Answer:
If a line is perpendicular to another line, that means that the slope is completely opposite that of the original line. The first thing that we do to the slope is we negate the number which means that if we have a slope of [tex]-7[/tex] our slope because [tex]7[/tex] in this step. In our case our slope is [tex]7[/tex] so in this step it becomes [tex]-7[/tex].
Moving onto the second part which is to get the reciprocal of the number which means that if we have [tex]\frac{1}{2}[/tex] then we would switch it to [tex]2[/tex]. In our case our number is [tex]-7[/tex] so we would make that into a fraction like this [tex]-\frac{1}{7}[/tex].
In conclusion, our final slope of the perpendicular line is [tex]-\frac{1}{7}[/tex].
Hope this helps! Let me know if you have any questions
Answer: " [tex]-\frac{1}{7}[/tex] " .
_____________
Step-by-step explanation:
Assume we have a two-dimension Cartesian plane graph;
in which equations of straight lines can be expressed in the form of:
" y = mx + b " ;
in which:
"m" is the slope; as well as the "coefficient" of "x" ;
and: "b" is the y-intercept; that is, the value "y" value of the "(x, y)" coordinate at the point which "x = 0" ; that is, where the graph crosses the "y-axis".
Given the ^aformentioned conditions:
Note that if we select a line that can be written in the format:
" y = mx + b " ; then another line that is "perpendicular" to that
[selected line] will have the slope, "m"; of the value that is the "negative reciprocal value" of the slope, "m" ; of the other line.
Note that is our problem, we select a line—in our given problem:
"Line a" —with a slope, "m = 7 " ;
which is perpendicular to the slope of "Line b" ;
→ then: the slope of "Line B" ; would be the "negative reciprocal value"
of "7" .
Note: " [tex]7 = \frac{7}{1}[/tex] " ; the recriprocal would be: " [tex]-\frac{1}{7}[/tex] " .
_____________
Hope this answer is helpful to you!
A circle has an arc of length 36 with central angle 40°. Find the circumference of the circle.
Answer: 324.02
Step-by-step explanation:
Radius 51.57
Which trigonometric function does the graph below represent?
Answer:
(d) 2sin(2θ +π/4) -1
Step-by-step explanation:
The graphed function has a midline of -1 (eliminates choice A). It will be a cosine function shifted right π/8 units, or a sine function shifted left π/8 units.
__
The shift is accomplished by replacing θ with (θ -π/8) in the sine function, or (θ +π/8) in the cosine function. That means, we're looking for an expression that is either of ...
2(cos(2(θ-π/8)) -1 = 2cos(2θ -π/4) -1 . . . . . no match
or
2(sin(2(θ+π/8)) -1 = 2sin(2θ +π/4) -1 . . . . . matches choice D
_____
Additional comment
In the form ...
g(x) = K·f(C(x -A)) +B
the factor K is a vertical stretch factor, C is a horizontal compression factor, A is a right shift, and B is an up shift. In this function, we have its amplitude stretched by a factor of 2, a down shift of 1 unit, and a horizontal shift of π/8. The horizontal compression factor is 2.
__
The amount of horizontal shift for the cosine function is found at the peak nearest the y-axis. The amount of horizontal shift for the sine function is found at the upward midline crossing nearest the y-axis.
Find |27|.
27
-27
i don't get it.
Answer:
|27| is 27
Step-by-step explanation:
What are you trying to ask?
Answer:
27
Step-by-step explanation:
Always in absolute value, if the number inside it is negative it will be positive. But if a number is already positive it will stay positive. Absolute value is just another way of making things positive. So always nothing will ever be negative.
The mean shoe size of the students in a math class is 7. 5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9. What is the standard deviation of the shoe size data for the math class? 1. 5 2. 7 3. 0 3. 8.
Answer: 1.5
Step-by-step explanation:Let the standard deviation of the shoe size be represented by ' ' and the mean shoe size be represented by ' = 7.5'. Also, the sizes of the shoe be represented by ' '. So, . Hence, the standard deviation of the shoe size data for the math class is 1.5.
