Answers
[tex]\dfrac{2x-3}x = \dfrac{14}{x+5}\\\\\implies (2x-3)(x+5) = 14x\\\\\implies 2x^2 +10x -3x -15 -14x=0\\\\\implies 2x^2-7x-15=0\\\\\text{Apply quadratic formula,}~~x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}.\\\\\text{In this case,}~ a=2, b=-7~ \text{and}~ c = -15. \\\\\\x = \dfrac{-(-7) \pm \sqrt{(-7)^2 -4\cdot 2 \cdot (-15)}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{7 \pm 13}4\\\\\\[/tex]
[tex]\text{Hence} ~x = \dfrac{7+13}{4} = \dfrac{20}4 = 5 ~\text{or}~ x = \dfrac{7-13}4 = -\dfrac{6}4 = -\dfrac 32[/tex]
Related Questions
Josephine is looking for a new job as a plumber. She responds to a classified ad for a position that pays 54K. What would her weekly salary be to the nearest cent if she gets this job? A. $855.77 B. $1,038.46 C. 1,125.00 D. $1,057.69
Answers
Based on the information given, it should be noted that her weekly salary will be B. $1,038.46.
It should be noted that there are 52 weeks in one year.
Based on the information given, the annual salary is given as 54000.
Therefore, the weekly salary will be:
= Annual salary / Number of weeks.
= 54000 / 52
= $1038.46
Her weekly salary is $1038.46.
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2.0,3.1,4.2,5.3 what is the next three numbers and what are they adding by
Answers
Answer:
6.4, 7.5, 8.6adding 1.1 each time
What is the quotient? StartFraction 3 y 2 Over 3 y EndFraction divided by StartFraction 6 y squared 4 y Over 3 y 2 EndFraction StartFraction 1 Over 2 y EnDfraction StartFraction 3 y 2 Over 6 y squared EndFraction StartFraction 1 Over y EndFraction StartFraction 2 (3 y 2) Over 3 EndFraction.
Answers
The quotient of the expression is [tex]\frac{1}{2y}[/tex]
The expression is given as:
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2}[/tex]
Divide 3y^2 by 3y
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \div \frac{6y^4}{3y^2}[/tex]
Rewrite the equation as a product
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \times \frac{3y^2}{6y^4}[/tex]
Divide 6 by 3
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \times \frac{y^2}{2y^4}[/tex]
Multiply y and y^2
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = \frac{y^3}{2y^4}[/tex]
Divide y^3 by y^4
[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = \frac{1}{2y}[/tex]
Hence, the quotient of the expression is [tex]\frac{1}{2y}[/tex]
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Answer:
its B
Step-by-step explanation:
Find the 63rd term of the arithmetic sequence 17, 26, 35
Answers
Answer:
a₆₃ = 575
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 17 and d = a₂ - a₁ = 26 - 17 = 9 , then
a₆₃ = 17 + (62 × 9) = 17 + 558 = 575
my Christmas present to you
Answers
I need helpppoppppppppppppp
Answers
Answer:
Step-by-step explanation:
2 1
Determine whether each quadrilateral is a parallelogram. Justify your answer.
Answers
Answer:
4. Parallelogram
5. Parallelogram
6. Parallelogram
Step-by-step explanation:
4. This is a parallelogram because the longer sides are parallel to each other and the shorter sides are also parallel to each other. Hence, this is a parallelogram.5. This is a parallelogram because it's angles are the same to the opposite angles. Hence, this is a parallelogram.6. This is a parallelogram because the longer sides are parallel to each other and the shorter sides are also parallel to each other. Hence, this is a parallelogram.Hoped this helped.
A car travels 15 km in 13 minutes. What is its average speed in km/h?
Answers
Answer:
69.45 km/hStep-by-step explanation:
Speed = Distance/Time=> Speed = 15 km ÷ 13/60 => Speed = 15 km ÷ 0.216=> Speed = 15 km/0.216=> Speed = 15 x 4.63/0.216 x 4.63=> Speed = 69.45 km/1 h (Approximate)Conclusion:
Therefore, the speed is 69.45 km/h (Approximate)Hoped this helped.
A cable company has a one time installation fee and then a monthly charge to use their service. The total cost of modeled by the function y=130x+119. Which statement represents the meaning of each part of the function?
Answers
Answer:
130=monthly charge
119=one time installation fee
Step-by-step explanation:
119 is the y-intercept and in problems like these, it is always the one time fee. 130 is the monthly payment because it has an x, which could account for the number of months. For example , say six months passed, you could multiply 130 * 6 to get the monthly fee for six months. I hope that makes sense!
Anand's garden is 70m long. If it is a square type and he has to fence with barbed wire of 3 rounds. What is the total length of the wire?
please give a valid and step by step explanation and answer this will give u an extra 5 points
Answers
Answer:
If her garden is 70m long, and it's a square type, wouldn't that suggest that her garden is 280m long?(70m X 4) And if this is the case, her garden would be 280 X 3=840 since there are 3 rounds?
