The answers are:
[tex]x=15\\y=-10[/tex]
Why?Solving systems of equations using elimination means multiplying/dividing the factors of the given equations in order to reduce variables and make the isolating process simpler, so, solving we have:
We are given the equations:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right.[/tex]
We have that the terms that contains the variable "y" are equal with opposite signs, so, we can eliminate both directly, and then, isolate the variable "x", so, solving we have:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right\\\\\left \{ {{-9x=-115} \atop {-6x=-110}} \right\\\\-9x-6x=-115-110\\\\-15x=-225\\\\x=\frac{-225}{-15}=25[/tex]
Now, that we know "x" we need to substitute it into any of the given equations in order to find "y", so, substituting we have:
[tex]-9x-2y=-115\\\\-9*(15)-2y=-115\\\\-135+115=2y\\\\2y=-20\\\\y=\frac{-20}{2}=-10[/tex]
Hence, we have that:
[tex]x=15\\y=-10[/tex]
Have a nice day!
ANSWER
(15,-10)
EXPLANATION
The given equations are:
–9x – 2y = –115 ...(1)
–6x + 2y = –110...(2)
Add equation (1) from equation (2) to eliminate y.
-9x+-6x=-110+-115
This implies that,
-15x=-225
Divide both sides by -15
[tex]x = 15[/tex]
Put the value of x into equation (2) to find y.
[tex] - 6(15 ) + 2y = - 110[/tex]
[tex] - 90+ 2y = - 110[/tex]
[tex]2y = - 110 + 90[/tex]
[tex]2y = - 20[/tex]
[tex]y = - 10[/tex]
The solution is (15,-10)
what is the difference of scientific notation. 0.00067 - 2.3 x 10^-5
A. 6.47 x 10⁻⁴
B. 6.47 x 10⁻⁵
C. 4.4 x 10⁻⁵
D. 4.4 x 10¹
Answer is letter A
it is the answer
For this case we must find the difference of the following expressions:
[tex]0.00067\\2.3 * 10 ^ {- 5}[/tex]
For the second expression we must run the decimal 5 times to the left, because the exponent is negative, that is:
[tex]0.000023[/tex]
We subtract:
[tex]0.00067-0.000023 = 0.000647[/tex]
Represented in scientific notation we have:
[tex]6.47 * 10 ^ {- 4}[/tex]
Answer:
Option A
50 POINTS
Tyrone rolls a standard number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he has rolled 155 sixes. Find the experimental probability of rolling a six, based on Tyrone’s experiment. Round the answer to the nearest thousandth.
Answer:
Step-by-step explanation:
Unless I'm reading this incorrectly, he throws 155 6's.
There are 1000 throws altogether (according to the table)
So the experimental probability is 155/1000 = 0.155
The answer is B. It is a bit tricky to read.
In the form of a paragraph, explain the difference between a ray and a segment. Include, in your explanation, a physical description of each defined term. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
Answer:
Step-by-step explanation:
Segment
A segment is a line that has 2 end points. We can measure the segment length. A segment is represented by [tex]\overline{AB}\\[/tex] where A and b are the two end points of the segment.
Ray
A ray is an line that has one end point and one point goes in infinity. We cannot measure ray as it's one end goes to infinity. A ray is represented by [tex]\overrightarrow{AB}[/tex] where A is the end point and B is the infinite point.
Figures of ray and segment are attached.
A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground. to the nearest 10th of a foot how far from the building is the base of the ladder a. 20.5 feet b. 30.5 feet C.32.3’ or D.39.5 feet
Answer:
a. 20.5
Step-by-step explanation:
because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x
therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a
Answer:
The correct answer option is a. 20.5 feet.
Step-by-step explanation:
We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.
We are to find the distance of the building from the base of the ladder.
For this, we will use tan:
[tex] tan 70 = \frac { 2 5 } { x } [/tex]
[tex] x = \frac { 2 5 } { tan 7 0 } [/tex]
x = 20.5 feet
MELVIN MOWS A LAWN. THE FRACTION OF THE AWN THAT MELVIN HA MOWED SO FAR IS REPRESENTED BY THE SHADED MODEL SHOWN. MELVIN WILL MOW 3/10 MORE OF THE LAWN BEFORE HE TAKES HIS FIRST BREAK. WHAT FRACTION OF THE LAWN WIK MELVIN HAVE MOWED WHEN HE TAKES HIS FIRST BREAK?