Simplify x = cos[2 arcsin(3/5)].
-7/25
7/25
4/5
Answer:
7/25
Step-by-step explanation:
Let [tex]\theta= \arcsin(\frac{3}{5})[/tex] so we have [tex]x=\cos(2\theta)[/tex]
As [tex]\cos(2\theta)=\cos^2\theta-\sin^2\theta[/tex], we'll have [tex]\cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2[/tex]
To determine [tex]\cos(\arcsin(\frac{3}{5}))[/tex], construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since [tex]\theta=\arcsin(\frac{3}{5})[/tex], then [tex]\sin\theta=\frac{3}{5}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus, [tex]\cos\theta=\frac{4}{5}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]. This means that [tex]\cos(\arcsin(\frac{3}{5}))=\frac{4}{5}[/tex].
Hence, [tex]\cos[2\arcsin(\frac{3}{5})]=(\frac{4}{5})^2-(\frac{3}{5})^2=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}[/tex]
An initial deposit of $6300.00 is made into a savings account that compounds 5.2% interest semi-annually. how much is in the account after 10 years?
question 1 options:
$414,740.48
$10,526.59
$10,459.19
$9,289.13
Answer:
$10459.19
Step-by-step explanation:
A linear model A. always predicts a straight line B. always predicts a curved line C. sometimes predicts a straight line and sometimes a curved line D. usually predicts a straight line
A linear model always represents a straight line which is x + y = c. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A linear model is given as
x + y = c
In the linear model, the power of the variable is one and the equation represents on the graph as a line.
More about the linear system link is given below.
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Ruby owns a small business selling bagels. She knows that in the last week 4
customers paid cash, 10 customers used a debit card, and 74 customers used a credit
а
card.
If next week, she is expecting 1600 customers, about how many would you expect to
pay with cash? Round your answer to the nearest whole number.
Answer:
73 people
Step-by-step explanation:
4/10/74=88
1600/88=18.18
18.18 x 4= 73
18.18 x 10= 182
18.18 x 74= 1345
Answer: 73
Step-by-step explanation:
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in a table, shown above. Use technology to find the equation of the least squares regression line. Then use the regression equation to predict the number of cans sold on a day that is 90*F Round your answer to the nearest whole number.
The regression equation to predict the number of cans sold on a day that is 90°F will be 871.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.
Then the regression line will be passing through (55, 340) and (84, 780). Then we have
y - 340 = 15.17(x - 55)
Then the regression equation to predict the number of cans sold on a day that is 90°F will be
y - 340 = 15.17 (90 - 55)
y = 871
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The distribution of professional baseball player salaries has a mean of $3.2 million. an analyst believes that the mean salary for teams on the east coast is different. the analyst randomly selects 50 baseball players from teams on the east coast and records their annual salaries. the mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. a significance test at an alpha level alpha = 0.05 of produces a p-value of 0.02. what is the correct interpretation of the p-value?
a. assuming the true mean salary is $3.2 million, there is a 2% probability that the null hypothesis is true by chance alone.
b.assuming the true mean salary is $3.2 million, there is a 2% probability of getting a sample mean of $3.9 million by chance alone.
c.assuming the true mean salary is $3.2 million, there is a 2% probability of getting a sample mean at least as extreme as $3.9 million by chance alone.
d.assuming the true mean salary is $3.2 million, there is a 98% probability that a sample mean of $3.9 million or one more extreme will occur by chance alone.
Answer:
c
Step-by-step explanation:
Help please..........................................................
Answer:
A) YXWZ
Step-by-step explanation:
W) 57.4*10^4 = 574 000
X) 5.11*10^5 = 511 000
Y) 0.17*10^6 = 170 000
Z) 7.3*10^5 = 730 000
Y, X, W, Z: A
If you shift the exponential parent function, f(x) = 2^x , right 2 units, what is the equation of the new function?
