The hypotenuse hall will be cheaper .
Both places charge $200 for 20 people .
The linear system of equation gives C = 20 + 10 n
Where ,
C = total cost
N = number of cost
What is linear system of equation?A system of linear equations in mathematics is a grouping of one or more linear equations that share the same variables. A collection of one or more linear equations involving the same variables is known in mathematics as a system of linear equations (or linear system). A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display significantly simpler traits and properties. A line equation is referred to as a linear equation. Or, for example, y + 0.5x 3.5 = 0 and more. The linear equation in each case is the same (remember this!) When two or more linear equations cooperate, this is known as a system of linear equations.
To know more about linear system of equation ,visit:
brainly.com/question/2420285
#SPJ1
[tex] |4x - 5 \leqslant 7| [/tex]here's my absolute value equation
2.
The inequation is given as,
[tex]\lvert4x-5\rvert\leq7[/tex]Consider the analogy,
[tex]\lvert a\rvert\leq b\Rightarrow-b\leq a\leq b[/tex]Applying this analogy to the given inequality,
[tex]-7\leq4x-5\leq7[/tex]Now, we just need to obtain the solution set for this inequality.
Add 5 to each term,
[tex]\begin{gathered} -7+5\leq4x-5+5\leq7+5 \\ -2\leq4x\leq12 \end{gathered}[/tex]Divide by 4 each term of the inequality,
[tex]\begin{gathered} \frac{-2}{4}\leq\frac{4x}{4}\leq\frac{12}{4} \\ -0.5\leq x\leq3 \end{gathered}[/tex]Thus, the solution set to the given inequation is obtained as,
[tex]-0.5\leq x\leq3[/tex]Calculate the distance between the points G=(-2,-6) and N=(-9, 2) in the coordinate plane.Give an exact answer (not a decimal approximation).
To find the diatance between two points you use the next formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the given two points:
[tex]\begin{gathered} d=\sqrt[]{(-9-(-2))^2+(2-(-6))^2} \\ \\ d=\sqrt[]{(-7)^2+8^2} \\ \\ d=\sqrt[]{49+64} \\ \\ d=\sqrt[]{113} \end{gathered}[/tex]Then, the distance between points G and N is the square root of 113
what is the reference angle for four radians rounded to two decimal places?
The reference angle can be calculated 4 radians is in the third quadrant, of the coordinate
reference angle=angle - 3.14
reference angle=4-3.14
the reference angle of 4 radians is 0.8584 rounded to two decimal places is 0.86 radians
Parallelogram ABCD is below. m
The consecutive angles of a parallelogram are supplementary. therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180 \\ 41+x+8.5=180 \\ x+49.5=180 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=180-49.5 \\ x=130.5 \\ x\approx131 \end{gathered}[/tex]Given the standard restricted domains, which of the following relationships does not hold for x=-1? (Assume angles are in radians.)
Answer:
[tex]D:\text{ arccos\lparen cos\lparen-1\rparen\rparen= 1}[/tex]Explanation:
From the restricted domain, we want to check for the relationship that does not hold
All we have to do here is to substitute the value -1 for x, after which we evaluate each of the given equations
We proceed as follows:
[tex]\begin{gathered} a)\text{ sin\lparen}\sin^{-1}(-1))\text{ = -1} \\ b)\text{ arcsin\lparen sin\lparen-1\rparen\rparen = -1} \\ c)\text{ cos\lparen arc cos \lparen-1\rparen\rparen = -1} \\ d)\text{ arc cos\lparen cos\lparen-1\rparen\rparen = 1} \\ e)\text{ tan\lparen arc tan\lparen-1\rparen\rparen = -1} \\ f)\text{ arctan\lparen tan\lparen-1\rparen\rparen = -1} \end{gathered}[/tex]The correct option is thus D
Find the diameter of a circle with a circumference of 28.26 centimeters. Use 3.14 for π.
Answer:
The diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]Explanation:
Given that the circumference of the circle is 28.26 centimeters.
