The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Can someone help me with this question?
Try this solution:
1. m∠A=m∠L; m∠B=m∠M and m∠C=m∠N;
2. m∠B=m∠M=35° and m∠C=m∠N=95°;
3. m∠A=m∠L=180°-(m∠B+m∠C)=180-35-95=50°
answer: 50°
PLEASE KNOW BEFORE YOU ANSWER. I CAN'T GET THIS WRONG.
Identify and EXPLAIN the ERROR
Show CORRECT WORK and SOLUTION
Show CORRECT WORK and SOLUTION
THE FIRST PIC IS THE QUESTION!!!!
Answer:
a) Error: Moving the decimal point without changing the exponent changes the value of the number. The final number reported is different from the one computed.
b) Correct work: (see below)
... Correct solution: 1.035×10¹¹
Step-by-step explanation:
a) When the decimal point is moved to the left in the mantissa, its value is divided by 10 for each place the decimal point is moved. To keep the overall value of the number the same, the power of 10 must be increased to compensate. The increase in the exponent is the number of places the decimal point is moved left.
In this problem, the decimal point is moved 1 place left, so the exponent needs to be increased from 10 to 11.
b) Correct work:
[tex]\displaystyle(7.14\cdot 10^{10})+(3.21\cdot 10^{10})=(7.14+3.21)\cdot 10^{10}\\\\=10.35\cdot 10^{10}=1.035\cdot 10^{11}[/tex]
Which of the following is 2/11 closest to?
0.
1/2.
1.
2/11 is 0.181818 as a decimal so closest to 0.
Answer:
The answer is the first one which is 0
Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. a. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values.
The expected value of business profit is the sum of probability times profit:
... 0.2×(-10,000) + 0.4×0 + 0.3×5,000 + 0.1×8,000
... = -2000 + 1500 + 800
... = 300 . . . dollars
The expected value of the business return is slightly positve, so Claire should invest in the business.
Answer:
The answer above is correct
While in college, why did Euler work through advanced math books on his own? His father required it. The quality of education offered was not satisfactory. His teacher advised it because he did not have time to tutor Euler privately. He wanted to come up with a method that would help builders find the best arrangement for a ship’s masts.
The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I just did the assignment and got it correct.
While in college, Euler work through advanced math books on his own because his teacher advised it because he did not have time to tutor Euler privately.
Leonhard Euler was a renowned Swiss mathematician who made significant contributions to various branches of mathematics. While in college, Euler worked through advanced math books on his own not because of his father or the quality of education, but because his tutor, Johann Bernoulli, advised it. Bernoulli recognized Euler's talent and encouraged him to pursue mathematics independently, as Bernoulli did not have enough time to tutor Euler privately.
A kite is flying on 39 feet of string. How high is it above the ground if it’s height is 22 feet more than the horizons distance from the person flying it. Assume that the string is being held at ground level.
Answer:
about 36.3 feet
Step-by-step explanation:
Let x represent the height of the kite in feet. Then (x-22) is the horizontal distance to the kite. The Pythagorean theorem tells you the string length is related to these distances by ...
... 39² = x² + (x-22)²
... 2x² -44x -1037 = 0 . . . . rearrange to standard form
Using the quadratic formula, the positive solution is ...
... x = (-b+√(b²-4ac))/(2a) . . . . for a=2, b=-44, c=-1037
... x = (44 + √((-44)² -4(2)(-1037)))/(2·2)
... x = 11 + √639.5 ≈ 36.288
The kite is about 36.3 feet above the ground.
HELP!! WORTH 20 POINTS
( anything )² = anything × anything
5² = 5 × 5 = 25
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is not given, identify the requirements that are not satisfied. Probability Distribution 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 P(x)
Does the table show a probability distribution? Select all that apply.
A.
Yes, the table shows a probability distribution.
B.
No, the sum of all the probabilities is not equal to 1.
C.
No, the random variable x's number values are not associated with probabilities.
D.
No, the random variable x is categorical instead of numerical.
E.
No, not every probability is between 0 and 1 inclusive.
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
Answer:
A.
Yes, the table shows a probability distribution.
Step-by-step explanation:
Given that a sociologist randomly selects single adults for different groups of three. And the random variable x is the number in the group who say that the most fun way to flirt is in person.
Since sample size is only 3, x cannot be more than 3.
So x can take values as 0 1 2 3
Prob distribution is given as
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
We find that x values are from 0 to 3.
