(5x-7)^2-1=8 solve for x
Answer:
[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex] or [tex]x = 2[/tex]
Or:
[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex] or [tex]x = \frac{4}{5}[/tex]
Step-by-step explanation:
Step 1 - Simplify by expanding the brackets:
[tex](5x - 7)^2\\(5x - 7)(5x - 7)\\25x^2 - 35x - 35x + 49\\25x^2 - 70x + 49 - 1\\25x^2 - 70x + 48 = 8[/tex]
Step 2 - Subtract 8 from both sides so the equation equals 0:
[tex]25x^2 - 70x + 48 - 8 = 8 - 8\\25x^2 - 70x + 40 = 0[/tex]
Step 3 - Use the quadratic formula:
[tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\a = 25\\b = -70\\c = 40[/tex]
Plug variables in:
[tex]\frac{-(-70) +- \sqrt{(-70)^2 - (4 * 25 * 40)} }{2 * 25}[/tex]
[tex]\frac{70 +- \sqrt{4900 - 4000} }{50}\\\\\frac{70 +- \sqrt{900} }{50}\\[/tex]
So x is either:
[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex]
[tex]x = 2[/tex]
Or:
[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex]
[tex]x = \frac{4}{5}[/tex]
Hope this helps!
What is the least common denominator of
1/3 and 7/9
Answer:
9
Step-by-step explanation:
9 is the LCD. So you have to multiply 3 by 3 to get 9, so multiply the numerator (1) by 3. 3/9 is the answer to that.
Evaluate the algebraic expression if w= -0.5, x = 2, y= -3, and z = 2.5.
2w^2 - 3x + y - 8z
Answer:
-28.50
Step-by-step explanation:
Given the algebraic expression, 2w² - 3x + y - 8z, where w = -0.5, x = 2, y= -3, and z = 2.5:
Substitute the given values for the variables to evaluate the algebraic expression.
2w² - 3x + y - 8z
= 2(-0.5)² - 3(2) + (-3) - 8(2.5)
= 2(0.25) - 6 - 3 - 20
= 0.50 - 6 - 3 - 20
= -28.50
Therefore, 2w² - 3x + y - 8z = -28.50.
Answer:
-28.5
Step-by-step explanation:
Substitute the values for their given variables and evaluate.
[tex]2w^2-3x+y-8z\\\\2(-0.5)^2-3(2)+(-3)-8(2.5)\\\\2(0.25)-6-3-20\\\\0.5-6-3-20\\\\-28.5[/tex]
Original price of a comics book $2.95 Discount 10% Tax 5%
Answer:
The price of the comic book would be $2.79 after the discount and the tax.
We first take 10% of 2.95 or 0.295 from 2.95 to get our first value of 2.66.
Then we add 5% of 2.66 or 0.133 back to 2.66 to get our last value of 2.79.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
Can someone please help me
Answer: i don''t know the answer im sorry i hope someone helps you :)
Step-by-step explanation:
PLEASE HELP WITH THIS ONE QUESTION
Answer:
Shift 7 units down
Step-by-step explanation:
Shift 7 units down
itements are true.
Choose all answers that apply:
The equation represents a proportional relationship.
B
The unit rate of change of y with respect to z is 1.4.
o
5
The slope of the line is
7
50
A change of 2 units in I results in a change of 2.8 units in y.
-pts
A change of 3 units in a results in a change of 1.2 units in y.
All the statements that are true as regards the proportional relationship of the graph are;
A. The equation represents a proportional relationship
B. The unit rate of change of y with respect to x is 1.4
C. The slope of the line is 7/5
D. A change of 2 units in x results in a change of 2.8 units in y
What is the proportional relationship of the graph?The slope intercept form of the equation of a straight line is;
y = mx + b
where;
m is the slope.
b is the y-intercept.
Since the equation is given as y = 1.4x, then the slope is 1.4 and the y-intercept is 0.
A. The equation represents a proportional relationship;
This is true since the equation because y is always 1.4 times as large as x from the given equation relationship.
