A triangle cannot be formed with side lengths 3, 9, 17 because A. No, because 3 + 9 < 17
How to illustrate the triangle?In geometry, a triangle is a polygon with three sides, three edges, and three vertices. The main characteristic of a triangle is that the sum of its internal angles is 180 degrees.
This is referred to as the triangle's angle sum property. It should be noted that any two sides of a triangle must have a sum of lengths greater than the third side.
In this instance, the result of multiplying 3 by 9 equals 12, which is less than 17. Therefore, choice A is the right one.
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prove that a mewdian drawn to the base of an isosceles triangle divides the triangle intro two congruent triangles
The prove can be shown on the picture attached. And here the describe that support the picture:
Let the triangle be ABC with vertex at A and AB=AC.Let ad be the median, in triangles ABD and ACD, we haveAB=AC, given AD=ADBD=DC (AD is median)Then we can know the 2 triangles are identical or congruent.
What is the median of an isosceles triangle?The median drawn from the vertex bisects the angle whose two adjacent sides are equal in isosceles and equilateral triangles. In the case of equilateral and isosceles triangles, the median not only bisects the side opposite the vertex, but it also bisects the angle of the vertex.
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4) Look at this graph:
100
90
80
70
60
50
40
30
20
10
Y
0 10 20 30 40 50 60 70 80 90 100
) What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:4
Step-by-step explanation:
Directions - Match the equations for parallel lines. (Note: you will not use all choices on the right side).
The equations for parallel lines:
y = -1/2 x - 2 ----- y = -1/2 x + 6
y = 1/2 x + 4 ----- y = 1/2 x - 4
y = 2x -4 ----- y =2/1x + 2
y = 5x + 2 ----- y = 5x - 1
y = 1/5 x + 10 ---- y = 1/5 x + 3
What is slope of line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
If an equation in the form y = mx + c then m is the slope of the line.
Equation of line slope Slope parallel line
y = -1/2 x - 2 -1/2 -1/2
y = 1/2 x + 4 1/2 1/2
y = 2x -4 2 2
y = 5x + 2 5 5
y = 1/5 x + 10 1/5 1/5
Now identify the lines from the option whose slope are -1/2, 1/2, 2, 5, 1/5.
The slope of the line y = -1/2 x + 6 is -1/2.
The slope of the line y = 1/2 x - 4 is 1/2.
The slope of the line y = 2x -4 is 2.
The slope of the line y = 5x + 2 is 5.
The slope of the line y = 1/5 x + 10 is 1/5.
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y = 2x + 1
2x - y = 3
The slope of the equations is equal. Then the lines are parallel to each other.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y = 2x + 1 ....1
2x - y = 3
y = 2x - 3 ....2
The slope of both equations is 2.
The slope of the equations is equal. Then the lines are parallel to each other.
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What is the product of 3 over 4x and 8x + 3?
Answer:
[tex]\frac{24x+9}{4x}[/tex] or 6 + [tex]\frac{9}{4x}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4x}[/tex] × 8x +3
= [tex]\frac{3}{4x}[/tex] × [tex]\frac{8x +3}{1}[/tex]
= [tex]\frac{3(8x+3)}{4x}[/tex]
= [tex]\frac{24x+9}{4x}[/tex]
or 6x + [tex]\frac{9}{4x}[/tex]
4. Open Response The manager of Happy
Puppy dog boarding company begins the
month with 85.4 pounds of dog food and
tracks the weekly use, along with the supply
delivery received in the middle of the month.
(Lesson 2)
Week
1
02
3
4
Weekly Dog Food Use (lb)
CAN
310-28.4moqasi go
-21
bruol
97-3
-30.25
Worke
dijo m
How much dog food does the company have
on hand at the end of the month?
Answer:
the answer is 163.375 lbs
Step-by-step explanation:
Rational numbers are numbers that can be expressed in the form of a ratio of two integers, where the denominator is not equal to zero. Examples of rational numbers include fractions such as 1/2, -3/4, 0.5 and -2.5. The mathematical formula for a rational number is a/b, where a and b are both integers and b ≠ 0.
Solution:
85.4-28.4-215 +972-30.25
=85.4-28.4-21.625+97.75-30.25
=163.375
The quantity of food left at the end of the month is equal to the amount provided by the management at the beginning of the month plus the amount given in the middle of the month less the amount taken in previous weeks.
