Let:
x = Number of months
y1 = Total cost for Club A
y2 = Total cost for Club B
a = Fee of Club A per month
b = Fee of Club B per month
c = Initial fee of Club A
d = Initial fee of Club B
so:
[tex]\begin{gathered} y1=ax+c \\ y1=25x+20 \\ -------- \\ y2=bx+d \\ y2=24x+25 \end{gathered}[/tex]So, the total cost will be the same for:
[tex]\begin{gathered} y1=y2 \\ 25x+20=24x+25 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 25x-24x=25-20 \\ x=5 \end{gathered}[/tex]The cost will be the same for the month number 5. And the total cost will be:
[tex]\begin{gathered} y1(5)=25(5)+20=145 \\ y2(5)=24(5)+25=145 \end{gathered}[/tex]$145
The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.
Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:
[tex]\begin{gathered} \frac{12}{10}=\frac{6}{x}\rightarrow(1) \\ \frac{12}{6}=\frac{6}{y}\rightarrow(2) \\ \frac{6}{12}=\frac{3}{z}\rightarrow(3) \end{gathered}[/tex]Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:
[tex]\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}[/tex]Therefore the perimeter is as follows:
[tex]\begin{gathered} P=x+y+x=5+3+6=14 \\ P_{(KMP)}=14 \end{gathered}[/tex]A figure is made up of a triangle and a square. The square andthe triangle have the same base of 9 inches. The triangle has aheight of 7 inches, what is the total area of the figure?
To solve the exercise, it is helpful first to draw the situation that the statement describes:
The total area of the figure will be
[tex]A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}}[/tex]Then, we can calculate the area of the square using the following formula:
[tex]\begin{gathered} A_{\text{square}}=s\cdot s \\ \text{ Where s is one side of the square} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} s=9in \\ A_{\text{square}}=s\cdot s \\ A_{\text{square}}=9in\cdot9in \\ \boldsymbol{A}_{\boldsymbol{square}}\boldsymbol{=81in}^{\boldsymbol{2}} \end{gathered}[/tex]Now, we can calculate the area of the triangle using the following formula:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} b=9in \\ h=7in \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \\ A_{\text{triangle}}=\frac{9in\cdot7in}{2} \\ A_{\text{triangle}}=\frac{63in^2}{2} \\ \boldsymbol{A}_{\boldsymbol{triangle}}\boldsymbol{=31.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Finally, we calculate the total area of the figure
[tex]\begin{gathered} A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}} \\ A_{\text{total}}=81in^2+31.5in^2 \\ \boldsymbol{A}_{\boldsymbol{total}}\boldsymbol{=112.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.
Can you please help me out with a question
The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimetersHELP PLEASEEEEE!!!!!!
The two rational number D and point R are found as 2/7 and 4/7 respectively.
What is meant by the term rational number?Rational numbers are those that can be specified in the type p/q, for which p and q are integers and q≠0 is a negative number. The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the denominator and numerator of a fraction were all numbers (denominator q≠0), whereas the denominator and the numerator of rational numbers are integers.For the given question.
The number line is given with the rational number D and R to be plotted.
There are 7 units between the points 4 and 5.
D point is 2 units right of 4.
Thus, D = 2/7
R point is 4 units right of point 4.
Thus, R = 4/7
Thus, the two rational number D and R are found as 2/7 and 4/7 respectively.
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Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 21 = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.10SI10310101
We are given the following equation of a line.
[tex]-2x=0[/tex]Let us first solve the above equation for x.
Divide both sides of the equation by -2
[tex]\begin{gathered} -2x=0 \\ \frac{-2x}{-2}=\frac{0}{-2} \\ x=0 \end{gathered}[/tex]So, the solution is x = 0
This means that the two ordered pairs must contain the x-coordinate 0 and the y-coordinate can be any value you like.
For example:
(0, -5) and (0, 5)
Here the x-coordinate is 0 and the y-coordinate is -5 and 5.
Let us plot these ordered pairs and the line on the given graph.
The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length
Let me check your question
[tex]T\text{ = 2}\cdot\text{ 3.14}\cdot\text{ }\sqrt[]{L/\text{ 32}}[/tex][tex]\frac{T}{2\cdot\text{ 3.14}}\text{ = }\sqrt[]{L/\text{ 32}}[/tex]T= the period = 6.28
[tex]\frac{6.28}{6.28}\text{ = }\sqrt[]{L/\text{ 32}}[/tex][tex]L/32=1^2[/tex][tex]L=32[/tex]_________________
Answer
L= 32
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
suppose there are two types of tickets to a show . advance and same day. advance tickets cost $15 and same day tickets cost 30. for one more performance there are 55 tickets sold in all and the total amount paid for them was 1275. how many tickets of each typer were sold?
