x²
= 36x⁴
Q3. [tex](-\frac{5}{6} )^{3}[/tex] [tex]=-\frac{125}{216}[/tex]
Q4. [tex](\frac{3a^{5} }{4b^{4}}) ^{3}=\frac{27a^{15} }{64b^{12} }[/tex]
Q5. [tex](\frac{8a^{2} b^{4}c^{23} }{26a^{13}b^{5}c^{2} }) ^{3} = (\frac{4c^{21} }{13a^{11}b } )^{3}[/tex]
[tex]=\frac{64c^{63} }{2197a^{33}b^{3} }[/tex]
Q6. [tex]-4^{-1}= (-\frac{4}{1} )^{-1}[/tex]
[tex]=(-\frac{1}{4} )^{1}[/tex]
[tex]=-\frac{1}{4}[/tex]
Q7. [tex](2r)^{-2}=(\frac{2r}{1} )^{-2}[/tex]
[tex]=(\frac{1}{2r} )^{2}[/tex]
[tex]=[/tex] [tex]\frac{1}{2r}[/tex] × [tex]\frac{1}{2r}[/tex]
[tex]=[/tex] [tex]\frac{1}{4r^{2} }[/tex]
Q8. [tex](\frac{xy}{ab^{3} } )^{-1} = (\frac{ab^{3} }{xy} )^{1}[/tex]
[tex]=\frac{ab^{3} }{xy}[/tex]
Q9. [tex]9x^{0} = 9(1)[/tex]
[tex]=9[/tex]
Q10. [tex](-4r^{5}s^{6} t^{-7} )^{0} = 1[/tex]
A protractor is user on an angle. One ray of the angle is at 46 degrees and the other ray is at 95 degreesWhat is the measure of the angle? Choices are:141 degrees95 degrees49 degrees46 degrees
A protractor is used to measure angles. The range is from 0 degrees to 180 degrees. One ray of the angle is at 46 degrees and the other ray is at 95 degrees. The measure of the angle can be calculated below
[tex]undefined[/tex]please explain steps to get correct answer in pic below
Let's use the properties of the sum:
[tex]\begin{gathered} \sum ^{11}_{i\mathop=1}(3i^2+17)=\sum ^{11}_{i\mathop{=}1}3i^2+\sum ^{11}_{i\mathop{=}1}17 \\ =3\sum ^{11}_{i\mathop{=}1}i^2+17\cdot11 \end{gathered}[/tex]Therefore the answer is the last option.
To simplify this we use the properties listed below:
[tex]\sum ^n_{i\mathop{=}1}na_i=n\sum ^n_{i\mathop{=}1}a_i[/tex][tex]\sum ^n_{i\mathop{=}1}(a_i+b_i)=\sum ^n_{i\mathop{=}1}a_i+\sum ^n_{i\mathop{=}1}b_i[/tex][tex]\sum ^n_{i\mathop{=}1}c=cn[/tex]an inequality is shown[tex] \frac{x}{8} \ \textless \ x \ \textless \ \sqrt{0.25} [/tex]choose all the options that worka. [tex] \sqrt{0.25} [/tex]b.[tex] \frac{ x}{4} [/tex]c.[tex]46 \: pecent[/tex]d.[tex] \frac{2}{5} [/tex]
Looking at the given inequality,
pi/8 = 0.392
pi/4 = 0.7
46% = 46/100 = 0.46
2/5 = 0.4
square root of 0.25 is 0.5
Therefore, the values of x that would the inequality are 0.46 and 0..4
Therefore, the correct options are C and D
a boat can travel 57 miles upstream against the current in the same amount of time it can travel 84 miles down stream with the current. if the boat's average speed in still water is 20 miles per hour. find the speed of the current
a boat can travel 57 miles upstream against the current in the same amount of time it can travel 84 miles down stream with the current. if the boat's average speed in still water is 20 miles per hour. find the speed of the current
Let
x -----> the speed of the current
we have that
speed *time=distance
upstream
(20-x)t=57 --------> equation A
down stream
(20+x)t=84 -----> equation B
solve the system of equations
Adds the equation A and B
20t-xt=57
20t+xt=84
------------------
40t=141
t=3.525 hours
Find the value of x
(20+x)t=84
substitute the value of t
20+x=84/3.525
x=84/3.525 - 20
x=3.83 mph
therefore
the answer is
3.83 mphThe graph below shows the number of notepads that each location of a business used last year. The number of departments per location are presented in the table below. Four of the locations used the same number of notepads per department, but the Northwest and Central offices used fewer notepads per department. The graph shows that the Northwest location used the same number of notepads as the Southeast location overall. If the Northwest location used fewer notepads per department, which of the following could be the number of departments for the Northwest location?
