To solve the equation 8/x + 1/5 = 3/x, we multiply the entire equation by 5x to get rid of the fractions to get 40 + x = 15. Solving for x we get x = -25.
Explanation:To solve the given rational equation 8/x + 1/5 = 3/x, we first need to find a common denominator to combine the fractions. Hence, we multiply the entire equation by 5x to get rid of the denominators:
5 * 8 + x = 15
which simplifies to
40 + x = 15.
Then by subtracting 40 from both sides to solve for x, we get:
x = -25.
That is the solution to the rational equation.
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The rational equation 8/x + 1/5 = 3/x is solved by finding a common denominator, simplifying the equation and then factoring the resulting polynomial to find the roots.
Explanation:To solve the given rational equation 8/x + 1/5 = 3/x, we first find a common denominator for the fractions. Seeing x and 5, we can take the common denominator as 5x.
Next, we rewrite each term with the common denominator: (40/5x) + (x/5x) = (15/5x). This simplifies to 40/5x + x/5x - 15/5x = 0. Simplifying further we have 8/x - 3/x + 1/5 = 0.
After setting the equation to zero, one may notice that this equation can be solved by bringing the terms together and then trying to factorize the resulting polynomial. The solution of the equation are the roots of the factored polynomial.
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You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?
$4,618.81
$2,910.63
$5,722.23
$3,910.02
What is the quotient of -19/2 divided by 38/ 7
The diameter of a circle is 8 inches.What is the area?
A.8 inches
B.16 inches
C.32 inches
D.64 inches
The required correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the given information provides the diameter (twice the radius), we need to first find the radius by dividing the diameter by 2.
Given: Diameter = 8 inches
Radius = Diameter / 2 = 8 inches / 2 = 4 inches
Now we can calculate the area using the formula:
= πr² = π * (4 inches)²
≈ 3.14 * 16 square inches
≈ 50.24 square inches
Therefore, the correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
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Final answer:
The area of a circle with an 8-inch diameter is calculated using the formula A = πr². The correct area is around 50.27 square inches, not one of the provided options.
Explanation:
The question asks for the area of a circle with a diameter of 8 inches. To find the area, we use the formula A = πr², where π is approximately 3.14159, and r is the radius of the circle. Since the diameter is 8 inches, the radius (r) is half of that, which is 4 inches.
To calculate the area:
Divide the diameter by 2 to find the radius: 8 inches / 2 = 4 inches.Square the radius: 4 inches ² = 16 square inches.Multiply by π (pi): π × 16 square inches ≈ 50.26548 square inches.The area of the circle is approximately 50.27 square inches, which means none of the given options A, B, C, or D is correct.
Refer to narrative 14-1. a house is selling for $150,000. a deposit of $20,000 was made when the sales contract was signed. the down payment is 30% and the balance will be financed with a 25-year mortgage at 11% and 4 discount points. if the sellers are responsible for the broker's commission (6% of the purchase price); $1,300 in other closing costs; and the existing mortgage, with a balance of $40,000; what proceeds will they receive on the sale of the property?
hello can you please help me posted picture of question
-4 log8 x - 2 = 6
Round to the nearest ten - thousandth
A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.
Answer:
A,B,D,E
Step-by-step explanation:
did it on edge
a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own
After receiving an 8% stock dividend on his initial 75 shares, the man will own a total of 81 shares.
Explanation:The question is asking how many shares the man will own after a corporation where he holds stock declared a dividend payable in stock. The man initially owned 75 shares of stock, each worth $50, and the corporation declared an 8% dividend. To find out how many additional shares he receives as a dividend, we calculate 8% of his 75 shares:
Additional shares = 8% of 75 = 0.08 × 75 = 6 shares.
The man will then own his original 75 shares plus the 6 additional shares, for a total of:
Total shares owned = 75 + 6 = 81 shares.
(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =
a. m = (b) find equations of the tangent lines at the points (1, 8) and (2, 9). y(x) = (at the point (1, 8)) y(x) = (at the point (2, 9))
The slope of the tangent will be "[tex]10a-6a^2[/tex]". The equation at point (1, 8) is "[tex]y = 4x+4[/tex]" and at point (2,9) is "[tex]y = -4x+17[/tex]".
Given equation is:
[tex]y = 5+5x^2-2x^3[/tex](a)
The slope of the tangent to the curve point where [tex]x = a[/tex] is:
→ [tex]\frac{dy}{dx} = m = 10x-6x^2[/tex]
→ [tex]= 10a-6a^2[/tex]
(b)
The equation of tangent at point (1,8) will be:
→ Slope, [tex]m = 10-6[/tex]
[tex]= 4[/tex]
→ [tex]y-8=4(x-1)[/tex]
[tex]y = 4x-4+8[/tex]
[tex]y = 4x+4[/tex]
and,
The equation of tangent at point (2,9) will be:
→ Slope, [tex]m = 10\times 2-6\times 2^2[/tex]
[tex]= 20-24[/tex]
[tex]= -4[/tex]
→ [tex]y-9=-4(x-2)[/tex]
[tex]y-9=-4x+8[/tex]
[tex]y = -4x+17[/tex]
Thus the above answer is right.
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What is the area, in cm2, of the circle shown above? Round your answer to the nearest tenth.
Please help Thankyou
Which of the following is the domain of the function G(F(x))?
F(x) = x + 4, G(y) =
G(F(x)) =
A. All numbers less than or equal to 4
B. All numbers less than or equal to -4
C. All numbers greater than or equal to -4
D. All numbers greater than or equal to 4
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy boy when their fourth fourth child is born, given that the first three three children were all boys all boys.
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?
your drawer contains 6 black socks and 8 white socks. what is the probability that both socks are black
[tex] \displaystyle
|\Omega|=\binom{14}{2}=\dfrac{14!}{2!12!}=\dfrac{13\cdot14}{2}=91\\
|A|=\binom{6}{2}=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15\\\\
P(A)=\dfrac{15}{91}\approx16\% [/tex]
Evaluate Cot0 if sin0= square root of 6/5
hey can you please help me posted picture of question
The ratio of the length to the width of a map is 8 to 5. The map is exactly 32 inches in length. What is the width of the map? A. 13 inches B. 20 inches C. 24 inches D. 32 inches
Answer:
B. 20 inches
Step-by-step explanation:
Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?
[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]
So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.
Algebraically determine if the relation y=10x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry
A.) y-axis
B.)no symmetry
C.)the origin
D.)x-axis
Hey can you please help me posted picture of question
34 + 4 ⋅ 5 = ____
PLEASE HELP ASAP FOR BRAINLIEST!!!!!
Find the feet of c and d
There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose. To play you roll a die. If a six appears you win; all other rolls you lose. if 1000 people played this game during one afternoon what would you expect to be the outcome?
A. the game earns $3330
B. the game earns $1660
C. the game loses $3330
D. the game loses $1660
Correct answer is Option(A) . The game earns $3330
Carnival Game Expected Outcome
To determine the expected outcome, we first need to calculate the expected value of playing this game once.
The cost to play is $20. If a six is rolled, the player wins $100; otherwise, they lose their $20.
Calculations:
Probability of rolling a six = 1/6Probability of not rolling a six (1, 2, 3, 4, or 5) = 5/6Expected value (EV) for one game:
EV = (1/6 x ($100 - $20)) + (5/6 x (-$20))EV = (1/6 x $80) + (5/6 x -$20)EV = $80/6 - $100/6EV = -$20/6EV ≈ -$3.33This means that on average, each player loses approximately $3.33 per game.
Outcome for 1000 Players
If 1000 people play the game, the total expected loss for the players will be:
Total Expected Loss = 1000 x EVTotal Expected Loss ≈ 1000 x (-$3.33) = -$3330Therefore, the game earns approximately $3330.
a salesman's commission on 150,000 sale is 3000. what is the percent?
Michael bought a new soccer Jersey that was $24.99. after taxes the total cost was $28.99. What is the percent if increase
A line passes through the (1, -6) and has a slope of 5. write an equation for this line
Which statements is true
A: all rectangles are squares
B: some trapezoids are parallelogram
C: all square are rhombues
D: no rhombuses are rectangles
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