Answer:
[tex]g(x)=2^{x-2}[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=2^x[/tex]
Translated 2 units right: [tex]g(x)=f(x-2)=2^{x-2}[/tex]
We know the rule for shifting right(x is changed)
f(x) —» f(x-a)So
here
For a =2
f(x-2)[tex]\sf 2^{x-2}[/tex]Help me solve the volume for the sphere?
Answer:
38.77 yd³
Step-by-step explanation:
The volume of the sphere can be determined by using the formula 4πr³/3.
[Where "r" is the radius of the circle].
We are given that:
Radius of circle = 2.1 yd
When we substitute the radius in the formula, we get;
⇒ 4 × π × (2.1)³/3
Let π be substituted as 3.14. Then;
⇒ 4 × π × (2.1)³/3
⇒ 4 × (3.14) × (2.1)³/3
When evaulating the cube of 2.1, we get;
⇒ 4 × (3.14) × (2.1)³/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
When simplified, we get;
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (0.7)
⇒ 4 × (3.14) × (4.41) × (0.7)
⇒ (12.56) × (4.41) × (0.7)
⇒ 38.77272 ≈ 38.77 yd³ (Rounded to nearest hundredth)
Therefore, the volume of the sphere is 38.77 yd³.
Which parallelogram has an area of 60 square units?
Answer:
Finding the area of each parallelogram, applying the formula, it is found that the parallelogram D has an area of 60 square units
Step-by-step explanation:
Similarly to a rectangle, the area of a parallelogram is given by height multiplied by base, that is:
In item A, the height is of 15 units and the base is of 10 units, thus, the area, in square units, is of .
In item B, the height is of 6 units and the base is of 10.2 units, thus, the area, in square units, is of .
In item C, the height is of 15 units and the base is of 15 units, thus, the area, in square units, is of .
In item D, the height is of 10 units and the base is of 6 units, thus, the area, in square units, is of , which means that this is the correct option.
2 cm
6 cm
6 cm
What is the surface area of the solid above?
O A. 14 cm2
O B. 120 cm2
O C. 56 cm2
O D. 84 cm2
Answer:
O B. 120 cm2
Step-by-step explanation:
2×(6×6 + 6×2 + 6×2) = 120 centimeters2
X is greater than or equal -3 and less than 5
use x only once in your inequality
Answer:
[tex] - 3 \leqslant x \leqslant 5[/tex]
Which of the following expressions would give the number of ways to choose a group of 7 from a group
of 15?
151!/7!8!
7!/15!8!
7!15!7!
Answer:
A) 15!/(7!8!)Step-by-step explanation:
We are looking for the combination of 7 out of 15.
This is written as
15C7This is calculated as
15!/(7!(15-7)! = 15!/(7!8!)Correct choice is A
How many whole numbers are there from 25 to 38?
Answer:
there is 13 whole number between 25 and 38
Dylan has 20x + 17 baseball cards. He gives 3x - 2 cards to his friend Tristan. How many cards does Dylan now have?
Answer:
17x-15
Step-by-step explanation:
I think.
Answer:
17x+19
Step-by-step explanation:
20x+17-(3x-2) (Set up the equation)
20x+17-3x+2 (Distribute the negative to both, double negative cancel out)
17x+19 (Combine Like terms)
Which two Integers is 29 between
Answer:
28 < 29 < 30
Step-by-step explanation:
29 - 1 = 28
29 + 1 = 30
Then
The integer 29 is between the two integers 28 and 30
Please help! I asked this question the other day and nobody even looked at it. I need help!!!!
Cost of a CD: $23.50
Markup: 63%
Discount: 50%
pls help this is urgent
aiden’s teacher tells him that the values in the table represent a proportional relationship.
x y
1 5
2. 10
3. 15
Based on the table, Alden claims that in order for a coordinate point to be in the proportional relationship, both the
x-coordinate and y-coordinate must be integers.
Determine a coordinate point that proves that Alden's claim is false.
Enter the x-coordinate in the first response box.
Enter the y-coordinate in the second response box.
Answer:
Step-by-step explanation:
im passing this concept trust me the answer is 12
Find the product of (x + 3)(x - 3).
x^2 - 6x + 9
x^2 + 6x + 9
x^2 + 9
x^2-9
Step-by-step explanation:
So the question is easy ....the thing that you need to do is just to multiply the expression and organize the like terms....okay so lets solvee..
