Answer:
To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.
Setting x^2 - 10x + 31 equal to x + 1:
x^2 - 10x + 31 = x + 1
Rearranging the equation to standard quadratic form:
x^2 - 10x + 30 = 0
Now, we can factorize the quadratic expression:
(x - 5)(x - 6) = 0
Setting each factor equal to zero and solving for x:
x - 5 = 0 or x - 6 = 0
x = 5 or x = 6
So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.
Answer:
To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.
Setting x^2 - 10x + 31 equal to x + 1:
x^2 - 10x + 31 = x + 1
Rearranging the equation to standard quadratic form:
x^2 - 10x + 30 = 0
Now, we can factorize the quadratic expression:
(x - 5)(x - 6) = 0
Setting each factor equal to zero and solving for x:
x - 5 = 0 or x - 6 = 0
x = 5 or x = 6
So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.
Answer:
x = 5 or x = 6
Step-by-step explanation:
Given expressions:
[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]
To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:
[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]
Using the zero-product property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]
Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.
Answer:
x = 5 or x = 6
Step-by-step explanation:
Given expressions:
[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]
To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:
[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]
Using the zero-product property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]
Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.
what is the product of -6
Answer:
The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.
Step-by-step explanation:
Find the measure of each indicated side. Round your answer to the nearest tenth.
Answer:
m∠R = 78.9°------------------------------
We are given three sides and need to find one of angles.
Use the law of cosines:
[tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]
Here we are given:
R - angle A, a = 59.7, b = 52, c = 41Substitute above values into the given equation:
[tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]
Find m∠R:
m∠R = arccos (0.1925), use calculatorm∠R = 78.9° (rounded to the nearest tenth)What is the greatest commen factor of 72 and 96
the greatest common factor of 72 and 96 is 24
Diane is a camp counselor she did signs in new obstacle course and tested course with three friends the Doppler shows the time it takes to complete the obstacle course. What is the mean absolute deviation(MAD)of the times.
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.
To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.
MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.
Let's say the times taken by the four people are:
Diane: 2 minutes
Friend 1: 1.5 minutes
Friend 2: 2.5 minutes
Friend 3: 1.75 minutes
The mean of these times is:
Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes
Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:
|2 - 1.9375| = 0.0625
|1.5 - 1.9375| = 0.4375
|2.5 - 1.9375| = 0.5625
|1.75 - 1.9375| = 0.1875
Then, we find the mean of these absolute deviations:
MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
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For each SSA case below, i) solve by the law of cosines, (ii) solve by the law of sines; use degrees for angles, and round each answer to its nearest 100th:
The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.
How to explain the angleSSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.
By sine rule,
Y = sin156.78 × 44 / 34
= 29
sin Y = 0.499
Y = 29.93°
By the angle sum property. The last angle will be:
180 - 156.78 - 29.93
= 6.67°
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What is the surface area of this cylinder?
Use 3.14 and round your answer to the
nearest hundredth.
2 ft
5 ft
square feet
The surface area of this cylinder is 942 millimeter square
How to determine the surface areaThe formula for the surface area of a cylinder is expressed as;
SA = 2πr h + 2πr²
Given that the parameters are identified as;
SA is the surface area of the cylinder.r is the radius of the cylinder..h is the height of the cylinderFrom the information given, we have that;
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 10²
Find the square values
Surface area = 2 × 3.14 × 10 × 5 + 2× 3.14 × 100
Multiply the values
Surface area = 314 + 628
Now, add the values
Surface area = 942 mm²
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The circle below has center O, and its radius is 5 m. Given that m LAOB = 30°, find the area of the shaded region and the length of the arc ADB. Give exact answers in terms of it, and be sure to include the correct units in your answer.
Measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and arc length ADB is 10.67π m
Given that the circle has a center O.
The radius of the circle is 8 m.
The measure of ∠AOB is 120°
We need to determine the area of the shaded region and the length of the arc ADB.