Advanced tickets(x): $15
Same day tickets(y) : $30
For one more performance there are 55 tickets sold
x+ y= 55 (a)
The total amount paid for them was 1275
15x+30y= 1275 (b)
System of equations:
x+y= 55 (a)
15x+30y = 1275 (b)
Solve for x in (a)
x=55-y
Replace x on (b)
15(55-y)+30y = 1275
82
i need help with this asap please check work when done
Given the parent function
[tex]y=\cos x[/tex]From the graph,
The range of the function is best modelled by the interval
Comparing the function with general equation of the cosine function,
[tex]B=1[/tex]The formula for the period is,
[tex]T=\frac{2\pi}{B}[/tex]There
3/3=_/21Fill the blank space with the answer
In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.
[tex]\frac{3}{3}\times\frac{7}{7}=\frac{21}{21}[/tex]So, 21 is to be filled at blank space.
Two towns are 1050 miles apart, a group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels 1 1/2 miles Per hour faster than the other group, find the rate of each group
Answer:
Rate of the faster group = 3.38 miles per hour
Rate of the slower group = 1.88 miles per hour
Explanation:
Let x = rate of the slower group
Therefore the rate of the faster group will be x + 1 1/2 = x + 3/2 = x + 1.5
From the question, we're told that the two groups traveled for a total hiking time of 200 hours.
We know that distance = rate x time
So the distance of the slower group will be = 200x
And the distance of the faster group will be = 200(x + 1.5)
So if the distance between each town is 1050, we can then solve of x as shown below;
[tex]\begin{gathered} 200x+200(x+1.5)=1050 \\ 200x+200x+300=1050 \\ 400x=750 \\ x=\frac{750}{400} \\ x=1.88\text{ mph} \end{gathered}[/tex]Therefore the rate of the faster group = 1.88 + 1.5 = 3.38 mph.
Haven’t done this type of math before could use some help:)
Third row:
The balance stays the same as the previous row ($337.52).
We have 12 days between 9/7 and 9/18, so we can calculate the product/sum as:
[tex]S=12\cdot337.52=4050.24[/tex]NOTE: the product/sum will be used to calculate the average balance for the month.
Fifth row:
The balance stays the same as the previous row ($399.78).
We have 11 days between 9/20 and 9/30.
Then, the product/sum is:
[tex]S=399.78\cdot11=4397.58[/tex]Total:
The total product/sum is:
[tex]S_{\text{Total}}=1937.60+337.52+4050.24+399.78+4397.58=11122.72[/tex]Average daily balance:
We can take the total product/sum and divide by the total amount of days.
[tex]\text{average daily balance}=\frac{11122.72}{30}=370.76[/tex]Finance charge:
[tex]\text{ finance charge}=\frac{1.25}{100}\cdot370.76=4.63[/tex]New balance:
[tex]\begin{gathered} \text{New balance = previous balance - payment/credits + finance charge + new purchases} \\ \text{New balance = }387.52-50+4.63+62.26=404.41 \end{gathered}[/tex]The new balance is $404.41.
MEASUREMENT Choosing metric measurement units Fill in the blanks below with the correct units. (a) Amanda bought a candy bar. Its mass was about 50 ? (b) A dollar bill is about 15 ? long (c) The can of soda held about 350 .
Explanation
We are asked to fill in the missing blanks
Part 1
The weight of a Candy bar is in grams
So the answer will be
Amanda bought a candy bar. Its mass was about 50 grams
Part 2
A dollar bill should be about 15 centimeters
Therefore, the answer is
A dollar bill is about 15 centimeters long
Part 3
A can of soda should a capacity in mililiters
Therefore, the answer will be
The can of soda held about 350 mililiters
The functions and are defined as follows.
r(x)= -x+1
s(x)= x^2+2
Find the value of r(s(5))
Answer: [tex]r(s(5))=-26[/tex]
Step-by-step explanation:
[tex]s(5)=5^2 +2=27\\\\r(s(5))=r(27)=-27+1=-26[/tex]
Solve for x8x-11=6x-5Simplify your answer as much as possible
Solve the given equation for x as shown below
[tex]\begin{gathered} 8x-11=6x-5 \\ \Rightarrow8x-11-6x=6x-5-6x \\ \Rightarrow2x-11=-5 \\ \Rightarrow2x-11+11=-5+11 \\ \Rightarrow2x=6 \\ \Rightarrow\frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]Therefore, the solution to 8x-11=6x-5 is x=3.Classify the following triangle. Check all that apply.A. ScaleneB. IsoscelesC. AcuteO D. RightE. EquilateralF. Obtuse
Answer
Options A and C are correct.
