Answer:
The [tex]y[/tex]-coordinate of this midpoint is [tex]5[/tex].
Step-by-step explanation:
Let [tex]{\sf A}[/tex] and [tex]{\sf B}[/tex] denote two points in the cartesian plane.
If point [tex]{\sf A}[/tex] is at [tex](x_{a},\, y_{a})[/tex] while point [tex]{\sf B}[/tex] is at [tex](x_{b},\, y_{b})[/tex], the midpoint of [tex]{\sf AB}[/tex] would be at:
[tex]\begin{aligned}\left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2} \right)\end{aligned}[/tex].
In other words, the [tex]y[/tex]-coordinate of the midpoint of [tex]{\sf AB}[/tex] would be the average of the [tex]y\![/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex].
In this question, the [tex]y[/tex]-coordinates of point [tex]{\sf A}[/tex] and point [tex]{\sf B}[/tex] are [tex]3[/tex] and [tex]7[/tex], respectively. The [tex]y\![/tex]-coordinate of the midpoint of [tex]{\sf A}\![/tex] and [tex]{\sf B}[/tex] would be the mean [tex](3 + 7) / (2) = 5[/tex].
h is a trigonometric function of the form h(x)=a\cos(bx+c)+dBelow is the graph of h(x)h(x)h, left parenthesis, x, right parenthesis. The function has a maximum point at (-2\pi,3) and a minimum point at(− 2 π ,−4). Find a formula for h(x). Give an exact expression.
Answer is h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π ) - [tex]\frac{1}{2}[/tex]
∵The maximum point (- 2π. 3 )
minimum point (- π / 2 , - 4)
and h(x) = a cos (b x + c)+ d
∴ a + d = 3 d = - 1/ 2
⇒
-a + d = -4 a = 7 / 2
{solve the equation}
and -2πb + c = 0 b = 2 / 3
⇒
- ( π/ 2) b + c = λ c = 4 / 3 π
∴ h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π) - [tex]\frac{1}{2}[/tex]
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant
here detail explanation:
Sine Function
Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:
Sin a =Opposite/Hypotenuse = CB/CA
Cos Function
Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.
Cos a = Adjacent/Hypotenuse = AB/CA
Tan Function
The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.
Tan a = Opposite/Adjacent = CB/BA
Also, in terms of sine and cos, tan can be represented as:
Tan a = sin a/cos a
Secant, Cosecant and Cotangent Functions
Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:
Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB
Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB
cot a = 1/(tan a) = Adjacent/Opposite = BA/CB
Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.
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HELP ME PLEASE TY
Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.
Explain the concept of rational numbers.?It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.
It is possible when decimals and numbers have worked effectively.
In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.
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Florencia depositó algún dinero en una cuenta en la que ganaba interés.
La tabla a continuación nos muestra la cantidad en la cuenta en distintos momentos.
AYUDAAAA PORFA
Usando una función lineal, tenemos que:
Con cada año adicional, la cantidad en la cuenta es incrementada en 60.
¿Qué es una función lineal?Una función lineal es modelada por:
y = mx + b
En el cual:
m es la pendiente, que es la tasa de cambio, es decir, cuánto cambia y cuando x cambia en 1.b es la intersección con y, que es el valor de y cuando x = 0, y también se puede interpretar como el valor inicial de la función.En este problema, hay que la pendiente es de 60, puesto que en cada año la cantidad aumenta en $60, por eso:
Con cada año adicional, la cantidad en la cuenta es incrementada en 60.
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Write and solve an equation for the situation.
4. The sum of 7 and u is 14. (1 point)
7+u = 14; u = 7
14+7=u: u = 21
7+u = 14: u = 8
7+14=u: u = 21
Answer:
=> 7+u = 14; u = 7
Step-by-step explanation:
The sum of 7 and u is 14
=> u + 7 = 14
=> u = 14-7
=> u = 7
PLS EXPLAIN THIS ITS URGENT HOW DO YOU DO THISSSS
Answer:
It means you will have to match the name with the correct numbers on the right hand side.example:Animal bread
food dog
answeranimal— dog
food — bread
The real question answer:Zero slope — ( 16,3), (16,-80)Negative slope — (-5,-20), (-11,-20)undefined slope— (-1000,2500), (500,4000)Positive slope— (0,4,25), (1,25,1,75)Incase you aren't still convinced, you can try using the slope formula to solve it yourself .
slope = Y2 - Y1
————
X2 - X1
Hope this helpsGood luck ✅
How much will a person pay for 6.8 pounds of bananas at a price of $0.79 per pound?