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Martin’s car averages 32 miles per gallon of gasoline. He lives 12 miles from work. How
many gallons of gasoline does Martin use to drive to and from work in 22 days?
We know that Martin will need 16.5 gallons of gasoline using mathematical operations.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, each day Martin travels:
12 * 2 / 24 miles from home to work and back home.
As she works for 22 days: 24*22 = 528 miles
So, the equation can be:
32x = 528
x = 528/32
x = 16.5
Therefore, we know that Martin will need 16.5 gallons of gasoline using mathematical operations.
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Adam is wanting to start saving for retirement but they don’t know how much they can afford to save from their monthly budget. Help Adam find their monthly cash flow.
Adam works at Tim Horton’s making $15/hour, 32 hours a week. (Assume they take no vacations.)
Expenses are: Rent: $650/month, Groceries: $75/week, Utilities: $120/month, Car Insurance: $118/month, Gasoline: $30/week, and Miscellaneous: $400/month
Saving for Retirement (20 Pts)
Now, let’s pretend you are Adam. How much of your ending cash flow would you want to save for retirement? This will be the amount they will put in the IRA monthly.
Retirement Amount (20 Pts)
If Adam retires in 35 years and finds an IRA for 4.8%, how much money will be in their retirement account when they retire?
Amount Deposited (20 Pts)
How much will Adam deposit in total to their IRA?
Interest Accrued (20 Pts)
How much will Adam accrue in interest from their IRA?
1) Adam's monthly cash flows are:
Cash Inflows = $2,080Cash Outflows = $1,743.2) I would save $300 monthly from the ending cash flow balance for retirement savings.
3) If Adam retires in 35 years and finds an IRA for 4.8%, the future value of their retirement account will be $326,070.43 when they retire.
4) In 35 years, Adam will deposit $126,000 in total to their IRA.
5) The accrued interest from the IRA will be $200,070.43.
What is the future value?The future value represents the balance in Adam's retirement savings account after 35 years of depositing $300 monthly at 4.8% interest.
The future value is computed by compounding the periodic deposits (present values).
Adam's total monthly earnings = $2,080 ($15 x 32 x 52 x 1/12)
Monthly Expenses:
Rent $650
Groceries $325 ($75 x 52 x 1/12)
Utilities $120
Car Insurance $118
Gasoline $130 ($30 x 52 x 1/12)
Miscellaneous $400
Total monthly expenses = $1,743
Ending cash flows = $337 ($2,080 - $1,743)
Retirement period = 35 years
IRA interest rate = 4.8%
Monthly savings = $300
N (# of periods) = 420 months (35 years x 12)
I/Y (Interest per year) = 4.8%
PV (Present Value) = $0
PMT (Periodic Payment) = $300
Results:
Future Value (FV) = $326,070.43
Sum of all periodic deposits = $126,000 ($300 x 420)
Total Interest = $200,070.43
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Which equation is equivalent to 1/3 (9x+12)+4x+6
Answer:
[tex]7x+10[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}(9x+12)+4x+6 \\ \\ =3x+4+4x+6 \\ \\ =7x+10[/tex]
Simplify:
10 x²y³ / 2xy
Answer:
Step-by-step explanation:
A company offers a starting yearly salary of $31,000 with raises of 3,500 per year. Find the total salary over a ten-year period.
The starting salary of $31,000 and the annual raise of $3,100 indicates that the series is an arithmetic series and the total salary over a ten-year period is $467,500
What is an arithmetic series?An arithmetic series consists of the addition of the terms of an arithmetic progression.
The starting salary offered by the company = $31,000
The amount by which the company raises the salary every year = $3,500
The total salary over a ten year period can be found by expressing the situation using an arithmetic progression formula as follows;
The sum of n terms of an arithmetic progression can be found using the formula;
Sₙ = (n/2)·(2·a + (n - 1)·d)
Where;
Sₙ = The sum of n terms of the series
n = The number of terms in terms in the series
a = The first term of the series
d = The common difference between the terms of the series
The details from the question indicates;
n = 10
a = $31,000
d = $3,500
Therefore; S₁₀ = (10/2) × (2 × 31,000 + (10 - 1) × 3,500) = 467,500
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use synthetic division
The required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]
In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[3x^3+5x^2-18x+39\right]}{x+4}[/tex].
