true or false, a trapezoid is a quadrilateral with one or more parallel side
Answer:
A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
Andrew is building a gate in his fence in the shape of a trapezoid.
What is the area of the gate?
ANSWER: 16FT
SOLUTION IN IMAGES
I need help with there’s problems
Answer:
3. x = 3, y = 1 --> = (3,1)
4. x = 2, y = 1 --> = (2,1)
Step-by-step explanation:
3.
x+5y =8
x = 8-5y
-x+2y=-1
-8+5y+2y=-1
7y-8=-1
7y=-1+8
7y=7
Divide 7 from both sides
y = 1
x=8-5y
x=8-5(1)
x = 3
4.
y=x-1
y=-2x+5
-2x+5=x-1
5=x-1+2x
5=3x-1
5+1=3x
6=3x
Divide 3 from both sides
2=x
x=2
Fractions:
4/5 is greater, less than, or equal to 8/10?
Answer:
Equal to.
Step-by-step explanation:
multiply both numbers by 2
the muscular muscle is 75kg and the muscle is pulling on the bone at an angle of 15 degrees. what are the vertical and horizontal components of this muscular force?
a. which of these forces would be responsible for the rotation of this bone around the joint
b. which of these forces would cause a compressive force at the joint?
please show work and draw a diagram and label
Answer:
Step-by-step explanation:
To find the vertical and horizontal components of the muscular force, we can use trigonometry. Let F be the force exerted by the muscle, and θ be the angle it makes with the horizontal.
Horizontal component of the force Fx = F cos θ
Vertical component of the force Fy = F sin θ
Given that the muscular force is 75kg and the angle of pull is 15 degrees, we have:
Fx = 75kg x cos(15) = 72.62 kg (approx.)
Fy = 75kg x sin(15) = 19.34 kg (approx.)
To determine which force would be responsible for the rotation of the bone around the joint, we need to consider the torque or moment created by the force. The torque is given by the force times the lever arm, which is the perpendicular distance from the line of action of the force to the axis of rotation. In this case, the axis of rotation is the joint, and the lever arm is the distance from the joint to the point where the muscle attaches to the bone.
The torque due to the horizontal component of the force is zero, since it acts perpendicular to the lever arm. The torque due to the vertical component of the force is:
Torque = Fy x d
where d is the lever arm. If we assume that the lever arm is 5 cm, we have:
Torque = 19.34 kg x 0.05 m = 0.967 Nm
Therefore, the vertical component of the force would be responsible for the rotation of the bone around the joint.
To determine which force would cause a compressive force at the joint, we need to consider the direction of the force. A force that acts perpendicular to the bone would cause compression at the joint. In this case, the vertical component of the force is perpendicular to the bone, while the horizontal component is parallel to it. Therefore, the vertical component of the force would cause a compressive force at the joint.
Here is a diagram of the situation:
|\
Fy | \ /|
| \ / |
| \ / |
| \ / |
| \ / |
| \/ |
| /\ |
| / \ |
| / \ |
| / \ |
| / \ |
| / \|
|/______\
Fx
In the diagram, Fx is the horizontal component of the force, Fy is the vertical component of the force, and the bone is represented by the vertical line. The angle θ is the angle between the force and the horizontal. The lever arm d is the distance between the joint and the point where the muscle attaches to the bone.
Come someone explain/help me how to do this? really appreciate it!
The monthly periodic rate is 1.25%, the finance charge is $6.99 and John's new balance is $566.24.
How to determine the monthly periodic rateThis monthly periodic rate calculated as
Monthly periodic rate = Annual percentage rate / 12
So, we have
Monthly periodic rate = 15% / 12
Monthly periodic rate = 1.25%
The finance chargeThis is the interest charged for the month.
So, we start by calculating the average daily balance using:
Average daily balance = ((Previous month's balance + Current month's purchases and cash advances) - Current month's payments and credits) / Number of days in the month
Substitute the known values in the above equation, so, we have the following representation
Average daily balance = (428.10 + 281.15) - 150.00) / 31
Average daily balance = $18.04
So, we have
Finance charge = Average daily balance x Monthly periodic rate x Number of days in the month
Finance charge = $18.04 x 1.25% x 31
Finance charge = $6.99
The value of John's new balanceThe new balance is calculated as
New balance = Previous month's balance + Current month's purchases and cash advances + Finance charge - Current month's payments and credits
Substitute the known values in the above equation, so, we have the following representation
New balance = $428.10 + $281.15 + $6.99 - $150.00
New balance = $566.24
Hence, the new balance is $566.24
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9-65 Eric set up this ratio for two similar triangles:
x/12 = 5/9
He solved the problem and found x = 6.67. What was his mistake? What does x REALLY equal?