Step-by-step explanation:
Answer: 840m
What is the leading coefficient of a third degree function that has an output of 221 when x=2, and has zeros of −15, 3i, and −3i?
Answers
Answer:
1
Step-by-step explanation:
The function with the given zeros will factor as ...
f(x) = a(x +15)(x^2 +9) . . . . with leading coefficient 'a'
You have ...
f(2) = 221 = a(2+15)(2^2+9) = a(17)(13) = 221a
Then a = 221/221 = 1
The leading coefficient is 1.
_____
Additional comment
As you know, a function with zero x=p has a factor of (x -p). The given zeros mean the function has factors (x -(-15)), (x -3i). and (x -(-3i)). The product of the last two factors is the difference of squares: (x^2 -(3i)^2) = (x^2 -(-9)) = (x^2 +9). This is how we arrived at the factorization shown above.
1 mi = 1.6 km
How many miles are in 39.2 kilometers?
Answers
Answer:
24.35775
Step-by-step explanation:
Ty for points xd
Answer:
24.35 miles
Step-by-step explanation:
just divide 39.2 by 1.6
Brianna received an overall IQ score of 117 on the Wechsler Scale. This means that Brianna has scored approximately____________ standard deviation above the mean IQ score of ____________. A. 2; 90 B. 1; 110 C. 2; 75 D. 1; 100
Answers
Using the normal distribution, it is found that the correct option is:
D. 1; 100In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean.In this problem:
The mean on the Wechsler Scale is of 100, hence [tex]\mu = 100[/tex].The standard deviation is of 17, hence [tex]\sigma = 17[/tex].Brianna had an score of 117, hence [tex]X = 117[/tex]Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{117 - 100}{17}[/tex]
[tex]Z = 1[/tex]
Hence, the option d is correct.
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Which expression is equivalent to x6 - 16x^2?
o x2(x - 2)2(x2 + 4)
o x2(x - 2)2(x + 2)2
o x2(x - 2)(x + 2)(x2 + 4)
o x2(x - 4)(x2 + 4)
Answers
Answer:
[tex]x^2(x - 2)(x + 2)(x^2 + 4)[/tex]
Step-by-step explanation:
[tex]x^6-16x^2[/tex]
[tex]x^2\left(x^4-16\right)[/tex]
[tex]x^2\left(x^2+4\right)\left(x+2\right)\left(x-2\right)[/tex]
[tex]\boxed{\bold{HOPE \:IT \:HELPS!\: :)}}[/tex]
The required expression that is equivalent to the given expression is x²(x - 2)(x + 2)(x² + 4). Option C is correct.
Given that,
To determine the equivalent expression equivalent to x⁶ - 16x²
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= x⁶ - 16x²
= x²[x⁴- 16]
= x²[x² + 4] [x² - 4] [ Following the rule (a² - b²) = (a + b)(a - b)}
= x²[x² + 4](x + 2)(x - 2)
Thus, the required expression that is equivalent to the given expression is x²(x - 2)(x + 2)(x² + 4). Option C is correct.
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Help me out please number 10 and if you can answer 13 please
Answers
25 divided by 25 /100 divided by 25 = 1/4
40% of 58 and 34% of 76
pls subscribe to aphmau it'll help her alot
Answers
Answer:
See below
Step-by-step explanation:
40% of 58 = 0.40(58) = 23.2
34% of 76 = 0.34(76) = 25.84
Answer:
23.2
25.84
Step-by-step explanation:
To calculate percentage, multiply the number by the percentage's decimal.
for example, 20% of 300
20%-->20/100---->0.20
300×0.20=60
40% of 58--->
40/100--->0.40
58×0.40=23.2
34%--->34/100--->0.34
0.34×76=25.84
In 2012, New York had a population of about 19 million people,
and Vermont had a population of about 626,000 people. What
is the difference in populations between New York and
Vermont?
A) 13.4 x 106
B) 1.8374 x 107
C) 1.34 x 107
D) 1.7964 x 107
Answers
Answer:
B(if the option is 10^7 instead of 107
Step-by-step explanation:
no. of people in New York=19000000
no. of people in Vermont =626,000
difference in populations = 19000000-626,000 =18374000
therefore, the difference in populations is 18374000
(which can also be written as 1.8374x10^7)
Write and solve a system of THREE inequalities that models the situation below. Terrence is going to make and sell cupcakes and giant cookies as a fundraiser to earn money for his bank uniform. He sells the cupcakes for $1.25 each and the cookies for $0.75. He knows he will sell at least 10 cupcakes and 24 cookies. He wants to make at least $50. Find a possible combination of cupcakes and cookies he needs to sell to meet his goal.
Answers
Answer:
x = cupcakes
y = cookies
3x + 1y ≥ 205
x cupcakes at $3 each plus y cookies at $1 each is greater than or equal to $205
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
i think its b
Step-by-step explanation:
A recipe that makes 4 servings calls for Two-thirds cup of flour. How much flour is required to make 20 servings?