B. The unit rate of change of y with respect to x is 1.4;
This is true because when we divide both sides by 1.4, we will get;
y/x = 1.4
C. The slope of the line is 7/5;
This means that the slope is 7/5 = 1.4. This is same as the slope given and it is true.
D. A change of 2 units in x results in a change of 2.8 units in y;
This means that the slope is 2.8/2 = 1.4. This is same as the slope given and it is true.
E. A change of 3 units in a results in a change of 1.2 units in y;
This means that slope = 1.2/3
This is not equal to our given slope and so is not true.
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P(E') = P(F) = 0.6 and P(E n F) = 0.24:
a. Write down P(E).
b. Explain how you know E and F:
i are independent
ii are not mutually exclusive
c Find P(E u F').
Answer:
(4- x)(x - 4) = 16 - x2 help me sir please
Choose the equation that is best represented by the graph.
Answer:
D
Step-by-step explanation:
Because the y-intercept is -3
please help :,) it’s due tomorrow and i’m so confused
I cant really interpret it for you, but here's what all the numbers mean in context:
Constant
Coefficient
This is the y-intercept of the regression line. With 0 wins, this model predicts that there will be 10834 attendants.The other 3 values for the constant can usually be ignored.
Wins
Coefficient
This is the slope of the regression line. For every win, this model predicts that there will be an additional 235 attendants.SE Coefficient
This is the standard error of the slope. If the data were to be collected again, you would expect the slope to vary by about 119. This also means about 68% of samples should be between 235 ± 119, or between 116 and 354. The same would apply for 95% between 2 standard errors away, and 99.7% between 3 standard errors away.T-value
Quoting minitab's blog here, "The t-value measures the size of the difference relative to the variation in your sample data."This is equal to the coefficient divided by the standard error of the coefficient: [tex]\frac{235}{119} =1.98[/tex].This t-value is calculated only on this sample, and would differ on another sample from the same population.The t-value is also directly linked to the p-value below.Before moving on, I'll use these hypothesis:
H₀ slope = 0 (null hypothesis, there is no relationship between the variables)H₁ slope ≠ 0 (alternative hypothesis, there is a relationship)P-value
This is the probability of getting a t-value farther away from 0 than our t-value (1.98).The p-value can be calculated from the t-value and the degrees of freedom (number of samples) depending on if this is a one-tailed or two-tailed test.The p-value of 0.058 here is greater than the common alpha value of 0.05 (95%, below), so we cannot reject the null hypothesis, suggesting that there is no statistically significant relationship between wins and attendants. It's close though, and with a slightly lower confidence interval like 0.06 (94%), we can reject the null hypothesis and conclude that there is a statistically significant relationship.Alpha value
The alpha value is a threshold used to judge if the test value is statistically significant.An alpha value of 0.05 is the most common, and this is a 95% confidence level, meaning you are 95% confident that the test results are accurate.Other things
S
This is the standard deviation of the residuals. 68% would fall within 7377 away from the line, 95% would fall within 14754, etcR²
This is the proportion of the variance that can be explained by the predictor. r² = 12.29% means only 12.29% of the variation in attendance can be explained by the number of wins.Adjusted R²
This one doesn't make too much sense to me in this context. An adjusted r² typically looks at whether any additional predictor variables are contributing to the predictions, but there are no additional predictors here, just wins.Conclusion
Based on all that information, I wouldn't say attendances are influenced by the number of wins. The high p-value, high standard error, and low r² all contribute to my conclusion. Especially looking at the p-value, assuming a common alpha value of 0.05, the relationship between wins and attendances is not statistically significant. It's likely that the positive slope is due to an unknown 3rd variable that influences both attendances and wins, like the popularity of the baseball team. A more popular baseball team is more likely to be skilled, and therefore, a more popular baseball team will get more wins. A more popular baseball team will also obviously have more attendees.
However, if all you have to do is just interpret the slope all on its own, then you could say that the positive slope of the regression line means more wins = more attendees.
