The scale on the map shows that 4 cm = 52 miles. How many miles apart are two towns if the measurement is 22 cm?

The two given triangles are congruent because of SAS.

In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other.  Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.

The given triangles are RTP and STP

P is the midpoint of RS and TP is the altitude of triangle RTS.

In the triangles RTP and STP

TP = TP (common)

∠RPT = ∠ SPT (90°)

RP = SP (median divides the side equally)

So, both triangles are congruent using SAS property.

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The number of brown notebooks is 40.

What is the ratio?

A ratio displays the multiplicity of two numbers. For example, if there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.

We have,

24 red notebooks,

∴ 5/3 = x/24.

Cross-multiply, and we now have

120 = 3x.

Divide both sides by 3,

x = 120/3

x = 40

x = 40 brown notebooks.

Hence, the number of brown notebooks is 40.

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Answer:

7 cm

Explanation:

The area of a parallelogram:

From the diagram:

• Base = y cm

• Height = y cm

Thus:

The value of y is 7cm.

internal angles of the polygon

angle a = 180 - 45 = 135°

angle b = 180 - 90 = 90°

angle c = 180 - 60 = 120°

angle d = 540 - 135 - 90 - 120 - 77 = 118°

angle e = 180 - 103 = 77 °

angle x = 180 - 118 = 62°

the polygon is not a regular polygon because the measure of its angles are different

we have

f(x) = |x – 1] + 2

g(x) = -2f(x) + 8

substitute the value of f(x) in g(x)

so

g(x)=2(|x – 1] + 2) +8

g(x)=2|x – 1] + 4 +8

g(x)=2|x – 1] + 12

Using a graphing tool

see the attached image

Therefore, 27/72 simplified to lowest terms is 3/8.

Let the first number be x.

The second number is 5 times less than x => x - 5

Therefore, we can write the statement as

Solving the quadratic equation:

Let us replace -5x in the equation with -4x and -x to be able to factorize.

Hence,

Hence,

Therefore, the number can be 1 or 4.

The second number can be

Therefore, the pair of numbers can be

Answer: 1/4

Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4

Answer:

49.5 minutes

Step-by-step explanation:

Amount of time that Philip took

= [tex]\frac{distance}{speed}[/tex]

= [tex]\frac{66km}{80km/h}[/tex]

= [tex]0.825h[/tex]

= [tex]49.5 min[/tex]

Given,

PD = 8 and DC = 9

Required

The length of line BC.

Here, PB and PD are the ardius of the circle. By the definition of circle, the measure of all radius is equal.

So, PB = PD = 8.

The tangent is always perpendicular to the radius at the point of tanjency.

By the pythagoras theorem,

Hence, the measure of BC is 15 units.

Answer:

Step-by-step explanation:

1 Simplify  (-3,5)y(−3,5)y  to  -3,5y−3,5y.

-3,5y=\frac{2}{3}x+1

−3,5y=

3

2

​

x+1

2 Simplify  \frac{2}{3}x

3

2

​

x  to  \frac{2x}{3}

3

2x

​

.

-3,5y=\frac{2x}{3}+1

−3,5y=

3

2x

​

+1

3 Switch sides.

\frac{2x}{3}+1=-3,5y

3

2x

​

+1=−3,5y

4 Break down the problem into these 2 equations.

\frac{2x}{3}+1=-3

3

2x

​

+1=−3

\frac{2x}{3}+1=5y

3

2x

​

+1=5y

5 Solve the 1st equation: \frac{2x}{3}+1=-3

3

2x

​

+1=−3.

x=-6

x=−6

6 Solve the 2nd equation: \frac{2x}{3}+1=5y

3

2x

​

+1=5y.

x=\frac{3(5y-1)}{2}

x=

2

3(5y−1)

​

7 Collect all solutions.

x=-6,\frac{3(5y-1)}{2}

x=−6,

2

3(5y−1)

​

Houston to NY= 1608

NY to Chicago=802

Chicago to Houston=1067

Step-by-step explanation:

(-5p + 8)(-3p - 5)

[tex]15p^2 +25p - 24p -40[/tex]

[tex]15p^2 +p -40[/tex]

As per the given interest rates, she have to pay $103.95  in fees for her actively managed fund.

Interest:

Interest means the amount to be paid on the borrowed money or the amount received on the money lent.

Given,

Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return.

Here we need to find the fees for her actively managed fund.

First we have to change rate of return percent to decimal form,

That is,

5% = 0.05

Now, we have to multiply the amount and decimal to get Alizeh 's profit,

=> 9000 x 0.05

=> 450

Therefore, the fund's total after 1 year, including initial investment and profit is

=>9000 + 450

=> 9450.

