what is the correct postulate to prove these two triangles congruent?

A. SAS
B. ASA
C. SSS
D. AAS
E. HL

The monthly payment for the first condition is $1750.11 and the total number of payments is 156.

What is the monthly payment?

Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.

The formula for monthly payments on the mortgage is given:

                                [tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]

where, MP = monthly payment

            P = principal amount

             r = rate of interest

             n = number of payments per year

              t = number of years

Given, a couple buys a house for $290000 and makes a down payment of 15%

Down payment = 0.15*290000 = $ 43500

First condition,

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

number of years (t) = 15 years

Then, the monthly payment is calculated by:

             [tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]

Therefore, monthly payment = $1750.11

Second condition,

monthly payment (MP) = $1950

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

time in years (t) = x years

Then,

or,  [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]

or, [tex]x = 13.06 = 13[/tex]

So, the total number of payments =  13*12 = 156

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Answer: x= 9

Step-by-step explanation:

I just checked that its right!

Answer:

The correct answer would be 9

Step-by-step explanation:

The correct statement regarding whether the graph is a one-to-one function is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

An one-to-one function is a function in which each output is related to only one input, that is, there are no horizontally aligned points.

These horizontally aligned points happen when an horizontal line is traced on the graph of the function, and crosses the function more than once.

From the graph of the function given by the image at the end of the answer, it can be seen that this line would cross the function twice for values of y between 0 and 2, hence the correct option is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

The problem asks for the correct statement regarding the function given on the image at the end of the answer.

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The solution to the equation given as √|x|² = x is x ≥ 0

From the question, the representation of the equation is given as

√|x|² = x

To start with;

We evaluate the square root expression in the equation

So, we have the following representation

|x| = x

The above implies that the absolute value of a number equals the number

As a general rule of absolute values, the absolute value of a number is positive

This can be represented as

x ≥ 0

Hence, the solution to the equation is x ≥ 0

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Answer:

Step-by-step explanation:

16/(2+6)

16/8=2

The absolute value equation graphed is defined by the rule given as follows:

y = |x - 3| + 6.

The function graphed is an absolute value equation, due to it's v format.

The equation that represents an absolute value function with vertex (h,k) is given by the rule presented as follows:

y = |x - h| + k.

On the graph, this vertex is the turning point of the absolute value function.

For the graphed function, the coordinates of the vertex are given as follows:

Then the coordinates of the vertex are:

(3,6).

The equation of the graphed absolute value function is:

y = |x - 3| + 6.

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y-intercept: (0,60)

This is given in the table.

Slope: [tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Using (1,50) and (2,40):

   [tex]m = \dfrac{40 - 50}{2-1} = \dfrac{-10}{1} = -10[/tex]

The slope is -10.

Using the slope-intercept form (y=mx+b) and the fact that we found m=-10 and b=60 from the table, the equation is:

   y = -10x + 60

If Two planes are parallel and each plane contains a line, the two lines are  not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.

Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.

The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.

Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.

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Prior to cellular radio, mobile radio and telephone services required

a. high-power transmitter/receiver.

A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.

Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.

Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.

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Answer:

31-6/1-1

=25/0

=undefined

Answer:

No

Step-by-step explanation:

The value that corresponds with the other value on a data (34 to 2, 51 to 3, 68 to 5 etc.) needs to have the same quotient (or ratio) when you compare them.

34/2 = 51/3 ? Yes (but you can't stop here because you need to test ALL the values, what I mean is ALL the values UNTIL you found one that is not equal to each other, if all of them are equal, then the data are proportional.

34/2 = 68/5 ? No (Now you can stop here and say it's not proportional because we already found one pair that are not equal).

Answer:

sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1

The length AC of the triangle will be 10.6 units

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is a right angled ΔABC as shown in the figure.

We have the image as shown in the figure. In the right angled triangle -

Sin(62°) = CA/CB

Sin(62°) = CA/12

CA = 12 x Sin(62°)

CA = 12 x 0.88

CA = 10.6

Therefore, the length AC of the triangle will be 10.6 units

Therefore, by following the steps above, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

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[Refer to image attached for full question]

Answer:

[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]

x-5=0

x=5

the length of smaller rectangle= 8 m

and breadth of s. rectangle= 7 m

l x b = 8 x 7

[tex]56 {m}^{2} [/tex]

hopefully this will u

The x-intercept and y-intercept of the graph is (5,0) and (0,4)

How to find the intercept ?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

1. To find the x-intercept we put y=0

The equation becomes

4x + 5(0) = 20

4x = 20

 x =  [tex]\frac{20}{4}[/tex]

 x = 5

∴ The x-intercept is (5,0)

2. To find the y-intercept we put x=0

The equation becomes

4(0) + 5y = 20

5y = 20

 y =  [tex]\frac{20}{5}[/tex]

 y =  4

∴ The y-intercept is (0,4)

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The answer to be entered in the boxes for the area model is 17, 0 and 17

An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle

Given:

    ....60.....1.............

36|2160 | 36 | 17

2160 ÷ 36 = 60 R 0

36 ÷ 36 = 1 R 0

17  ÷ 36 =  0 R 17

Note:  (0 x 36) + 17 = 17

Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively

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The probability that the sample mean is less than 200 pounds is 33% or 0.33

Given that,

The average annual meat consumption in the United States was 218.4 pounds, with a standard deviation of 42 pounds, and was normally distributed. A random sample of 30 individuals was chosen.