Answer:
A person will pay $5.37
Step-by-step explanation:
6.8 pounds of bananas x $0.79 per pound = $5.37.
I hope this helps and have a blessed day! :)
Graph the following system of equations.
3x + 6y = 6
2x + 2y = 6
What is the solution to the system?
A)There are infinitely many solutions.
B)There is one unique solution, (4, -1).
C)There is one unique solution, (6, -2).
D)There is no solution.
The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is
B) There is one unique solution, (4, -1).
What is a solution for a system of equations?The solutions for a system of equation is the intersecting points between them
We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.
Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.
The system of equations has no solution when they are parallel to each other.
So, now we'll graph this system of equations and observe where they lie in XY coordinate.
Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).
We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).
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Quadrilateral WXYZ with vertices W(0,-4), X(13,0), Y(9,-12), and Z(5,-12); scale factor: k = 3/4, center of dilation: (1,0)
Dilation involves changing the size of a quadrilateral or any shape
The coordinates of the image of the dilation are: [tex]W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$[/tex] and [tex]$Z^{\prime}=(4,-9)$[/tex]
This is further explained below
How to determine the vertices of the image?The vertices of the pre-image are given as:
W=(0,-4)
X=(13,0)
Y=(9,-12)
Z=(5,-12)
The scale factor is given as:
k=3 / 4
The center of dilation is given as:
(a, b)=(1,0)
To calculate the vertices of the image, we make use of the following formula [tex]$\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$[/tex]
So, we have:
W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)
W'=(1 / 4,-3)
X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)
X'=(10,0)
Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)
Y'=(7,-9)
Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)
Z'=(4,-9)
Hence, the coordinates of the image of the dilation are:
W'=(1 / 4,-3),
X'=(10,0),
Y'=(7,-9)
Z'=(4,-9)
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A woman has a total of $9,000to invest. She invests part of the money in an account that pays7%per year and the rest in an account that pays9%per year. If the interest earned in the first year is$710, how much did she invest in each account? She invested $___ at 7% and $___ at 9%.
She invested $5,000 at 7% and $4,000 at 9%
How much is invested at each rate of return?
The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%
total interest at 7%=interest rate*amount invested
interest rate=7%
amount invested=x
total interest at 7%=7%*x=0.07x
total interest at 9%=9%*(9000-x)
total interest at 9%=810-0.09x
total interest on both accounts=0.07x+810-0.09x
total interest on both accounts=810-0.02x
total interest earned=$710
710=810-0.02x
0.02x=810-710
0.02x=100
x=100/0.02
x=amount invested in the account which earns 7%=$5,000
amount invested at 9%=$9000-$5000
amount invested at 9%=$4,000
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i’m not sure on how to solve this equation. 10(2y+2)-y=2(8y-8)
Answer:
-12
Step-by-step explanation:
Distribute
20y+20-y=16y-16
Combine like terms
19y+20=16y-16
subtract 16y from 19y and subtract 20 from -16
3y=-36
Divide by 3
y=-12
3. What is the cardinality number of the set {2, 4, 6, 8, 10, 12}?
a. 2
b. 6
c. 8
d. 10
The cardianality of the set {2, 4, 6, 8, 10, 12} is 6.
According to the given question.
We have a set {2, 4, 6, 8, 10, 12}.
Here, we have to find the cardianality of the set {2, 4, 6, 8, 10, 12}.
As we know that, the cardinality of a set is a measure of the number of elements of the set.
From the given set {2, 4, 6, 8, 10, 12} we can say that the total number of elements in the given set is 6. So, the cardianality of the set is 6.
Hence, the cardianality of the set {2, 4, 6, 8, 10, 12} is 6.
Thus, option b is correct.
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a runner wants to run 11.7 kmkm . her running pace is 8.1 mi/hrmi/hr . how many minutes must she run?
The runner should run for roughly around 54 minutes.
What do we mean by conversion factors?A conversion factor is an amount that is used to multiply or divide one set of units into another. When converting to an equal value, the appropriate conversion factor must be used. To convert inches to feet, for example, the suitable conversion value is 12 inches equal to 1 foot.To find how many minutes must the runner run:
1 mile = 1.6 kmSo, 8.1 miles = 1.6 kmMinutes required are:
11.7 × 60 / 8.1 × 1.6 = 54.16Therefore, the runner should run for roughly around 54 minutes.