Please help if you can I'll even give you a brainiest answer.
whats the answer can someone answer please
Answer:
8. b
9. d
Step-by-step explanation:
5(x+6)-8x=3(10-x)n no solution, one solution, or all real numbers are solutions
Answer:
Infinite, any number
Step-by-step explanation:
Simplify
30 - 3x = 30 - 3x
A cable is 40 decimeters long. How long is the cable in meters?
Be sure to include the correct unit in your answer.
Answer:
4 Meters
Step-by-step explanation:
Formula
divide the length value by 10
A submersible is a type of underwater vessel. Suppose a submersible starts at a depth of 40 feet below sea level, represented by –40 feet. The table shows the submersible's change in depth from one minute to the next.
Answer the questions to find the depth of the submersible after 3 minutes.
1. Write and evaluate a subtraction expression to find the depth of the submersible at 2:16 p.m. (2 points)
2. Write and evaluate a subtraction expression to find the depth of the submersible at 2:17 p.m. (2 points)
3. Write and evaluate a subtraction expression to find the depth of the submersible at 2:18 p.m. (3 points)
4. If the submersible dove straight down, what is the distance between the submersible's starting position at 2:15 and its position at 2:18? Show your work. (3 points)
1. -40 - 180 = -220
2. -40 - 175 = -135
3. -40 - 185 = -225
4. 2:15 = -40
2:18 = 185
distance b/w them is = -40 - 185 = - 225
hope this answer helps you dear! btw I'm not sure but hope so this helps...!!
I agree with the first person that answered.
A chemist has three different acid solutions. The first acid solution contains 20 % 20% acid, the second contains 30 % 30% and the third contains 60 % 60% . They want to use all three solutions to obtain a mixture of 90 90 liters containing 35 % 35% acid, using 2 2 times as much of the 60 % 60% solution as the 30 % 30% solution. How many liters of each solution should be used
Answer:
Step-by-step explanation:
37,4gam
Solve the equation for x:
x2 = 196
Answer: x= 1/196
Step-by-step explanation:
Operations
Five football players ate
15/17
of a lasagna. The 5 players ate equal
amounts. How much of the lasagna did each player eat?
Answer:
3
Step-by-step explanation: because 15 divided by 5 equals 3
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
If the spectator has an angle of 115° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
hole?
25.6°
39.4°
64.3°
65.0°
Using the law of sines, it is found that the angle that the golfer has between the spectator and the hole is of 25.6º.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lenghts and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, in this problem, we have that:
[tex]\frac{\sin{115^\circ}}{200} = \frac{sin{x}}{140}[/tex]
[tex]sin{x} = \frac{140\sin{115^\circ}}{200}[/tex]
[tex]x = \arcsin{0.6344}[/tex]
x = 39.4º.
Considering that the sum of the internal angles of the triangle is of 180º, the angle that the golfer has between the spectator and the hole is given by:
A = 180 - (115 + 39.4) = 25.6º.
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Answer:
25.6
Step-by-step explanation:
I got it right
What is the quotient of -9 Divided by 3 ?
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\large\text{\bf Guide to remember}\downarrow\\\large\textsf{2 negatives = positive}\\\large\textsf{1 negative \& 1 positive = negative}\\\large\textsf{2 positives = positve}\\\large\textsf{1 positive \& 1 negative = negative}[/tex]
[tex]\large\text{This means your answer will most likely be a \boxed{\text{negative}} because}\\\large\text{you have a negative number (-9) \& a positive number (3).}[/tex]
[tex]\large\boxed{\mathsf{-9 \div 3}}\\\large\boxed{\mathsf{= \dfrac{-9}{3}}}\\\large\boxed{\mathsf{= \dfrac{-9\div3}{3\div3}}}\\\large\boxed{\mathsf{= \dfrac{-3}{1}}}\\\large\boxed{\mathsf{= -3\div 1}}\\\large\boxed{\mathsf{= -3}}\\\\\\\\\\\huge\boxed{\text{Therefore. your answer is: \boxed{\textsf 3}}}\huge\checkmark[/tex]
[tex]\huge\text{\bf Good luck on your assignment \&}\\\huge\text{\bf enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A wall that is 12 feet high and 15 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). If each window is 3 feet by 5 feet, determine the area of the space to be painted.