The measure of ∠ADB is given by
∠ADB = 360 - ∠AOB
= 360 - 120
=240 degrees
The area of the shaded region can be determined using the formula,
A = (θ/360) πr²
A = (θ/360) ×3.14× 8²
A = 42.67 m²
Thus, the area of the shaded region is 42.67π m²
The length of arc ADB can be determined using the formula,
Arc length = (θ/360) 2πr
=10.67π m
Hence, measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and length of arc ADB is 10.67π m
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Jen works for a cellular phone company. She earns a salary of $250 per
week plus a bonus of 10% of the value of any phones and accessories
that she sells. In the past four weeks, Jen sold $312 worth of phones
and accessories.
Circle the amount that correctly completes the statement.
In the past four weeks, Jen earned a total income of $
1,031.20
562.00
312.00
281.20
31.20
Okay, here are the steps to solve this problem:
* Jen earns a weekly salary of $250
* She gets a 10% bonus on any sales
* In the past 4 weeks, she sold $312 worth of phones and accessories
* 10% of $312 is $31.20
* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80
* Her weekly salary is $250
* So in 4 weeks, her salary would be $250 * 4 = $1000
* Her total income over 4 weeks is $1000 + $124.80 = $1124.80
* The choices are:
** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20
So the correct choice is $1,031.20.
I need help please I can’t figure this out
Answer: Area=3.125 square feet
Step-by-step explanation:
2.5x2.5=6.25
6.25/2= 3.125
Answer:
A = 50 ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
given that 1 inch equals 4 feet , then
b = 2.5 in = 2.5 × 4 feet = 10 feet
h = 2.5 in = 2.5 × 4 feet = 10 feet
then
A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²
point(s) possible
Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1093 and x = 538 who
said "yes." Use a 90% confidence level.
Click the icon to view a table of z scores.
b) Identify the value of the margin of error E.
(Round to three decimal places as needed.)
c) Construct the confidence interval.
if you rotate cars tires at 10,000 miles, if a car tire has 25,200 rotations per day, how many weeks will it be until you rotate the tires
It will take 4. 09 weeks for the tires to be rotated at the current rate.
How to find the time till rotation ?When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.
25, 200 rotations / day x 7 days / week = 176, 400 rotations per week
To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:
C = 2πr
Rotation per mile is:
1 mile / 87.96 inches / rotation = 72.26 rotations / mile
Number of weeks:
10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations
722, 600 rotations / 176, 400 rotations/week = 4.09 weeks
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Which of the following is the expanded form of a number? Select all correct answers.
(A) 7·1000+8·100+3· 1/100
(B) 4·100+9·100+3· 1/10 +4· 1/10
(C) 71·10+4·1+6· 1/100 +5· 1/1000
(D) 5·1000+5·100+5·1+5·1/100
(E) 3·1000+8·1000+9·1/1000
(F) 9·1000+3·101+5· 1/10
Find the sales tax. Then find the total cost of the item.
$50.00
Sales Tax
Rate of Sales Tax Sales Tax
7%
?
As a result, the item's final price is $53.50 and the sales tax is $3.50.
What is sales tax?The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax
We can multiply the item's price by the applicable sales tax rate to determine the sales tax:
Price of Item x Sales Tax Rate equals Sales Tax
Sales Tax: $50.00 x 7% = $3.50
We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:
Price of Item + Sales Tax = Total Cost
$50.00 plus $3.50 equals $53.50 as a total
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$550 is deposited in an account with 8.5%
interest rate, compounded continuously.
What is the balance after 6 years?
F = $[?]
the balance after 6 years is approximately $926.45.
What is Continuous compounding ?
Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.
We can use the formula for continuous compounding to find the balance after 6 years:
[tex]F = Pe^{(rt)}[/tex]
where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.
[tex]F = 550e^{(0.085*6)}[/tex]
F ≈ $926.45
Therefore, the balance after 6 years is approximately $926.45.
