Answers
5/8 = x+7/ 2
We need to start by doing cross multiply
(8)(2) = (x+7)*5
16 = 5x + 35
5x = 35 - 16
5x =-19
x = -19/5
The correct answer is -19/5
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The mistake is easy to see.
Instead of doing 35 - 16 { they did 35+16 which is wrong because you are transferring 16 to the opposite so you must change the positive sign as well.}
I hope that helps, please let me know if you have further questions about my answer.
Related Questions
Write the equation in logarithmic form.
25 = 32
A. log32 = 5 • 2
B. log232 = 5
C. log32 = 5
D. log532 = 2
Answers
The equation in logarithmic form is B.log₂32 = 2.
To convert the equation 2⁵ = 32 into logarithmic form, you need to identify the base, the exponent, and the result. The given equation can be interpreted as 2 raised to the power of 5 equals 32.
The general form of a logarithmic equation is: log_base (result) = exponent
In this specific case, we have:
base = 2
result = 32
exponent = 5
Putting it into the logarithmic form, we get: log₂32 = 5
So, the correct option is: B.log₂32 = 2
determine the valie of x for which v || w if m2 =100 and. m7 =4x+10
Answers
Find the equation of the tangent line of f^-1(x) at the point where it intersects the x-axis
Answers
note :
1 ) f(X0) = Y0 equiv : X0 = f^-1(Y0)
2 ) ( f^-1(Y0) )' = 1/ f'(X0)
in this exercice : X0 = 0
he equation of the tangent line for graph of : f
Y - Y0 = f'(X0) (X- 0)
sp : he equation of the tangent line for graph of : f^-1(x) is :
X -X0 = f'(Y0) (Y -0)
A bond payable is similar to which of the following?
Answers
A Bond payable is are likely similar to note payable. They are similar because they have both written premises to pay the interest and the principal amount on a specific futures dates. They are both liability and also the interest is accrued in current liability.
The answer to your question is "Notes Payable."
If y = 4x + 3 were changed to y = -4x + 3, how would the graph of the new function compare with the original?
Answers
-4x-3 adding 6 moves the graph upwards by 6 units
-4x-3+6
-4x+3
Answer:
The graph of y=-4x+3 will be as a reflexion in a mirror of y=4x+3
Step-by-step explanation:
y=4x+3 y=-4x+3
. .
. .
. .
solve for x in the diagram (right triangle smallest side 9,bottom side 12,longest x)
Answers
Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 numbers. there are 26,000 possible codes. what is the probability that you will be assigned the code a123?
Answers
What is the simplified expression for ?
Answers
George plays basketball in a week-long camp. On Day 2, he scored 8 points. On day 4, he scored 12 points. Explain how to measure his average rate of change
Answers
avg rate of change is x+2=y
Simplify 10x - 3x + (-5x).
-2x
2x
18x
-18x
Answers
its 10x - 3x - 5x
= 10x - 8x = 2x Answer
The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.
Answers
A = LW = 33
L = 2W-5
Substituting the second equation to the first,
A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3
Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,
L = 2(5.5)-5
L = 6 m
Therefore, the dimensions of the rectangle is 6 m by 5.5 m.
How many three-letter "words" can be made from 5 letters "fghij" if repetition of letters (a) is allowed?
Answers
Also, for the second letter of the word, we can also have 5 choices because it is stated that repetition is allowed. Similarly, there are also 5 choices for the last letter of the word. By fundamental principle of counting, we multiply the numbers identified in the sentences above,
n = 5 x 5 x 5 = 125
Thus, 125 words can be formed from the given letters.
What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?
Answers
9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6
First term: a1 = 3
Sn = n*(a1 + an)/2
Sn = n*(a1 + a1 + (n-1)*d)/2
Sn = n*(2*a1 + (n-1)*d)/2
substitute 26 for n
S26 = 26*(2*a1 + (26-1)*d)/2
substitute 3 for a1
S26 = 26*(2*3 + (26-1)*d)/2
substitute 6 for d
S26 = 26*(2*3 + (26-1)*6)/2
S26 = 2,028
S = n*(a_1+a_n)/2, that easy.
n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!
a_n = a_1 + (n-1)*d, the difference, d, is 6.