Mean  (μ) = 218.4

Standard deviation (σ) =42        

Probability = P(X< 200) = P[(X-μ ) / σ < (200-218.4) /42 ]

= P(z <-0.44 )

Using z table                                            

=0.3300

Probability=0.3300                                                        

Therefore, 33% or 0.33 of the time, the sample mean will weigh less than 200 pounds.

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================================================

Explanation:

Part A)  Find P(-2)

We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so

P(x)/(x+2) = quotient + remainder/(x+2)

P(x)/(x+2) = Q(x) + 8/(x+2)

When multiplying both sides by (x+2), it clears out the fractions and we're left with this

P(x) = (x+2)*Q(x) + 8

From here, plug in x = -2 and simplify

P(x) = (x+2)*Q(x) + 8

P(-2) = (-2+2)*Q(-2) + 8

P(-2) = (0)*Q(-2) + 8

P(-2) = 0 + 8

P(-2) = 8

Luckily we don't need the value of Q(-2) since it cancels out with the zero.

-----------------------------------

Part B) Find P(2)

This time we'll plug in x = 2 and we'll get...

P(x) = (x+2)*Q(x) + 8

P(2) = (2+2)*Q(2) + 8

P(2) = 4*Q(2) + 8

P(2) = 4*5 + 8

P(2) = 20+8

P(2) = 28

Answer:

Length would be 6ft

Width would be 4ft

Step-by-step explanation:

24ft^2 is the area as we know 6x4 = 24 and 4 is two less than 6, therefor your answer is 4 and 6.

Dad's car's gas tank holds 14.8 gallons of the gas.

A mixed fraction is one generated by integrating a whole number as well as a fraction.

Changed the mixed fraction in decimal.

Total gas purchased = 37/2 = 18.5 gallons of gas.

Let x be the gallons of gas tank contains.

Then,

(1/2)x + (3/4)x = 18.5

Multiply both sides by 4,

2x + 3x = 74

5x = 74

x = 14.8 gallons

Thus, Dad's car's gas tank holds  14.8 gallons of the gas.

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Answer: -19 49/50 ==> a

Step-by-step explanation:

(−5 2/5) ⋅ 3 7/10=

(−5 - 2/5) ⋅ (3 + 7/10)=

(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators

((-25-2)/5) ⋅ ((30+7)/10)=

-27/5 ⋅ 37/10 =

-27 ⋅ 37 / (5 ⋅ 10) =

-999/50=

(-950-49)/50=

-950/50 - 49/50=

-19 - 49/50=-19 49/50 ==> a

Answer:

[tex]x=12, y=0[/tex]

Step-by-step explanation:

[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]

Setting the real and imaginary parts of the left hand side equal to 0,

[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]

The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.

How to find the time for a rocket to hit the ground?

The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.

Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.

According to the given question:

We are given equation for height as

h(x) = -4x² + 16x

where x is the time in seconds

When object hits the ground the height becomes 0

So, we can set h(x) = 0 and then we can solve for x

-4x² + 16x = 0

Dividing by -4x from both sides

x - 4 = 0

x = 4 sec

So, the time it takes for a rocket  to hit the ground is 4 seconds.

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The scientist will take 23 seconds to get back to the sea level.

Let us calculate the distance covered by the scientist at the given speeds and at the specified times.

She travels down for 41 seconds at speed of 4.9 feet per second.

Distance travelled = 41 × 4.9 = 200.9 feet

Elevation = -200.9 feet

She then goes up for 49 seconds at speed of 3.2 feet per second.

Distance travelled = 49 × 3.2 = 156.8 feet

Elevation = -222.9 + 156.8 = -44.1

So she is at a depth of 44.1 feet below the sea level.

Time taken = 44.1 / 3.6 = 12.25 seconds

Therefore it will take her about 12.25 seconds to go back to the sea level.

The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.

There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.

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The product of the improper fraction 3 1/4 and 1/2 is 1 5/8.

What is mixed fraction?

 A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. a fraction when the denominator (bottom number) and the numerator (top number) are both more than or equal (the bottom number). When the numerator is equal to or more than the denominator, the fraction is said to be improper fraction. It always has a value of one or higher.

Here the given fraction 3 1/4 convert into 13/4.

Now the product of the fractions is

=> 13/4 × 1/2

=> 13/8

=> 1 5/8.

Therefore product of the given fraction is 1 5/8.

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The sum of three consecutive even numbers is 558, The first number is 184.

The Sum of three consecutive even numbers is 558

We have to find the first number

Let the three consecutive even numbers be:

First number = x

Second number = x + 2

Third number = x + 4

Since their sum is 558

Therefore,

x + x + 2 + x + 4 = 558

3x + 6 = 558

3x = 558 - 6

3x = 552

Divide both sides by 3

Then the first number is 184.

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Answer:

Y-int = -45, X-int =-11.25

Step-by-step explanation:

Please read this before moving on :)

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.

We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.

Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

2 points; (0,-40), (-10,0)

0-(-40)/(-10)-0 = 40/-10 = -4

Y=MX+B

Y=MX+(-45)

Y=MX-45

Y-int = -45

Y=MX+B

0=(-4)x+-45

45=-4x

X-int =-11.25