Final answer:
To find the total fraction of the lawn mowed by Melvin before his first break, one would add the additional 3/10 to the already mowed fraction represented by the shaded model.
Explanation:
The student's question is about calculating the fraction of the lawn that will be mowed by Melvin before he takes his first break. Initially, the question does not specify what fraction of the lawn is already mowed, but indicates that Melvin will mow an additional 3/10 of the lawn. Assuming that the shaded model represents the fraction already mowed (let's say x), the total fraction mowed before Melvin's first break would be x + 3/10. Without the specific value of the initially mowed fraction, we cannot provide the exact answer; however, generally, the operation would involve adding the given fraction to Melvin's progress before he mows the additional 3/10.
Find a: 2x+2y=a 2y−4a=2x
Answer:
a=4/5y
Step-by-step explanation:
If we assume that all possible poker hands (comprised of 5 cards from a standard 52 card deck) are equally likely, what is the probability of being dealt: a. a flush? (A hand is said to be a flush if all 5 cards are of the same suit. Note that this definition means that straight flushes (five cards of the same suit in numeric sequence) are also considered flushes.) b. one pair? (This occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct.) c. two pairs? (This occurs when the cards have numeric values a, a, b, b, c, where a, b and c are all distinct.) d. three of a kind? (This occurs when the cards have numeric values a, a, a, b, c, where a, b and c are all distinct.) e. four of a kind? (This occurs when the cards have numeric values a, a, a, a, b.)
Answer:
See the attached photo for the calculations and answers
Step-by-step explanation:
The calculations and explanations are shown in the 3 attached photos below.
The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024
What is probability?
It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.
The probability of being dealt a flush:
For a suit there are 4 choices and 13C₅ choices for a card in that suit
Probability of flush = 4.( 13C₅)/52C₅
Probability of flush = 0.0019
The probability of being dealt one pair:
There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.
P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅
P(one pair) = 0.4225
The probability of being dealt two pairs:
There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.
P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475
The probability of being dealt three of a kind:
There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.
P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211
The probability of being dealt four of a kind:
There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.
P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ2
Martha buys a surfboard that cost $405 for 40% off. How much money does she save?
Answer:
$162
Step-by-step explanation:
Discount = percentage discount ÷ 100 × original cost
Discount = [tex]\frac{40}{100}[/tex] × $405 = $162
15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.
Answer:
y = -2(x -1)^2 -2
Step-by-step explanation:
My "work" consists of providing a table of values to a calculator and asking it for a quadratic model. The result is ...
y = -2(x -1)^2 -2
__
If you like to do these "by hand", you can write the model, then solve for its parameters using the given points.
We observe that the first and third points have the same y-coordinate. Then the vertex of the quadratic will be halfway between the corresponding x-values, at ...
h = (-2 +4)/2 = 1
So, one of the parameters of the model is found already. Using the second point and one other, we can find the remaining parameters for our model:
y = a(x -1)^2 +k
for (4, -20) ...
-20 = a(4 -1)^2 +k = 9a +k
for (0, -4) ...
-4 = a(0 -1)^2 +k = a + k
Subtracting the second equation from the first, we get
-16 = 8a
-2 = a . . . . . divide by 8
Substituting this value of a into the second equation, we have ...
-4 = -2 +k
-2 = k . . . . . . add 2
So, our model is ...
y = -2(x -1)^2 -2
Is 12y -20 factorable
Answer:4(3y-5)
Step-by-step explanation: Factor out 4 from the expression. 4 goes into 12 3 x's, 4 goes in to 20 5 x's Hope this helpedYes. 4(3y-5) is the factored version
Consider the following claim: if the point (2 + d, y) is on the graph of the function
f(x) = x(x-4), then the point (2 - d, y) is also on the graph.
Use algebra to show that the claim is true
What is the relationship between the line x = 2 and the graph of f(x)? Justify your reasoning.