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Use spherical coordinates to evaluate the triple integral ∫∫∫Ex2+y2+z2dV
, where E is the ball: x2+y2+z2≤81
.
[ rate 5stars~ and give thanks for more po! welcome! ]
Step-by-step explanation:
We have the triple integral:
∫∫∫E x^2 + y^2 + z^2 dV
where E is the ball x^2 + y^2 + z^2 ≤ 81.
In spherical coordinates, the volume element is given by:
dV = ρ^2 sin φ dρ dθ dφ
where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).
Substituting into the integral, we get:
∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ
= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π
= (2π/5)(9^5)(-(-1 - 1))
= (4π/5)(9^5)
≈ 114413.73
Therefore, the value of the triple integral is approximately 114413.73.
riangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
Will give brainliest if you get correctly!
Guessing = Report
Answer:
Step-by-step explanation:
A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 2 comma 5, 8 comma 2, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 7, and 10 comma 4 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 1 comma 8, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 5.33, and 6 comma 4.33 Question 11(Multiple Choice Worth 5 points) (Scatter Plots MC) A large retailer calculated the average hourly wage of employees over 6 years. The following table shows the years since 2016 and the average hourly wage of an employee at that time. Years (since 2016) 0 1 2 3 4 5 6 Hourly Wage (in dollars) 10 10.5 11 11.5 12 13 14 Which of the following representations is most appropriate for showing the change in the average hourly wage each year? scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 10, 1 comma 10 and a half, 2 comma 11, 3 comma 11 and a half, 4 comma 12, 5 comma 13, 6 comma 14 scatter plot with the title average hourly wage and the x axis labeled hourly wage in dollars and the y axis labeled years since 2016, with points at 10 comma 0, 10 and a half comma 1, 11 comma 2, 11 and a half comma 3, 12 comma 4, 13 comma 5, and 14 comma 6 line graph with the title average
A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?
To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
How long must the person leave the money in the bank until it reaches 20400 dollars?We can use the formula for compound interest:
A = P[tex](1 + r/n)^{nt}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.
Let's solve for t:
20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]
2.55 = [tex](1.00013)^{(365t)}[/tex]
Taking the natural logarithm of both sides, we get:
after solving
Using a calculator, we find:
t ≈ 15.5
So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
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If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is
fo =
c + vo
c − vs
fs
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 32 m/s and accelerating at 1.1 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.5 m/s2, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)
Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.
It can be calculated as:
[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]
where:
c is the speed of light (c = 332m/s)
all the subscripted s is related to the Source (frequency, velocity);
all the subscripted o is related to the Observer (frequency, velocity);
As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.
So, the frequency perceived by the observer:
[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]
[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]
[tex]f_o=460(1.247)[/tex]
[tex]f_o= 573.6 \ \text{Hz}[/tex]
At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz
Answer:
The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time
The perceived frequency you hear is
370.9 Hertz
The function is given as:
[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x [tex]f_{s}[/tex]
From the question
[tex]c=332[/tex] --- speed of the sound
[tex]V_{o} =32[/tex] ---current speed of the train
[tex]V_{s} = 40[/tex] --- speed of the opposite train
[tex]f_{s} =460[/tex] --- frequency of the sound wave
This gives:
[tex]f_{o}= \frac{332-32}{332+40}[/tex] ×[tex]460[/tex]
[tex]f_{o}= \frac{300}{372} x460[/tex]
Rewrite as:
[tex]f_{o}= \frac{300x460}{372}[/tex]
[tex]f_{o}= 370.9[/tex]
ASAP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Given
ABCΔ is a triangle.
D is a point on [BC]
|BD|=4
|AD|=|CD|
m(CBAˆ)=α=30∘
m(ACBˆ)=β=20∘
To Find
What is |AC|=x?