So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)
Now a_26 = 6*26-3 = 153, so finally:
S = 26*(3+153)/2 = 26*78 = 2028
2028 is the answer
Name a pair of supplementary angles.
A. angle A E B and angle C E D
B. angle A E B and angle B E D
C. angle A E C and angle B E D
D. angle B E A and angle C E B
Answers
Answer:
B.angle AEB and angle BED.
Step-by-step explanation:
We are given that a diagram .
We have to find a pair of supplementary angles.
Supplementary angles:The pair of angles whose sum is 180 degrees is called supplementary angles.
From given diagram
[tex]\angle AEB+\angle BED=180^{\circ}[/tex]
[tex]\angle AEC+\angle CED=180^{\circ}[/tex]
Hence, option B is true.
Answer:B.angle AEB and angle BED.
If there is a 0.3% chance of something happening one day, what is the possibility of it happening throughout twenty days?
Answers
Well if there is a 3/10 probability of it happening in any given day, there is a 7/10 probability of it not happening on any given day. The probability of it not happening at all in 20 consecutive days is:
(7/10)^20
So the probability of it happening at least once in 20 days is:
1-(7/10)^20≈9992/10000 (about 99.92%)
WILL GIVE A BRAINLIEST IF UR RIGHT PLEASE HELP!!
Determine which ordered pair is NOT a solution of y=3x-8.
a.
(8, 16)
b.
(3, 4)
c.
(–6, –26)
d.
(–10, –38)
Answers
The coordinates (3, 4) are not of this function:
y = 3x - 8
x = 3:
y = 3(3) -8
= 9 - 8
= 1 ≠ 4
∴ (3, 4) does not lie on the line y = 3x - 8
Line EF has an equation of a line y = −2x + 7. Which of the following could be an equation for a line that is perpendicular to line EF?
y = 2x − 3
y = 1 over 2x − 3
y = −2x − 3
y = −1 over 2x − 3
Answers
When a line is given in the form y=mx+n,
m is the slope of this line.
For example, the slope of the line y=-2x+7 is -2.
2.
If lines y=mx+n and y=kx+t are perpendicular, then the multiplication of their slopes is -1, that is
m*k = -1, so k=-1/m
3.
any line perpendicular to y=-2x+7 has slope = -1/(-2)=1/2
4.
Among the choices, y=(1/2)x-3 is a line perpendicular to the given line.
Answer:
b. y=(1/2)x-3
Answer:
[tex]y=\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Step 1
Find the slope of the line EF
we have
[tex]y=-2x+7[/tex]
The slope of the line EF is equal to
[tex]m=-2[/tex]
Step 2
Find the slope of the line perpendicular to the line EF
we know that
If two lines are perpendicular, then the product of its slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=-2[/tex] -----> slope of the line EF
Find the value of m2
substitute
[tex](-2)*m2=-1[/tex]
[tex]m2=1/2[/tex]
therefore
the equation [tex]y=\frac{1}{2} x-3[/tex] could be an equation for a line that is perpendicular to line EF
The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.4 radians
1.2 radians
2.8 radians
0.4 radians
Answers
L = (2πr) x (θ /360)
where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.
Substituting the known values to the equation,
36 = (2π)(15) x (θ / 360)
We translate the equation to find the value of θ,
θ = (36)(360) / 2π(15)
The value of θ is equal to 137.51°.
This can be coverted to radians through the equation below,
θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad
(05.02 LC)
Which equation does the graph below represent?
y = fraction 1 over 4x
y = 4x y
fraction negative 1 over 4x
y = −4x
Answers
Answer:
y=-4x
Step-by-step explanation:
WE need to write the equation for the given graph
In the graph y intercept is (0,0)
The equation of linear graph is y=mx+b
where m is the slope and b is the y intercept
From the given graph y intercept is 0 so b=0
to find slope pick two points from the graph
(0,0) and (1, -4)
slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-4-0}{1-0} = -4[/tex]
m=-4 and b=0
So the equation becomes
y= -4x+0
y= -4x
Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x
Answers
sin5x+sinx=sin3x
this can be written as:
(sinx)^5+sinx=(sinx)^3
dividing through by sin x we get:
(sinx)^4+1=(sinx)^2
let y=(sinx)^2
thus our expression will be given by:
y^2+1=y
y^2-y+1=0
solving the quadratic equation above we get:
y=(-1)^(1/3) or -(-1)^(2/3)
the above is a complex equation, therefore our expression has no defined answer
How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $9000 in three years?