Please show steps
Answer:
The point (2 - d, y) is on the graph of f(x)
The line x = 2 is the axis of symmetry of the graph of f(x)
Step-by-step explanation:
* Lets explain how to prove that a point lies on a graph Algebraically
- Substitute the value of the x-coordinate of the point in the equation
of the graph the answer must be equal the y-coordinate of the point
- The function is a quadratic because the greatest power of x is 2,
then it represented by parabola
- The parabola has a vertex point (h , k), where h is the x-coordinate
and k is the y-coordinate
- This vertex divides the parabola into two equal parts, then the axis
of symmetry of the parabola is a vertical line passing through it
∴ The equation of the axis of symmetry is x = h
- The vertex of the parabola could be minimum point if the parabola
opened upward or maximum if it opened downward
- The minimum value and the maximum value are the value of k
# Look to the attached figures for more understand
* Now lets solve the problem
∵ f(x) = x(x - 4)
∵ Point (2 + d , y) is on the graph of f(x)
- Replace each x in f(x) by 2 + d
∴ f(2 + d) = (2 + d)(2 + d - 4) ⇒ add 2 and -4
∴ f(2 + d) = (2 + d)(-2 + d)
∵ f(2 + d) = y
∴ y = (2 + d)( -2 + d)
* Multiply them to simplify
∴ y = 2(-2) + 2(d) + d(-2) + d(d) = -4 + 2d - 2d + d²
∴ y = -4 + d²
* Lets do these steps again with point (2 - d , y)
- Replace each x in f(x) by 2 - d
∴ f(2 - d) = (2 - d)(2 - d - 4) ⇒ add 2 and -4
∴ f(2 - d) = (2 - d)(-2 - d)
∵ f(2 - d) = y
∴ y = (2 - d)( -2 - d)
* Multiply them to simplify
∴ y = 2(-2) + 2(-d) - d(-2) - d(-d) = -4 - 2d + 2d + d²
∴ y = -4 + d²
- The value of y of the point (2 - d , y) = the value of y of the point on
the graph
∵ f(2 + d) = f(2 - d)
∵ The point (2 + d , y) is on the graph of f(x)
∴ The point (2 - d , y) is on the graph of f(x)
* It is true the point (2 - d, y) is also on the graph.
* To find the relation between the line x = 2 and the graph of f(x)
lets find the vertex of the parabola
- If f(x) = ax² + bx + c in the general form, where a, b , c are constant
then h = -b/2a, where h is the x-coordinate of the vertex point, a is
the coefficient of x² and b is the coefficient of x
∵ f(x) = x(x - 4) ⇒ multiply the bracket by x to put it in the general form
∴ f(x) = x² - 4x
- Find the value of a and b to find h
∵ a = 1 and b = -4
∵ h = -b/2a
∴ h = -(-4)/2(1) = 4/2 = 2
∴ The x-coordinate of the vertex point = 2
∵ The axis of symmetry of the parabola passing through the
vertex point
∴ The equation of the axis of symmetry of the parabola is x = 2
* The line x = 2 is the axis of symmetry of the graph of f(x)
Answer:
Step-by-step explanation:
AYOOO
If a = 7, what is the value of the expression 2(a + 8)? A. 2 B. 15 C. 17 D. 23 E. 30
The answer is 30.
if 7=a and 2(a+8)
all you need to do is replace a with 7
so the formula would then be 2(7+8)
next you would solve in the parentheses.
2(15)
and 2(15) is the same as 2 x 15
so the answer would be 30
Answer: E. 30
Step-by-step explanation:
Cause a=7 and the equation is 2 (a+8) and it the same as 2 × (7+8) which if you use PEMDAS it's 2 × 15 =30
An athlete was having her blood pressure monitored during a workout. The doctor found that the periodic function, P= 20 sin (8pi/3 t) + 90 models her blood pressure as a function of time in seconds.
a. What is the systolic pressure (the maximum blood pressure)?
b. What is the diastolic pressure (the minimum blood pressure)?
c. What is the length in time, of her heartbeat cycle?
d. Sketch a wall labeled graph.
Answer:
(a) 110 mm Hg
(b) 70 mm Hg
(c) 3/4 second
(d) see the attachment
Step-by-step explanation:
(a) The sine function has a maximum value of +1, so the maximum value of p is ...
pmax = 20·(+1) +90 = 20+90 = 110 . . . . . mm Hg
__
(b) The sine function has a minimum value of -1, so the minimum value of p is ...
pmin = 20·(-1) +90 = -20+90 = 70 . . . . . mm Hg
__
(c) The period of the sine function is 2π, so the value of t that makes the argument be 2π will be the period.
8π/3·t = 2π
t = 2π·3/(8π) = 3/4 . . . . . . multiply by the inverse of the coefficient of t
The period of her heartbeat cycle is 3/4 seconds.