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Need an explanation, thx
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula and equate to the given slope
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(a)
(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )
[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then
[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )
y + 4 = 6 ( subtract 4 from both sides )
y = 2
ordered pair is (0, 2 )
(b)
(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )
[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then
[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )
3(x + 2) = 21 ( divide both sides by 3 )
x + 2 = 7 ( subtract 2 from both sides )
x = 5
ordered pair is (5, 5 )
(c)
(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )
[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then
[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )
- 5(1 - x) = - 20 ( divide both sides by - 5 )
1 - x = 4 ( subtract 1 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
ordered pair is (- 3, 5 )
(e)
(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )
[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then
[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )
- 7(2 - y) = 14 ( divide both sides by - 7 )
2 - y = - 2 ( subtract 2 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
ordered pair is (- 6, 4 )
You want to put a 5 inch thick layer of topsoil for a new 20 ft by 12 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:64
Step-by-step explanation: 12 x 2 = 24 and 20 x 2 = 40 and if you add it all up it equals 64 cubic yards please tell me if i'm wrong
On a city map, 5th Avenue is parallel to Main Street. If 5th Avenue is
represented by the equation y=2x-3, what is the equation representing Main Street if Main Street passes through the point (5, 2)?
The equation representing Main Street if Main Street passes through the point (5, 2) is; y = 2x - 8
How to find the equation in slope intercept form?
We are given the linear equation that represents 5th Avenue as;
y = 2x - 3
Now, main street is parallel to 5th avenue and as such will have the same slope.
Thus, equation of the line passing through (5, 2) representing main street is;
y - 2 = 2(x - 5)
y - 2 = 2x - 10
y = 2x - 10 + 2
y = 2x - 8
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What did lambert call the difference between the angle-sum of a triangle and 180 degrees?
Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
Who is Lambert?Johann Heinrich Lambert (26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made significant contributions to mathematics, physics (particularly optics), philosophy, astronomy, and map projections. Lambert pioneered the use of hyperbolic functions in trigonometry. He also proposed theories about non-Euclidean space. Lambert is credited with being the first to demonstrate that is irrational by employing a generalized continued fraction for the function tan x. Euler believed the conjecture but was unable to prove it was irrational, and it is speculated that Aryabhata believed it as well in 500 CE. Lambert also developed theorems about conic sections that simplified the calculation of comet orbits.Lambert refers to the defect as the difference between the angle-sum of a triangle and 180 degrees.Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
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highest number impossible to make using 5,7
Answer:
Step-by-step explanation:
can someone help me with 13 and 14 please and fast
Answer:
24 25 26
Step-by-step explanation:
guess and check..................
L is the midpoint of JM. K is the midpoint
of JL. JL = 1. What is the length of KM?
Answer:
KM = 1.5
Step-by-step explanation:
The first piece of info we get is that L is the midpoint of JM. This means that L = JM/2. The second piece of information provided is that K is the midpoint of JL, which means K = JL/2. We know that JL = 1, so we can plug it into the equation to help us figure out the problem. You can also illustrate to solve this problem, as I do here.
Since JL = 1...
K = 1/2, K = 0.5
________________________________________________
J K(0.5) L M
___________ __________
0.5 0.5
Now with this information, we know that 0.5 represents the distance of 1/4 of JM. We know that KM is 3/4 of the number line, and we know that 1/4 of the line is 0.5. We multiply 0.5 * 3 to get our final answer.
FINAL ANSWER: KM = 1.5
The lines 4x+6y-5=0 and 2x+4y-3=0 intersect at N. Find the equation of the line through N perpendicular to the line x+2y=0.
4x+6y=5 and 2x+4y=3 are the 2 supplied lines. We must solve two simultaneous equations in order to determine the location at where these two lines cross.
When we multiply the second equation by two, we obtain the result 4x+8y=6. Next, we subtract this from the first equation to get -2y = -1, which equals y=1/2. N's coordinates are therefore (+1/2, +1/2).
The line we need to identify now goes through this point and is perpendicular to the line x+2y=0; its slope is -1/2 (the slope of the line [tex]ax+by+c=0[/tex] is -a/b). With m1*m2=-1, the line perpendicular to this one has a slope of 2. Consequently, the line that we must identify The slope of the equation is 2, and it goes through N. In order to simplify the equation, (y-1/2) = 2*(x-1/2), which results in 2y-1 = 2*(2x-1) and 2y-1 = 4x-2 and 4x-2y-1=0. The necessary equation is as follows.
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Juan and jaquan work for separate companies. juan earns $15 for each sale plus 5% commission. jaquan earns $21 for each sale plus 3.5% commission. in july, juan made 35 sales and jaquan made 29 sales. they made the same total salary. which equation can be used to find x, the amount juan & jaquan each had in sales in july?
The amount Juan & Jaquan each had in sales in July is approximately $725 and the equation for Juan's Earning is 525 + 1.75x and the equation for Jaquan's Earning 609 + 1.015x.