[tex](x + 3)(x - 3)[/tex]
Solution,
[tex] = x(x - 3) + 3(x - 3)[/tex]
[tex] = {x}^{2} - 3x + 3x - 9[/tex]
[tex] = {x}^{2} - 9[/tex]
If a job has salary of $470 a week, how much would it pay for a year
Answer:
$22560
step 1
$270 × 4month
=$1880 for a month
step 2
$1880×12months
= $22560
What is the value of x?
99°
35°
81
55
46
134
Answer: 46
Step-by-step explanation:
The angles add to form a straight angle, so x+99+35=180. It follows that x=46.
Q5 A and B
Unsure of how to go about this.
Thanks :)
Answer:
Step-by-step explanation:
the given angle measurments are x, (x + 18), and 2(x - 5)
knowing that the angles add up to 180, you can write the equation:
x + (x + 18) + 2(x - 5) = 180
Then you solve the equation
so our equation is:
x + x + 18 + 2(x - 5) = 180
*combine like terms
2x + 18 + 2(x - 5)
*distribute the 2
2x + 18 + 2x - 10
* combine like terms
4x + 8 = 180
* subtract 8 from both sides
4x = 172
* divide both sides by 4
x = 43
so knowing that x is 43, we can plug that in to the original given angle measurements:
the top angle which was x + 18 becomes 43 + 18, or 61
the bottom right angle was 2(x - 5), now it's 2(43 - 5) or 2(38) which is 76
and the other one was x so it's 43 degrees
We can check our work by adding them together.
61 + 76 + 43 = 180
they equal 180 as the angles of a triangle should.
Note: most of these numbers should have degree symbols, but I don't know how to type that.
PLEASE SOMEONE HURRY I NEED THE ANSWER PLS
7. After washing your hands there are 300 bacteria on your right hand. The amount of bacteria on each of
your hands is doubling each hour. When will the amount of bacteria on your right hand exceed 2000?
A) 2 hours
B) 2½ hours
C) 3 hours
D) 3½ hours
Answer: maybe c?
Step-by-step explanation:
Uh, 300+300 = 600
600+600= 1200
1200+ 1200= 2400
I need help with number 8….
Pls help
The equation properties are:
The distributive propertyThe associative property.The associative property.How to determine the properties?
The equations are given as:
3 * (6 + 2) = 3 * 6 + 3 * 25 * (7 * 8) = (7 * 5) * 85 * 3 * 7 = 7 * 3 * 5The distributive property of an equation states that:
a * (b + c) = ab + ac
This means that 3 * (6 + 2) = 3 * 6 + 3 * 2 is represented by the distributive property.
The associative property of an equation states that:
a * (b * c) = (a * b) * c
This means that 5 * (7 * 8) = (7 * 5) * 8 and 5 * 3 * 7 = 7 * 3 * 5 are represented by the associative property.
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You and your sister have been saving and decide to buy a Playstation 5 together. You need $500 to
buy the Playstation. Together you have $850 saved up. Since you have more money, you contribute
50% of your savings and your sister contributes 75% of hers toward the $500 cost. How much do each
of you have saved individually?
a. Write a system of equations in standard form to model this situation
b. Solve this system of equations using eliminations
According to the information given, we have that:
a) The system of equations is given by: x + y = 850, 0.5x + 0.75y = 500.
b) You has saved $550 and your sister has saved $300.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: The amount you have saved up.Variable y: The amount your sister has saved up.Item a:
Together you have $850 saved up, hence:
x + y = 850.
You contribute 50% of your savings and your sister contributes 75% of hers toward the $500 cost, hence:
0.5x + 0.75y = 500.
Item b:
From the first equation, we have that:
x = 850 - y
Replacing on the second:
0.5(850 - y) + 0.75y = 500
0.25y = 75
y = 75/0.25
y = 300
x = 850 - y = 550.
You has saved $550 and your sister has saved $300.
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