__
(d) a graph is attached.
Quick answer if you can help@
The domain is the input values, which are the X- values.
The domain would be -6, -1 , 0, 3
The first answer is the right one.
For this case, we have that by definition, the domain of a function is given by all the values of "x" for which the function is defined. The values of the domain are represented in the starting point.
Then, it is observed in the figure that the values of the domain are:
[tex]{x | x = -6, -1,0,3}[/tex]
ANswer:
Option A
Fine Furniture Company had a net income of $50,000. Accounts receivable increased by $30,000; inventory decreased by $20,000; amounts payable increased by $4,000; and salaries payable decreased by $1,000. The amount of cash flow from continuing operating activities under the indirect method is
Cash flow from operating activities is $43,000. Calculated by adjusting net income for changes in working capital items.
To calculate the cash flow from operating activities using the indirect method, we start with net income and adjust for changes in working capital.
Net Income = $50,000
Changes in Working Capital:
1. Accounts Receivable increased by $30,000, so we subtract $30,000.
2. Inventory decreased by $20,000, so we add $20,000.
3. Amounts Payable increased by $4,000, so we add $4,000.
4. Salaries Payable decreased by $1,000, so we subtract $1,000.
Now, let's calculate the cash flow from operating activities:
Cash flow from operating activities = Net Income + Changes in Working Capital
= $50,000 - $30,000 + $20,000 + $4,000 - $1,000
= $50,000 - $7,000
= $43,000
So, the amount of cash flow from continuing operating activities under the indirect method is $43,000.
Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y plus five squared divided by nine = 1
Answer:
The vertices are (3 , -5) , (-5 , -5)
The foci are (4 , -5) , (-6 , -5)
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the x-axis is
(x - h)²/a² - (y - k)²/b² = 1
- The length of the transverse axis is 2 a
- The coordinates of the vertices are (h ± a , k)
- The coordinates of the foci are (h ± c , k), where c² = a² + b²
- The distance between the foci is 2c
* Now lets solve the problem
- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1
* From the equation
# a² = 16 ⇒ a = ± 4
# b² = 9 ⇒ b = ± 3
# h = -1
# k = -5
∵ The vertices are (h + a , k) , (h - a , k)
∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)
* The vertices are (3 , -5) , (-5 , -5)
∵ c² = a² + b²
∴ c² = 16 + 9 = 25
∴ c = ± 5
∵ The foci are (h ± c , k)
∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)
* The foci are (4 , -5) , (-6 , -5)
Answer:
Vertices: (3,-5) (-5,-5)
Foci: (-6,-5) (4,-5)
Step-by-step explanation:
(x+1)^2/16-(y+5)^2/9 =1
formula: (x-h)^2/a^2 -(y-k)^2/b^2=1
in this case...
a^2=16 b^2=9
h=-1 k=-5
a=4 b=3
v=(h+/-a,k)
v1=(-1+4,-5)=
v1=(3,-5)
v2=(-1-4, -5) =
v2=(-5,-5)
Foci=(h+/-c,k)
F1=(h-c,k)
=(-1-5,-5)
f1=(-6,-5)
F2=(h+c,k)
=(-1+5, -5)
F2=(4,-5)
Hope this helps! :)
if f(×)=-5,tgen f(-3)=
Answer:
f(-3) = -5
Step-by-step explanation:
Put -3 where x is and evaluate the expression:
f(-3) = -5
_____
The function describes a horizontal line. It doesn't matter what x is, the value of the function is -5.
according to the line plot how many more Runners ran 1/3 of a mile for their warm-up than ran 1/4 of a mile
Answer:
2
Step-by-step explanation:
count how many more
What is the x-intercept and the y-intercept of the line on the graph
Answer:
X-intercept: (0,4)
Y-intercept: (-4,0)
Help! Please help me with these two questions!!
1.What is the volume of below composite figure?
2.What is the value of x?
Answer:
2. area = 504 cm^2
3. x = 30°
Step-by-step explanation:
2. The figure can be divided across the middle into a rectangular bottom part and a triangular top part. The triangle will have a base length of 21 cm and a height of 32 -16 = 16 cm. Its area is ...
triangle area = (1/2)bh = (1/2)(21 cm)(16 cm) = 168 cm^2
The area of the rectangle is the product of its base (21 cm) and height (16 cm). Its area is ...
rectangle area = bh = (21 cm)(16 cm) = 336 cm^2
Then the total area of the figure is the sum of the areas of its parts:
total area = triangle area + rectangle area
= (168 cm^2) + (336 cm^2) = 504 cm^2
A plane figure has no volume. The volume is zero.