Solution
Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b
and applying law of cosines to all three triangles yields;
x=2acos20∘16=a2+b2+2abcos70∘(a+4)2=b2+x2+2bxcos50∘respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4
The complete question is -
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
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Can someone actually help me with this!!!! please do A through D, I attached the picture. BRAINLIEST!!!!!
Supplementary angles
Answer: ∠EGF and/or ∠CGB
Step-by-step explanation:
Starting Angle: ∠CGE
Possible Supplements: ∠EGF and ∠CGB
Tell whether the given side lengths can represent the sides of a right triangle
10, 12, 20
Determine if the segment lengths form an acute, right, or obtuse triangle,
10, 11, 14
26.
Need help with all of these please need this asap. Please show work
23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]
24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex] and finally the side length opposite the [tex]60^\circ[/tex] is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.
So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]
25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20
For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.
Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.
26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
The correct equation is C. d = 163t.
This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).
Step-by-step explanation:
Which parent functions have a domain of all real values of x? Select all that apply.
A. Absolute value
B. Linear
C. Reciprocal
D. Quadratic
E. Cube root
F. Cubic
Answer:
D. Quadratic
Step-by-step explanation:
The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative
Of the following Z-score values, which one represents the location closest to the mean?
A. Z=+0.5
B. Z=+1,0
C. Z=-1.5
D. Z=-0.3
Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean so option A is correct.
What is?In mathematics, the absolute value (also known as modulus) of a real number is its distance from zero on the number line. It is denoted by enclosing the number between two vertical bars, such as |x|.
For example, the absolute value of 5 is 5, because 5 units to the right of zero on the number line is at a distance of 5 units from zero. Similarly, the absolute value of -5 is also 5, because 5 units to the left of zero on the number line is at a distance of 5 units from zero.
According to the given informationTo determine which Z-score represents the location closest to the mean, we need to know the sign of each Z-score, as well as the absolute value of each Z-score.
The sign of the Z-score indicates whether the location is above (+) or below (-) the mean. The absolute value of the Z-score indicates how far away the location is from the mean, measured in standard deviations.
Looking at the options provided, we see that:
A. Z=+0.5 is positive, indicating a location above the mean, and has an absolute value of 0.5.
B. Z=+1.0 is positive, indicating a location above the mean, and has an absolute value of 1.0.
C. Z=-1.5 is negative, indicating a location below the mean, and has an absolute value of 1.5.
D. Z=-0.3 is negative, indicating a location below the mean, and has an absolute value of 0.3.
Since we want to find the Z-score closest to the mean, we should look for the option with the smallest absolute value. Therefore, the answer is A. Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean.
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The volume of blood in a person's body is proportional to body weight. A person who weighs 200 pounds has approximately 6 quarts of blood. Estimate the number of quarts of blood
in a person who weighs 90 pounds.
Complete the proportion, where the ratios have volumes of blood in the numerators and body weights in the denominators.
X
(Doshot simplify.)
X
More
The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.
How to calculate the number of quarts of blood the individual has?The body weight of the first individual = 200 pounds
The volume of blood = 6 quarts.
Therefore a person of 90 pounds = X quarts.
That is;
200 pounds = 6 quarts
90 pounds = X quarts
make X quarts the subject of formula;
X = 90×6/200
= 540/200
= 2.7 quarts
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Find the sum of the interior angles of the following polygon:
115⁰
4
130⁰
115
95⁰
Sum of interior angles =
Part 2:
Find the measure of x:
degrees.
degrees.
The Sum of interior angles of the given polygon is: 540°
The value of the angle x is: 85°
What is the interior angle of the polygon?The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.
Sum of interior angles in a n-sided polygon is:
Sum = (n - 2)180
where:
n is the number of sides of the irregular polygon.
This is a 5-sided irregular polygon
Thus:
Sum = (5 - 2)180
Sum = 540°
Thus:
x + 115 + 115 + 130 + 95 = 540
x + 455 = 540
x = 540 - 455
x = 85°
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