Each probability is positive but less than 1.
Also total probability = 1
So this is a perfect probability distribution.
A.
Yes, the table shows a probability distribution.
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
I would add 7 to get ...
... 2x² = 16
then divide by 2 to get
... x² = 8
Now, I would take the square root, recognizing that both positive and negative values will solve the problem.
... x = ±√8
The root can be simplified, so we have ...
... x = ±2√2
_____
The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.
... 2x² -16 = 0 . . . . subtract 9
... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula
... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result
Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.
help please...........
1. y = 3 x
y = -8x
2. y = - 7x
y =-4x - 12
(1)
both equations express y in term of x, hence equate the right sides
- 8x = 3x ( subtract 3x from both sides )
- 11x = 0 ( divide both sides by - 11 )
x = 0
substitute x = 0 into y = 3x → y = 0
solution is : (x, y ) → (0, 0)
(2)
both equations express y in terms of x, hence equate the right sides
- 4x - 12 = - 7x ( add 7x to both sides )
3x - 12 = 0 ( add 12 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
substitute x = 4 into y = - 7x → y = - 28
solution is : (x, y ) = (4, - 28 )
Partial results of a survey about students who wear glasses are shown in the two-way table.
Which of the following statements are true? Check all that apply.
225 students were surveyed.
25 girls always wear glasses.
15 girls sometimes wear glasses.
52 boys never wear glasses.
75 boys were surveyed.
65 students sometimes wear glasses.
Answer:
a. True, b. False, c. True, d. True, e. False, f. True
Step-by-step explanation:
Partial results of a survey about students who wear glasses are shown in the two-way table.
First we complete the table to understand options easily
Always Sometimes Never Total
Boys 25 50 52 127
Girls 35 15 48 98
Total 60 65 100 225
Now we can solve all the options easily.
a. 225 students were surveyed - True
b. 25 girls always wear glasses - False (35)
c. 15 girls sometimes wear glasses - True
d. 52 boys never wear glasses - True
e. 75 boys were surveyed - False (127)
f. 65 students sometimes wear glasses -True
Perform the indicated operation and write the result in the form a+bi. -9i(-9i+4)+3(8+8i)
- 57 - 12i
distribute the parenthesis
= 81i² - 36i + 24 + 24i
[ note that i² = (√- 1 )² = - 1 ]
= - 81 - 36i + 24 + 24i ( collect like terms )
= - 57 - 12i
Answer:
D^^
Step-by-step explanation:
Edge
Write the equation of the line parallel to the given line and passing through the given point. y= 1/2 x+2 through (0,4)
Parallel lines have the same slope, so the slope of the new line is 1/2.
The line passes through (0,4), and this gives the y-intercept, which would equal 4.
The equation now would be: y = 1/2x + 4
Find the values of x and y in the following equation
(x+yi)+(4+9i)=9-4i
A. x = 9 and y = -4
B. x = 5 and y = -13
C. x = -9 and y = 4
D. x = 5 and y = 13
Answer:
B. x = 5 and y = -13
Step-by-step explanation:
Equating real parts, we have ...
... x + 4 = 9
... x = 9 - 4 . . . . subtract 4
... x = 5
___
Equating imaginary parts, we have ...
... yi +9i = -4i
... yi = -4i -9i = -13i . . . . subtract 9i
... y = -13 . . . . . . . . . . . divide by i
[tex](x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}[/tex]
Please Help ASAP 20 points
Find the slope of the line through the given points.
(−1, 2) and (−5,10)
(1,3) and (0,−9)
(18, 6) and (−7, 7)
(−7, 10 ) and (1, 10)
if the x-intercept (–68, 0), and the y-intercept (0, –34), what is the equation?
y = - [tex]\frac{1}{2}[/tex] x - 34
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 68, 0 ) and (x₂, y₂ ) = (0, - 34 )
m = [tex]\frac{-34-0}{0+68}[/tex] = [tex]\frac{-34}{68}[/tex] = - [tex]\frac{1}{2}[/tex]
the y-intercept = (0, - 34 ) ⇒ c = - 34
y= - [tex]\frac{1}{2}[/tex] x - 34
Answer:
Y=-.5x-34
Step-by-step explanation:
this is because you can do y2-y1/x2-x1 to get slope
-34/68
Which equals one half so currently
Y=-1/2x
To get the y intercept we can look at the number when x=0 so it would be -34. So here is the equation
Y=-.5x-34
Genes are responsible for:
A. all inherited traits of an organism.
B. all traits of an organism.
C. no traits of an organism.
D. all preferences of an organism.
A. all inherited traits of an organism.
Genes are something you inherit from a family and are passed on. Sometimes you might skip your parents and inherit a trait from a another past relative.