Eric made the wrong ratio of the sides of the triangle. As corresponding sides of both triangles are in proportion to each other. So, the proportion will be x/12=9/5. x equal to 21.6.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. If the corresponding sides and angles of two triangles are proportionate, then the triangles are similar. As a result, using another triangle, we may determine the dimensions of one triangle.
So, the right ratio of the sides of the triangle is x/12=9/5
12 * 9 / 5 =x
108/5 = x
21.6 = x
Therefore, x is equal to 21.6
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can someone help me with this problem please
here is the picture is just one
What is Function?
Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.
How to determine
Where F(x) = 2x^4 + x^2 - 10x + 1
So, to calculate f(-10)
f(x) = y
Where x = -10
f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1
f(-10) = 2(10000) + 100 + 100 + 1
f(-10) = 20000 + 100 + 100 + 1
f(-10) = 20201
For f(2),
f(x) = y
Where x = 2
f(2) = 2(2)^4 +2^2 -10(2) + 1
f(2) = 2(16) + 4 -20 + 1
f(2) = 32 + 4 -20 + 1
f(2) = 17
For f(3)
f(x) = y
Where x = 3
f(3) = 2(3)^4 + 3^2 -10(3) + 1
f(3) = 2(81) + 9 -30 + 1
f(3) = 162 + 9 - 30 + 1
f(3) = 142
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Can you answer the question? TKSSS
Answer:
[tex]\frac{7}{2}[/tex] π
Step-by-step explanation:
To find the arc length of the partial circle, you have to find a fourth of the circumference
C = [tex]\frac{1}{4}[/tex] πd - Formula
C = [tex]\frac{1}{4}[/tex] 14π - Plug in values
C = [tex]\frac{14}{4}[/tex] π - Simplify/Solve
C = [tex]\frac{7}{2}[/tex] π
Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end
of the month to go to a concert. A movie ticket costs $5. Write and solve an inequality to determine how many times Robin can go to the
movies this month. Then interpret the solution.
PLEASE WRITE THE INEQUALITY WITH THE ANSWER AND A SUMMARY OF HOW TO SOLVE IT
Answer:
If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.
Step-by-step explanation:
Two or more expressions with an Equal sign is called as Equation.
Given,
Robin was given a $40 monthly allowance.
She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.
The amount spent on movies
40-12.5
$27.5
A movie ticket costs $5.
We need to find how many times can she go to the movies.
To find this we need to divide $27.5 by 5
$27.5/5=5.5
Robin can go 6 times to the movies.
Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Z′(−1, 4). 4 units down 4 units up 4 units to the right 4 units to the left
The translatiοn directiοn is 4 units tο the left.
What is Triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.
A pοlygοn with three edges and three vertices is called a triangle. It is οne οf the fundamental geοmetric shapes. Triangle ABC is a triangle with vertices A, B, and C. In Euclidean geοmetry, any three nοn-cοllinear pοints give rise tο a distinct triangle and a distinct plane.
The translatiοn directiοn is 4 units tο the left because Z' has mοved frοm (3,4) tο (-1,4), and the x-cοοrdinate has decreased by 4.
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ML
is tangent to the circle at L. Find the value of x.
Write your answer as a whole number or a decimal.
x=
The value of x for the given tangent angle is 1.5.
What is the value of x?The value of x can be determined by applying the following circle theorem about tangle angles as shown below.
2 x ∠LMN = 16x - 12 ( angle at tangent is half of the angle subtended at the arc)
2 ( 4x ) = 16x - 12
8x = 16x - 12
16x - 8x = 12
8x = 12
x = 12/8
x = 1.5
Thus, if ML is tangent to the circle at L, then the value of x is 1.5 (Written as a decimal)
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Mathilde has 30 pints of green paint. She uses 3/5 of it to paint a landscape and 3/10 of it while painting a clover. She decides she that, for her next painting, she will need 16 pints or green paint. How much more green paint will she need to buy?
Answer: 13 pints
Step-by-step explanation:
she used 27 pints at first (9/10 of the 30)
so she has 3 pints left.
and 16-3 = 13 pints.
Simplify the expression. x8• (2x)3 =
Subtract 4x 4 x from 6x 6 x . Divide each term in 2x=−12 2 x = - 12 by 2 2 and simplify. Divide each term in 2x=−12 2 x = - 12 by 2 2 . Simplify the left side.
Answer:
8x^11
Step-by-step explanation:
x^8 * (2x)^3
x^8 * (8x^3)
8x^11
Question 1 of 24
In right -angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. What is the measure of the hypotenuse of the triangle?
The measure of the hypotenuse of the triangle is 15 cm.
What is a hypotenuse?The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.