__
3. The angle whose measure is 4x is supplementary to the angle marked 60°, so is 180° -60° = 120°. That means ...
4x = 120°
x = 120°/4 = 30° . . . . divide by the coefficient of x
The value of x is 30°.
Can someone explain to me how to do this
See the attached picture for the solution.
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Note: Images may not be drawn to scale.
Triangle ABC is shown. Side AB is labeled 9. Side BC is labeled 9. Side CA is labeled 18. Triangle A prime B prime C prime is shown. Side A prime B prime is labeled 4 and a half. Side B prime C prime is labeled 4 and a half. Side C prime A prime is labeled 9.
Answer:
1/2
Step-by-step explanation:
The ratio of corresponding side lengths of the dilation are 1/2 those of the original, so the scale factor is 1/2.
___
For example, A'C'/AC = 9/18 = 1/2.
Detroit, Michigan covers an area of 142.9 square miles. There are approximately 672,800 people living in Detroit. Grand Rapids, Michigan has an area of 45.3 square miles and has a population of approximately 195,100 people. How many more people, per square mile, live in Detroit verses Grand Rapids? Round to the nearest person per square mil
Answer:
401 people per square mile
Step-by-step explanation:
First find the number of people per square mile in Detroit by dividing people by square miles:
672,800/142.9 = 4708.18754374
Then do the same for Grand Rapids:
195,100/45.3 = 4306.84326711
Subtract:
4708.2-4306.8 = 401.4
Round to the ones place:
401
The number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.
Explanation:To find the number of more people per square mile living in Detroit versus Grand Rapids, we need to find the population density for each city. Population density is calculated by dividing the population by the area. Let's do the calculations:
Detroit population density = Detroit population / Detroit area = 672,800 / 142.9 = 4,706.42 people per square mile
Grand Rapids population density = Grand Rapids population / Grand Rapids area = 195,100 / 45.3 = 4,305.97 people per square mile
To find the difference in the number of people per square mile, we subtract the population density of Grand Rapids from the population density of Detroit. Therefore, the number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.
A foam kickboard to use for swimming has two identical hand grips.
a. Find the volume of the kickboard
b. One cubic inch of the phone weighs about 0.007 lb. How much does the kickboard weigh?
Answer:
a. 215.6 in^3
b. 1.51 lb
Step-by-step explanation:
The area of each hand grip hole is that of a circle of radius 0.6 in together with a rectangle 2 in long and 1.2 in wide. So, that area is ...
π·(0.6 in)^2 + (2 in)(1.2 in) = (0.36π +2.4) in^2
The area of the kickboard before the hand grip holes are put in is that of a semicircle of radius 5.5 in together with a rectangle 12 in long and 11 in wide. So, that area is ...
(1/2)·π·(5.5 in)^2 + (12 in)(11 in) = (15.125π +132) in^2
Taking the hand grip holes out, the top area of the board is ...
((15.125π +132) -2(0.36π +2.4)) in^2
= (14.405π + 127.2) in^2
___
a. The volume is the product of the area and the thickness, so is ...
((14.405π +127.2) in^2)·(1.25 in) ≈ 215.568 in^3
__
b. The weight of the kickboard is the product of its volume and its density:
(215.568 in^3)(0.007 lb/in^3) ≈ 1.509 lb
To find the volume of the foam kickboard, its length, width, and height are needed. The weight is then calculated by multiplying the volume by the weight per cubic inch. Without specific dimensions, we cannot provide exact answers for the volume and weight.
Explanation:To find the volume of the foam kickboard, we would need its dimensions such as length, width, and height. If we had these measurements, the volume (V) can be calculated using the formula V = length × width × height. Unfortunately, the question does not provide specific dimensions, so we cannot calculate an exact volume without this information.
To calculate the weight of the kickboard, once the volume is determined, you would multiply the volume by the weight per cubic inch of the foam. Assuming we had a volume of V cubic inches, the weight (W) of the kickboard can be found with W = V × 0.007 lb/in3.