[tex]C=28.26\text{ cm}[/tex]Recall that the formula for the circumference of a circle is;
[tex]\begin{gathered} C=2\pi r=\pi d \\ d=\frac{C}{\pi} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} d=\frac{28.26\text{ cm}}{3.14} \\ d=9.0\text{ cm} \end{gathered}[/tex]Therefore, the diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]As the number manu fucture increase from soo+200. manufactute (ost increase from 350 to 650 birr. Assume that the given data establishes relationship between Cost. cand number of units made. Q and asume that the the relation This is linear. Assuum the thice unit is birr 13.
y = 3x + 50 is the linear equation relating the total cost to the number of units produced.
We know that a linear equation is of the form
y = mx + b
Where m is the slope (rate of change of y with respect to x) and b is the value when x is 0.
With the given information, the cost increased by
$650 - $350 = $300
When the number of units produced increased by 200 - 100 = 100.
So the rate of change of cost (y) with respect to x (number of units) is 300/100=3.
So the equation is of the form
y = 3x + b
Use one of the two given data points to determine b.
When the production was 100, the total cost was $350:
So,
350 = 3(100) + b
350 = 300 + b
b = 50
Hence the answer is y = 3x + 50 is the linear equation relating the total cost to the number of units is produced.
To learn more about linear equations click here https://brainly.com/question/26310043
#SPJ9
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in NYC each year between 2000 and 2013. A line was fit to the data to model the relationship. Which of these linear equations best describes the given model?A) ŷ = ⅖x + 800B) ŷ = 40x + 800C) ŷ = 800x + ⅖D) ŷ = 800x + 40Based on the equation, use this equation to estimate the average rent in 2020.Round your answer to the nearest dollar.$___.
From the graph, we can conclude:
[tex]\begin{gathered} b=y-intercept_{}\approx800 \\ m\approx\frac{900-800}{3-0}\approx33.33\approx40 \end{gathered}[/tex]So, the linear equation that best describes the given model is:
[tex]\hat{y}=40x+800[/tex]Therefore, for 2020 or x = 20:
[tex]\begin{gathered} \hat{y}(20)=40(20)+800 \\ \hat{y}(20)=1600 \end{gathered}[/tex]TWO-Variable SystemsThe two lines graphed below are parallel. How many solutions are there to thesystem of equations?O A. TwoO B. ZeroO C. OneO D. Infinitely manyPREVIOUS
Answer:
B. Zero
Explanation:
The solutions of a system of equations are the points where the graphs intersect. If the lines are parallel, the lines will not intersect, so there will be no solutions to the system.
Therefore, the solutions to the system of two parallel lines are
B. Zero
Use the formula P(B\A)=n(A and B)÷n(A) to find the probability P(kinglface card) when a single. card is drawn from a standard 52 card deck. P(king face card)=
In a deck of 52 cards, there 4 faces of Kings. These are the King of Hearts, King of Diamonds, King of Spades, and King of Clubs. Therefore, the chance of drawing a king face card in a deck of cards would be 4 out of 52 or 1 out of 13.
Answer: P(king face card) = 1/13
7/8 of a watermelon weight is water. if the watermelon weighs 24 kilograms, how many of the kilograms come from water?
ANSWER
21 kg of the watermelon are water.
EXPLANATION
We have to divide the weight of the watermelon by 8 and then multiply by 7 - or in other words, multiply by 7/8:
[tex]24\times\frac{7}{8}=\frac{24}{8}\times7=3\times7=21[/tex]21 of the 24 kilograms of the watermelon are from water.
For positive acute angles A and B, it is known that sin A= 7/25 and cos B= 21/29. Find the value of sin(A + B) in simplest form.
Answer
sin A = 7/25
cos B = 21/29
To find sin(A + B), we use double angle formula.
sin(A + B) = sin A cos B + sin B cos A
sin A = 7/25 , cos B = 21/29
From trigonometric identity, sin²θ + cos²θ = 1
cos A = √(1 - sin²A) = √(1 - (7/25)²)
cos A = √(1 - (49/25))
cos A = √(576/625)
cos A = 24/25
Also, sin B = √(1 - cos²B) = √(1 - (21/29)²)
sin B = √(1 - (441/841))
sin B = √(400/841)
sin B = 20/29
Recall that sin(A + B) = sin A cos B + sin B cos A
sin (A + B) = (7/25 x 21/29) + (20/29 x 24/25)
sin (A + B) = (147/725 + 480/725)
sin (A + B) = (147 + 480)/725
sin (A + B) = 627/725
Use the intercepts to graph the equation. y = -6 x-intercept: Enter as a coordinate: such as (a, b). If there is no x-intercept, enter DNE. Enter as a coordinate: such as (a, b). If y-intercept: there is no y-intercept, enter DNE. 8 6 5 4 ربا
Answer:
x -intercept: DNE
y-intercept: (-6, 0)
Explanation:
The x-intercept is the point where the line intersects the x-axis.