Given that, in a right-angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. we need to find the measure of the hypotenuse of the triangle
Using the Pythagoras theorem,
9² + 12² = h²
h² = 81+144
h² = 225
h = 15
Hence, the measure of the hypotenuse of the triangle is 15 cm
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2
A worker earned #80 per hour for a 38-hour week in a company. The company pays overtime at
a time and a half. In one week he earned #3640. Find the total numbers of hours he worked that
week.
3
Kasham travelled from Lagos to Akure, a distance of 350km. The first 210km she spent 3hours
and the remaining distance she spent 2hours 45minutes. (a) Calculate the speed for each part
of the journey. (b) Calculate the average speed for the whole journey in (i) km/h (ii) m/s to 1d.p
Answer:
2. Total Hours= 38+5 = 43
Step-by-step explanation:
2. Wage at Normal rate80 *38 = 3040
Extra Sum of Money then Normal wage 3640-3040 = 600
Overtime rate 80*1.5= 120
Overtime hours 600/120=5
3. (a) 210/3 = 70km/hr
140/(2.75*) = 50.91 km/hr
*2.75= 2+ (45/60)
The Clarke's son suggests that they rent a car that costs $250 for the week plus $0.22c/km. Their daughter does not want to drive far, so she suggests a car that is only $96 for the week but $0.50/km.
a) Write an equation to represent the cost of the car suggested by the son
b) Write an equation to represent the cost of the car suggest by the daughter
c) When will the two cars cost the same? Used the method of elimination to solve.
d) If the Clarke's plan to drive 500km, which option is less expensive?
Answer: a) The equation to represent the cost of the car suggested by the son is:
C1 = 250 + 0.22k
where C1 represents the total cost of renting the car, and k represents the number of kilometers driven.
b) The equation to represent the cost of the car suggested by the daughter is:
C2 = 96 + 0.5k
where C2 represents the total cost of renting the car, and k represents the number of kilometers driven.
c) To find when the two cars cost the same, we need to solve the equation:
C1 = C2
Substituting the expressions for C1 and C2 from parts a and b, we get:
250 + 0.22k = 96 + 0.5k
Simplifying this equation, we get:
0.28k = 154
Dividing both sides by 0.28, we get:
k = 550
Therefore, the two cars cost the same when the number of kilometers driven is 550.
d) If the Clarke's plan to drive 500km, we can calculate the total cost for each car by substituting k=500 into the equations from parts a and b:
C1 = 250 + 0.22(500) = 360
C2 = 96 + 0.5(500) = 346
Therefore, the car suggested by the daughter is less expensive for a 500km trip, as it would cost $346 compared to $360 for the car suggested by the son.
Step-by-step explanation:
Four transformations of the function ()
f
(
x
)
are given below.
For each transformation, drag the graph that shows the result of that transformation into the box under it.
On a coordinate plane, a line f goes through (0, 1) and (1, negative 1).
CLEAR CHECK
On a coordinate plane, a line f begins at the top of the second quadrant, extends downward toward the fourth. The line is shifted 4 units to the right.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units up.
On a coordinate plane, a line f begins at the top of the second quadrant, goes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units down.
On a coordinate plane, a line f begins at the top of the second quadrant and extends toward the bottom of the fourth. The line is shifted 4 units to the left.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 3 units up.
()=(−4)
m
(
x
)
=
f
(
x
-
4
)
()=()−4
n
(
x
)
=
f
(
x
)
-
4
()=(4+)
p
(
x
)
=
f
(
4
+
x
)
()=4+()
q
(
x
)
=
4
+
f
(
x
)
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 5 units down.
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Reference
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formulas
glossary
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Language
Changes the language of the audio snippets and the glossary
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Answer:
Step-by-step explanation:
300000000000000000000000000
Writing linear equations. Only 4 questions.
The linear equations that represents the problem are c = 40d + 20, P = 6.07 + 0.17(y - 2002), c = fixed fee + 7.75p and d = -93t + 1007
What is the linear equation that models the problemTo solve this problem, we need to write linear equations that represent each scenario
1. Total cost (C) to rent the trench digger for d days can be represented as:
C = 40d + 20
2. The amount of renewable power (P) produced in year y between 2002 and 2005 can be represented as:
P = 6.07 + 0.17(y - 2002)
3. The cost (C) of a birthday party for p people can be represented using the two given data points as:
For 10 people: 97.50 = fixed fee + 10(cost per person)
For 20 people: 175 = fixed fee + 20(cost per person)
Subtracting the first equation from the second equation gives:
77.50 = 10(cost per person)
Hence, the cost per person is:
cost per person = 7.75
Therefore, the rule for the cost (C) of a birthday party for p people is:
C = fixed fee + 7.75p
4. Jimmy's distance (d) from home after t hours of driving can be represented using the two given data points as:
After 3 hours: d = 740
After 6 hours: d = 461
Subtracting the first equation from the second equation gives:
d - 740 = -279
Hence, the distance (d) from home after t hours of driving can be represented as:
d = -93t + 1007
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A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $70,000 saved up for when she goes to college in 15 years, assuming the account earns a 5% return.
