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Drag an answer to each box to complete this paragraph proof.
Given: ∠PQR and ∠RQS are supplementary angles and m∠PQR=115°
Prove: ∠RQS is an acute angle.
It is given that ∠PQR and ∠RQS are supplementary angles. So, m∠PQR+m∠RQS=180° using the ________ . It is also given that m∠PQR=115° . Using the substitution property of equality, ________ + m∠RQS=180° . Using the subtraction property of equality, m∠PQR=65° . Therefore, ∠RQS is an acute angle by ________ .
A. definition of complementary angles
B. definition of supplementary angles
C. definition of acute angle
D. definition of obtuse angle
E. 180°
F. 115°
Image uploaded below:
V V V
Answers
Answer: The correct options for blank 1,2 and 3 are B, F and C respectively.
Explanation:
It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.
The two angles are called supplementary angles if they are lies on the same arc of a straight line and their sum is 180 degree.
Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.
[tex]\angle PQR+\angle RQS=180^{\circ}[/tex] .... (1)
Therefore, the correct option for first blank is option B.
It is given that ∠PQR=115°.
Using the substitution property of equality, the equation (1) can be written as,
[tex]115^{\circ}+\angle RQS=180^{\circ}[/tex]
Therefore, the correct option for second blank is option F.
Using the subtraction property of equality, ∠PQR=65° .
An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.
Since 65 is less than 90, so by the definition of acute angle the ∠RQS is an acute angle.
Therefore, the correct option for third blank is option C.
Related Questions
What are the roots of the polynomial equation? 0= x^2 +18x+45
Answers
First factor 45
Second you have (x+3)(x+15)
Third to find you zeros in this form it will be x=-3 and x=-15
Because it would be the opposite pf those numbers in the factored form
Answer:
-15 and -3
Step-by-step explanation:
What is the maturity value of a 3-month, 14% note for $50,000? (round your answer to the nearest dollar.)
a.$57,000
b.$51,750
c.$50,000
d.$52,000?
Answers
The maturity value of a 3-month, 14% note for $50,000 is calculated by first determining the interest over the 3-month period and then adding it to the principal. The interest is $1,750, resulting in a maturity value of b) $51,750.
The maturity value of a 3-month, 14% note for $50,000 can be calculated using the formula for simple interest: M = P + (P × r × t), where M is the maturity value, P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years. Let's calculate the interest first and then add it to the principal to find the maturity value.
First, convert the annual interest rate to decimal: 14% = 0.14.
Then, because the note is for 3 months (which is 3/12 or 0.25 of a year), the time period t is 0.25.
Now, calculate the interest: I = P × r × t = $50,000 × 0.14 × 0.25 = $1,750.
Finally, add the interest to the principal to get the maturity value: M = P + I = $50,000 + $1,750 = $51,750.
So, the correct answer is b. $51,750.
How long does it take for a deposit of $900 to double at 2% compounded continuously?
Answers
What is the equation of a circle with center (-3, -1) that contains the point (1, 2)?
Answers
hmmm what's the radius anyway? well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point? well, is the radius, let's check then.
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ -1}})\quad % (c,d) &({{ 1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5[/tex]
so, what's the equation of a circle with center at -3, -1 and a radius of 5?
[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{\quad k}})\qquad radius=&{{ r}}\\ &-3&-1&5 \end{array} \\\\\\\ [x-(-3)]^2+[y-(-1)]^2=5^2\implies (x+3)^2+(y+1)^2=25[/tex]
Answer:
(x + 3)^2 + (y + 1^)2 = 25
Step-by-step explanation:
The distance formula gives the length of the radius:
r = √(-3-1)^2 + (- 1-2)^2 = √25 = 5
Substituting h = -3, k = -1, and r = 5 into the standard form (x - h)2 + (y - k)2 = r2, you get (x + 3)2 + (y + 1)2 = 52 = 25.
edmentum :)
A bread recipe calls for 1/3 cup of white flour and 2 3/4 cups of whole wheat flour. What is the total amount of flour needed?
Answers
Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)
Answers
y = 5x + 10
The slope-intercept form is y = mx + b, where m = slope, and b = y-intercept.
In this case, the 5 is the slope.
Parallel lines have equal slopes, so the line we need to find also has a slope of 5. Its equation is
y = 5x + b
We need to find what b is.
We can use the given point, (3, 10), in for x and y and solve for b.
10 = 5 * 3 + b
10 = 15 + b
-5 = b
Now that we know that b = -5, we replace b with -5 to get our equation
y = 5x - 5
The equation of the required line is [tex]y=5x-5[/tex].
Given:
The eqation of paralle line is [tex]y-5x=10[/tex]. The required line passes through the point [tex](3,10)[/tex].To find:
The equation of the required line in slope-intercept form.
Explanation:
The given equation can be rewritten as:
[tex]y=5x+10[/tex]
On comparing this equation with [tex]y=mx+b[/tex], we get
[tex]m=5[/tex]
Slopes of parallel lines are always equal.