Answer:Measure length of each wall including doors and windows. Find the total square feet of the wall(s) by multiplying ceiling height by total wall length.
Step-by-step explanation:
The required area that is to be painted is given as 150 square feet.
Given that,
A wall that is 12 feet high and 15 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). each window is 3 feet by 5 feet,
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,
Area of the wall = 12 × 15 = 180 square feet
Area of the two windows, = 2 × 3 × 5 = 30 square feet
Area to be painteded = 180 - 30 = 150 square feet,
Thus, the required area that is to be painted is given as 150 square feet.
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What is 20% of $1575.00
step:
20% = 20/100
of = ×
20/100 × $1575.00
answer : $315
Step:
20% = 20/100
of = ×
20/100 × $1575.00
Answer : $315
5. What does the following addition equal?
3 and 7 eights + 6 and 5 eights
3 7/8 + 6 5/8 =
9 12/8 = 10 4/8
10 4/8 = 10 1/2
The answer is 10 1/2
If you are not looking for a mixed fraction it should be..
21/2
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
___ feet, ___ feet, ___ feet
Answer:
Step-by-step explanation:
Let the other leg = x
x^2 + 4^2 = (3x)^2
x^2 + 4^2 = 9x^2
4^2 = 9x^2 - x^2
16= 8x^2
16/8 = x^2
x^2 = 2
x = sqrt(2)
The lengths of the sides
x = sqrt(2)
other side =4
hypotenuse = 3*sqrt(2)
x = 1.4
other side= 4
hypotenuse = 3*1.4142
hypotenuse = 4.2
15-3x when x = to -2
Answer:
21 is the answer
Step-by-step explanation:
Given:
x = -2Let's use the given clue to solve the problem.
15 - 3x = Solution
=> 15 - 3(-2) = Solution
=> 15 + 6 = Solution
=> 21 = Solution
After working on this problem, we can conclude that 21 is our answer.
- [tex]GenuisUser[/tex] -
Answer:
21
Step-by-step explanation:
So, when given a question like this, we must plug in the number give for "x" in the equation.
[tex]15-3x = 15-3(-2)[/tex]
Now, we can simplify using PEMDAS
[tex]15+6 = 21[/tex]
Dont forget that a negative times a negative equals a positive!
PLEASE HELP WITH THIS ONE QUESTION
FACTOR THE FOLLOWING COMPLETELY:
PLease help middle school math 40 points
Answer:
b
Step-by-step explanation:
2/5 * 2x = 4/5
2/5 * 3 = 6/5 = 1 1/5
Answer:
B.
Step-by-step explanation:
Using the distributive property (multiplying 2/5 to both 2x and 3) we can get the answer 4/5x + 1 1/5.
I hope this helps :)
Sarah mowed 3 lawns in 9 hours what is her rate of mowing in hours per lawn?
Answer:
Sarah mowed 1 lawn in 3 hours
Step-by-step explanation:
3 lawns divided by 3 is 1 lawn
9 hours divided by 3 is 3 hours
Answer:
See below:
Step-by-step explanation:
So we know that she moves 3 lawns in 9 hours, to find how much time she takes per lawn we can divide both sides by three to get our number. We can do this due to the reason below:
[tex]\frac{3}{9}=3:9[/tex]
Due to this, we can simplify both sides by 3 and get our rate of 1 lawn per 3 hours.
Have a nice day and feel free to ask me if you need more help :D
4 4/6 + 3 7/8 = ? ........................................
Answer:
[tex]8\frac{13}{24\\}[/tex]
Step-by-step explanation:
[tex]4\frac{4}{6}+3\frac{7}{8}[/tex]
[tex]\frac{28}{6}+\frac{31}{8}=\frac{205}{24}=8\frac{13}{24}[/tex]
What is the quotient of 0 and 15?
15
-15
0
Undefined
ANSWER :
it's 0Step-by-step explanation:0 / 15 = 0 + 0/15 = 0