The triangle is a Scalen triangle and it is also an Acute triangle.
Explanation
To answer this question, we first explain what these type of triangles are
According to side lengths,
- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.
- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.
- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.
According to the angles,
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
For this triangle,
We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.
Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.
Hope this Helps!!!
What’s the correct answer answer asap for brainlist please
Answer:
c. you can't be feeling alive with wearing,weakness of body and mind.
Terry invested $2,200 in the stock market for 2 years. If the investment earned 12%, how muchmoney did Terry earn in 2 years?
We will have that $2200 represent the 100%, then how much money does 12% represent.
In order to solve for the ammount of money we multiply the invested ammount ($2200) times the percentage we want to know (12%) and divide it by 100%, that is:
[tex]m=\frac{2200\cdot12}{100}\Rightarrow m=264[/tex]Here we can see, he earned $264 in those 2 years.
Circumference of a circleThe radius of a circle measures 16 m. What is the circumference of the circle?Use 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
Which of the following equations represents a line that passes through thepoints (6,-5) and (-6, -7)?
Problem
Which of the following equations represents a line that passes through the
points (6,-5) and (-6, -7)?
Solution
For this case the equation for a line is given by:
y= mx +b
And we can find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And replacing we got:
[tex]m=\frac{-7+5}{-6-6}=\frac{-2}{-12}=\frac{1}{6}[/tex]Then we can find the intercept with this formula:
-5 = 1/6 (6)+b
And solving for b we got:
b= -5-1 =-6
And our equation would be:
y= 1/6 x -6
And the best option would be:
I.
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a card with number from 2 to 9.
The probability that we do not dealt a card with number 2 to 9 is 5/13
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
A pack of card = 52 cards
The Cards having Hearts = 13
The Cards having Spade = 13
The Cards having Diamond = 13
The Cards having Clubs = 13
According to question
The cards numbered from 2 to 9 are 8 cards, specifically 2, 3, 4, 5, 6, 7, 8, and 9.
But there are four suits: diamonds, hearts, spades, and clubs.
Therefore you multiply 8 by 4 to get 32
The probability of getting dealt one of those cards would be:
32/52, or
8/13
But we have to find the probability of not getting such cards
Thus,
1 - 8/13 = 5/13
Hence, the probability that you are not dealt a card with number from 2 to 9 will be 5/13
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Solve the system by elimination. 2x+3y=06x+9y=0
We have the next system of equations
2x+3y=0 ...(1)
6x+9y=0 ...(2)
I order to solve this system by elimination we will multiply the first equation by -3
So we will have
-6x-9x=0
then we add the equation above with the second equation
-6x-9x=0
+6x+9y=0
As we can see we obtain 0=0 which means that we have infinity solutions
ANSWER
Infinity solutions
hello im stuck on this hw problem and need help ty
The amount of money that Abdul is going to donate to the City Youth Fund is denoted by x, and the amount of money that Abdul is going to donate to the Educational Growth Foundation is denoted by y.
Since Abdul will donate up to $500, the sum of those amounts must be less or equal to 500.
[tex]x+y\leq500[/tex]It is not possible to donate less than zero, therefore, we also have the following constrains
[tex]\begin{gathered} x\geq0 \\ y\geq0 \end{gathered}[/tex]Abdul wants the amount of money donated to the Educational Growth Foundation to be at least 4 times the amount of money donated to the City Youth Fund, therefore, we have our final constrain
[tex]4x\leq y[/tex]Combining those four regions, the solution is their interception, which is
The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?