The slope of reqired line is [tex]m=5[/tex] and it passing through the point [tex](3,10)[/tex]. Using the point slope form, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-10=5(x-3)[/tex]
[tex]y=5x-15+10[/tex]
[tex]y=5x-5[/tex]
Therefore, the equation of the required line is [tex]y=5x-5[/tex].
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a googol is a large number that is the digit one followed by one hundred zeros.if you multiply a googol by 100, how many zeros will that product have
Answers
Question 3 e and f are sets of real numbers defined as follows.
Answers
Kevin has a box of cereal that contains 10 1/2 cups of cereal. A serving size of the cereal is 3/4 cup. How many servings are in the box of cereal? Enter your answer in the box
Answers
29 servings
The number of servings in the box of cereal is:
14
Step-by-step explanation:It is given that:
Kevin has a box of cereal that contains 10 1/2 cups of cereal.
i.e. the number of cups of cereal= 21/2 cups
Also,
A serving size of the cereal is 3/4 cup.
This means that:
The number of servings in the box are:
Ratio of number of cups of cereal in box to the number of cups of cereal in one serving
which is calculated as:
[tex]\text{Number of servings}=\dfrac{\dfrac{21}{2}}{\dfrac{3}{4}}\\\\\\\text{Number of servings}=\dfrac{21\times 4}{3\times 2}\\\\\\\text{Number of servings}=14[/tex]
What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?
Answers
center(-2,4)
Answer: The required center of the given circle is 2 units.
Step-by-step explanation: We are given to find the radius of a circle with the following equation:
[tex]x^2+y^2+8x-6y+21=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The standard equation of a CIRCLE with radius 'r' units and center at the point (h, k) is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2+8x-6y+21=0\\\\\Rightarrow (x^2+8x+16)+(y^2-6y+9)-16-9+21=0\\\\\Rightarrow (x^2+2\times x\times 4+4^2)+(y^2-2\times x\times 3+3^2)-4=0\\\\\Rightarrow (x+4)^2+(y-3)^2=4\\\\\Rightarrow (x-(-4))^2+(y-3)^2=2^2.[/tex]
Comparing the above equation with the standard equation (i), we get
radius, r = 2 units and center, (h, k) = (-4, 3).
Thus, the required center of the given circle is 2 units.
what is 0.81% written as a decimal
Answers
Hope it helped! Have a great day
Answer: 0.0081
I need help on how to figure out this question! A track coach made a two way table to show his runners gender and running category. Male: Sprints- 16 Middle distance- 11 Long distance- 9 Female: Sprints- 12 Middle distance- 14 Long distance- 5 To the nearest hundredth, what is the probability that a randomly chosen female runs sprints? This obviously says that order doesn't matter as they mention "randomly chosen". I am just having trouble figuring out how to solve this.
Answers
Answer: Approx 0.39 will be the required probability.
Step-by-step explanation:
Here,Number of,
Male: Sprints=16, Middle distance=11, Long distance= 9
So, total males=36
And, Female: Sprints= 12, Middle distance=14, Long distance=5
So, total females=31
Thus, If one female randomly chosen,
Then, The probability that female runs sprint= Number of females who run sprint / total number of females
⇒ The probability that female runs sprint=12/31= 0.38709677419≈0.39
N a trip to his grandparents, donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. how many miles did donny drive?
Answers
The solution is, donny drove 70 miles.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
we know that,
Speed: The ratio of distance to time.
To find the distance we use the following formula.
Given that
donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes.
so, we get,
In 45 minutes, she traveled = ( 60/60 * 45)
= (1 * 45)
=45 miles.
again, we have,
The she drove 50 miles per hour for 30 minutes.
so, we get,
In 30 minutes, she traveled = ( 50/60 * 30 )
=50/2
= 25 miles
Therefore donny drove (45+25) miles= 70 miles.
Hence, The solution is, donny drove 70 miles.
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In a couple of sentences and your own words describe how to re-write an expression that's in radical form into an expression with rational exponents?
Answers
Using this information, we will make the power of the radical the denominator of our exponent, and whatever exponent is contained in the radical will become the numerator.
Example:
√(x³) = square root of x³ = x^(3/2)
You are ordering pizzas for a birthday party and getting them delivered to your house. you order 12 pepperoni pizzas, 8 cheese pizzas, and 4 hawaiian pizzas. there is a delivery fee of $5.50 if your total comes to 184.54. how much was each pizza
Answers
The answer would be $7.46. If you subtract the delivery fee then divide by how much pizzas there are you would find the amount per each pizza.
Select all that apply. If p is a statement, which of the statements is the negation of p. not p. and p. p is false. or p. p is true.
Answers
bill is on the school archery team. the target has a center bull's-eye and two rings around the bull's-eye. the table gives the probabilities of each outcome. what is the probability that bill will get the next arrow in the inner or outer ring?express your answer as a decimal
Answers
Given the table below that gives the probabilities of outcomes.
[tex]\begin{tabular} {|c|c|c|c|c|} \bold{Outcome}&Bull's-eye&Inner ring&Outer ring&Miss\\ \bold{Probability}&0.036&0.297& 0.423&0.244 \end{tabular}[/tex]
The probability that Bill will get the next arrow in the inner or outer ring is given by
P(inner ring) + P(outer ring) = 0.297 + 0.423 = 0.72
Therefore, the probability that Bill will get the next arrow in the inner or outer ring is 0.72
Which is true of a melting point and a boiling point?
