Answers
Step-by-step explanation:
In figure:
∠PRT+∠RTP+∠TPR=180
O
(angle sum property of triangle)
⇒x+(180
O
−∠RTQ)+60
O
=180
O
(linear pair)
⇒x+(180
O
−97
0
)+60
o
=180
O
⇒x=31
o
Now, ∠PRT+∠TRQ+∠QRS=180
O
(angle of straight line)
⇒x+48
o
+y=180
O
⇒31
o
+48
o
+y=180
O
⇒y=101
0
Related Questions
simply an surds
√75+ √48 -2√675
Answers
The simplification of √75+ √48 -2√675 is -21√3.
What is a surd?Surds are irrational numbers.
To simplify the surd in the question above, we use the addition and subtraction of surds.
Addition and subtraction of surdsTwo or more surds can be added or subtracted if they are in the same basic form.
E.g
a√b+c√b = (a+c)√ba√b-c√b = (a-c)√bUsing the above example,
Given:
√75+√48-2√675Express the surds to the same basic form
5√3+4√3-(2×15)√35√3+4√3-30√39√3-30√3 = -21√3Hence, the simplification of √75+ √48 -2√675 is -21√3.
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please need help involve steps for better understanding conic section
Answers
It has a vertical transverse axis (it lies on the y-axis). There is a vertex at (0, 4) and (0,0).
See the lines creating an X? Where they meet is the hyperbolas center point: (0, 2).
The general equation for this is ((y-k)^2)/a^2 - ((x-h)^2)/b^2. The center is (h, k), a = distance from center to vertex, c = distance from center to foci. b^2 = a^2 - c^2.
a = 2; center (0,2) to vertex (0,0).
b =5; from center (0,2) to the right (or left, either works) line of the box outlined inside of the hyperbola.
Now start substituting values into the hyperbola equation: ((y - 2)^2)/2^2 - ((x - 0)^2)/5^2. Also, since x-0 is just x, instructors might appreciate:
((y - 2)^2)/2^2 - (x^2)/5^2. That’s it!
I hope this helps, I’m very tired so I’m sorry if I don’t explain very good. Best of luck :)
Can anyone solve number 20?
Answers
Answer:
X=80
Step-by-step explanation:
Angle OAB=50(Properties of isosceles traingle)
X+50+50=180(sum of the interior angles of the traingle)
X=180-100
X=80
im stuck need help me i don't get it
Answers
Answer:
J. 12 : 18
Step-by-step explanation:
Amy used 2 tea bags for every 3 cups of water to make iced tea
the ratio here is 2:3
x = 2:3
lets simplify our ratios
6 : 10 = 3 : 5 ≠ 2 : 3
5 : 6 = (doesn't simplify evenly) ≠ 2 : 3
9 : 15 = 3 : 5 ≠ 2 : 3
12 : 18 = 2 : 3 = 2 : 3
Simplifying
find their highest common factor and divide both the numbers by the same amount (HCF).
Ex.
12 : 18
12 ÷ 6 = 2
18 ÷ 6 = 3
2 : 3
Use the the limit of sin of x all over x as x approaches 0 equals 1 to determine the limit of x times cosine of the quantity 5 times x all over sine of the quantity 5 times x as x approaches 0.
Answers
The limit of x times cosine of the quantity 5 times x all over sine of the quantity 5 times x as x approaches 0 is determined as ¹/₅.
Limit of the function
The limit of the function is determined as follows;
[tex]\lim_{x \to 0} \ \frac{sinx}{x} = 1\\\\ \lim_{x \to 0} \ \frac{x(cos5x)}{sin5x}[/tex]
The derivative of the function;
[tex]\frac{xcos(5x)}{sin5x} = \frac{-5x(sin(5x)) + cos(5x)}{5cos(5x)}\\\\= \frac{-5x(sin(5x))}{5cos(5x)} + \frac{cos(5x)}{5cos(5x)} \\\\ \lim_{x \to 0} \\\\= 0 + \frac{1}{5} = \frac{1}{5}[/tex]
Thus, the limit of x times cosine of the quantity 5 times x all over sine of the quantity 5 times x as x approaches 0 is determined as ¹/₅.
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Find the area of the figure. Round to the nearest hundredth where necessary.
55 mm
32.5 mm
12.5 mm
12.5 mm
Answers
[tex]\bold{ANSWER:}[/tex]
746 mm^2
[tex]\bold{SOLUTION:}[/tex]
Which of the following are solutions to the quadratic equation below?
Check all that apply.
x^2+ 6x + 9 = 2
Answers
Answer:
C & D
Step-by-step explanation:
x^2+6x+7=0
Delta=b^2-4ac=6^2-(4*1*7)=36-28=8
X=((-b)+-(delta)^(1/2))/2
X=((-6)+-(2^(3/2)))/2
[tex]x1 = - 3 - \sqrt{2} \\ x2 = - 3 + \sqrt{2} [/tex]
The perimeter of a rectangular painting is 304 centimeters. If the width of the painting is 61 centimeters, what is its length?