So we plot the values over the bars
Now we identify that each line is separated by 2
Answer: Then we get central as 8 and northwest as 6
(03.01 LC)
Simplify (√5)(35)
Answer:5/35=1/7
Step-by-step explanation:
Calculate the maturity value of simple interest a seven months loan of $6,000 if the interest rate is 7.6%
ANSWER
[tex]6266[/tex]EXPLANATION
Given;
[tex]\begin{gathered} p=6000 \\ R=7.6\% \\ T=\frac{7}{12} \end{gathered}[/tex]Now using the formula for simple interest
[tex]I=\frac{PRT}{100}[/tex]substituting the values we have;
[tex]\begin{gathered} I=\frac{6000\times7.6\times7}{100\times12} \\ =266 \end{gathered}[/tex]Now the interest after 7 months would be
[tex]266[/tex]The maturity value is
[tex]\begin{gathered} P+I \\ =6000+266 \\ =6266 \end{gathered}[/tex]What is the result of performing these steps?1. Draw a line segment with endpoints A and B.2. Draw point Canywhere on AB.3. Fold the paper through C So As lies on top of itself.4. Draw a line segment from C to any point along the fold.O A. A line segment parallel to ABB. A line segment perpendicular to ABC. A bisected angleD. The perpendicular bisector of AB
As AB lies on top of itself after folding the paper, the fold would be perpendicular to AB. Drawing a line from C to any point of the fold would result in a line segment perpendicular to AB.
Answer:
B. A line segment perpendicular to AB
x² + x+49
14
7
712
+ 49
Answer:
x 2^x=49. 2x=49 2 x = 49.
Step-by-step explanation:
Step 1. Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
PLEASE HELP ME I NEED YOU TO SOLVE FOR C
Solve the equation 8 −710c = 6−15c for c.
Answer: C =0.006
Step-by-step explanation:
step by step on how to solve -6.43 - 22.3
The given expression is
[tex]-6.43-22.3[/tex]Given that the numbers have the same sign, we have to sum.
The result must be negative because both numbers are negative.
Hence, the result is -28.73.Answer:
-28.73.
Step-by-step explanation:
5. Read the givens about the diagram shown and then state all conclusions you can draw from these givens. Explain your conclusions
We are given the following information
[tex]\bar{TV}\perp\bar{US}[/tex]Which says the line TV is perpendicular to the line US.
From this we can conclude that the angle VRU, angle TRU and angle TRS are 90°
We are also given that
[tex]undefined[/tex]Which of these systems of equations could be used to choose a ticket plan ?
Answer:
A. y = 0.50x + 12
y = 1.25x
Explanation:
The equation that model the total cost of plan A is:
y = 12 + 0.50x
Because there is a cost of $12 that is independent of the number of rides x and there is a cost of $0.5 for each ride.
In the same way, the equation that model the total cost of plan B is:
y = 1.25x
Because there is only a cost of $1.25 for each ride.
Therefore, the system of equations that could be used to choose a ticket plan is:
A. y = 0.50x + 12
y = 1.25x
26 is what % of 65.
Suppose that 65 is the 100%, then we can find the percentage that is 26 from 65 using a rule of three:
[tex]\begin{gathered} 65\rightarrow100\% \\ 26\rightarrow x\% \\ \Rightarrow x=\frac{26\cdot100}{65}=\frac{2600}{65}=40 \\ x=40\% \end{gathered}[/tex]therefore, 26 is 40% of 65
what is 2x exponent 3 - 4x exponent 2 -3x divide 2x
Equation
[tex]\frac{2x^3-4x^2-3x}{2x}[/tex]
To operate this fraction we will separate the numerator and divide each term with the denominator.
[tex]\begin{gathered} \frac{2x^3}{2x}-\frac{4x^2}{2x}-\frac{3x}{2x} \\ x^2-2x-\frac{3}{2} \end{gathered}[/tex]The answer would be
[tex]x^2-2x-\frac{3}{2}[/tex]PLS HELP MATH WILL MARK BRAINLIEST
Look at this diagram: GHIJKLMNIf HJ and KM are parallel lines and mJIG = 43°, what is mKLN?
