Answers
PR = QR
5n = 32 +n
subtract 1 n from each side
4n = 32
divide both sides by 4
n = 32/4 = 8
n=8
PR = 5n = 5*8 = 40
PR = 40
The measure of PR from the diagram given is 40
The given diagram is an isosceles triangle, For an isosceles triangle, two of sides and angles are equal. hence;
PR = QR
5n = 32 + n
Collect the like terms;
5n - n = 32
4n = 32
n = 32/4
n = 8
Get the measure of PR;
PR = 5n
PR = 5(8)
PR = 40
Hence the measure of PR from the diagram given is 40
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Related Questions
On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?
Answers
Chance of two 6s: (1/6)² = 1/36
The chance of rolling a 6 on 2 dice is 1/6 x 1/6.
1/6 x 1/6 = 1/36.
The average number of times for the first 6 would be 6
I'm not sure how to explain this part
But the average number of times for the second one would be 7.
To get the consecutive number of times, multiply them together:
6 x 7 = 42.
It would take an average of 42 times.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.
A.682
B.2044
C.2048
D.678
Answers
Answer: The correct option is (B) 2044.
Step-by-step explanation: We are given to find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024.
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
According to the given information, we have
[tex]a=4[/tex]
and
[tex]ar^{9-1}=1024\\\\\Rightarrow 4\times r^8=1024\\\\\Rightarrow r^8=\dfrac{1024}{4}\\\\\Rightarrow r^8=256\\\\\Rightarrow r^8=2^8\\\\\Rightarrow r=2.[/tex]
Therefore, the sum of the 9-term geometric sequence is given by
[tex]S_9\\\\\\=\dfrac{a(r^9-1)}{r-1}\\\\\\=\dfrac{4\times(2^9-1)}{2-1}\\\\\\=\dfrac{4\times(512-1)}{1}\\\\=4\times511\\\\=2044.[/tex]
Thus, the required sum of the 9-term sequence is 2044.
Option (B) is CORRECT.
Describe the change that occurs to the coordinates of a vertex of a figure when it is reflected across the Y axis
Answers
The sign of the x-coordinate changes; the y-coordinate stays the same.
Please help!!
Graph each pair of parametric equations.
x = 2t – 1
y = t^2 + 5, -4 ≤ t ≤ 4
Answers
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~
Sorry brainly kept of freezing on me...
Solving this is pretty simple, we plug in what t equals in both equations based upon our lovely given notice -4 ≤ t ≤ 4...
(My work will be attached below)
Now we will have to plot all the points we gathered onto our graph...
(The Graph will be attached below)
And there you are!
Answer:
B
Step-by-step explanation:
100% edge 2021
Which statement is true about the equations –3x + 4y = 12 and x – y = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answers
Answer:
C
Step-by-step explanation:
Its C just did the test
The african bush elephant weighs between 4.4 tons and 7.7 tons. What are its least and greatest wieghts rounded to the nearest ton
Answers
7.7=8 tons rounded
7.7 rounds to i
What is the smallest natural number n, greater than 1, for which (1×2×3× . . . ×n) + 01 is not prime?
Answers
The smallest natural number is 4 which is not prime.
What are Natural Numbers?Natural numbers are defined as which range from 1 to infinity and are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.
What are Prime numbers?Prime numbers are defined as any number that is any integer with exactly two factors 1 and the number itself. is said to be a prime number.
Given that
⇒ (1×2×3× . . . ×n) + 1
We have to determine the smallest natural number n, greater than 1, for which (1×2×3× . . . ×n) + 1 is not prime.
Here we substitute the value of n = 4 in the given expression,
⇒ (1×2×3×4) + 1
⇒ (24) + 1
⇒ 25
Therefore, the smallest natural number is 4 which is not prime.
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PLEASE HELP
Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box.
Answers
-32 + 5 < 9x
-27 < 9x
-3 < x
x > -3
hope that helps, God bless!
Inequality is a statement of an ordered relationship
The value of x as inequality is less than -3.
x < -3 is our answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
Example:
x > 3
y < 5
x ≤ 6
y ≥ 2
We have,
-32 > -5 + 9x
Add 5 on both sides.
-32 + 5 > -5 + 9x + 5
[ -32 + 5 = -27 ]
-27 > 9x
Divide both sides by 9.
-27/9 > 9x/9
-9 x 3 / 9 > 9x / 9
-3 > x
This can be written as:
x < -3
Thus,
The value of x as inequality is less than -3.
i.e x < -3
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Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function for Ronald’s wall. Let x be the number of minutes he walks.
B) what should the domain of the function be?
Answers
[tex]d=vt[/tex]
where d[tex]y= \frac{1}{15}x [/tex]= distance,
v = velocity,
t = time
In this case, d = 2 mi., t = 30 min. So we get
[tex]2=30v[/tex]
Dividing both sides by 30, we get
[tex]v= \frac{2}{30}= \frac{1}{15} [/tex]
Thus a function for his walk would be
[tex]y= \frac{1}{15} x[/tex]
where y = distance and x = number of minutes he walks.
b) Domain of a function is a set of x-values on which the function defined. In this case, the number of minutes is 30 at maximum. So the domain of the function is [0, 30].
