One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

The diagonal EG is a line of symmetry for rhombus EFGH

A rhombus is a quadrilateral with equal sides. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.

Given rhombus EFGH

We have to prove that diagonal EG is a line of symmetry for rhombus EFGH

According to the property of the rhombus

Four sides of EFGH are equal

So EF = EH

FG =HG

Meanwhile EG =EG(common side)

So triangle EFG = triangle EHG

The diagonal EG is a line of symmetry for rhombus EFGH

Therefore the diagonal EG is a line of symmetry for rhombus EFGH

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The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3), and the minima of the given function at the point (-3, -12), and maxima at point (3,2).

A graph can be defined as a pictorial representation or a diagram of any function that represents data or values.

According to the given graph,

We can see that the function is decreasing at the interval (-∞, -3), then the function is increasing at the interval (-3, -1), then the function is decreasing at the interval (-1, 1), the function is increasing at the interval (1, 3), and the function is decreasing at the interval (3, ∞).

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3).

Thus, the minima of the given function at the point (-3, -12), and maxima at point (3,2).

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Answer:

An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

Step-by-step explanation:

The time taken for the increase in temperature by 4 degrees Celsius is 1/2 minute.

Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is given in the form of a graph. The coordinates of the points through which the line passes are (2, 10) and (4.5, 30). We can find the slope of the straight line. If the coordinates of two points are (x1, y1) and (x2, y2), then the slope of the passing line is given as below.

m = (y2 - y1)/(x2 - x2)

m = (30 - 10)/(4.5 - 2)

m = 20/2.5

m = 8

This means there is an increase of 8 degrees in temperature in one minute. We need to calculate the time taken for a 4-degree increase in temperature.

m = Δy/Δx

8 = 4/Δx

Δx = 4/8 = 1/2

Hence, the increase in temperature by 4 degrees Celsius took half a minute.

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Answer:

Step-by-step explanation:

Halie,  find angle EAD.... see it?   next think about the definition of vertical angles: each of the pairs of opposite angles made by two intersecting lines.

which angle is EAD  an opposite pair of?   ∠IAH  looks like a good one.  

Answer:

Step-by-step explanation:

the question is about 15% tax equaling 19 cents.  So what amount of principle would be needed to make 19 cents worth of tax.

.19/.15=1.26666666

round up to $1.27 since we don't have parts of pennies for money.

8.25-1.27=$6.97 for the watermelon.  

Answer:

B . 72 you have to skip count by 12

C . 18 because 54 divide by 3 is 18 because they frame 3 houses in one week

Sorry I tried to do the rest but got confused I hope this helps u

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps :)

Answer:

1.01 g/cm³

Explanation:

The density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and

280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

Let us find the mass of each drink mixed to make the new drink

mass = density × volume

mass of apple juice =  1.05 × 25

                                = 26.25 g

Mass of fruit syrup = 1.4 × 15

                              = 21 g

Mass of carbonated water = 0.99 × 280

                                           = 277.2 g

Total mass of the drink = 26.25 g + 21 g + 277.2 g

                                      = 324.45 g

Volume of the given drink =  320 cm³

Density of the drink = total mass of liquids/ volume

                                = 324.45g/320cm³

                                 = 1.01 g/cm³

Thus, the density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The algebraic expression for the verbal description:

The amount of acid in x liters of a 45% acid solution is

0.45x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The amount of acid in x liters of a 45% acid solution.

This can be written as an expression as,

= 0.45x

We know that,

45% = 45/100 = 0.45

Thus,

The algebraic expression for the verbal description:

The amount of acid in x liters of a 45% acid solution is

0.45x

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The rate of interest half yearly is 8.25 and monthly is 1.375%.

In the given question we have to find the effective rate of intereset, if a amount of money is borrowed an interest rate of 16.5% p.a. and is compounded.

The interest rate annually = 16.5%

(a) We have to calculate rate of interest half yearly.

In a half year have 6 months and in total have 12 months. So their is rate of interest for 2 times.

So the rate of interest half yearly = 16.5%/2

The rate of interest half yearly = 8.25%

(b) We have to calculate rate of interest monthly.

As we know that in a year have 12 months.

So the rate of interest monthly = 16.5%/12

The rate of interest monthly = 1.375%

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The number of mini hotdogs in the combination meal is 4.

The number of pizza rolls in the combination meal is 10.

The variables that you use to write the system are x and (x + 6).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation

We have,

Number of hot dogs = x

Number of pizza = x + 6

Hot dogs calories = 90

Pizza calories = 50

Now,

90x + 50(x + 6) = 860

Solve for x.

90x + 50x + 300 = 860

140x = 860 - 300

140x = 560

x = 560/140

x = 4

We can cross-check.

90 x 4 + 50 x 10 = 860

360 + 500 = 860

860 = 860

Thus,

The number of hot dogs is 4.

The number of pizzas is 10.

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Answer: 4v so this would be the correct answer.

Step-by-step explanation:

y = 3

Step-by-step explanation:

Calculate the slope between the 2 points using the slope formula, then equate to - 3

m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }

x

2

−x

1

y

2

−y

1

with (x₁, y₁ ) = (12, - 12 ) and (x₂, y₂ ) = (7, y )

m = \frac{y-(-12)}{7-12}

7−12

y−(−12)

= \frac{y+12}{-5}

−5

y+12

= - 3 ( multiply both sides by - 5 )

y + 12 = 15 ( subtract 12 from both sides )

y = 3

Answer:

Step-by-step explanation:

The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

From the figure:

MZ is a perpendicular bisector of ∆GHJ.

GM = MJ

GM = 14.5

KZ is a perpendicular bisector of ∆GHJ.

GK = KH

GK = 18.6

Z is the circumcenter of ∆GHJ.