6 cups
3 and one-third cups
two-thirds cups
StartFraction 2 over 15 EndFraction cups
PLEASE HURRY ITS A TEST AND TIMED
Answers
20/4=5
(5*2)/3= 3 1/3
orignal price on a comb 0.99 discount 55%
Answers
Answer:
I think 5.45? Sorry, not the best at math
Step-by-step explanation:
if you get a 55% discount off of 0.99 cents you pay 0.45 $
you're saving 0.54 $
[tex]\sf 12(3+5)[/tex]
Answers
Hi,
12(3 + 5) = 12*3 + 12*5 = 36 + 60 = 96
I hope it helped.✅
Answer:
[tex]12(3 + 5) = 12 \times 3 + 12 \times 5 \\ = 36 + 60 \\ = 96[/tex]
Sarah use a gift card to buy for $47 worth of food she has $18 left on her gift card write an equation to represent a situation
Answers
47
-18
29 try that
And if can try division
Answer: 1.50
Step-by-step explanation:
The sum of a number f and 9 is equal to 38. Write an equation to represent this situation.
Kim rented skates for h hours. The rental fee was $2 per hour. She paid a total of $8. Write an equation to represent this situation.
The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Write an equation to represent this situation.
John is paid $8 more than the number of bags of peanuts he sells at the baseball stadium. The table given below shows the relationship between the money John earns and the number of bags of peanuts John sells. Identify the independent and dependent variables, and write an equation to represent this situation.
A taxi charges a flat rate of $3, plus an additional $1.50 per mile. Write an equation to represent this situation.
Kim is playing an online trivia game. she has 25 points and earns 1 point for each correct answer .she will advance to the next round if her score is over 34 points
Answers
Answer: 10 points
Step-by-step explanation:
She must get 10 answers right to get into the next round, if it need to be over 34
25+10=35
Can i have brainliest
Answer:
1x + 25 > 34
Step-by-step explanation:
test says its right
* 5.) Write the following in standard form.* 5.8709 x 107
58, 709
58,709,000
5,870,900
587,090
Answers
Answer:
5.8709 x 10 to the 4th power = 58,709
5.8709 x 10 to the 7th power = 58,709,000
5.8709 x 10 to the 6th power = 5,870,900
5.8709 x 10 to the 5th power = 587,090
Step-by-step explanation:
Hoped that helped:P
Calculate the area of the quarter circle estimate using 3.14 for pi
(Please do say click this link for the answer and I didn’t mean to click that answer)
Answers
The area of the quarter circle with radius 3ft is [tex]7.065 ft^2[/tex]
Area of a quarter circle is given by the formula:
[tex]Area = \frac{\pi r^2}{4}[/tex]
Where r represents the radius of the circle
In the quarter circle shown, the radius, r = 3 feet
π = 3.14
Substitute π = 3.14 and r = 3 into the formula [tex]Area = \frac{\pi r^2}{4}[/tex]
[tex]Area = \frac{3.14 \times 3^2}{4}\\\\Area = \frac{3.14 \times 9}{4}\\\\Area = \frac{28.26}{4}\\\\Area = 7.065 ft^2[/tex]
The area of the quarter circle with radius 3ft is [tex]7.065 ft^2[/tex]
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Five Identical semicircles are arranged as shown.
Find the diameter of one circle
Answers
The diameter of one circle is 28 units
Find the diagram shown below:
Considering the semi-circle at the centre.
Let the unknown distance from the left be x:Let the unknown distance from the right be y:To get the value of "x"
x + 16 = 22
x = 22 - 16
x = 6
To get the value of "x"
16 +y = 22
y = 22 - 16
y = 6
Diameter of one of the circle = x + 16 + y
Diameter of one of the circle = 6 + 16 + 6
Diameter of one of the circle = 28
Hence the diameter of one circle is 28 units
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What is the common ratio for the geometric sequence?
4/3,4, 12, 36,...
Enter your answer in the box.
Answers
Answer:
3 is the correct answer
u can find common ratio by dividing a specific term in GP by its preceding term. ...just as here
4/(4/3) = 3
also 12/4 = 3
also 36 /12 = 3
hence the common ratio for this GP is 3
hope it helped
Step-by-step explanation:
3 4/9 - 1 1/6 answer please
Answers
Whole part = 2
Fractional part = 5/18
=========================================================
Explanation:
4/9 = 8/18 after multiplying top and bottom by 2
1/6 = 3/18 after multiplying top and bottom by 3
So the fractional parts subtract to:
4/9 - 1/6 = 8/18 - 3/18 = (8-3)/18 = 5/18
The whole parts subtract to
3-1 = 2
Overall, we end up with the mixed number of [tex]2 \frac{5}{18}[/tex]
We can write this as 2 & 5/18 or as 2 5/18
Side note: This mixed number converts to the improper fraction of 41/18.
what is 1+1-2+3+1-4+5-5+6+2-8+8 x 2-16+4x5-20 = ?
first to answer correctly gets marked brainliest
Answers
Answer: The answer is 0.