The perimeter of triangle XYZ is 48 units
What is the perimeter of a triangle?
The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.
Here, we have
In The triangle XYZ
A is the midpoint of XY
B is the midpoint of YZ
AB = 1/2 XZ
AB = 5 units
Substitute the value of XZ in AB
5 = 1/2 × XZ
XZ = 10 units
B is the midpoint of YZ
C is the midpoint of XZ
BC = 1/2 XY
XY = 24 units
BC = 1/2 × 24 = 12 units
A is the midpoint of XY
C is the midpoint of XZ
AC = 1/2 YZ
AC = 7
7 = 1/2 YZ
YZ = 14
The perimeter of a triangle = the sum of the lengths of its sides
Perimeter ΔXYZ = XY + YZ + ZX
Perimeter ΔXYZ = 24 + 14 + 10
Hence, the perimeter of triangle XYZ is 48 units
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Is 5x-8+7y=y-6 linear or nonlinear
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inNeed Awnser asap
Right Awnser gets branliest
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
An area code has three digits. How many different area codes are possible
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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If 1+3+5+7+…+49 =625, what is 2+4+6+8+…+50?
If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.
What is arithmetic series?
A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Here, we have
Given: 1+3+5+7+…+49 =625
We have to find the value of 2+4+6+8+…+50.
Here, we calculate the sum of all even numbers and we get
2+4+6+8+…+50 = 650
Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.
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A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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Give expressions for the following:-
1) x is multiplied by -10 and then 5 is added to the result
2) 5 is multiplied by p and the result is subtracted from 26
3)y is multiplied by -5 and the result is added to 6
Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
3. What type of angle is angle A?
obtuse
acute
right
straight
The angle A is an obtuse angle of the regular polygon.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The interior angle of a polygon is [(n-2)180°]/n.
Where n is the number of sides of the polygon.
The number of sides of the polygon is 8.
The measure of the interior of the polygon is [(8-2)180°]/8
= 135°
The obtuse angle is an angle that more than 90°.
Therefore angle is an obtuse angle.
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You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
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Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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Which quantity is multiplied by pi in the formula for the area of a circle?
The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius
How to determine the multiplied quantity?From the question, we have the following parameters that can be used in our computation:
Area of a circle
The formula for the area of a circle is represented as
A = πr²
Express the formula as a product
So, we have the following representation
A = π * r²
In the above formula, we can see that the square of r is multiplied by pi
Hence, the required quantity is the square of the radius of the circle
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A recipe for a sports drink calls for 5/8 cup of powder for every 2 quarts of water. If Dionne uses 3 quarts of water, how many cups of powder are needed?
Answer: i think 15/8 but, im not sure
Step-by-step explanation:
In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
Status
Review
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
0 - 10,000
10,001 - 50,000
50,001 - 100,000
Progressive
Tax Rate
3%
5%
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
h
Answer:
final answer would be $6,550
Step-by-step explanation:
To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:
Income Range: $0 - $10,000
Progressive Tax Rate: 3%
Tax Owed: $0 - $10,000 * 3% = $0 - $300
Income Range: $10,001 - $50,000
Progressive Tax Rate: 5%
Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500
Income Range: $50,001 - $100,000
Progressive Tax Rate: 5.5%
Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500
Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.
look at attached photo
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
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A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
The retail cost of a computer is 37% more than its wholesale cost?which statement is true?1. THe retail cost of the computer is 132% more than the wholesale price.2. THe wholesale cost of the computer is 68% if the retail price.3. THe retail cost of the computer is 132% of the wholesale price.4. the retail cost of the computer is 37% of the wholesale price.
when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price
Retailers who acquire products in bulk are subject to wholesale pricing.
Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.
Retail pricing is what merchants decide to charge customers as their ultimate selling price.
Consumers are the primary focus of retail pricing.
According to the question,
The retail cost of a computer is 37% more than its wholesale cost
Let Retail cost be "x" and wholesale cost be "y"
So , x = y + 0.37y
=> x = 1.37y
Therefore , The retail price is 1.37times the wholesale price
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Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
70
Step-by-step explanation:
In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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