The graph of an inequality has a closed circle at 2.6, and the ray moves to the left. What inequality is graphed?
x Greater-than-or-equal-to 12
A closed circle is used on the graph.
The arrow on the graph points right.
The inequality representation is x ≤ 2.6 and has been graphed.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of before example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
The graph of inequality has a closed circle at 2.6, and the ray moves to the left.
The closed circle represents that point x = 2.6 is included.
Suppose the variable is x then x ≤ 2.6 represents the inequality.
Hence "The inequality representation is x ≤ 2.6 and has been graphed".
For more about inequality,
brainly.com/question/20383699
#SPJ2
half the quotient of a number and 3 is ten. find the number.
call that number x.
[tex]\frac{1}{2}\frac{x}{3}=10\\\frac{x}{3}=20\\x=60[/tex]
PICK MORE THAN ONE ANSWER:
Eva earned the following test scores in science:
82, 100, 96, 90, 91
Ms. Wade entered the next score as 0 because Eva was absent on test day and hadn’t had a chance to make up the test. Which statements are true based on the data? Check all that apply.
After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data.
After adding the 0 test score, the mean would be affected.
After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
Before the missed test, Eva’s median score was 96.
Before the missed test, Eva’s median score was 91.
Before the missed test, Eva’s mean score was 91.8.
Answer:
The correct answers are "After adding the 0 test score, the mean would be affected.", ad "Before the missed test, Eva’s median score was 91".
Step-by-step explanation:
We know that the mean and median scores would not be helpful in determining Eva's abilities since the 0 is not a representation of how much she knows. However, it will affect the average as adding a 0 to the numerator and a 1 to the denominator will lower the average.
Finally, we can tell the median is 91 before added as when we line up the scores in ascending order, the middle number is 91.
82, 90, 91, 96, 100
Answer:
Statements that are true based on the data:
-After adding the 0 test score, the mean would be affected.
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
-Before the missed test, Eva’s median score was 91.
-Before the missed test, Eva’s mean score was 91.8.
Step-by-step explanation:
-After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data: NO, it won't because the data now has an extreme value that shifts the mean value significantly.
-After adding the 0 test score, the mean would be affected: YES, The mean value would be greatly impacted by adding the 0, (mean=76.5 with the 0; 91.8 without the 0),
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data: YES, because the median won't be affected as much as the mean by the extreme value.
-Before the missed test, Eva’s median score was 96: NO, the median score was 91 at that point.
-Before the missed test, Eva’s median score was 91: YES, the median score was 91, the median is defined as the value where 50% of sorted values are below and 50% are above
-Before the missed test, Eva’s mean score was 91.8: YES, the mean is defined as the sum of all values divided by the total number of values
The formula for calculating the median is:
-odd number of values: [tex]$ x_m = x_\frac{n+1}{2}[/tex]
-even number of values: [tex]$ x_m = \frac{x_\frac{n}{2}+x_\frac{n+2}{2}}{2}[/tex]
MEDIAN BEFORE ADDING THE 0: 82,90,91,96,100
[tex]$ x_m = x_\frac{5+1}{2}[/tex]=3 (third value)
MEDIAN AFTER ADDING THE 0: 0,82,90,91,96,100,
[tex]$ x_m = \frac{x_\frac{6}{2}+x_\frac{6+2}{2}}{2}[/tex]=average between the 3 and 4 values
[tex]$ x_m = \frac{90+91}{2}[/tex]=90.5
The formula for calculating the mean is: [tex]mean ={\frac{1}{n} \sum_{i=1}^n (x_i) $[/tex]
MEAN BEFORE ADDING THE 0
[tex]mean ={\frac{1}{5} \sum_{i=1}^5 (x_i) $[/tex]=[tex]\frac{459}{5}[/tex]=91.8
MEAN AFTER ADDING THE 0
[tex]mean ={\frac{1}{6} \sum_{i=1}^6 (x_i) $[/tex]=[tex]\frac{459}{6}[/tex]=76.5
use subtraction 14 x 25 x 4
Answer:
The correct answer would be -15
Step-by-step explanation:
Although you have the multiplication symbols here, if we were to use subtraction as your instructions indicate, we would just complete the operations from left to right.