Now, we have to change fee percent  that is the expense ratio into decimal form,

=> 1.1% = 0.011

Therefore, the fees for her fund is,

=> 9450 x 0.011

=> 103.95

Therefore, she have to pay $103.95 for her managed fund.

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An equation for the distance between the two friends after time (t) in hours is given by: c = 50t

Given,

Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour.

We have to find the equation for the distance between the friends after t hours.

Here,

The distance covered by each friend should be calculated as follows:

For the first friend heading North, we have;

Distance, a = speed × time

Distance, a = 30t

For the second friend heading East, we have:

Distance, b = speed × time

Distance, b = 40t

By applying Pythagorean theorem, the distance between these two friends after an amount of time (t) is given by:

Distance, c² = a² + b²

Distance, c² = (30t)² + (40t)²

Distance, c² = 900t² + 1600t²

Distance, c² = 2500t²

Distance, c = √(25 × 100t²)

Distance, c = √25t² × √100

Distance, c = 5t x 10

Distance, c = 50t

Therefore,

The equation for the distance between the friends after t hours is c = 50t

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The probability of the event that the first digit is nine and the last letter is a is 1/260.

The building security code has 2 numeric digits in between 0-9 and 2 letters.

The choices for letters is 26 each and the choices for digits is 10 each.

So, the total possible security code can be,

Total security codes possible  = 10 × 10 × 26 × 26

Total security codes possible = 67600

Now, the number of codes that starts with 9 and end with a are,

= 1 × 10 × 26 × 1

= 260

The probability that the first digit is nine and the last letter is a is,

P(E) = 260/67600

P(E) = 1/260

So, the probability that the first digit is nine and the last letter is a is 1/260.

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Answer:

the program I will get back to you on that date is approaching the

Step-by-step explanation:

the program I will get back to you on that date is approaching the

On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "

A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.

Here,

12y - 1/2 = 9y +8/5

3y=8/5+1/2

3y=(16+5)/10

3y=21/10

y=7/10

According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.

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Answer: 2x^3 + 3x^2 - 11x - 6

Step-by-step explanation: simplified

Answer: A

Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,

First, combine the x's on the RHS, and the integers on the LHS.

1.69x - 0.44x = 1.25x

24 - 19 = 5

So the equation will be 1.25x = 5

Divide both sides by 1.25 to isolate the x.

x = 4

Given

A) The angles A and B are supplementary.

If,

B) The figure,

To find

A) The value of x.

B) The value of x.

Explanation:

A) It is given that,

Angle A and angle B are supplementary.

Then,

Hence, the error is in the statement,

Since the angles are supplementary, when added together they equal 90.

As, the correct answer is when added together they equal 180.

That implies,

Hence, the value of x is 18 degrees.

B) It is given that,

From, the figure the given angles are interior angles.

Also, the interior angles on the same side of the transversal is supplementary.

Which means when you add them they equal 180.

Hence, the error is in the statement,

Since the angles are adjacent, they are complementary angles.

Which means when you add them they equal 180.

As, the angles are interior angles on the same side of the transversal.

Also,

Hence, the value of x is 116 degrees.

The equation of the line that represents the data in the table is y = 30x + 30.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

From the data;

Point 1( 0,30 )

Point 2( 2,90 )

First, we determine the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 90 - 30 )/( 2 - 0 )

Slope m = ( 60 )/( 2 )

Slope m = 30

Next, we determine the y-intercept b by substituting the given values into the equation of line formula.

y = mx + b

30 = (30)0 + b

30 = b

b = 30

Now, plug these values into y = mx + b to determine the equation of the line.

y = mx + b

y = 30x + 30

Therefore, y = 30x + 30 is the equation of the line.

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Verify each equation

option A

For x=3 ------> y=216(3^3)=

Answer:

Step-by-step explanation:

Answer:

2.5×10 to the sixth power

Step-by-step explanation:

6÷2.4=2.5

10^9÷10^3=6

Answer: 66/2 or in simplest form, 33/1

Step-by-step explanation:

11/2 divided by 1/6

*Keep the first fraction, flip the sign to multiplication, reciprocal or flip the fraction*

= 11/2 x 6/1

=66/2

=33/1

To find out the slope we need two points

from the table

we take

(0,1) and (1,3)

so

m=(3-1)/(1-0)

m=2/1

The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

According to the question,

We have the following information:

A line is passing through two points (2,7) and (-4,19).

We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:

m = (y2-y1)/(x2-x1)

(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)

In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.

m = (19-7)/(-4-2)

m = 12/(-6)

m = -2

Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

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To find the time that Priya spent practicing violin, calculate what is 152% of 74 minutes by multiplying 74 times 152/100:

Therefore, Priya practiced for 112.48 minutes.