The y-intercept is the point where the line intersects the y-axis.
Now when we draw the line y = -6, we get
We see that the red line does not intersects the x-axis at any point; thereffore, the x-intercept does not exist.
x -intercept: DNE
The red line intersects the y-axis at y = -6; therefore, the y-intercept is the point (0, -6)
if H & J equals 7 and 10s equals 10 find LK
The trapezoid HJKL has T and S as midpoints of the legs
The length of TS can be calculated as the mean or average of the lengths of HJ and LK, i.e.:
[tex]TS=\frac{HJ+LK}{2}[/tex]We are given the lengths HJ=14, LK=42, thus:
[tex]TS=\frac{14+42}{2}=\frac{56}{2}=28[/tex]Now if we have HJ=7 and TS=10, we can find LK by solving the equation for LK
[tex]LK=2TS-HJ[/tex][tex]LK=2*10-7=20-7=13[/tex]The length of LK is 13
A car travels at a steady speed of 40 mph. How far will it go in 15 minutes?
The distance travelled by the car in 15 minutes can be determined as,
[tex]\begin{gathered} D=s\times t \\ D=40\text{ mph}\times15\text{ min}\times\frac{1\text{ h}}{60\text{ min}} \\ D=10\text{ miles} \end{gathered}[/tex]Thus, the required distance is 10 miles.
is 0.5 a integer but not a whole number
...
Natural Numbers are the numbers 1 through infinity.
Whole numbers.
So, they start from 1 and go on...
1, 2, 3, 4, .....
Now, Whole numbers are very same just that they start from 0, so it would be:
0, 1, 2, 3, ....
Integers would include the negatives fo the naturals and 0, so they would be:
...-2, -1, 0 , 1, 2, ....
We want a number NOT natural but integer, that would be 0.
So,
Natural Numbers = 1, 2, 3, 4, 5, ....
Whole Numbers = 0, 1, 2, 3, 4, 5, .....
Integers = ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
3. Which situation could be represented by the graph shown?3027242118A. Garrett buys limes for $0.80 each.B. Sophia buys 12-packs of soda for $1.75 each.C. Jacob buys packs of gum for $1.50 each.D. Allison purchases lemons for $0.75 each.15129631 2 3 4 5 6 7 8 9 10
Find the slope of the graph, use 2 points on the line (0,0) and (4,3)
[tex]m=\frac{3-0}{4-0}=\frac{3}{4}=0.75[/tex]The equation of the graph is y=0.75x, it represents the situation in option D. Allison purchases lemons for $0.75 each
what is the intermediate in the form (x+a)^2=b as a result of completing the square for the following equation?Answer:()^2=
Step 1: Write out the equation
[tex]x^2-12x+32=4[/tex]Step 2: Subtract 32 from both sides of the equation
[tex]\begin{gathered} x^2-12x+32-32=4-32 \\ x^2-12x=-28 \end{gathered}[/tex]Step 3: Complete the square by adding 1/2 of the square of the coefficient of x to both sides
That is
[tex]x^2-12x+(-6)^2=-28+(-6)^2[/tex]This implies that
[tex](x-6)^2=-28+36=8[/tex]Hence the intermediate step is (x - 6)² = 8
7. Solve this riddle. I am an even number. I am between 10 and 20. And when I am divided by 7, I have no remainder. What number am I?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
solve the riddle = ?
Step 02:
We must analyze the exercise to find the solution
a. even number
b. 10 ----- 20
c. x / 7 ===> no remainder
11 , 13 , 15 , 17 , 19 ===> even numbers
2) The mass of a radioactive element decays at rate given by m(t) = m0e^-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay.Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? (Use e = 2.71828.]A) 28.54387 gB) 30.58254 gC) 32.14286 gD) 32.68034 g
Solution
- We are given the following formula:
[tex]\begin{gathered} m(t)=m_0e^{-rt} \\ \text{where,} \\ r=\text{decay rate} \\ t=\text{time} \\ m_0=\text{ Initial mass} \\ m=\text{mass after time t} \end{gathered}[/tex]- We are told that the Initial mass is 50g, the decay rate is .0491593745, time (t) is 10 hours, and e = 2.71828.