It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
As performing synthetic division of polynomials, the terms in the product remaining as fractions will be the remainder of the division while the polynomial is said to be the quotient of the division.
[tex]= \frac{\left[3x^3+5x^2-18x+39\right]}{x+4}\\=3x^2-7x+10-\frac{1}{x+4}[/tex]
Thus, the required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]
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TEXT ANSWER Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more ev- ery week at a constant rate. The line y = 3x + 12 rep- resents this scenario. a. How many rolls of towels did he start with? I b. How many rolls of towels is be buying every week?
Gavin already had 12 rolls of towels, and he is buying 3 rolls per week.
What is slope?Slope tells us the change between two points given, and is shown by the change in the y coordinate divided by the corresponding change in the x coordinate.
Given that, Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more every week at a constant rate. The line y = 3x + 12 represents this scenario.
Here the equation is y = 3x+12
When comparing with standard equation of the line, y = mx+c where m is slope, we get,
m = 3 and c = 12
Therefore, the change is 3, that means, he is buying 3 rolls per week,
and the constant is 12 that tells that he already have 12 rolls in stock.
Hence, a) he is buying 3 rolls every week, b) he has 12 rolls in stock.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equation (i), (ii), and (v) are the equivalent.
What is the equivalent expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
We have,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
If we take x =3,
the sums would be true.
for the equation (i) take x = 3,
2 + x = 5
2 + 3 = 5
LHS = RHS = 5
for equation (ii) take x = 3,
x + 1 = 4
3 + 1 = 4
LHS = RHS = 4
for equation (iii) take x = 3,
9 + x = 6
9 + 3 = 6
12 ≠ 6
LHS ≠ RHS
for the equation (iv) take x = 3,
x + (-4) = 7
3 + (-4) = 7
-1 ≠ 7
LHS ≠ RHS
for the equation (v) take x = 3,
-5 + x = -2
-5 + 3 = -2
-2 = -2
LHS = RHS = -2
Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.
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compute the arc length of the curve:
x(t)=2t^(3/2)+2, y(t)=2t-3, 0<=t<=2
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
What is Integration ?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
According to the given information
We can find the length of the arc by
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
Find the derivative of x w.r.t to t
dx/dt = [tex]3t^{\frac{1}{2} }[/tex]
Find the derivative of y w.r.t to t
dy/dt = 2
Putting the values in above equation
We get
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]
L= [tex]\int\limits^2_0 {\sqrt{9t+4} } \, dt[/tex]
L = [tex]\frac{2}{27}(9t+4)^{\frac{3}{2} }[/tex]
limit approaches from 0 → 2
Hence
The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m
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how do you solve for the y intercept ?
Y Intercept is the point where a line or curve crosses the y-axis of a graph or in other words where x=0.
Knowledge of the y-intercept can be used when graphing lines or when writing an equation in slope-intercept form.
Formula to calculate y-intercept.
We get the y-intercept by using the equation of a straight line which is;
y = mx + b
Where;
m is the gradient of the slope
b is the y-intercept.
We can use the following formula to calculate the y-intercept.
y – a = m ( x – b )
a and b being a point on a line.
Example:
Suppose you have a straight line whose gradient is 3 and a point 2,1, calculate its y-intercept.
Since the y-intercept is when x=0, therefore;
y – 2 = 3 ( x – 1 )
y – 2 = 3x – 1
y = 3x – 1
Therefore, the number that has replaced b is -1, which means that -1 is the y-intercept.
Select the inequality which represents the gragh shown below -6-y>=x2-7x
Answer:
The inequality which represents the graph shown is -6-y >= x^2 - 7x.
Simplify -x-(-4x-6)=6
Answer:
To simplify the given equation, we can start by using the rules of algebra to rearrange the terms and combine like terms on both sides of the equation. This gives us:
-x - (-4x - 6) = 6
We can then distribute the negative sign on the left side of the equation to get:
-x + 4x + 6 = 6
We can then combine like terms on the left side of the equation to get:
3x + 6 = 6
We can then subtract 6 from both sides of the equation to get:
3x = 0
We can then divide both sides of the equation by 3 to get the final result:
x = 0
Therefore, the simplified form of the given equation is x = 0.