14 - 25 - 4
-11 - 4
-15
The functions f(x) and g(x) in the table below show Kim's and Ben's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Kim's savings in dollars 3 9
f(x) = 3x + 5
Ben's savings in dollars 8 11
Which statement best describes Kim and Ben's savings in the long run?
The savings will increase by the same factor for both.
The savings will increase by the same amount for both.
Kim will save more than Ben.
Ben will save more than Kim.
pleaseeee help will give brainliest
The table can be filled in as follows:
[tex]\begin{array}{r|cccc}x(days)&1&2&3&4\\g(x)=3^x&3&9&27&81\\f(x)=3x+5&8&11&14&17\end{array}[/tex]
After 3 days, Kim's savings already exceeds Ben's, and is increasing at a faster rate. The appropriate descriptor is ...
... Kim will save more than Ben
_____
An exponential function increases faster than any polynomial function. (A linear function is a polynomial function.)
If Kim keeps up her savings for 28 days, her account balance will exceed the US Gross National Product of more than $20 trilliion. (Exponential functions tend to increase very rapidly!) Meanwhile, Ben's savings will be $89 on day 28.
_____
Please note the discrepancy in the problem statement. The verbiage says "days", but the table shows "years".
Find the angle complementary to the angle 80°.
The answer is 10 degrees since 90 - 80 = 10
the angle = 10°
Complementary angles sum to 90°
the complement of 80° is 90° - 80° = 10°
Gina is making pancakes for breakfast. Each batch of pancakes calls for 1/4 of a teaspoon of salt. Gina has 9/10 of a teaspoon of salt left. How many batches of pancakes can she make?
Divide the total amount she has by how much she needs per batch.
When dividing fractions, flip the second one over and then multiply straight across.
9/10 / 1/4 becomes: 9/10 x 4/1
9/10 x 4/1 = 36/10 = 3 6/10 = 3 3/5
She can make 3 more batches and have 3/5 of a teaspoon left over.
plz help asap geometry
Answer:
i think its d
Step-by-step explanation:
Answer:
I think it is C triangle ABD and triangle ADC. I hope that helped.
3.5x10^-2 of salt in one liter of water this is how much
2.64x10^20of liters water
Answer:
Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].
Step-by-step explanation:
If 1 liter of water contains [tex]3.5*10^-2[/tex] amount of salt,
Then,
[tex]2.64*10^20[/tex] liters of water will contain,
[tex]3.5*10^-2[/tex] should be multiplied by [tex]2.64*10^20[/tex].
Therefore,
Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].
PLZ HELP ME WITH GEOMETRY
B a counterclockwise rotation about the origin of 90°
under a counterclockwise rotation about the origin
a point ( x , y ) → (- y, x)
figure Q to figure Q'
( 4,2 ) → (- 2, 4 )
(7, 5 ) → (- 5, 7 )
(3, 7 ) → (- 7 , 3 )
(2, 4 ) → (- 4, 2 )
(5, 4 ) → (- 4, 5 )
the coordinates of the original points of the vertices of Q map to the corresponding points on the image Q'
Point M belongs to AN , point N belongs to BM , AB = 18 in and AM : MN : NB = 1:2:3. Find MN.
MN = 6 in
add the parts of the ratio, 1 + 2 + 3 = 6
divide AB by 6 to find 1 part of the ratio
[tex]\frac{18}{6}[/tex] = 3 ← 1 part
AM = 3 in ← 1 part
MN = 2 × 3 = 6 in ← 2 parts
NB = 3 × 3 = 9 in ← 3 parts
and 3 + 6 + 9 = 18 in = AB
HHELLLP IDEK HOW TO DO THIS THIS IS DUE TODAY!!!!!
The slope is 8/5 because you are increasing 8 units in the y axis and 5 units in the x direction. So the equation here would be d = 8/5t which means for every increase in t by 1, d will increase by 8/5.
PLZ HELP GEOMETRY BELOW
c (16, 7 )
the transformation which maps KLMN to K'L'M'N' is a translation < 10, 3 >
Applying the same translation to STUV
T(6, 4 ) → T'(6 + 10, 4 + 3 ) = T'(16, 7 )