Annual deposit: $
Using Simple interest, savings account for her needed to deposit $1,842.82 each year.
What is simple interest?A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
t can also be computed using the annuity factor of 5% for 17 years to divide the total sum of $50,000.
The 529 plan, according to available data, is a tax-advantaged or tax-qualified savings plan designed to encourage individuals to save for future education costs of their relations or for themselves.
Data and Calculations:
N (number of intervals) = 17 years
Interest every year is equal to 5%.
Present Value = $0 PV
FV (Future Value) = $50,000 ($31,327.88 + $18,672.12)
Results: PMT = $1,842.82
Sum of all periodic payments = $31,327.88 ($1,842.82 x 17)
Total Interest = $18,672.12
Hence, in order to save $50,000 in 17 years at a 5% return for his granddaughter, the man who wanted to open a 529 college savings account for her needed to deposit $1,842.82 each year.
Hence the interest the bank will collect will be $117.53.
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Eighteen cyclists were each asked the number of miles they biked last week. Their responses are given below.
Answer:
You didn't give the answers
Bob’s school is selling tickets to a concert. On Monday, the school sold 3 student tickets and 1 adult ticket for a total of $38. On Tuesday, the school made $52 by selling 3 student tickets and 2 adult tickets. Find the price of a student ticket and the price of an adult ticket. SHOW YOUR WORK.
Answer:
Let's call the price of a student ticket "s" and the price of an adult ticket "a".
From the first day's sales, we know that:
3s + 1a = 38
From the second day's sales, we know that:
3s + 2a = 52
We can use these two equations to solve for "s" and "a".
First, we'll use the first equation to solve for "a":
3s + a = 38
a = 38 - 3s
Next, we'll substitute this expression for "a" into the second equation:
3s + 2(38 - 3s) = 52
Simplifying and solving for "s", we get:
3s + 76 - 6s = 52
-3s = -24
s = 8
So the price of a student ticket is $8.
We can substitute this value back into the first equation to solve for "a":
3(8) + a = 38
24 + a = 38
a = 14
So the price of an adult ticket is $14.
Janet hikes a trail at a local forest each day. The trail is 23.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week?
Answer:18
Step-by-step explanation:
Tic-tac-toe: In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is 0.127. How is 0.127 figured in this problem?
There are 5 methods to determine which player has less pieces, 5! ways probability to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.
What is probability?Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.
Case 1: There are 5 Xs and 4 Os on the board, and there is a one-point difference in the number of Xs and Os. In this situation, starting with the player who has less pieces on the board, we must alternately put the Xs and Os in the squares. There are 5 methods to determine which player has less pieces, 5! ways to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.
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Jose receives a dividend of $1.36 on each of his 398 shares. How many shares can he buy at $15.88?
Answer:
Jose can buy 0.086 shares at $15.88 with his dividend of $1.36 on each of his 398 shares.
Step-by-step explanation:
PLEASE HELP ME ON QUESTION D. THE answer is not Kite.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year.
P = $590, r = 3%, t = 2 years
By answering the above question, we may state that As a result, $35.40 interest in simple interest is due for the use of the funds.
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to compute interest. The most typical technique to figure out interest is as a portion of the principle sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
For simple interest, use the formula:
I = P * r * t
where I represents the amount of interest payable, P the amount borrowed, r the interest rate, and t the length of time in years.
Inputting the values provided yields:
I = $590 * 0.03 * 2
I = $35.40
As a result, $35.40 in simple interest is due for the use of the funds.
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5. The numbers 3.111... and 3.222... are both rational numbers. What is an irrational number that is between these two rational numbers?
The irrational number that is between the numbers is 3.112...
How to determine the irrational number that is between the numbers?Given that
Numbers = 3.111... and 3.222....
The question states that the numbers are ratonal numbers
This is not true because the numbers are irrationa number dues to the ... appended to the numbers
Having said that
The irrational number between 3.111... and 3.222 is 3.112...
This is so because
3.111... < 3.112... < 3.222
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ASAP 40 points
Graphs of exponential functions either increase or decrease for all x-values.
True or
False
It is true that graphs exponential functions either increase or decrease for all x-values.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change, as a decimal.An exponential function can either increase or decrease depending on the values of a and b, however the behavior is uniform, meaning that it is true that graphs exponential functions either increase or decrease for all x-values.
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which choice is equivalent to the product below? √5x • √x+3
Answer:
Below
Step-by-step explanation:
sqrt(5x) * sqrt(x+3) = sqrt ( 5x * x + 5x * 3) = sqrt ( 5x^2 + 15x)