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answers
Answer:
Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.
Step-by-step explanation:
based on the pattern of the drawings which conjecture is reasonable to make?
A. when a pair of parallel lines is intersected by a third line, the corresponding angles are complementary
B. when a pair of parallel lines is intersected by a third line, all of the angles formed are congruent.
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
D. when a pair of parallel lines is intersected by a third line, the corresponding angles are supplementary.
Answers
the 2 angles in each picture are the same - meaning they are congruent,
so the answer is:
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
Conjectures are simply opinions from a given information.
The conjecture that can be formed is: C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
From the three diagrams, we can see that:
[tex]\mathbf{30^o = 30^o}[/tex][tex]\mathbf{35^o = 35^o}[/tex][tex]\mathbf{50^o = 50^o}[/tex]From the figures above, we have the following observations
The angles are congruentThe angles are correspondingThe congruence of the angles is based on parallel lines, intersected by a third line (i.e. the transversal)Hence, the conjecture that can be formed is: option (c)
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Help me i hate word problems
Answers
so the question would be: how many times does fit into 3.5?
if you want to divide by a fraction, you need to multiply by the reverse of it.
so the answer is: 10 servings of lemonade ( and a little bit will be left over for half a serving).
Hope this helps!
Write the next two terms in the pattern. 3, 10, 17, 24, . . .
Answers
So next values would be 31 and 38
10-3 =7
each term increases by 7
so 24 +7 = 31
31+7 = 38
next 2 terms are 31 & 38
a pyramid with a square base of length 3cm and height 16cm
Answers
s = 16.0702 cm
a = 3 cm
e = 16.14 cm
r = 1.5 cm
V = 48 cm3
L = 96.421 cm2
B = 9 cm2
A = 105.421 cm2
The volume of a square pyramid:V = (1/3)a2hSlant Height of a square pyramid:By the Pythagorean theorem, we know thats2 = r2 + h2since r = a/2s2 = (1/4)a2 + h2, ands = √(h2 + (1/4)a2)This is also the height of a triangle sideLateral Surface Area of a square pyramid (4 isosceles triangles):For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a, and for this calculation our height for the triangle is slant height s. With four
sides we need to multiply by 4.L = 4 x (1/2)as = 2as = 2a√(h2 + (1/4)a2)Squaring the 2 to get it back inside the radical,L = a√(a2 + 4h2)Base Surface Area of a square pyramid (square):B = a2Total Surface Area of a square pyramid:A = L + B = a2 + a√(a2 + 4h2))A = a(a + √(a2 + 4h2))
A rectangular picture frame measures 83 cm by 42 cm What is the perimeter or distance around the picture frame in meters
Answers
[tex]P=2w+2l[/tex]
We can find our answer by direct substitution of known values:
[tex]P=2(83cm)+2(42cm)[/tex]
[tex]P=166cm+84cm[/tex]
[tex]P=250cm[/tex]
We can then convert to meters:
[tex]250cm * \frac{1m}{100cm} = 0.25m[/tex]
The perimeter of the picture frame is 0.25m.
Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than 4/5 of Terrance’s score. If t represents Terrance’s score, which inequality represents the situation?
Answers
Answer:
The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Step-by-step explanation:
Score earned by Jenny on her most recent test = 77
Let the Terrance's score is represented by t
[tex]\frac{4}{5}\text{ of the Terrance's score is = }\frac{4}{5}\cdot t[/tex]
If Terrance's score is 5 points greater then the points earned by Terrance's in the test is represented by :
[tex]\bf\frac{4}{5}\cdot t+ 5.......(1)[/tex]
Now, according to the given condition in the question , Jenny's score is not less than the score represented by (1)
⇒ Jenny's score is greater than equal to the score represented by (1)
Hence, The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Answer:
B
Step-by-step explanation:
2.What is the correct equation of the line shown below ?
Answers
Since the line enters the y-axis at (0,3) the y-intercept of the equation would be 3 (as according to the y=mx+b format where b is the y-intercept and m is the slope). The slope would be 3/2 since when you find two perfect points (I used (0,3) and (2,6)) and you use the rise over run method (move up 3 from (0,3) and 2 to the right to get to (2,6)), your slope is 3/2.
The equation of the line shown is y = (3/2)x + 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now given points from the line passes are (0,3) and (-4,-3)
Therefore we have,
x₁ = 0
y₁ = 3
x₂ = -4
y₂ = -3
Now since the slope of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
⇒ m = (-3 - 3)/ (-4-0)
⇒ m = -6/(-4)
⇒ m = 6/4
or, ⇒ m = 3/2
Now, for intercept c we can put any of points in the equation of line.