For example, if the kickboard's volume was 100 cubic inches, then the weight would be 100 × 0.007 lb/in3 = 0.7 lb.
David wants to build a rectangular fencing with the 5 identical parts for his animals. He has 780 feet of fencing to make it. What dimensions of each part will maximize the total enclosed area?
Answer:
Step-by-step explanation:
So we're looking at a rectangle split into 5 smaller rectangles. If the height of each rectangle is y and the width of each rectangle is x, then the amount of fencing is:
P = 6y + 10x
And the area of the large rectangle is:
A = 5xy
We know that P = 780:
780 = 6y + 10x
10x = 780 - 6y
5x = 390 - 3y
If we substitute this into our area equation:
A = (390 - 3y) y
A = -3y² + 390y
This is a vertical parabola pointing down, so we know the maximum is at the vertex, which is at -b/(2a). Or, we can use calculus to take the derivative and set to 0.
dA/dy = -6y + 390
0 = -6y + 390
y = 65
Solving for x:
5x = 390 - 3y
5x = 390 - 3(65)
5x = 195
x = 39
So each part will have a width of 39 feet and a height of 65 feet.
With a base salary of $250 and a commission of 4% of all sales, compute Cindy Nelson’s salary for the following weeks:
Week : 1 2 3 4
Base Salary. $250. $250 $250 $250
Sales. $890. $1,126 $975 $ 824
Commission ? ? ? ?
Total Salary ? ? ? ?
Answer:
Part 1) The commission is $35.6 and the total salary for week 1 is $285.6
Part 2) The commission is $45.04 and the total salary for week 2 is $295.04
Part 3) The commission is $39 and the total salary for week 3 is $289
Part 4) The commission is $32.96 and the total salary for week 4 is $282.96
Step-by-step explanation:
Let
x-----> the amount in sales
y----> Cindy Nelson’s salary
we know that
4%=4/100=0.04
so
The linear equation that represent this situation is
y=250+0.04x
case 1) week 1
Sales $890
For x=890
substitute in the linear equation
y=250+0.04(890)
y=250+35.6=$285.6
therefore
The commission is $35.6
The total salary for week 1 is $285.6
case 2) week 2
Sales $1,126
For x=1,126
substitute in the linear equation
y=250+0.04(1,126)
y=250+45.04=$295.04
therefore
The commission is $45.04
The total salary for week 1 is $295.04
case 3) week 3
Sales $975
For x=975
substitute in the linear equation
y=250+0.04(975)
y=250+39=$289
therefore
The commission is $39
The total salary for week 1 is $289
case 4) week 4
Sales $824
For x=824
substitute in the linear equation
y=250+0.04(824)
y=250+32.96=$282.96
therefore
The commission is $32.96
The total salary for week 1 is $282.96
equation find three points that solve the equation then plot on the graph -3y = 5x -7
ANSWER
See attachment.
EXPLANATION
The given equation is
-3y=5x-7
when y=0,
-3(0)=5x-7
0=5x-7
5x=7
[tex]x = \frac{7}{5} [/tex]
we plot (7/5,0)
when x=0
-3y=5(0)-7
y=7/3
we plot (0,7/3)
when x=1,
-3y=5(1)-7
-3y=-2
y=2/3
we plot (1,2/3)
what is the measure arc PD?
a) 35°
b) 90°
c) 110°
d) 180°
Answer:
c) 110°
Step-by-step explanation:
Arc FP is twice the measure of the marked angle, so is 70°. If FD is supposed to be a diameter, then arc FPD is a semicircle (180°) and arc PD is 180° -70° = 110°.
Elevation and depression? Someone help me please
5 x tan 66 = 7.140
your welcome :)
Answer:
11.2Step-by-step explanation:
What is the length of AC?
A is at -8 and C i5 at 5
-8 to 0 is 8 units and 0 to 5 is 5 units.
8 +5 = 13
AC is 13 units long.
For this case, we have that by definition, the distance between two points any A and B will be the absolute value of the subtraction of their coordinates in the order that is preferred. (the distances can not be negative)
So:
We find the distance from A to a point x located at 0. ENtonces:
[tex]| -8-0 | = | -8 | = 8[/tex]
Now we add the distance from x to C. From point x (located at zero) to point C there are 5 spaces, then:
[tex]8 + 5 = 13[/tex]
Thus, the distance from A to C is 13
Answer:
13