- With the above information, we can proceed to substitute the values given into the formula and get the mass of Uranium after 10 hours.
- This is done below:
[tex]\begin{gathered} m=50\times2.71828^{-(0.0491593745)\times10} \\ \\ m=50\times0.611651003817 \\ \\ \therefore m=30.5825\ldots\approx30.58254g \end{gathered}[/tex]Final Answer
The answer is 30.58254g (OPTION B)
2. The following is a graph of the function f(x) = 2^x. Graph thetransformation f(x+3) on the blank coordinate axis.yy
Explanation:
The transformation f(x+3) indicates that we have to translate the graph of f(x) 3 units to the left.
In the graph of f(x) the y-intercept is at y = 1. For f(x+3) this point is moved 3 units to the left, so it is (-3, 1).
Answer:
The graph of f(x+3) is
If X = 7 units, Y = 11 units, Z = 14, and H = 4 units, what is the surface area of the triangular prism ?
we know that
The surface area of a triangular prism is equal to
SA=2B+PL
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the prism
step 1
Find the area B
B=(1/2)*y*h
substitute the given values
B=(1/2)*11*4
B=22 units^2
step 2
Find teh value of P
P=X+X+y
substitute the given values
P=7+7+11
P=25 units
step 3
Find the surface area
SA=2*22+25*14
SA=394 units^2Find and graph the intercepts of the following linear equation: x-4y=16
The given function is:
[tex]x-4y=16[/tex]The x-intercept is the value of x when y = 0.
[tex]\begin{gathered} x-4(0)=16 \\ x=16 \end{gathered}[/tex]The y-intercept is the value of y when x = 0.
[tex]\begin{gathered} (0)-4y=16 \\ -4y=16 \\ \text{ Dividing both sides of the equation by }-4 \\ y=-4 \end{gathered}[/tex].
The average amount of water used per person each day in a country is 45 gallons. How much water does the average person use in one year?
Proportions
It's assumed the amount of water consumed by one person is proportional to the time.
The contant of proportionality is given as 45 gal/day.
Since one normal year has 365 days, then we use the same proportion to calculate the water used in one year as follows:
Water used = 45 * 365 = 16,425 gallons.
The average person uses 16,425 gallons.of water in one year
y = x2 + 5x - 10y=-x² + 2x + 10
Since in both given equations, the variable y is already clear, then you can equal the two equations and then solve for x. So, you have
[tex]\begin{cases}y=x^2+5x-10\text{ (1)} \\ y=-x^{2}+2x+10\text{ (2)}\end{cases}[/tex][tex]\begin{gathered} x^2+5x-10=-x^2+2x+10 \\ \text{ Add }x^2\text{ to both sides of the equation} \\ \text{ Subtract 2x to both sides of the equation} \\ \text{ Subtract 10 to both sides of the equation} \\ x^2+5x-10+x^2-2x-10=-x^2+2x+10+x^2-2x-10 \\ 2x^2+3x-20=0 \end{gathered}[/tex]To solve for x you can use the quadratic formula, that is,
[tex]\begin{gathered} \text{ For }ax^2+bx+c=0\text{ where a}\ne0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In this case
a=2
b=3
c=-20
So,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{(3)^2-4(2)(-20)}}{2\cdot2} \\ x=\frac{-3\pm\sqrt[]{9+160}}{4} \\ x=\frac{-3\pm\sqrt[]{169}}{4} \\ x=\frac{-3\pm13}{4} \\ x_1=\frac{-3+13}{4}=\frac{10}{4}=\frac{5}{2}=2.5 \\ x_2=\frac{-3-13}{4}=\frac{-16}{4}=-4 \end{gathered}[/tex]Now you can plug in the solutions found in any of the given equations to find their respective y-coordinates.