65 adult's ticket and 85 children's ticket was sold
Explanation:Let the number of tickets for children = x
Let the number of adults ticket = y
Total tickets = 150
x + y = 150 ....equation 1
The cost of tickets per child = $4.75
The cost of tickets per adult = $7.50
Total revenue from tickets = $891.25
Total revenue from tickets = The cost of tickets per child × number of children ticket +
The cost of tickets per adult * number of adults ticket
891.75 = 4.75(x) + 7.5(y)
891.75 = 4.75x + 7.5y ...equation 2
x + y = 150 ....equation 1
891.75 = 4.75x + 7.5y ...equation 2
Using substitution method by making x the subject of formula in equation 1:
x = 150 - y
Substitute for x in equation 2:
891.25 = 4.75(150 - y) + 7.5y
891.25 = 712.5 - 4.75y + 7.5y
891.25 = 712.5 + 2.75y
891.25 - 712.5 = 2.75y
178.75 = 2.75y
y = 178.75/2.75
y = 65
Substitute for x in equation 1:
x + 65 = 150
x = 150 - 65
x = 85
Hence, 65 adult's ticket and 85 children's ticket was sold
A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.
A line can be written as an equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know the slope:
[tex]m=3[/tex]The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.
We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:
[tex]b=3[/tex]Thus, we have the equation:
[tex]y=3x+3[/tex]To calculate the other points, we just need to substitute their x values and get their y values:
x = 1:
[tex]y=3\cdot1+3=3+3=6[/tex]So, when x = 1, y = 6
x = 2:
[tex]y=3\cdot2+3=6+3=9[/tex]So, when x = 2, y = 9.
x = 3:
[tex]y=3\cdot3+3=9+3=12[/tex]So, when x = 3, y = 12;
So, the complete table is:
x | 0 | 1 | 2 | 3
y | 3 | 6 | 9 | 12
Which describes a number that cannot be irrational?A. a number that represents the ratio of the circumference to the diameter of a circle B. a number that can be written as the ratio of two integers C. a number that can be used to solve an algebraic equation D. a number that represents the length of the diagnostic of a square
a number that can be written as the ratio of two integers (option B)
Explanation:Irrational number cannot be written in the fractional form
Rational numbers can be written in the form of fraction
Checking the options:
a) Circumference = πd
where d = diameter
π = Circumference/diameter
π is an irrational number
b) A number written as ratio of two intergers can be written in the form of fraction
Hence, it is rational
c) A number that we can use in solving an algebraic equation can be any real number.
From a real number, we have rational and irrational numbers. So, there is the likelihood we get an irrational number
d) side of a square = a
diagonal² = a² + a²
length of diagonal of a square = √(a² + a²) = √2a²
This can also yield either irrational or rational numbers.
A number that cannot be irrational means a number that is rational.
From the option, the only one without doubt that it is rational is a number that can be written as the ratio of two integers (option B)
Algebra Find the value(s) of the variables in each kite.
56º,34º
1) A kite is a quadrilateral that according to the following theorem:
2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.
3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following
So we can pick one triangle and write out the following according to the Triangle sum theorem:
[tex]\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ \frac{13x}{13}=\frac{91}{13} \\ x=7 \end{gathered}[/tex]4) Finally, let's plug into each one the quantity of x and get the measure of those angles:
Helppppppppppppppppppp
Perpendicular line are reciprocals
slope of the original line = -1/9
slope of the perpendicular line = 9
can you please help me solve this practice problem I really need help
Question:
Solution:
Step 1: Find the equation of a line:
Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-2-3}{4-0}\text{ = }\frac{-5}{4}\text{ =-}\frac{5}{4}[/tex]now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:
[tex]y\text{ = -}\frac{5}{4}x+3[/tex]Step 2:
note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]and it is shown graphically like this:
So that, we can conclude that the correct answer is:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]Find the equation for thefollowing parabola.Vertex (0,0)Focus (2, 0)A. 2x^2 = yB. y^2 = 8x2C. X^2 = ByD. y^2 = 8x
To answer this question we need the equation of a parabola that uses the distance from the focus to the vertex.
This formula is,
[tex]4p(y-k)=(x-h)^2[/tex]where,
p is the distance from the focus to the vertex, and the point (h,k) is the vertex.
[tex]\begin{gathered} \text{focus (2,0)} \\ \text{Threrefore} \\ p=2 \end{gathered}[/tex][tex]\begin{gathered} \text{vertex (0 , 0)} \\ \text{Therefore,} \\ h=0 \\ k=0 \end{gathered}[/tex]Let us now substitute the data into the equation of the parabola,
[tex]\begin{gathered} 4\times2(y-0)=(x-0)^2 \\ 4\times2(y)=x^2 \\ 8y=x^2 \end{gathered}[/tex]Hence, the equation for the parabola is, x² = 8y.
Option C is the correct answer.