Step-by-step explanation:
Challenge The members of the city cultural center have decided to put on a play once a night for a week. Their
auditorium holds 500 people. By selling tickets, the members would like to raise $2,050 every night to cover all expenses.
Let d represent the number of adult tickets sold at $6.50. Let s represent the number of student tickets sold at $3.50 each.
If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise
exactly $2,050? At one performance there were three times as many student tickets sold as adult tickets. If there were
480 tickets sold at that performance, how much below the goal of $2,050 did ticket sales fall?
There are 100 students and 400 adults.
The 480 tickets sold had a $10 fall in ticket sales.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Let d be the number of adults and y be the number of students.
⇒ d + s = 500 ..(1)
The number of adult tickets sold at $6.50 and the number of student tickets sold at $3.50 each.
⇒ 6.5d + 3.5s = 2050 ..(2)
From equation (1) d = 500 - s
Plug the value of d in equation (2)
6.5(500 - s) + 3.5s = 2050
3250 - 6.5s + 3.5s = 2050
3250 - 3s = 2050
3s = 3250 - 2050
3s = 1200
s = 400
Plug s = 400 in d = 500 - s
⇒ d = 500 - 400 = 100
Hence, there are 100 students and 400 adults.
Now, at one performance there were three times as many student tickets sold as adult tickets.
⇒ s = 3d
3d - s = 0 ..(3)
d + s = 480 ..(4)
⇒ 4d = 480
d = 120 Adults
Plug d = 120 in equation (4)
120 + s = 480
s = 480 - 120
s = 360 Students
The money earned from these 480 people is
120 * 6.5 + 360 * 3.5 = 780 + 1260 = $2040.
$2040 - $2040 = $10
Hence, the 480 tickets sold had a $10 fall in ticket sales.
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Solve this system of equations using the Substitution method. All work and a brief phrase/sentence explaining what you're doing needs to be shown for each step for full credit. Write final answer as a coordinate point.
12x+4y=−8
y = 2x + 3
pls help
Answer: (-1,1)
Step-by-step explanation:
since y is equal to 2x+3 you can sub 2x+3 into the y value of 12x+4y=-8
12x+4(2x+3)=-8
Multiply the numbers inside the parentheses using the distributive property
12x+8x+12=-8
Combine like terms
20x+12=-8
Isolate x by moving all other numbers to the right side
Subtract 12 on both sides
20x+12-12=-8-12
20x=-20
divide both sides by 20 to isolate and get the value of x
x=-1
Now that we know the x value substitute the value of x in any of the above equations. I am using y=2x+3
y=2(-1)+3
Multiply the numbers inside the parentheses
y=-2+3
y=1
The x value is -1, and the y value is 1.
Use them as coordinate points
(x,y)
(-1,1)
The solution to the given system of equations is the point (-1, 1) which is determined by the substitution method.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of equations is given as:
12x + 4y = −8
y = 2x + 3
To solve this system of equations using the substitution method, you can substitute the second equation into the first equation to eliminate one of the variables.
Substituting y = 2x + 3 into the first equation gives:
12x + 4(2x + 3) = -8
12x + 8x + 12 = -8
20x + 12 = -8
20x = -20
x = -1
Substituting this value of x back into the second equation gives:
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, the solution to the system of equations is the point (-1, 1).
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4. What is the length of b?
b=16
b=24
b=12
b=15
Answer:
b=12
Step-by-step explanation:
θ is an acute angle. Find the value of θ in degrees.
sec(θ)=2
The value of θ is 60°.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin, cos , tan , cosec , sec and cot
Let the angle be θ , that is;
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Thus, tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data that the angle be represented as θ
Now , we are given that the angle θ is acute
Since Acute angles measure less than 90 degrees
So , the value of θ < 90°
when the value of sec θ = 2
cos θ = 1/sec θ
, cos θ = 1/2
The value of θ when cos θ is 1/2.
when the angle θ is 60°
Therefore ,
the value of θ is 60°
sec 60° = 2
Hence , The value of θ is 60°
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After a dilation with a scale factor of 2 about the origin,ΔABC maps onto ΔDEF Which of the following statements is true?