Unitary method:
Unitary method is defined as the process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Given,
Juan and Jaquan work for separate companies.
Juan earns $15 for each sale plus 5% commission.
Jaquan earns $21 for each sale plus 3.5% commission.
In July, Juan made 35 sales and Jaquan made 29 sales.
They made the same total salary.
Here we need to find the amount Juan & Jaquan each had in sales in July.
Let x be the total number of sales in July.
So, based on the given details we can written it as,
Juan earns,
=> 15 + 5%x
=> 15 + 0.05x
And Jaquan earns,
=> 21 + 3.5%x
=> 21 + 0.035x
So, in July, Juan made 35 sales and Jaquan made 29 sales,
Then
=> 35(15 + 0.05x)
=> 525 + 1.75x -----------(Juan's Earning)
=> 29(21 + 0.035x)
=> 609 + 1.015x -----------(Jaquan's Earning)
And also in July, they made the same total salary.
So,
Juan's Earning = Jaquan's Earning
Then,
=> 525 + 1.75x = 609 + 1.015x
=> 1.75x - 1.0.15x = 609 - 525
=> 0.735x = 84
=> x = 84 / 0.735
=> x = 114.28
So, the total amount they earned in July is,
=> 525 + 1.75(114.28) = 609 + 1.015(114.28)
=> 525 + 199.99 = 609 + 115.99
=> 724.99 = 724.99
So, they earned approximately $725 in July.
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A survey from the Department of Motor Vehicles was given to residents in the city of Smallville. The results showed that 80% held a valid driver’s license. Of the individuals who held a value driver’s license, 10% has at least one traffic violation, whereas 30% who did not have a valid driver’s license has at least one traffic violation. What percent of Smallville residents have at least one traffic violation?
A. 14%
B. 28%
C. 38%
D. 40%
Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.
As given,
A=Person has a driver license
A'=Person does not have a driver license
P(A)=0.80
P(A')=0.20
For A, 10% has at least one traffic violation
For A', 30% had at least one traffic violation.
Probability with at least one traffic violation
=Probability of( A and one traffic violation +A' and one traffic violation)
=0.80(0.10)+0.20(0.30)
=0.08+0.06
=0.14
=14%
Therefore, percent of the residents with at least one traffic violation is 14%.
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X to the power of 2 minus 6 minus 7
Answer:
[tex]x=\sqrt{13}[/tex]
Step-by-step explanation:
[tex]x^{2} - 6 - 7 = 0 \\x^{2} =13\\x=\sqrt{13}[/tex]
A standard ream of paper plus another half ream of paper contains 750 sheets of paper
The number of the sheets in a ream of paper is a 500 sheets.
According to the statement
We have to find that the number pf paper sheets in a one ream.
So, For this purpose, we know that the
The standard form of a number is a way of writing the number in a form that follows certain rules.
From the given information:
A standard ream of paper plus another half ream of paper contains 750 sheets of paper.
It means
total number of sheets = 750 sheets
Then
one full ream + half ream = 750 sheets
Let x be a number of sheets
then
x + x/2 = 750
2x+x /2 = 750
3x/2 = 750
3x = 1500
x = 1500/3
x = 500.
So, The number of the sheets in a ream of paper is a 500 sheets.
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At Zoe's Beading Boutique, 15 out of the 20 beads on clearance are plastic. What percentage
of beads on clearance are plastic?
Write your answer using a percent sign (%).
Submit
+
Work it out
Answer:
75%
Step-by-step explanation:
15 over 20 is equal to 3/4 and 3/4 is 75%
8xy(x^3 y) fully simplify
Answer:
8x^4y^2
Step-by-step explanation:
Just plug it in to the calculator and that will be your result.
pls help find interval notation
Step-by-step explanation:
-2x - 7 > 1
-2x > 8
-x > 4
x < -4
that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).
x - 2 >= -1
x >= 1
that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.
On a map with a scale 1 : 100,000, the distance between two cities is 12 cm. What would be the distance between these two cities on a different map with a scale 1 : 300,00?
Answer:
36 cm
Step-by-step explanation:
8th grade Mathematics
A line has a slope of -3 and a y-intercept of 3.
What is the slope of the line?
O. -9
O. -1
O. 1
O. 9
I appreciate all of your answers even if they are wrong, thanks!! :)
Answer:
1
Step-by-step explanation:
5. Which value of a satisfies this equation? x + 7 = 28
A) x = 35
B) x = 21
C) x=4
D)x = 14
Answer:
21
Step-by-step explanation:
Subtract 7 from both sides to get the answer.