A. The melting point is a higher temperature than the boiling point.
B. The melting point is a lower temperature than the boiling point.
C. The melting point and the boiling point depend on the size of the sample.
Answers
Answer:
B - The melting point is a lower temperature than the boiling point.
Step-by-step explanation:
Melting point is the temperature at which any given solid will melt. The state of the solid changes from solid to liquid.
Boiling point is the temperature at which a given liquid boils and changes to vapor state. Like water starts to boil at 100 degrees Celsius.
The boiling point of a substance cannot be lower than its melting point.
So, the answer here is - The melting point is a lower temperature than the boiling point.
Write an equation for the line parallel to line AB that contains point C (0,3)
AB: y=-2x+1
Answers
y-3=-2(x)
y-3=-2x
y=-2x+3
y = -2x + 3
Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 4 vertices and 6 edges have?
7
4
6
5
Please Help!
Answers
4 vertices mean V=4
6 edges mean E=6
4-6+F=2
-2+F=2
F=4
A polyhedron with 4 vertices and 6 edges would have 4 faces, according to Euler's formula.
Explanation:This question involves the understanding of Euler's formula applied on polygons. Euler's formula, as given in the question is V – E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. To answer your question, we need to solve the formula for F. Let's replace V and E with the given numbers, which are 4 for vertices and 6 for edges.
So the formula becomes 4 – 6 + F = 2. Simplifying this, we get -2 + F = 2. Solving for F, we find F = 1 + 2, which means F = 4. So, a polyhedron with 4 vertices and 6 edges would have 4 faces.
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For what value of b does
Answers
Note that (1/12)^-2b is the same as 12^2b. When we add the exponents we get 2b-2b+2=2, hence 12² on the left.
Tracey paid $170 for an item that was originally priced at $580. What percent of the original price did Tracey pay? Round your answer to two decimal places.
Answers
Michael, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Michael also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2.20 dollars, Basic Proofreading 2.80 dollars, Extended Proofreading 3.90 dollars, and Deep Editing 12 dollars Maria has a 25-page manuscript. The equation below shows the relationship between the total cost of editing 25 pages, T, and the cost per page, c, if she gets the 5% discount: 25c − 0.05(25c) = T Using the equation, what is the best quality of editing that Maria can get done for a maximum of $66.50?
Answers
25c - 1.25c = 66.50
23.75c = 68.50
c = 68.50 / 23.75
c = 2.88
The best quality of editing she can get is basic Proofreading
Kate has some dimes and quarters. if she has 1919 coins worth a total of $2.95, how many of each type of coin does she have?
Answers
Translate the variable expression into a word phase
2 x (3 - x)
Answers
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
answer choices in pics
Answers
Answer:
[tex]V = (10a^3+91a^2+54a-792)[/tex]
Step-by-step explanation:
We have
[tex]V = lwh[/tex] (I), and
[tex]l=2a+11[/tex] (II)
[tex]w=5a-12[/tex] (III)
[tex]h=a+6[/tex] (IV)
We substitute the expression (II),(III) and (IV) in (I), that is
V= (2a+11)(5a-12)(a+6), solve the first one terms
[tex]V = (10a^2-24a+55a-132)(a+6)[/tex]
[tex]V = (10a^2+31a-132)(a+6)[/tex]
[tex]V = (10a^3+31a^2-132a+60a^2+186a-792)[/tex], simplifying
[tex]V = (10a^3+91a^2+54a-792)[/tex]
X= -75/y; X=6
what's the answer & how do u solve this?
Answers
[tex]x = \frac{-75}{y} For x = 6 Well, first replace x by 6 6 = -75/y Cross multiply 6*y = -75 6y = -75 Divide both sides by 6 to find y 6y/6 = -75/6 y= -25/2 Best of luck with your studies! [/tex]
The length of a rectangle is 55 meters longer than the width. if the area is 2929 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Answers
length = L = (w + 55)
w * (w + 55) =2,929 sq meters
w^2 +55w -2,929,= 0
width = 33.206 = 33.2 meters (rounded)
Length = 33.2 + 55 = 88.2 meters
The expression V = 2x3 + 6x2 can be used to find the volume of the trapezoidal prism below. If x = 12 cm, what is the volume of the prism?
Answers
x = 12
V = 2(12^3) + 6(12^2)
V = 2(1728) + 6(144)
V = 3456 + 864
V = 4320
The volume of the prism is 4320 cubic units
The expression for the volume is given as:
V = 2x^3 + 6x^2
When x = 12, the expression becomes
V = 2 * 12 ^3 + 6 * 12^2
Evaluate the exponent
V = 2 * 1728 + 6 * 144
Evaluate the products
V = 3456 + 864
Evaluate the sum
V = 4320
Hence, the volume of the prism is 4320 cubic units
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Help this is urgent due tomorrow... The lowest price for a play is $15 and the highest ticket price is $45. Write and graph a compound inequality that describes the price of all tickets for the play.