For the first solution, you have
[tex]\begin{gathered} x_1=\frac{5}{2} \\ y_{}=-x^2+2x+10\text{ (2)} \\ y_1=-(\frac{5}{2})^2+2(\frac{5}{2})+10 \\ y_1=-\frac{25}{4}+5+10 \\ y_1=\frac{35}{4} \\ y_1=8.75 \\ \text{ Then} \\ (2.5,8.75) \end{gathered}[/tex]For the second solution, you have
[tex]\begin{gathered} x_2=-4 \\ y=-x^2+2x+10\text{ (2)} \\ y_2=-(-4)^2+2(-4)+10 \\ y_2=-16-8+10 \\ y_2=-14 \\ \text{Then} \\ (-4,-14) \end{gathered}[/tex]Therefore, the solution set of the given system of equations is
[tex]\mleft\lbrace(-4,-14),(2.5,8.75)\mright\rbrace[/tex]Help meeee please!!!!
The coordinates of B' are (1, 0) after transforming the parallelogram down 4 units and right 3 units.
What are coordinates?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions or in space of three dimensions. These are the set of values that shows the exact position. Coordinates are the set of points, or numbers, that locates a point on a line, on a plane, or in space. The points at the coordinates are called coordinate points. The coordinate plane has two axes. Those are horizontal and vertical axes. The two axes intersect each other at a point called the origin. Coordinate axes are one of the fixed reference lines of a coordinate system. It is a two-dimensional number line. It is used to locate the position of any point.
From the graph, the coordinates of B are (-2, 4).
Translating 4 units down means the value of the y-axis is changing. Therefore, new coordinates will be
(-2-0, 4-4)
=(-2, 0)
Then the parallelogram is translated to 3 units to the right. So, the x-axis is changing to a positive end.
The coordinates of B' will be
(-2+3, 0+0)
= (1,0)
To know more about coordinate, visit:
https://brainly.com/question/19187448
#SPJ1
Which situation can be represented by the equation y = 9x?Question 3 options:Michael drove x amount of hours in his car. This is 9 times the amount of miles as y.Michael drove x amount of miles in his car. He drove y amount of hours in 9 miles.Michael has y amount of miles to drive. This amount is 9 times x, the amount of miles to drive in hours.Michael has x amount of hours. This amount is 9 times y, the amount of miles to drive in hours.
Solution:
Given:
[tex]y=9x[/tex]This is a linear equation that relates distance, speed, and time.
where;
[tex]undefined[/tex]An arithmetic sequence has a 10th term of 15 and 14th term of 35. show that the equation (y=mx+b) of this graph equals an =-30+(n-1)5.
The arithmetic sequence follows
[tex]a_n=-30+(n-1)5[/tex]Lets see if the 10th term is 15 by replacing the n for 10
n=10
[tex]a_{10}=-30+(10-1)5[/tex][tex]a_{10}=-30+(9)5=-30+45=15[/tex]Now, Lets see if the 14th term is 35 by replacing the n for 14
n=14
[tex]a_{14}=-30+(14-1)5[/tex][tex]a_{14}=-30+(13)5=-30+65=35[/tex]Then so, the sequence follows the equation an =-30+(n-1)5.what is 7/8 - 3 1/5? i cant firgure it out
Answer:
-93/40 or -2 13/40
Step-by-step explanation:
7/8 - 16/5
Adjust based on the LCM
35/40 - 128/40
35-128/40
Graph the line from the table you found in (5). Remember to scale and label your axes!
We are asked to draw a line by using the values given in the table.
Let x denotes the first column of values and y denotes the second column of values
So, the (x, y) ordered pairs are
(0, 4), (2, 0), (1, 2), (3, -2), (-1, 6)
Let us plot these points on the graph then we would draw a line connecting these points.
Therefore, this is how the graph of the line looks like.
The y-intercept of the line is the point where the line intersects the y-axis.
From the above graph, we see that the line intersects the y-axis at y = 4
Therefore, the y-intercept of the line is 4
The slope of the line is given by
[tex]slope=\frac{\text{rise}}{\text{run}}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
As you can see, we selected two points on the line. (you may select any two points)
The two points are (2, 0) and (3, -2)
The vertical distance is -2 (negative because it is going down) and the horizontal distance is 1
[tex]slope=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}=-2[/tex]Therefore, the slope of the line is -2