So, put (0,3)in the equation of line
3 = m(0) + c
3 = 0 + c
⇒ c = 3
Hence the required equation of line is given as,
y = mx + c
put the values of m and c,
y = (3/2)x + 3
which is the required equation of the line shown
Hence,the equation of the line shown is y = (3/2)x + 3.
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The relative frequency of a car travelling through a road junction having exactly two occupants is 0.26.If 5,000 cars are observed passing through the junction, how many of the cars could be expected to have only two occupants?
Answers
5000 x 0.26 = ??
What is the average of 5.24,6.875,3.298,5.7,4.98? Round the answer to 2 decimal points
Answers
8 less than one third of x is y
Answers
I think this is what you were looking for seeing that you cannot solve this problem without an 'x' or 'y'.
Which transformation is not isometric?
Answers
A game show contestant must randomly select a door. one door doubles her money while the other three doors leave her bankrupt. what is the probability she selects the door that doubles her money
Answers
A new truck that sells for $25,000 depreciates (decreases in value) 11% each year. What will be the value of the truck in 2 years
Answers
Depreciation rate = 11%
Note that 1 - 0.11 = 0.89.
Value after 1 year = $25,000 (0.89) = $22,250
Value after 2 years = $22,250 (0.89) = $19,802.50
Answer: $19,802.50
Answer:
Price of Truck after 2 year = $ 19802.50
Step-by-step explanation:
Given: Price of truck = $ 25,000
Price depreciate at rate of 11% in a year
To find: Price of truck after 2 years
If we let Price of truck to be P = $ 25000
And Rate of deprecation to be R = 11%
And time to be n = 2
now by using formula of deprecation, we get
[tex]A=P\times(1-\frac{R}{100})^n[/tex]
[tex]A=25000\times(1-\frac{11}{100})^2[/tex]
[tex]A=25000\times0.7921[/tex]
A = $ 19802.50
Therefore, Price of Truck after 2 year = $ 19802.50
evaluate the expression a3 -b/c for a = 3, b = 2 and c = 4. write in simplest form
Answers
Write out your equation:
[tex](a^3 - b)/c[/tex]
Substitute the values in:
[tex](3^3 - 2)/4[/tex]
Simplify:
[tex](27 - 2)/4[/tex]
[tex]25/4[/tex]
Solve:
It is 6.25.
Therefore, your answer is 6 1/4.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Final answer:
To evaluate the expression a³ - b/c for a = 3, b = 2, and c = 4, substitute the values and simplify to get 27 - 1/2, which equals 53/2 in simplest form.
Explanation:
To evaluate the expression a³ - b/c when a = 3, b = 2, and c = 4, you need to substitute these values into the expression and simplify.
Step 1: Substitute the given values. The expression becomes 3³ - 2/4.
Step 2: Calculate the power of 3. The expression is now 27 - 2/4.
Step 3: Simplify the fraction 2/4, which is equivalent to 1/2.
Step 4: The expression now reads 27 - 1/2.
Step 5: To subtract, convert 27 to a fraction which has the same denominator as 1/2. This gives us 54/2 - 1/2.
Step 6: Subtract the fractions which results in 53/2, which is the simplest form.
Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most
d. Find the value of
d.
Answers
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]
There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05
Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]
The greatest deviation from the mean is d = 0.86.
Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567
Answer:
d = 0.86
Help with math please.
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).
Question 1 options:
The rate of change is –3, and the y -intercept is 18.
The rate of change is 3, and the y -intercept is –6.
The rate of change is 1/3, and the y intercept is 4 2/3
The rate of change is -1/3, and the y intercept is 7 1/3
Answers
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years. A. 6.5 years B. 7.2 years C. 12.5 years D. 10.2 years
Answers
with an initial starting balance of $1,000.00Balance after 6 years with annual interest of 12.05% $1,979.12
7 years- 2,217.60$
12 years- 3,916.90
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).
A. 2x3 − x2 + 4x − 3
B. x2 − 4x + 3
C. 2x3 − x2 − 4x + 3
D. 2x3 − 4x2 + 3
Answers
so the answer should be C
Find the domain of the following piecewise function.
[-4,3)
(-4,3]
[-4,6)
(-4,6]
Answers
Graph both the you can easily find the answer
Answer:
c
Step-by-step explanation:
in 2003, a gallon of gas cost $1.75. In 2013 a gallon of gas cost $3.25. Write an equation to model this situation.
Answers
To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.
Explanation:To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m):
The change in cost of gas is $3.25 - $1.75 = $1.50The change in years is 2013 - 2003 = 10Therefore, the slope (m) is $1.50 / 10 = $0.15.
Next, let's find the y-intercept (b):
Using the point (2003, $1.75), we can substitute the values into the equation and solve for b:$1.75 = $0.15(2003) + b
b = $1.75 - $0.15(2003)
b = $1.75 - $300.45
b = -$298.70
Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.
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