JZ = GZ

JZ = 19.9

Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

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Answer:

$1.2

Step-by-step explanation:

If the tax is 3% then we will have to multiply the price($40) by .03

40*.03= 1.2

Answer:

B

Step-by-step explanation:

The rate of change is the slope.  See the picture.  The blue line (Function B) is steeper than the red line (Function A).

The general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

The given arithmetic sequence is -2, -8, -14, -20

The first term = a = -2,

The common difference = d = -8 -(-2) = -8 +2 = -6

The general term of the arithmetic sequence is given by

[tex]T_{n} = a + (n-1)d[/tex]

Now, putting the values of the first term and common difference in the general term.

[tex]T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4[/tex]

Hence, the general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

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The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.

Total quantity she took

Total quantity = 4.5 × 17

Total quantity = 76.5 milliliters

Original quantity = 148.5 + 76.5

Original quantity = 225 milliliters

b. Time taken to drink all

Time =225 milliliters /2.5

Time = 50 seconds

Therefore original quantity  225 milliliters  and the time is 50 seconds.

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Answer: -28w + 7x -35

Step-by-step explanation:

[tex]-7(-4w -x +5)\\\\= -7*-4w + (-7)*(-x) + (-7)*5= -28w + 7x -35[/tex]

Answer:

28w+7x-35

Step-by-step explanation:

The working of T critical value calculator is explained

What is t test?

t test is the test used  if the sample standard deviation is known and population standard deviation is unknown.

t test is used if the sample standard deviation is known and population standard deviation is unknown.

Here, t value is calculated by the formula

[tex]t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]\bar{x}[/tex] = mean of the sample

[tex]\mu[/tex] = mean of the population

s = standard deviation of sample

n = Number of samples

Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be [tex]t_{critical}[/tex]

if the value of t lies between [tex]-t_{critical}[/tex] and [tex]+t_{critical}[/tex] then the null hypothesis is accepted, otherwise the null hypothesis is rejected.

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Cesium would remain 10g after 2 years in 9.55 gram.

A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionally as the quantity shrinks. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Given,

Cesium 134 decays exponentially. the half life of cesium-134 is 2 years.

The half-life of cesium is approximately 30 years.

The formula for half-life decay is A = P(1/2)t/d.

The half life is D. A Equals 9.55 gram when 10 gram and 2 years are entered into the equation.

Cesium would remain 10g after 2 years in 9.55 gram.

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Answer:      6 × (10 × 40)

Answer:

6 × (10 × 40)

Step-by-step explanation:

6 × 14 = 84

6 × (10 + 4) = 6 × 14 = 84

6 × 7 + 6 × 7 = 42 + 42 = 84

6 × 10 + 6 × 4 = 60 + 24 = 84

6 × (10 × 40) = 6 × 400 = 2400

Answer:

1898

Step-by-step explanation:

Multiply both numbers together to find the area.

clinical prediction is not the fairest way to combine assessment information about job applicants, but the other methods (unit weighting, rational weighting, and multiple regression) are more fair

Clinical prediction appears to have a serious shortcoming in terms of overall fairness for applicants because it is a subjective process of bringing information and hence clinical prediction is not the fairest way to combine assessment information about job applicants .

unit weighting is the simple method which add scores of each candidate at each level of assessment in order to arrive at a total score

Thus the other methods (unit weighting, rational weighting, and multiple regression) are more fair

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The probability of the next customer paying with a debit or credit card other than cash is =94.82%

We have given,

Genesis owns a small business selling clothing.

She knows that in the last week 6 customers paid cash, 66 customers used a debit card, and 44 customers used a credit card.

we are asked to determine  the probability that the next customer will pay with something other than cash as a percent to the nearest whole number

P(A)= number of favorable outcome in event A divided by the total outcome in a sample space

customers will pay through debit or credit card other than cash.

last week of customers paid cash: 6

last week of customers paid w/ a debit card: 66

last week of customers paid w/ a credit card: 44

Therefore, 6+66+44= 116

=110/116

=0.9482

= 94.82% is the probability that the next customer will pay with

something other than cash as a percent to the nearest whole number.

Hence we get the required answer.
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The rearranged form of equation 4(x-3)/a=y will be x=ay+3.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the expression is, 4(x-3)/a=y

First, we open the bracket to make x the variable in the equation.

4x - 12/a = y

4x - 12 = ay

4x = ay + 12

x = ay + 12/4

x = ay + 3

Thus, the rearranged form of equation 4(x-3)/a=y will be x=ay+3.

The question is incomplete,

The complete question is"Rearrange to make x the subject of 4(x-3)/a=y:

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Answer:The mean of combined group is 71.12 kg

Step-by-step explanation:

Mean of 35 students test score=75.3

Total score of 35 students=mean×test score

=35×75.3

=2635.5

Mean of 26 students test score=65=65.6

Total score of 26 students= 26×65.6

=1705.6

Mean of combined group=(Total score of 35 students+Total score of 26 student ÷Number of total students

=(12635.5+1705.6)÷61

=71.16

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The combined group's average is 71.16.

Given;

If the average test score for one class of 35 students is 75.3 while the average test score for another class of 26 students is 65.6

Mean of 35 student's test scores = 75.3

The total score of 35 students is the mean * test score

=35 * 75.3   =2635.5

Mean of 26 student's test scores = 65.6

The total score of 26 students = 26 * 65.6  =1705.6

Mean of combined group = (Total score of 35 students + Total score of 26 students) / Number of total students

                                          = (12635.5 + 1705.6)  / 61

                                           = 71.16

Hence, the mean of the combined group is 71.16

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The number which when increased by 12 is two times its opposite. is

N = -4

final equation N + 12 = -2N

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

The problem says

N + 12 = -2N

N + 2N = -12

3N = -12

N = -4

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