Answers
Answer:
The width of the rectangle is 91 cm
Step-by-step explanation:
61 × 2 = 122
304 - 122 = 182
182 ÷ 2 = 91
Answer:
91 cm
Step-by-step explanation:
61 x 2 (because there are 2 sides with length 61) = 122
304 - 122 = 182
182 / 2 = 91
165 divided by 11 =
154 divided by 14 =
306 divided by 17 =
322 divided by 14 =
Answers
Answer:
165 divided by 11 = 15
154 divided by 14 = 11
306 divided by 17 = 18
322 divided by 14 = 23
please help me!! I’m bad at math!!
Answers
Answer:
50.24
-
And, you're not bad at math! You goot this correct! :)
Step-by-step explanation:
c=25.12
we can use this to find the raidus!
-
plug it back into the circumference formula first.
c=(pi)(d)
25.12=3.14*d
divide both sides by 3.14!
d=8 but we need the radius, so we just divide by 2. 8/2 = 4. so the raidus is 4!
-
now we plug it into the area of a circle formula.
π · r2
3.14 * 4^2
3.14*16
50.24
2. Answer each of the following based on the scenario below.
Scenario: You bought a brand new iphone 13 for $1,200. Unfortunately your phone
loses 10% of its value every year.
a. Does this scenario represent exponential growth or decay? De
b. What is the initial value of your phone? 2000
c. What is the growth/decay factor? 10
d. Create a function in exponential form that models how much your phone will be worth
after x years.
f(x) =
e. After 3 years how much will your phone be worth?
. After 8 years how much will your phone be worth?
Answers
a) losing value is exponential decay.
b) Initial value is the price you paid = $1,200
c) decay factor is 100% - the percent lost per year = 90%
d) value = starting value x decay factor^ time
f(x) = 1200 x 0.90^x
e) replace x with 3 then 8 and solve:
f(3) = 1200 x 0.90^3 = 874.80
after 3 years it is worth $874.80
f(8) = 1200 x 0.90^8 = 516.56
after 8 years it is worth $516.56
Find the sum of the n terms using the formula a(1-r^n)/1-r 1,3/2,9/4,27/8,81/16, …
Answers
Answer:
[tex]S_5=\frac{211}{16}[/tex]
Step-by-step explanation:
We can easily see that the common ratio is [tex]r=\frac{3}{2}[/tex] and we are to find the first [tex]n=5[/tex] terms:
[tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_5=\frac{1(1-(\frac{3}{2})^5)}{1-\frac{3}{2}}\\\\S_5=\frac{1-\frac{243}{32}}{-\frac{1}{2}}\\ \\S_5=\frac{-\frac{211}{32}}{-\frac{1}{2}}\\ \\S_5=\frac{422}{32}\\\\S_5=\frac{211}{16}[/tex]
Evaluate the following when n = 7: 5(n - 5)
Answers
Hey! there
Answer:
10 is the answerStep-by-step explanation:
In this question we are given value of n as 7 and an expression that is 5 ( n - 5 ) .
And we are asked to evaluate the expression .
SOLUTION : -
Expression :
[tex] \quad \longmapsto \qquad \: 5(n - 5)[/tex]
We are substituting value of n as 7 :
[tex] \quad \longmapsto \qquad \:5( \bold{7} - 5) [/tex]
Solving parenthesis that is subtracting 5 from 7 :
[tex] \quad \longmapsto \qquad \:5(2)[/tex]
Now we are multiplying 5 with 2 and We get :
[tex] \quad \longmapsto \qquad \: \underline{\boxed{ \frak{{10}}}} \quad \bigstar[/tex]
Henceforth , value of expression when n is equal to 7 is ❝ 10 ❞#Keep LearningStep-by-step explanation:
Answer:
10 is the answer
Step-by-step explanation:
In this question we are given value of n as 7 and an expression that is 5 ( n - 5 ) .
And we are asked to evaluate the expression .
SOLUTION : -
Expression :
[tex] \quad \longmapsto \qquad \: 5(n - 5)[/tex]
We are substituting value of n as 7 :
[tex] \quad \longmapsto \qquad \:5( \bold{7} - 5) [/tex]
Solving parenthesis that is subtracting 5 from 7 :
[tex] \quad \longmapsto \qquad \:5(2)[/tex]
Now we are multiplying 5 with 2 and We get :
[tex] \quad \longmapsto \qquad \: \underline{\boxed{ \frak{{10}}}} \quad \bigstar[/tex]
Henceforth , value of expression when n is equal to 7 is 10
For Halloween, Sue wears a monocle that, its packaging claims, has a circumference of
18.212 centimeters. What is the monocle's radius?
Use 3.14
Answers
the measure of the radius is 2.9
A submarine starts 15 meters above sea level and travels 95 meters below sea level. How far did the submarine travel? *
Answers
The height attained by the submarine in the sea will be 80 meters.
What is the height?
Height is a vertical distance travelled by any object. Here the submarine is going down in the sea from 15 meters to 95 meters below the sea.