Answers
A=p (1+r/k)^kt
A future value 9000
P present value?
R interest rate 0.06
K compounded monthly 12
T time 3years
We need to solve for p
P=A÷(1+r/k)^kt
P=9,000÷(1+0.06÷12)^(12×3)
P=7,520.80
Assume that adults have iq scores that are normally distributed with a mean of 100100 and a standard deviation of 15. find the third quartile upper q 3q3, which is the iq score separating the top 25% from the others.
Answers
Final answer:
The third quartile (Q3) of IQ scores, which separates the top 25% of scores, is approximately 110.125 for a normal distribution with a mean of 100 and a standard deviation of 15.
Explanation:
To find the third quartile (Q3) of IQ scores, which is the value that separates the top 25% from the others in a normally distributed data set, we use the properties of the normal distribution. The mean IQ score is 100 and the standard deviation is 15. Q3 corresponds to the 75th percentile in a normal distribution.
To find the third quartile (Q3), we often refer to the z-score table or use a statistical software or calculator that can handle normal distribution calculations. The z-score corresponding to the 75th percentile is approximately 0.675. We can then use the formula for z-scores:
Q3 = mean + z*(standard deviation)
Q3 = 100 + 0.675*15
Q3 = 100 + 10.125
Q3 = 110.125
Thus, the third quartile IQ score, separating the top 25% of scores from the rest, is approximately 110.125.
To find Q3 for IQ scores (mean 100, SD 15), calculate 75th percentile: [tex]\( Q3 = 100 + 0.674 \times 15 = 110.11 \).[/tex]
To find the third quartile (upper Q3) of IQ scores, we need to determine the IQ score that separates the top 25% from the rest. Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to find this value.
1. Identify the z-score corresponding to the third quartile (Q3):
- The third quartile (Q3) corresponds to the 75th percentile of the normal distribution.
- Using the standard normal distribution table or a calculator, the z-score for the 75th percentile is approximately 0.674.
2. Convert the z-score to an IQ score:
- Use the formula for converting a z-score to a value in a normal distribution:
[tex]\[ X = \mu + z \sigma \][/tex]
where:
- [tex]\( \mu \)[/tex] is the mean (100)
- [tex]\( \sigma \)[/tex] is the standard deviation (15)
- [tex]\( z \)[/tex] is the z-score (0.674)
3. Calculate the IQ score:
[tex]\[ Q3 = 100 + (0.674 \times 15) = 100 + 10.11 = 110.11 \][/tex]
Therefore, the third quartile (Q3) IQ score, which separates the top 25% from the others, is approximately 110.
If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answers
rope = 36 feet
first piece = x
2nd piece = 2x ( twice as long as the first piece)
3x=36
x=12
first piece = 12 feet
2nd piece = 2 x 12 = 24 feet
Solve |x| + 7 < 4.
........................
Answers
|x| + 7 < 4.
|x| < 4.-7
|x| < -3
no reals solutions because for all reals x : |x| ≥ 0
For Jane's Uber business, she charges $5 initial fee and $0.10 a mile. Joe's Uber business charges $4 initial fee and $0.20 per mile.
1. Write a function for jane's Uber buisiness
2. write a function for joe's Uber business
Answers
Joe : y = 0.20x + 4...or f(x) = 0.20x + 4
The linear equations to calculate the earning by Jane and Joe's Uber business per ride, given the initial fee and charge per mile:
Jane: y = 5 + 0.1x
Joe: y = 4 + 0.2x
What is a linear equation ?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
For Jane's Uber business, she charges $5 initial fee and $0.10 a mile.
Let Jane's earning from a ride be $y.
Let the number of miles she drove in that ride be x miles.
Linear equation to calculate the earning from a ride given the number of miles rode: y = 5 + 0.1x
For Joe's Uber business, he charges $4 initial fee and $0.20 a mile.
Let Joe's earning from a ride be $y.
Let the number of miles he drove in that ride be x miles.
Linear equation to calculate the earning from a ride given the number of miles rode: y = 4 + 0.2x
Learn more about linear equation here
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A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true?