2. AB=DF
m ∠B=2. m ∠E
CA≅FD
BC/EF=CA/FD
Hello, I'm pretty sure this answer is D
Answer: D) BC/EF=CA/FD
Step-by-step explanation:
1. Bank AAA is charging 4% in total fees to borrow money for a car loan. You want to buy a car that costs $25,000.
Calculate the total price for the car and the bank fees. Then, find the monthly payment if you get a $5 year loan to buy
the car from Bank AAA?
The total price for the car is $26000.
The monthly payment is $500.
How to calculate the price?From the information illustrated, Bank AAA is charging 4% in total fees to borrow money for a car loan and the person want to buy a car that costs $25,000.
The total amount that will be paid will be:
= Amount of car + Interest
= $25000 + ($25000 × 4%)
= $26000
The amount on a 5 year loan will be:
Interest = PRT
= ($25000 × 4% × 5)
= $5000
Total amount to be paid = $25000 + $5000
= $30000
Monthly payment = Total amount / Number of months
= $30000 / 60
= $500
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A public health official claims that more than 5.8 percent of the population suffers from long-term COVID symptoms. Use p, the true percentage of the population that suffers from long-term COVID. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, ρ, σ) for the indicated parameter. A. H0 : p = 5.8% H1 : p < 5.8% B. H0 : p = 5.8% H1 : p > 5.8% C. H0 : p = 5.8% H1 : p ≤ 5.8% D. H0 : p = 5.8% H1 : p ≥ 5.8%
Answer:
B. H0 : p = 5.8% H1 : p > 5.8%
The null hypothesis, denoted H0, is a statement that asserts that there is no significant difference between a sample statistic and a population parameter. In this case, the null hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is equal to 5.8 percent. This is represented symbolically as H0 : p = 5.8%.
The alternative hypothesis, denoted H1, is a statement that contradicts or negates the null hypothesis. In this case, the alternative hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is greater than 5.8 percent. This is represented symbolically as H1 : p > 5.8%.
Read the following statement: If the sum of two angles is 90º, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90º.
the angles are complementary.
angles are complementary if their sum is 90º.
The correct option is angles are complementary if their sum is 90º.
What are complementary angles?When the sum of two angles is 90°, then they are complements of each other and hence called complementary angles.
Given is a statement, If the sum of two angles is 90º, then the angles are complementary.
Rewriting the sentence to check the hypothesis, in it.
It should be this:
The two angles are complementary if the sum of the two angles are 90 degrees.
A.) There are two angles.
While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.
B.) The sum of two angles is 90 degrees.
This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.
C.) The angles are complementary.
This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.
D.) Angles are complementary if their sum is 90 degrees.
This is an accurate statement, and provides details to support its claim, also rewriting the original sentences into one properly.
Hence, the correct option is option D.
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Find the value of x in the image
Answer:
Step-by-step explanation:
73 = x + 85
x + 85 = 73
x = -12
(-12) is the value of x.
Please helpppp thank you
can someone who loves math do this and tell me the answers or do step by step please
Answer:
Step-by-step explanation:
3.) Slope: 15x
Y-int: 120
Y=15x+120
4.) For this one i'm not sure maybe..
5.) Slope: 5x
Y-int: 250
Y=5x+250
NO LINKS!! Help me with these 2 column proofs 9aa
Answer:
Step-by-step explanation:
ok this is hella easy what kind of geometry is this
ok on to the answers
statement 1: angle 1 is a right angle, angle 2 is a right angle
reason 1: given
statement 2: angle 1 is congruent to angle 2
reason 2: all right angles are congruent theorem
second problem
statement 1: angle 1 and angle 2 are vertical angles
reason 1: either say given or shown in diagram (id do both if ur teacher is picky)
statement 2: angle 1 is congruent to angle 2
reason 2: vertical angles are congruent theorem
Here is the two column proof:
Statement Reason
∠1 is a right angle Given∠2 is a right angle Given∠1 ≅ ∠12 Right angles theoremProved===================================================
Statement Reason
Diagram Given∠1 and ∠2 are vertical angles Definition of vertical angles∠1 ≅ ∠2 Vertical angles theoremProved