Answers
The values of variable x are x₁ = 16, x₂ = - 4.
The measure of angle R is 60°.
The lengths of side RS are RS₁ = 256 and RS₂ = 16.
The lengths of side RT are RT₁ = 256 and RT₂ = 16.
How to find the variables associated to a given triangle
In this problem we need to find the values of four variables related to a triangle, which is seen in the picture, indicating an equilateral triangle. The solution of this question must be done by using definitions and theorems from Euclidean geometry:
Value of variable x
According to Euclidean geometry, the measures of the three sides in an equilateral triangle are the same. Then, the variable x can be found by solving the following equation:
RT = RS
x² = 12 · x + 64
x² - 12 · x - 64 = 0
(x - 16) · (x + 4) = 0
There are two possible solutions:
x₁ = 16, x₂ = - 4
Measure of the angle R
Equilateral triangles have three internal angles of 60°. Therefore, m ∠ R = 60°.
Length of side RS
There are two options:
RS₁ = 16²
RS₁ = 256
RS₂ = (- 4)²
RS₂ = 16
Length of side RT
There are two options:
RT₁ = 12 · 16 + 64
RT₁ = 256
RT₂ = 12 · (- 4) + 64
RT₂ = 16
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Related Questions
Which linear inequality is represented by the graph?1. y>2/3x-22. y<2/3x+23. y
Answers
To identify the inequality of the given graph:
1. Identify the equation of the borderline in slope-intercept form (y=mx+b)
- Find the slope (m): Use two points in the line in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=\frac{1-(-3)}{3-(-3)}=\frac{1+3}{3+3}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)
b= -1
Equation of the border line:
[tex]y=\frac{2}{3}x-1[/tex]2, Identifify the inequality sing:
-When the inequality is < or > the borderline is a dotted line
-When the inequality is ≥ or ≤ the border line is a full line
-When the inequality is < or ≤ the shaded area is under the borderline
-When the inequality is > or ≥ the shaded are is over the borderline
In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:
[tex]y<\frac{2}{3}x-1[/tex]Select all the equations that have the same solution as 2x-5=15
Answers
Answer:
B, D, E
Step-by-step explanation:
2x - 5 = 15
2x = 20
x = 10
B) 2x = 20
x = 10
D) 2x - 20 = 0
2x = 20
x = 10
E)4x - 10 = 30
4x = 40
x = 10
3,4,16/3 find the 10 term
Answers
The 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The [tex]n^{th}[/tex] term of the Geometric Sequence is
given by the formula
aₙ = a*rⁿ⁻¹
where , a is the first term , r is the common ratio .
in the question ,
the sequence is given as {3,4,16/3....}
here we need to find the common ratio(r) ,
we know , r = a₂/a₁
So , r= 4/3 .
Since we need to find the 10th term , so n=10 .
Substituting the values in the nth term formula , we get
a₁₀ = (3)*(4/3)¹⁰⁻¹
= 3* (4/3)⁹
= 4⁹/3⁸
= 262144/6561
The 10th term is 262144/6561.
Therefore , the 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The given question is incomplete , the complete question is
Find the 10th term of the Sequence {3,4,16/3....} ?
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Jordan and his children went into a restaurant and he bought $26 worth of drinks
and tacos. Each drink costs $2.50 and each taco costs $2. He bought 4 more tacos
than drinks. Write a system of equations that could be used to determine the number
of drinks and the number of tacos that Jordan bought.
Answers
The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's assume that number of drinks that Jordan and his children bought is x while the number of tacos is y.
The cost of drinks = 2.50x
Cost of tacos = 2y
Total cost 2.5x + 2y
2.5x + 2y = 26
Given that,
He bought 4 more tacos than drinks.
Therefore,
y = x + 4.
Hence "The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4".
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If f(x) =5x2 - 3x + 1, calculate the following
Answers
Answer:
a) 199
f(-6)= 5(-6)^2 - 3 (-6) + 1 =199
b) 37
f(3)= 5(3)^2 - 3 (3) + 1 =37
Hi please help me on the q
Answers
Answer:
x = 30°
Step-by-step explanation:
The angles of a pentagon add up to 540°
Make an equation adding up the angles to equal 540°
x + 4x + 4x + 135° + 135° = 540°
Simplify
9x = 270°
Divide
x = 30°
5. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the x-axis of the graph off(x) = -(x+3)^2 - 2. Write a rule for g.
Answers
Answer:
[tex]g(x)=-f(x-2)+2[/tex]Explanation:
Given the function f(x)
A translation of 2 units up = f(x)+2
Next, a translation of 2 units right = f(x-2)+2
When we reflect the result above in the x-axis, we have:
[tex]g(x)=-f(x-2)+2[/tex]A rule for g is therefore:
[tex]g(x)=-f(x-2)+2[/tex]A store is having a sale in which all items
are discounted 20%. Including tax, Colin paid $21 for a picture. If the
sales tax rate is 5%, what was the original price of the picture?
Answers
In linear equation, that price of shorts before discount was $25
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Assume that the price of shorts after the discount is x
Total payment = price of shorts + taxes
We know that:
total payment = $21
taxes = 5% = 0.05 of the price
This means that:
21 = x + 0.05x
21 = 1.05x
x = $20
Therefore, the price of the shorts is $20 after the discount
Now, we will get the price of the shorts before the discount:
Assume that the price of shorts before discount is y
We know that:
The discount was 20%
This means that Jennifer paid:
100% - 20% = 80% of the price of the shorts
Therefore:
80% of the price = $20
0.8y = 20
y = $25
This means that price of shorts before discount was $25.
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does anybody know what 6x+24 means
Answers
= 6(x+4)
WILL GIVE BRAINLIEST find center, vertices, and foci of the ellipse.
Answers
The vertices is (5, 1 - 4 square root of 2) and (5,1 + 4 square foot of 2)
The foci is (5, 1 + 2 square root of 6) and (5, 1 - 2 square root of 6)
Hope this was helpful :)
A dinner set was marked $ 532 and a discount of 12% was offered on its marked price. Find the sale price of the dinner set.
Answers
Answer:
$468.16
Step-by-step explanation:
answer key
in recent years the state of alaska issued license plates consisting of 7 characters. the first three characters are the letters of the alphabet excluding i, o, and x. the last four characters are the numeral digits. how many different license plates can be issued using this configuration (with repetition)?
Answers
121670000 different license plates are possible.
A license plate consists of 7 characters.
The first 4 characters are numerals from 0 to 9.
each character can be in 10 ways
so possible ways = 10 * 10 * 10 * 10 = 10000
The last 3 characters are letters excluding I, O, and X.
Each character can be in 26 - 3 = 23 Ways
Possible ways = 23 *23 * 23 = 12167
Number of possible different license plates = 10000 * 12167
= 121670000
What is car registration ?
Motor vehicle registration is the registration of a motor vehicle with a public authority, whether compulsory or otherwise. The purpose of registering a motor vehicle is to establish a link between the vehicle and the owner or user of the vehicle. This link may be used for taxation or criminal investigations.
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A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work? On a graph
Answers
The equation in slope intercept form is C(h) = 50h+25 ,the total cost for 8 hours of work is $425 , and for 10 hours of work is $525.
In the question;
it is given that
the fixed charge of plumber = $25
charge for per hour of service = $50
the hours of service be "h"
and the total cost be "C"
according to the question
C(h) = 50h+25
the equation in the slope intercept form is C(h) = 50h+25
to find the total cost for 8 hours of work , put h=8
C(8) = 50(8) + 25
= 400+25
= 425
to find the total cost for 10 hours of work , put h=10
C(10) = 50(10) + 25
= 500+25
= 525
Therefore , total cost for 8 hours of work is $425 , and for 10 hours of work is $525 .
The given question is incomplete , the complete question is
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?
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a company has its employees choose a password which consists of 9 characters: 3 letters, followed by 2 symbols, followed by 4 digits. there are a total of 11 symbols that the employees can choose from. letters, symbols and digits can be repeated. how many possible passwords are there?
Answers
The total possible choices of password that are available is 21,266,960,000.
The length of the password has to be of 9 characters.
Three of them should be letters, 2 should be symbols from the 11 choices of the symbols and 4 have to be digits.
Any of the following can be repeated in the password,
So, making the combination of 9 characters.
As we know, letters are 26, so, there are 26 choices each for three places.
Also, if 11 symbols are available, then there are 11 choices each are available for the two places and the total number of 10 which are 0 to 9, so, there are 9 choices each for the last four places,
Hence the final combination would be,
= 26 x 26 x 26 x 11 x 11 x 10 x 10 x 10
= 21,266,960,000
Hence the total password available are 21,266,960,000.
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(Order of Operations with Radicals LC)
Simplify the expression.
square root of 49 minus 2 squared
Answers
Answer:
3Step-by-step explanation:
Given expression[tex]\sqrt{49}-2^2[/tex]Simplify it as follows[tex]\sqrt{49}-2^2 =[/tex][tex]7-4=[/tex][tex]3[/tex]Answer:
3
Step-by-step explanation:
i got it right on the exam!
$ Given T is the midpoint of SU. Prove x = 5 3x + 20 STATEMENTS REASONS 1. 1. Given 2. ST = TU 2. Definition of midpoint W 3. Definition of congruent segments 3. ST = TU 4. 7* = 3x + 20 4. 5. 5. Subtraction Property of Equality 6. r = 5 6. 1. What should be the statement for Reason 1? SU = SU
Answers
In the images, we are given an exercise which is solved by taking T as the midpoint of SU. This is the
7) 5x - 125 5x-:5 OTROW VOITA U Name Samantha Date 3/3 Kuta Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. 1) yz-2x-2 9) y 25 *2=5 2) ys-*+1 Yst
Answers
It is not possible to write a linear inequality such that the solution contains only positive values of x and y.
This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.
-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
Answers
The result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
The equation is
(-2/3)w - 4/5 = -3/2
Here we have to rearrange the terms and combine the like terms.
Mover 4/5 to the right hand side of the equation
(-2/3)w = -3/2 + 4/5
(-2/3)w = -7/10
Move the number (-2/3) to the right hand side of the equation
x = -7/10 ÷ (-2/3)
To make it multiplication, take the reciprocal of the the second number
x = -7/10 × (-3/2)
Multiply the numbers
x = 21/20
Hence, the result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
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How many positive factors of 96 are also multiples of 12?
Answers
The number of positive factors of 96 which are also multiples of 12 are 4 which are 12,24,48, and 96.
Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96
Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96
Common numbers between the two are 12,24,48 and 96.
Hence, there are only 4 positive factors of 96 which are also the multiples of 12
Factors
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.
Multiples
A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.
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Select all rational numbers.
O√75
0-√25
02. √7
100
√0.36
✓0.0144
√
0-√√
36
49
Answers
All the rational numbers are;
2. - √25
4. 100
5. √0.36
6. √0.0144
7. √36
8. √ 49
What is Rational number?
A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Given that;
All the numbers are,
1. √75
2. - √25
3. 2√7
4. 100
5. √0.36
6. √0.0144
7. √36
8. √ 49
Now,
1. √75 = 8.660250
Clearly, It cannot be written as the form of p / q.
So, It is not a rational number.
2. - √25 = - 5
It can be written as;
- √25 = - 5 / 1
So, It is a rational number.
3. 2√7
Since, √7 is an irrational number.
So, 2√7 is not a rational number.
4. 100
It can be written as;
100 / 1
So, It is a rational number.
5. √0.36 = 0.6
= 6 / 10
= 3 / 5
Thus, It is a rational number.
6. √0.0144 = 0.12
= 12 / 100
= 3 / 25
So, It is a rational number.
7. √36 = 6
= 6 / 1
So, It is a rational number.
8. √ 49 = 7
= 7 / 1
So, It is a rational number.
Therefore, All the rational numbers are;
2. - √25
4. 100
5. √0.36
6. √0.0144
7. √36
8. √ 49
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At the 6th grade school dance, there are 130 boys, 100 girls, and 20 adults. Write the ratio of the number of girls to the number of adults.
Answers
The ratio of the number of girls to the number of adults is 5 : 1.
What is the ratio?Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.
The ratio of the number of girls to the number of adults = number of girls : number of adults
number of girls = 100
number of adults = 20
The ratio of the number of girls to the number of adults = 100 : 20
Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.