So the height attained by the submarine will be:-
H= 95-15
H= 80 meters.
Therefore the height attained by the submarine in the sea will be 80 meters.
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I need help in 17 & 18 & 19 :(
Answers
Answer:
The perimeter of the rectangle is 28 units
Based on a sample of 55 people, the sample mean GPA was 3.33 with a standard deviation of 0.08
The test statistic is:
(to 2 decimals)
The p-value is: (to 2 decimals)
Answers
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = 2.78.The p-value is of 0.01.What are the hypotheses tested?At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:
[tex]H_0: \mu = 3.3[/tex]
At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:
[tex]H_1: \mu \neq 3.3[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 3.33, \mu = 3.3, s = 0.08, n = 55[/tex]
Hence, the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.33 - 3.3}{\frac{0.08}{\sqrt{55}}}[/tex]
t = 2.78.
We are testing if the mean is different of a value, hence we have a two-tailed test. Using a t-distribution calculator, with 55 - 1 = 54 df and t = 2.78, the p-value is of 0.01.
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What is the volume of the rectangular prism?
Type the answer in the boxes below.
Answers
Answer:
3.75 cubic centimeters
Step-by-step explanation:
1.5*2.5*1 cubic centimeters
Answer:
3/20
Step-by-step explanation:
1/2 x 3/5 x 1/2
L x W x H is the formula
Length x Width x Height
count the squares, they're each 1/2 so multiply the number of squares with 1/2.
For example, the rectangular prism is 3 squares high, which means it's 3/6, and that simplifies to 1/2. Now you have your height. You do the same for the width and length.
Hope this helps <3
What is the length of side a rounded to the nearest 12.9 cm tenth of a centimeter? a a 15.3 cm
Answers
Answer:
8.227 then rounded to tenth is 8.2
Step-by-step explanation:
just smart.
please rate good. have a good day.
Can you guys help me please :(
Answers
Answer:
circumference formula = πd or 2πr .. they are the same thing
G is the answer
What type of solution is this expression (one solution, no solution, or infinite solutions)
4x + 2x - 2 = 3x + 7
Answers
Answer: One solution
Step-by-step explanation:
6x-2=3x+7
3x-9
x=3
I need help.. can somebody help me understand inputs & outputs?
A) 8, 2, –12
B) 8, 0, 12
C) 8, 0, –12
D) –8, 0 12
Answers
substitute the input values into the equation
input (6) -> y = 2(6)-4
y = 12-4
y = 8
basically just substitute the
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, what is the volume of the water that was displaced (in cubic inches)?
Answers
The volume of the water that was displaced will be 0.06 cubic feet.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
mass = density × volume
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water.
Then the volume of the water that was displaced will be
We know that the density of the water is 62.4 pounds per cubic foot.
Then we have
3.7 = 62.4 × volume
Volume = 0.059
Volume ≅ 0.06 cubic-foot
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what is this help plssss
Answers
Answer:
C
Step-by-step explanation:
8- 3.14159265359 = 4.85840734641.
or
8-pi = 4.85>5 which is incorrect.
From the triangle, find the missing length
Answers
Solve for x.
32 exponet 5-3x=2 exponet-10x
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The value of x in the given expression 32⁽⁵⁻³ˣ⁾ = 2⁻¹⁰ˣ is 5.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of x in the given expression 32⁽⁵⁻³ˣ⁾ = 2⁻¹⁰x can be found,
[tex]32^{(5-3x)}=2^{-10x}\\\\2^{5(5-3x)}=2^{-10x}\\\\5(5-3x)=-10x\\\\25-15x=-10x\\\\25=-10x+15x\\\\25=5x\\\\x=5[/tex]
Hence, the value of x in the given expression 32⁽⁵⁻³ˣ⁾ = 2⁻¹⁰ˣ is 5.
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Tell whether the following ratios shows proportion or not. Write
your answer on the space provided before each number.
_________ 1. 2:10 = 1:5
_________ 2. 3:6 = 6:3
_________ 3. 5:15 = 1:3
_________ 4. 12:4 = 6:2
_________ 5. 5:15 = 1:3
Answers
Answer:
1. Proportion
2. Not Proportion
3. Proportion
4. Proportion
5. Proportion
Step-by-step explanation:
Hope it helps you :))))))
Have a good day
pls help plssssss thank you 20 points
Answers
Answer:
7x - 10 < 11
Step-by-step explanation:
B
Write a cosine function that has an amplitude of 4, a midline of 2 and a period of1
Answers
Answer:
see below
Step-by-step explanation:
start with cos (x)
amplitude 4
4 cos x
midline 2
4 cos (x ) + 2
period of 1 : 2 pi / 1 = 2 pi
multiply x by 2pi
4 cos ( 2 pi x) + 2
Is 8,11,14 a right triangle?
Answers
Answer:
NO
Step-by-step explanation:
For it to be a right triangle, 14 should be 13.6
8, 11, 13.6 is a right triangle
