Jacob wants to prove that AFGH = A/KL using SAS.
He knows that FG = J and F = J. What additional
piece of information does he need?
Answers
The piece of information does he need is ∠F ≅ ∠J.
What is triangle?
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.
Properties of triangle?
A triangle has three sides, three angles, and three vertices.The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.The sum of the length of any two sides of a triangle is greater than the length of the third side.Given,
ΔFGH = ΔJKL
By SAS property of triangle;
[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex], FG ≅ JK
third property ,
∠F = ∠J
By SAS property at least two side their ratio must be equal and one angle.
[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]
∠F = ∠J
So, option A is correct.
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Related Questions
A baseball team has three different pitchers. Randy allowed
2
22 runs and pitched
3
33 innings. Felix allowed
4
44 runs and pitched
5
55 innings. Johan allowed
5
55 runs and pitched
7
77 innings.
Which pitcher has the lowest number of runs allowed per inning?
Answers
The pitcher that has the lowest number of runs allowed per inning is Randy.
Which pitcher has the lowest number of runs per inning?In order to determine the pitcher that has the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.
Division is the mathematical operation that is used to calculate the quotient of two or more numbers. It entails grouping a number into equal parts using another number.
Number of runs per innings = number of runs / number of innings
Number of runs per innings for Randy : (2 / 3) = 0.667
Number of runs per innings for Felix : (4 / 5) = 0.80
Number of runs per innings for Johan: (5 / 7) = 0.714
Here is the complete question:
A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.
Which pitcher has the lowest number of runs allowed per inning?
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Give two ordered pairs on the line with equation x = 7
Answers
(7,0); (7,−5) ;(7,3); (7,10);. (7,y)
Step-by-step explanation:
Answer:
The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.
Step-by-step explanation:
For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.
A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.
Points that are on the line x = 7 include:
(7, 0)
(7, 1)
(7, 2)
(7, 4)
(7, 5)
(7, 6)
Please help with the ones that have a red x beside it would greatly and would give 100 pts so please help me!!!!!
Answers
Answer:
huhh
Step-by-step explanation:
Hi im new can u guys tell me how this work pease??
Answer:
Step-by-step explanation:
idek idek
Find the value of x in 4^x+64^x= 272
Answers
Answer:
1.342
Step-by-step explanation:
4^x+64^x=272
4^x+(4^3)^x=272
4^3x+4^x=272
(4^x)^3+4^x=272
(4^x)^3+4^x-272=0
u^3+u-272=0 ==> substitute 4^x with u
Now, use synthetic division to find roots:
[tex]\sqrt[3]{272}[/tex]31 | 1 0 1 -272
[tex]\sqrt[3]{272}[/tex]1 [tex]\sqrt[3]{272^2}[/tex] 272
1 [tex]\sqrt[3]{272}[/tex]1 [tex]\sqrt[3]{272^2}[/tex] 0
4^x=[tex]\sqrt[3]{272}[/tex]
log 4 (4^x)=log 4 ([tex]\sqrt[3]{272}[/tex])=1.342
Two consecutive odd integers have a sum of 40. Find the integers
Answers
Answer:
19 and 21|
Step-by-step explanation:
a + (a+2) = 40
2a + 2 = 40
2a = 40 - 2
2a = 38
a = 38/2
a = 19
a+2 = 21
Check:
19 + 21 = 40
The table below shows the cost of downloading songs from a website. \text{Number of Songs}Number of Songs \text{Total Cost}Total Cost 1313 \$9.36$9.36 1717 \$12.24$12.24 1919 \$13.68$13.68 What is the constant of proportionality between the total cost and the number of songs?
Answers
The constant of proportionality between the total cost and the number of songs is 0.72.
What is the constant of proportionality?The constant of proportionality is the ratio that supplies the variable cost per unit of each song.
Other names for the constant of proportionality include:
SlopeUnit rateConstant rateConstant ratioRate of changeConstant of variation.Determining the constant of proportionality can help us formulate the total cost equation as y = 0.72x.
Number of Songs Total Cost Unit Cost
13 $9.36 $0.72 ($9.36/13)
17 $12.24 $0.72 ($12.24/17)
19 $13.68 $0.72 ($13.68/19)
Check:
y = 0.72x
y = 0.72(13)
y = $9.36
Thus, the constant of proportionality is 0.72, showing that a downloaded song costs $0.72 each.
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How to solve: 24 - (5 + 3)^2 + 4 × 2^3 step by step.
Answers
The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value given will be expressed thus:
= 24 - (5 + 3)^2 + 4 × 2^3
= 24 - (8)² + 4 × 8
= 24 - 64 + 32
= -8
The value is -8.
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Calculate capital if assets are £451,100, liabilities are £20,500, income is £351,200 and expenses are £270,600.
Answers
The capital is £430,600.
Define capital.
The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).
The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.
Solution Explained:
Given, Assets = £451,100 and liabilities = £20,500
Capital = Assets - Liabilities
= 451100 - 20500
= £430,600
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math, pls help, will mark brainlest
Answers
Answer:
Step-by-step explanation:
3x + 3x equals 11x
A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. Find the probability that the mean actual weight for the 100 weights is greater than 25.2
Answers
The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.
How to determine the probability that the mean actual weight for the 100 weights?In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.
In a uniform distribution, the mean of a data set can be calculated by using this formula:
Mean, E(x) = [a + b]/2
Where:
a is the lowest boundary.b is highest boundary.Substituting the given parameters into the formula, we have;
Mean, E(x) = [24 + 26]/2
Mean, E(x) = 50/2
Mean, E(x) = 25.
For the standard deviation, we have:
Standard deviation, S(x) = √((b - a)²/12)
Standard deviation, S(x) = √((26 - 24)²/12)
Standard deviation, S(x) = √((2)²/12)
Standard deviation, S(x) = √(4/12)
Standard deviation, S(x) = 0.5774.
For the sample standard deviation, we have:
Standard deviation = S(x)/√n
Standard deviation = 0.5774/√100
Standard deviation = 0.5774/10
Standard deviation = 0.05774.
By applying the central limit theorem, we would determine the z-score as follows:
Z-score = (x - μ)/σ
Z-score = (25.2 - 25)/0.05774
Z-score = 0.2/0.05774
Z-score = 3.64
Therefore, the p-value is equal to 0.000136.
Probability (x > z) = 0.0136%.
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Complete the table: (Enter your answers as a whole dollar amount.) Units Unit Cost Dollar Cost Beg. Inventory Jan. 1 10 $ 7.00 A Apr. 11 30 $ 12.00 B May 17 40 $ 13.00 C Dec. 5 20 $ 15.00 D
Answers
The completion of the inventory table is as follows:
A = $70B = $360C = $520D = $300.What are the inventory methods?Some of the inventory methods that are used in completing the inventory table are:
FIFO (First-in, First-out) lies on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.Specification Identification does not rely on any assumptions in allocating the costs of goods sold and ending inventory.Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 10 $7.00 $70
Apri. 11 Purchases 30 $12.00 $360
May 17 Purchases 40 $13.00 $520
Dec. 5 Purchases 20 $15.00 $300
Total 100 $1,250
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what is 1357 mm in cm
Answers
An ice cream factory has 4 machines that make the same type of ice cream. The rate of production for each machine is shown in the table. Based on the date given, which machine works atthe fastest rate?
Answers
Using division operations and based on the rates of production, given, Machine D works the fastest.
How is the rate of production determined?The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).
The rate of production is the number of goods that can be produced during a given period of time.
The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.
There are, therefore, two ways of determining production rate. Firstly, we can divide the total production by the hours consumed.
Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.
Units Production Rate of
Produced Hours Production
Machine A 10,000 15 667 cups per hour
Machine B 25,000 20 1,250 cups per hour
Machine C 30,000 30 1,000 cups per hour
Machine D 15,000 10 1,500 cups per hour
Thus, using division operation, Machine D produces at the fastest rate than the other three machines.
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Question Completion:Units Production
Produced Hours
Machine A 10,000 15
Machine B 25,000 20
Machine C 30,000 30
Machine D 15,000 10
WILL MARK BRAINLIEST 30 POINTS
Each night Liz spends at least 45 minutes and no more than 120 minutes on her phone.
Choose which double inequality describes how long Liz spends on her phone each night.
"n" will be used as your variable.
WILL MARK BRAINLIEST
Answers
The double inequality describing the length of time (in minutes) that Liz spends on her phone each night is 45 ≤ f(x) ≤ 120.
What is double inequality?Double inequality is a mathematical expression that has two inequalities.
Double inequality is also known as a compound inequality. because there is more than one inequality in the expression
The form of double inequality is always written as: a ≤ f (x) ≤ b.
This double inequality gives the value of x as more than a and less than b.
The least number of minutes spent by Liz on her phone = 45 minutes
The maximum number of minutes spent by Liz on her phone = 120 minutes
Inequalities:Inequality 1: 45 ≤ f(x)
Inequality 2: f(x) ≤ 120
Thus, this double inequality 45 ≤ f(x) ≤ 120 shows Liz's time on the phone every night.
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simplify: 8x divided by 16+8 divided by 32
Answers
The value of 8x ÷ (16+8) ÷ 32 is x/96
What are basic operations?The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Discussing about division or quotient
The division is usually denoted by ‘÷‘ and is the inverse of multiplication. It constitutes two terms dividend and divisor.
To simplify
8x÷(16+8)÷32= 8x×1/24×1/32
= x/96
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Find the unit rate for this relationship
Answers
2/3 is the unit rate of the relationship
How to determine the unit rate of the relationship?
A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:
Slope = y2-y1 / x2-x1
Slope = 6-2 / 9-3 = 4/6 = 2/3
Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer
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Write two quadratic equations that are NOT equivalent, each forming a graph with -intercepts
(−3,0) and (1,0).
Explain in detail please
Answers
The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3
Given,
x - intercepts = (−3,0) and (1,0).
The x-intercepts are given by the point at which the y-value of the equation are zero.
Therefore;
The quadratic equation are;
(x + 3)·(x - 1) = 0
x² + 2·x - 3 = 0
Quadratic equations;-
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
Here,
The equation can also be written in the form;
(-x - 3)·(x - 1) = 0
-x² - 2·x + 3 = 0
The quadratic equations are;
y = x² + 2·x - 3 and y = -x² - 2·x + 3
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a student observes a blood sample with a compound microscope that has a 10x ocular lens and a 40x objective lens. How much larger do the blood cells appear under the microscope?
Answers
If they observes a blood sample with a compound microscope that has a 10x ocular lens and a 40x objective lens. The larger that the blood cells appear under the microscope is: 400x.
How to determine the blood cells?Given data:
Blood sample has:
10x ocular lens
40x objective lens
Using this formula to determine how large the blood cells appear
Blood cells = ocular lens × objective lens
Let plug in the formula
Blood cells = 10x × 40x
Blood cells = 400x or 400 times larger
Therefore the blood cells appear 400 times larger.
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400 times larger
what is (18x45) divided by 8
Answers
The solution for (18x45) divided by 8 = 101.25
Simplify (18x45) divided by 8
Step 1: Rewrite the equation in mathematical terms
we have:
[tex]\frac{18 x 45}{8}[/tex]= [tex]\frac{810}{8}[/tex]
= 101.25
Therefore, the solution for (18x45) divided by 8 = 101.25
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Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
Answers
If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.
How to determine the total possibilities?Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.
Hence,
Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)
Total possibilities = 26^4 × 10^5
Total possibilities = 456976×100000
Total possibilities = 45,697,600,000
Therefore we can assume that the total possibilities is : 45,697,600,000.
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Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
Answers
The integer in the set S:{−24, 2, 20, 35} that will make the inequality five-sixths m minus five is less than one-half m plus 3 false is 35
What is inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities imply that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 35. This will be illustrated thus:
= 5/6(35 - 5) < 1/2(35 + 3)
= 5/6(30) < 1/2(38)
= 25 < 19
In this case, 25 isn't less than 19. Therefore, 35 is the correct integer.
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-268=-6(-6-6k)+2k
k= ???
Answers
Answer:
k = - 8
Step-by-step explanation:
- 268 = - 6(- 6 - 6k) + 2k ← distribute parenthesis by - 6
- 268 = 36 + 36 k + 2k ( subtract 36 from both sides )
- 304 = 38k ( divide both sides by 38 )
- 8 = k
Jamison wants to run for office. The committee prints 18,800 flyers to fold and then mail out to the community. If there are 15 people on the committee, what is the number of flyers per capita to fold and distribute? Round to two decimal places if necessary.
Answers
Answer: 1253.33
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is:
[tex]x^{2} +y^{2} +2gx+2fy+c=0[/tex]
Given circle equation:
[tex]x^{2} +y^{2} -2x-8=0[/tex]
on comparing
2gx = -2x
g = -2
2fy = 0
f = 0
Center = (2,0)
radius r = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]
= [tex]\sqrt{9}[/tex]
r = 3 units.
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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James shares 5/8 of a cake between 6 people.
What fraction of the cake do they each receive?
Answers
Answer:
5/48
Step-by-step explanation:
The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
James shares 5/8 of a cake between 6 people.
Now, 1/6 of 5/8 will be as,
1/6(5/8) = 5/48
Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".
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Graph the line with slope 1/3 and y-intercept −2.
Answers
Explanation is
21. An artist created a piece of art with 675 round glass beads. There were
also 179 beads in the shape of a heart. Write a number sentence to
find about how many more round beads there were.