The ratio of the number of girls to the number of adults = 5 : 1
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pleas help quick
What is the value of the expression
Answers
PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} [/tex]
THE ANSWER IS OPTION C.
Simplify (10y - 5g)(3s + 6g) using foil method
Answers
The solution is on the paper.
ANSWER ASAPDonna received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left on your card how many pounds of coffee did she buy
Answers
The amount of coffee she bought is 5.16 pounds.
How to find the pounds of coffee she bought?She received a $70 gift card for a coffee store.
She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left.
Therefore, base on the card, the number of pounds of coffee she bought can be calculated as follows;
Hence,
let
the amount of coffee she bought in pounds = x
Hence,
70 = 8.36x + 26.85
70 - 26.85 = 8.36x
43.15 = 8.36x
divide both sides by 8.36
43.15 / 8.36 = x
x = 5.16148325359
Therefore, the amount in pounds is 5.16 pounds.
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change from radical form to exponential expression in fractional form. No need to evaluate just be put in simplest form
Answers
To convert from radical form to exponential in fractional form, we can follow:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]Firstly, notice that 9 is the same as 3 squared:
[tex]\sqrt[4x+2]{9}=\sqrt[4x+2]{3^2}[/tex]Now, we can apply the change:
[tex]\sqrt[4x+2]{3^2}=3^{\frac{2}{4x+2}}[/tex]Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:
[tex]3^{\frac{2}{4x+2}}=3^{\frac{2}{2(2x+1)}}=3^{\frac{1}{2x+1}}[/tex]So, the expression in the simples form and fractional exponent is:
[tex]3^{\frac{1}{2x+1}}[/tex]at a tree farm,there are nine rows of 36 Spruce trees . in each row 14 of the spruce trees are blue spruce how many Spruce tree‘s are not blue spruce?
Answers
Answer: 198
Step-by-step explanation:
9 * 36 = 324
9 * 14 = 126
324 - 126 = 198
Hope this helps!
Write the sum of (4 × 10³) + (3.2 × 10¹) in scientific notation.
A) 43.2 x 104
B 4.32 x 105
C) 43.2 x 105
D) 7.2 x 10¹
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(4\times10^3) + (3.2\times 10^1)}[/tex]
[tex]\mathsf{= 4\times10^3 + 3.2\times 10^1}[/tex]
[tex]\mathsf{= 4\times10\times10\times10 + 3.2\times10}[/tex]
[tex]\mathsf{= 4\times100\times10 + 3.2\times10}[/tex]
[tex]\mathsf{= 4\times1,000 + 3.2\times10}[/tex]
[tex]\mathsf{= 4,000 + 32}[/tex]
[tex]\mathsf{= 4,032}[/tex]
[tex]\mathsf{\approx 4.032\times10^3}[/tex]
[tex]\huge\text{Thus, your answer SHOULD be: \boxed{\mathsf{4.032\times10^3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
Answers
Answer:
1,730
Step-by-step explanation:
173x10 (pieces)= 1730
Write the equation of a line in slope intercept form that passes through (-15, 20) and is parallel to x - 5y = 5
Answers
First step is to write the equation in slope-intercept form
[tex]x - 5y = 5\\-5y = -x+5[/tex] To make simplification easier, multiply negative to both sides
[tex]5y = x-5\\[/tex] Now, you must divide 5 to both sides to isolate the variable
[tex]y = \frac{x}{5} - 1[/tex] To tell the slope more easily, turn [tex]\frac{x}{5}[/tex] into [tex]\frac{1}{5} x[/tex]
To rewrite the equation: [tex]y = \frac{1}{5} x - 1[/tex]
Now, you are able to see the slope(m) being [tex]\frac{1}{5}[/tex]
Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"
[tex]20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23[/tex]
Final Answer: [tex]y = \frac{1}{5} + 23[/tex]
Hope this helps :)
In parallelogram ABCD, diagonals AC and BD intersect at point E, BE=x+21, and DE=4x.
What is BD?
Enter your answer in the box.
Answers
Answer:
BD = 56
Step-by-step explanation:
x + 21 = 4x
3x = 21
x = 7
x + 4x + 21
5x + 21
35 + 21
56