Answers
A triangle has one leg measuring 10 inches and the hypotenuse measuring 20 inches. the other leg measures 10\sqrt[]{3} 10 3 inches. what type of triangle is represented here?
Answers
c^2 = a^2 + b^2
where c is the hypotenuse or the longest side and a, b are the two shorter sides.
To prove that the triangle is indeed a right triangle, we use the equation above.
c^2 = a^2 + b^2
c^2 = 20^2 = 10^2 + (10sqrt(3))^2
400 = 100 + (100(3))
400 = 400
Find three consecutive odd integers with the sum of 51.
Answers
bear in mind that, if you multiply any integer, odd or even, by 2, you get an even, no matter how you slice it and dice it, you always get an even number, 17 *2, 34*2, or whatever * 2, is always an EVEN integer.
you can always get an ODD integer, by simply adding or subtracting 1 from any even, say 4 - 1, or 4 + 1, is 3 and 5 respectively, both odd ones.
and you can always get another consecutive odd integer, by simply jumping 2 units from any odd, so 3, 5, 7, 9, 11 and so on, notice, you simply hop two spots from one, on either direction back or forth, and you get another ODD integer.
alrite, with that in mind, let's pick a reference value, say "a" is our reference integer.
so, 2*a or 2a, we know is an EVEN integer, however, we also know that 2a + 1 is an ODD integer, well, there you have it, our first odd integer is 2a + 1.
now, let's hop twice from there to get our second consecutive odd one, (2a + 1) + 2, or 2a + 3, now, let's hop again to get the next consecutive odd one, (2a + 3) + 2, or 2a + 5.
there you have it, our reference integer is "a", our odd integers are those.
alrite... now, we know their sum gives 51, alrite
[tex]\bf (2a + 1) + (2a + 3) + ( 2a + 5) = 51 \\\\\\ 2a + 1 + 2a + 3 + 2a + 5 = 51 \\\\\\ 2a + 2a + 2a +1 + 3 ++ 5 = 51\implies 6a+9=51\implies 6a=51-9 \\\\\\ 6a=42\implies a=\cfrac{42}{6}\implies \boxed{a=7}[/tex]
now, recall, "a" is only our reference integer, so... if you want to get the consecutive odd integers, well, they're just 2a + 1, 2a + 3 and 2a + 5, and since you already know what "a" is, well, just plug it in to get the integers.
A group of hikers are 675 ft from the base of Guadalupe Peak, which is 8,749 ft tall. What is the angle of elevation when they look at the top of the Peak? Round to the nearest hundredth.
Answers
x= arctan (8749/675) arctan = tan^-1
x=85.59 degrees
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n equals 123n=123, p equals 0.85
Answers
Variance = np(1-p) = (123)(0.4)(1-0.4) =(123)(0.4)(0.6) = 29.52
Standard. Deviation = √variance = √29.52 = 5.43
The mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .
To find the mean, variance, and standard deviation of a binomial distribution with given values of [tex]\( n \)[/tex] and [tex]\( p \)[/tex], we use the following formulas:
Mean [tex](\( \mu \)) = \( n \times p \)[/tex]
Variance [tex](\( \sigma^2 \)) = \( n \times p \times (1 - p) \)[/tex]
Standard Deviation [tex](\( \sigma \)) = \( \sqrt{\text{Variance}} \)[/tex]
Given:
[tex]\( n = 123 \)[/tex]
[tex]\( p = 0.85 \)[/tex]
Let's calculate each of these:
Mean [tex](\( \mu \))[/tex]:
[tex]\( \mu = n \times p \)[/tex]
[tex]\( \mu = 123 \times 0.85 \)[/tex]
[tex]\( \mu = 104.55 \)[/tex]
Variance [tex](\( \sigma^2 \))[/tex]:
[tex]\( \sigma^2 = n \times p \times (1 - p) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times (1 - 0.85) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 104.55 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 15.6825 \)[/tex]
Standard Deviation [tex](\( \sigma \))[/tex]:
[tex]\( \sigma = \sqrt{\sigma^2} \)[/tex]
[tex]\( \sigma = \sqrt{15.6825} \)[/tex]
[tex]\( \sigma \approx 3.9599 \)[/tex]
Therefore, the mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .