3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are each sisters ages

∠GJI ≅ ∠LKF is proved below.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical. If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Given Data

EF║GH

AB║CD

In given figure,

AB║CD,

While line segment GH is the transversal line.

So,

∠GJI ≅ ∠JLK (because it is corresponding angle) ..(1)

Also,

EF ║GH

Line segment DL  is the transversal line.

So,

∠JLK ≅ ∠LKF (because it is interior alternate angle)..(2)

From (1) and (2)

∠GJI ≅ ∠LKF

Hence, proved.

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1 .

Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2.

Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.

To estimate fractions using mental math, start by simplifying the fraction to the lowest possible denominator. Then, look at the fraction and round it to the nearest fraction that you feel comfortable working with which could be ¼, ⅓, ½, ¾, or even 1.

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The domain of a function is the set of x values the function uses as inputs; from a graph the domain is the x-values that the graph take on the x-axis; in this case, since we have an infinite amount of x-valeus the function uses we will write the domain as an interval. The domain is:

Similarly, the range is the set of values the function takes on the y-axis, from the graph we notice that the range is:

Answer:

7/8

Step-by-step explanation:

Answer:

-2, 6 or -2/6 is what im seeing i could be wrong though

Step-by-step explanation:

sub to imaginefn

Step 1:

Write the given vectors

Step 2

Resultant vector = [ 10 + (-6) , 9 + (-2) ]

= ( 4 , 7 )

Resultant vector = 4i + 7j

Step 3

Step 4:

Given data:

The given table is shown.

Draw the points on the graph paper as shown below.

The equation for the given summation is:

   [tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

Here we have a summation of unknown terms of the form:

uₙ

That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:

[tex]\sum_{n=1}^4 u_n[/tex]

Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:

[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

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The test statistic for the anova is an F test and it is said to be positively skewed which would be to the right of the F test statistic.

This is the term that is used to refer to the short form of the term that says analysis of variance.

The ANOVA is used to show the variation that would be in existence of a group of observations.

The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.

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Answer:

3 is missing in there numbers,the last pair

Isosceles triangle have 2 equal lengths

Square or Rectangle have 4 equal teiangles

Isosceles trapezoid also divides

Then answer is

Isosceles trapezoid. Option A)

Given:

solve for y:

Value of y is zero and

Part a

Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate

so

(x, 2x+1)

y=2x+1

Part b

x=(1/2)y^2

Part c

x^2+y^2=25

Part e

y=2

Part f

x=7

Part g

x=y

Part h

Part i

1) In this question, we can solve it in two different ways. Either algebraically, or by mental Math.

2) Algebraically we have:

By mental math, we just need to ask ourselves how much can I add to 4 and get 10,? The answer will be six.

3) Thus, the answer is 6

Part A: The vertex, domain, and range of the function g(x) = |x-5|  is

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y - coordinate of the vertex is shifted by 3 units.

In Part A:

The given function is;

g(x) = | x - 5 |.

Now, The x - coordinate of the vertex will be:

x - 5 = 0

x = 5

Therefore, the y- coordinate of the vertex will be:

y = g(x) = | x - 5 |

y = g(7) = | 5 - 5|

y = 0

So, The vertex of the absolute function is ( 5, 0 ).

Since, All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this case, the phrase is defined even if there is no real number.

Hence, In Interval Notation the domain is;

⇒ ( - ∞ , ∞ )

And, The set of all legitimate y values is the range.

Hence, In Interval Notation the range is:

⇒ [0, ∞ )

Now, In Part B:

Function h(x) = |x| + 3 is the transformed version of the parent function

f(x) = |x|.

For the parent function f(x) = |x|, the vertex is ( 0, 0).

Since, The range of an absolute function in the form c( | ax + b | ) + k is

f(x) ≥ k.

Therefore, The range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).

For the transformed function h(x) = |x| + 3.

The vertex of the function is ( 0, 3 ).

The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).

Hence, the y coordinate of the vertex is transformed by 3 from f (x) to h(x).

So, Part A: The vertex, domain, and range of the function g(x) = |x-7|  is  

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 2 units to get the function h(x) = |x| + 3. The y coordinate of the vertex is shifted by 3 units.

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Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:

Substraction of numbers in scientific notation:

1. Turn the numbers to get the same power of base 10.

You move to the left the decimal to increase the power of base 10 and move to the right to g

The absolute number of an integer is the distance that separates the number from position zero "0" so, if it is a distance it cannot be a negative value.

Then the absolute value of these numbers is:

The root mean square velocity of Neon, in m/s as required in the task content is; 18.45 m/s.

It follows from the task content that the root mean square velocity of Neon is to be determined.

Since the molar mass of Neon is; 20 while the gas constant, R = 8.314 and T = 273K.

It follows from the root mean square velocity formula that we have;

R.M.S = √(3RT/M)

R.M.S = √{(3×8.314×273)/20}

R.M.S = √340.46

R.M.S = 18.45 m/s.

Hence, the root mean square velocity of Neon, Ne under the given condition is; 18.45 m/s.

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Answer:

D) 10

Step-by-step explanation:

2x - 2 < 8 + x

add 2 to both sides:

2x - 2 + 2 < 8 + x + 2

2x < 10 + x

subtract x from both sides:

2x - x < 10 + x - x

x < 10

Answer:

3x^5y^8

Step-by-step explanation:

so the cube root of 27 is 3

to find the cube root of x^15 divide the exponent by 3 which gets you x^5

do the same thing for y^24 and that gets you y^8

mhm and i think thats right

6 bracelets Eva can make with the yarn she has left with .

The equation is [tex]\frac{3n}{2}=9[/tex]

Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.

Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend

Now she left with 11 -2 = 9

As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn

n braclet = [tex]\frac{3n}{2}[/tex]

9= [tex]\frac{3n}{2}[/tex]

n = [tex]\frac{18}{3}[/tex]

=6

6 bracelets Eva can make with the yarn she has left with .

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Answer:

1018.3

Step-by-step explanation:

The volume of a cylinder=πr2h

=22\7*6*6*9

=1018.3

therefore, the of the cylinder is 1018.3

We can conclude that Jeffry will reach his home in the time of 9 hours.

So, the time taken by Jeffrey to get home:

Now calculate time as follows:

Rounding off: 9 hours

Therefore, we can conclude that Jeffry will reach his home in the time of 9 hours.

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Answer:

47/68

Step-by-step explanation:

total candies=136

not red candies=94

94/136=47/68

3 per thousand?

10000 ------------------------- 1000

x ------------------------ 3

x = (3 x 10000)/1000

x = 30000/1000

x = 30

The answer is 30

X₁: science GPA for those who left their profession after graduation

X₂ science GPA for those who remained in their profession after graduation.

The working hypothesis is that the GPA of those who stayed is higher than those who left.

Which is the same as saying that the GPa of those who left is less than those who stayed.

μ₁ represents the population mean of the science GPA of those who left.

μ₂ represents the population mean of the science GPA of those who remained.

Part one

You can express the working hypothesis as follows:

The hypothesis does not include the equal sign, so this hypothesis can be considered as the alternative hypothesis.

The null hypothesis of this test will be the complement of the alternative hypothesis, and always carries the equal sign within. So if the alternative hypothesis states that "the mean of the leavers is less than the mean of the stayers", then the null hypothesis will be that "the mean of the leavers is greater than or equal to the mean of the stayers" you can symbolize this as:

Since the null hypothesis carries the equal sign you can also write it as:

Both options are equally valid.

So, the second answer is null hypothesis.

Part two

Considering that we are studying the population means of two normal variables and that we know the population standard deviation for both populations, the test statistic to use is the standard normal for the difference of means which is defined as follows:

Subindex 1 indicates the values corresponding to the "leavers":

X₁bar= 3.16

n₁= 103

σ₁= 0.52 → σ₁²= 0.2704

Subindex 2 indicates the values corresponding to the "stayers":

X₂bar= 3.28

n₂= 225

σ₂= 0.46 → σ₂²= 0.2116

Under the null hypothesis both population means are equal, which means that their difference is equal to zero:

If μ₁ = μ₂, then μ₁ - μ₂ = 0

Replace all values on the formula to determine the Z-value under the null hypothesis, i.e. the test statistic:

The equation to describe the relationship between the height of the plant and the number of weeks is

y = x + 5

Given,

The height of the plant = x

The number of weeks = y

The height of plant at 6th week = 11 inches

The height of plant at 8th week = 13 inches

The height of plant at 10th week = 15 inches

We have to find the equation to describe the relationship between the height of the plant and the number of weeks.

Lets see,

x = 6 and y = 11, y – x = 11 – 6 = 5

x = 8 and y = 13, y – x = 13 – 8 = 5

x = 10 and y = 15, y – x = 15 – 10 = 5

That is,

y – x = 5.

y = x + 5

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The first equation is increasing at highest rate.

Which function has highest increasing rate?

We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.

In equation first m = 2 and is highest among every slope.

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

In second equation m = 1

m = (-4 + 5)/(2-1) = 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

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Given the word problem, we can deduce the following information:

Principal amount = $4739

Future amount = $5336

Interest = 5.1 % =0.051

To determine the time to accumulate the $5336, we use the compound interest formula:

A=Future amount=$5336

P=Present amount=$4739

r=interest rate = 0.051

n=number of compounding periods =12

t=time in years

We also note that the number of compounding periods must be 12 since the investment is compounded monthly.

We plug in what we know:

Therefore, the answer is 2.33 years.