We are given that lines HJ and KM are parallel. We notice that the angles:
[tex]\begin{gathered} \angle KLN \\ \angle HIL \end{gathered}[/tex]Are corresponding angles, and therefore they are congruent, that is:
[tex]\angle KLN\cong\angle HIL[/tex]Also, angles:
[tex]\begin{gathered} \angle HIL \\ \angle JIG \end{gathered}[/tex]Are vertical angles, therefore, they are equal:
[tex]\angle HIL\cong\angle JIG[/tex]Therefore, combining the two statements we get:
[tex]\angle KLN\cong\angle JIG[/tex]Therefore:
[tex]\angle KLN=43[/tex]Angle KLN equals 43 degrees.
What is the value of the digit in the tens place?3,847O A. 3,000OB. 4C. 40D. 800
Expand the given number as,
[tex]3847=(3\times10^3)+(8\times10^2)+(4\times10^1)+(7\times10^0)[/tex]The tens place is the second from the right.
It is observed that the value of the digit at tens place is 4
So, option B is the correct choice.
18 is 32% of what number w? what is w?
Given: 18 is 32% of a number
To Determine: The number
Let the number be w. Therefore:
[tex]\begin{gathered} 32\%ofw=18 \\ \frac{32}{100}\times w=18 \end{gathered}[/tex][tex]\frac{32w}{100}=18[/tex][tex]\begin{gathered} 0.32\times w=18 \\ 0.32w=18 \end{gathered}[/tex]Divide both sides by 0.32
[tex]\begin{gathered} \frac{0.32w}{0.32}=\frac{18}{0.32} \\ w=56.25 \end{gathered}[/tex]Hence,
an equation is 18 = 0.32 . w
The solution is w = 56.25
Which of the following sa rational number? [tex] \sqrt{5} [/tex][tex] - \frac {3}{4} [/tex]Pi[tex] - \sqrt{7} [/tex]
First of all, we need to remember what is a rational number.
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Now, from your options we can deduce that:
[tex]\frac{3}{4}[/tex]is the rational number.
Bethany is paid time-and-a-half for each hour she works above her normal 40 hours each week. Last week, Bethany worked 44 hours and her gross pay was $575. how much did Bethany earn for each hour of overtime she worked?
Bethany worked a total of 44 hours, which means that she worked 40 normal hours and 4 extra hours.
Let x be the amount earned per 1 normal working hour since she earns a half more for each extra hour we can express the money earned above her 40 normal hours as 1.5 times x ( x+0.5*x = 1.5x), then we can express the gross pay like this:
gross pay = earnings per normal hour * normal hours + earnings per extra hour * extra hours
gross pay = x * normal hours + 1.5x * extra hours
As mentioned, she worked 40 normal hours and 4 extra hours, then we get:
gross pay = x*40 + 1.5x*4
gross pay = 40x + 1.5*4x
gross pay = 40x + 6x
gross pay = 46x
From the given information, we know that the gross pay equals $575, then we get:
575 = 46x
46x/46 = 575/46
x = 575/46
x=12.5
The amount earned with extra hours is 1.5x, then we get:
Extra hour earning = 1.5*12.5=18.75
Then, Bethany earned $18.75 for each extra hour
I A family of G holds a ceremony to determine each child's favorite Teenage Mutant Ninja Turtle. The ceremony involves each child's results of choosing 10 numbers out of a hat. If Raphael, Michelangelo, Donatello, and Leonardo are represented with the numbers 1, 2, 3, and 4, respectively, which Teenage Mutant Ninja Turtle would become the favorite of a Child having the following results? Construct a 90% confidence interval estimate of the mean to develop the reasoning for your answer 2 21 4 3 3 3 3 11
Solution
Step 1
Write an expression for the mean
[tex]\bar{x}=\text{ }\frac{\sum ^{\square}_{\text{ of terms}}}{\text{mumber of terms}}[/tex][tex]\begin{gathered} \bar{x}=\frac{2+2+1+\text{ 4 +3+3+3+3}+4+1}{10} \\ \bar{x}=\text{ }\frac{26}{10} \\ \bar{x}=2.6 \end{gathered}[/tex]Step 2
Find the standard deviation
[tex]SD=\sqrt[]{\frac{\sum |x-\bar{x}|^2}{n}}[/tex][tex]SD=\sqrt[]{\frac{|2-2.6|^2+|2-2.6|^2+|1-2.6|^2+|4-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|4-2.6|^2+|1-2.6|^2}{10}}[/tex][tex]\begin{gathered} SD=\sqrt[]{\frac{0.36+0.36+2.56+1.96+0.16+0.16+0.16+0.16+1.96+2.56}{10}} \\ =\sqrt[]{\frac{10.4}{10}}\text{ =}\sqrt[]{1.04} \\ =1.02 \end{gathered}[/tex]Find the Z (confidence interval level) value for 90%
[tex]Z_{90}=1.645[/tex]Find the confidence interval
[tex]\begin{gathered} CI=\bar{x}\pm_{}_{}z\times\frac{s}{\sqrt[]{n}} \\ \bar{x}\Rightarrow\operatorname{mean} \\ s\Rightarrow\text{standard deviation} \\ n\Rightarrow\text{sample size} \\ z\Rightarrow\text{confidence level} \end{gathered}[/tex][tex]\begin{gathered} CI=2.6\pm1.645\times\frac{1.02}{\sqrt[]{10}} \\ =2.6\pm1.645\times0.32 \\ =2.6\pm0.53 \\ \text{Thus,} \\ CI=2.6+0.53\text{ 0r 2.6-0.53} \\ CI=3.13\text{ or 2.07} \end{gathered}[/tex]Hence, a 90% confidence interval estimate of the mean lies between 2 and 3
Therefore, either Michelangelo or Donatello
Solve for x. 70° 37° 10x + 3x=
Let's suppose, the given equation is:
37 = 10x + 3
By solving it
37 - 3 = 10x
34 = 10x
34/10 = x
x = 17/5
Hence, the value of x is 17/5.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y= -3x-6
Step-by-step explanation:
I believe this is correct
10. There is a carnival at a local state park. It cost $5 to get in and $1.50 per ride. .Suppose Maya Mapleton has $25 to spend for the day. Which inequality wouldmodel this situation?5+ 1.50x 2 255x + 1.50 s 255 + 1.50x s 2525x + 1.50 s 5
Let:
B = Maya's budget = $25
c = cost of the entrance = $5
a = cost of each ride = $1.50
x = number of rides
T = total money spent
Therefore:
[tex]\begin{gathered} T\le B \\ where_{} \\ T=c+ax \\ so\colon \\ 5+1.5x\le25 \end{gathered}[/tex]3x² + 11x > 4
How to slove this and the answer for it with it I really do need help with this
Using the factorization, the solution of given inequality is x>1/3 and x< -4.
In the given question we have to solve the given inequality.
The given inequality is 3x^2+11x>4.
Solving the given inequality
Subtract 4 on both side we get
3x^2+11x-4>0
Now factoring the binomial equation.
The multiplication of first and third term is 12 and middle term is 11.
So the possible factors are 1 and 12
3x^2+(12-1)x-4>0
3x^2+12x-x-4>0
3x(x+4)-1(x+4)>0
(3x-1)(x+4)>0
Equating equal to zero
3x-1>0 or x+4>0
Solving for x
x>1/3 or x< -4
Hence, the solution of given inequality is x>1/3 and x< -4.
To learn more about inequality link is here
brainly.com/question/20383699
#SPJ1
Unit 3 homework 3 proving lines are parallelI need help on 1,2,3,4
ANSWER
Not enough information
EXPLANATION
2. We want to see if the lines l and m are parallel based on the information given in the diagram.
In the figure given, we have two angles that lie on the same line m (128 and 52 degrees).
This information is not enough to conclude that the two lines are parallel. To be able to determine that, we need at least an angle that lies on the line l.
Therefore, the information is not enough to determine that l and m are parallel.
For which inequality would x = 8 not be a solution?4x + 3 > 09x - 5 < 100x + 4 ≤ 1072 ÷ x ≥ 4
Given:
Given the inequalities:4
[tex]\begin{gathered} 4x+3>0 \\ 9x-5<100 \\ x+4\leq10 \\ 72\div x\ge4 \end{gathered}[/tex]Required: Identify the inequality in which x = 8 is a solution.
Explanation:
Substitute 8 for x in each inequality and check whether it satisfies the inequality.
Consider 4x + 3 > 0.
[tex]4\cdot8+3=35>0[/tex]So, x = 8 satisfies the inequality 4x + 3 > 0.
Consider 9x - 5 < 100.
[tex]9\cdot8-5=67<100[/tex]So, x = 8 satisfies the inequality 9x - 5 < 100.
Consider x + 4 ≤ 10.
[tex]8+4=12>10[/tex]So, x = 8 not satisfies the inequality.
Consider 72 ÷ x ≥ 4.
[tex]72\div8=9\ge4[/tex]So, x = 8 satisfies the inequality.
Final Answer: The inequality in which x = 8 is not a solution is x + 4 ≤ 10.