Answers
By using subtraction, it can be calculated that there were 496 round beads more than heart shaped beads
What is subtraction?
Suppose, there are two numbers and it is required to find out how much one number is bigger than the other. The operation used for this is subtraction.
The larger number is called minuend and the smaller number is called subtrehend.
Here, subtraction will be used
Number of round glass beads = 675
Number of beads in the shape of heart = 179
Number of more round beads there were = 675 - 179
= 496
There were 496 round beads more than glass beads
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8 (a) Write 0.000089 in standard form.
Answers
Answer: 0.000089
Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...
8.9 x 10⁻⁵
6) Tomás está haciendo compras en el supermercado. Primero eligió
una bandeja con naranjas cuya etiqueta dice 1.350 g. ¿Cuántos
gramos más debe comprar si quiere llegar a 5 kg?
Answers
With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
It is given to us that -
Tomás first chose a tray with oranges whose label says 1,350 gram
We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.
We know that
1 kilogram = 1000 grams
=> 1000 grams = 1 kilogram ----- (1)
By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.
From equation (1), we have
1000 grams = 1 kilogram
=> 1350 grams = (1/1000) * 1350
=> 1350 grams = 1.35 kilograms ----- (2)
Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.
This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -
(5 - 1.35) kilograms
= 3.65 kilograms
From equation (1), we have
1 kilogram = 1000 grams
=> 3.65 kilograms = 3.65 * 1000 grams
=> 3.65 kilograms = 3650 grams.
Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
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A bank representative studies compound interest, so she can better serve customers. She analyzes what happens when $2,000 earns
interest several different ways at a rate of 4% for 3 years.
Find the interest if it is computed using simple interest.
Find the interest if it is compounded annually.
Find the interest if it is compounded semiannually,
Find the interest if it is compounded quarterly.
Find the interest if it is compounded monthly.
Find the interest if it is compounded daily.
Find the interest if it is compounded hourly.
Find the interest if it is compounded every minute.
Find the interest if it is compounded continuously.
What is the difference in interest between simple interest and interest compounded continuously?
Answers
1) The interest if it is compounded using simple interest is $240
2) The interest if it is compounded annually is $249.73
3) The interest if it is compounded semiannually is $252.325
4) The interest if it is compounded quarterly is $253.650
5) The interest if it is compounded monthly is $254.543
6) The interest if it is compounded daily is $254.978
7) The interest if it is compounded hourly is $254.993
8) The interest if it is compounded every minute is $254.993
9) The interest if it is compounded continuously is $254.993
10) The difference in interest between simple interest and interest compounded continuously is $14.993
What is meant by compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.
Given, P=2000
r=4%
r=4/100
r=0.04
t=3 years
1) Simple interest⇒ A=P(1+rt)
=2000(1+3(0.04)
=2000(1+0.12)
=2240
S.I= 2240-2000
S.I=$240
2) Compound interest(yearly)
1st year= 2000(4/100)=80
2nd year=2080(4/100)=83.2
3rd year=(2080+83.2)(4/100)=86.528
P=2163.2+86.528
P=2249.728
C.I=2249.728-2000
C.I=249.728≈$249.73
3) Compounded semiannually
A= P(1+(R/200))²ⁿ
A=2000(1+(4/200))⁶
A=2000(1.12616)
A=2252.325
C.I= 2252.325-2000
C.I=$252.325
4) Compounded quarterly
A=P(1+(R/400))⁴ⁿ
A=2000(1+(4/400))¹²
A=2253.650
C.I=2253.650-2000
C.I=$253.650
5) Compounded monthly
A=P(1+(R/1200))³⁶
A=2000(1+(4/1200))³⁶
A=2254.543
C.I= 2254.543-2000
C.I=$254.543
6) Compounded daily
A=P(1+(R/36500))³⁶⁵ⁿ
A=2000(1+(4/36500))¹⁰⁹⁵
A=2254.978
C.I=2254.978-2000
C.I=$254.978
7) Compounded hourly
A=P(1+(R/876000))²⁶²⁸⁰
A=P(1+(4/876000))²⁶²⁸⁰
A=2254.993
C.I=2254.993-2000
C.I=$254.993
8) Compounded every minute
A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰
A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰
A=2254.993
C.I=2254.993-2000
C.I=$254.993
9) Compounded continuously
A= [tex]Pe^{rt}[/tex]
A=2000([tex]e^{0.04*3}[/tex])
A=2254.993
C.I=2254.993-2000
C.I=$254.993
10) The difference in interest between simple interest and interest compounded continuously is
254.993-$240=$14.993
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