Mrs.smith deposits $980 in a saving account that pays 3.1% interest compounded daily

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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Step-by-step explanation:

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

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

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

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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Answer:

[tex]\frac{5}{14}[/tex]

Step-by-step explanation:

First, find the total number of students:

[tex]252+140=392[/tex]

Then, divide the number of students at hand by the total number:

[tex]\frac{140}{392}[/tex]

When possible, reduce the fraction to its simpliest form:

[tex]\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}[/tex]

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

16+14i will the required simplified value as the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number having imaginary and real part.

A complex number is one with the formula a + bi, where a and b are real numbers and I is an imaginary number. Complex numbers are those that are expressed as a+ib, where a,b are real numbers and I is an imaginary number known as "iota." (√-1) is the value of i. 2+3i is a complex number, for example, where 2 is a real number (Re) and 3i is an imaginary number (Im). A complex number is one that can be expressed as a + bi, where a and b are real numbers and I is an imaginary unit, and which solves the equation i² =-1. In this expression, a represents the complex's real part and b represents its imaginary part.

Here,

-6(3i)(-2i)=2(3-i)(4i-2)

-6(-6i²)

=36i²

=-36

2(3-i)(4i-2)

=2(12i-4i²-6+2i)

=2(14i+4-6)

2(14i-2)=-36

14i-2=-18

on simplifying,

16+14i will the required simplified value.

As the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number with imaginary and real parts, the required simplified value is 16+14i.

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Answer:

−6(3i)(−2i) =

✔ –36

2(3 − i)(−2 + 4i) =

✔ –4 + 28i

Step-by-step explanation:

An order of 1 slice of cheese pizza and 3 sodas cost will be $5.25.

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.

Given data -

Cost of 3 slices of cheese pizza and 2 sodas = $8.75

Cost of  2 slices of cheese pizza and 4 sodas = $8.50

Let x be the cost of 1 slice of cheese pizza

and y be the cost of 1 soda

According to the given data,

3x + 2y = $8.75         -------------equation 1

2x + 4y = $8.50        -------------equation 2

Equation 1 by equation 2 multiplied results in

6x + 4y = $17.5          ------------equation 3

By subtracting equation 2 from equation 3 to get the cost of 1 slice of cheese pizza, we will get

4x = $9

x = $2.25

By substituting the value of x in equation 2 so that we can get the cost of 1 soda, we will get

2*2.25 + 4y = $8.50

4.5 + 4y =  $8.50

4y = $8.50 - 4.5

4y = $4

y = $1

To get the cost of 3 sodas, multiplying the value of y by 3

Therefore the cost of 3 sodas will be $1*3 = $3

The total cost of 1 slice of cheese pizza and 3 sodas cost = $2.25 + $3

= $5.25

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

Step-by-step explanation: simplified

Leah and Philip have same unit rate.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The table is shown for the number of pages and number of nights.

Now,

The unit rate to read the number of pages for Leah;

⇒ 45 / 3 = 15

The unit rate to read the number of pages for Rose;

⇒ 48 / 4 = 12

The unit rate to read the number of pages for Hannah;

⇒ 30 / 3 = 10

The unit rate to read the number of pages for Philip;

⇒ 150 / 10 = 15

Thus, Leah and Philip have same unit rate.

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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.

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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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.

When we rotate a figure 90° around a point, we need to check the difference in x and y coordinates between the point and the center of rotation.

Then these differences will swap among themselves.

The difference in x-coordinate between A and B is 1, so now this difference will be the difference in y-coordinate.

The difference in y-coordinate between A and B is 7, so now this difference will be the difference in y-coordinate.

So the coordinates of A'' will be:

Also, the point will be in the third quadrant, so all coordinates are negative:

Therefore the answer is C.

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.

Verify each equation

option A

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

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.

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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Answer:

2,6

Step-by-step explanation:

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

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]

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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The error is in step 2 that is 3x-3=2x+6 as in step 2 we shifted 2x to LHS side of calculation.

Error is the difference between a true value and an estimate, or approximate, representation of that value in applied mathematics. The difference between the mean of the entire population and the mean of a sample taken from that population is a frequent example in statistics. Three types of errors can occur when solving math problems: factual, procedural, and computational. Students can make a variety of math mistakes, and it's crucial to know how to avoid them and how to take lessons from them. An error is an inaccurate or incorrect action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake. The term "error" in statistics describes the discrepancy between the computed value and the correct value.

Here,

5x-3=2x+6

3x-3=6

3x=9

x=3

The mistake is in step 2, which reads 3x-3=2x+6 because we shifted 2x to the LHS side of the calculation in step 1.

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The required solutions are m∠1 + m∠7 = 143° + 37° = 180° and 'a' is parallel to 'b' due to the same-side exterior angle.

Transversal c intersects lines a and b which is given in the question.

As per the given figure,

m∠1 + m∠7 = 143 degrees + 37 degrees = 180 degrees

m∠1 = 143° and m∠7 = 37°.

First, we can write m∠1 + m∠7 and then substitute angles with their actual degree measure:

143° + 37° = 180 degrees

The first statement will be:

m∠1 + m∠7 = 143° + 37° = 180°

Exterior indicates that both angles are on the same side, or outside, of the parallel lines.

Angles a, b, c, and d in the figure are outside of the parallel lines.

We can then state;

a and b are parallel since they both agree with the same-side exterior theorem.

As a result, 'a' and 'b' are parallel because they both satisfy the same-side exterior theorem.

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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

Houston to NY= 1608

NY to Chicago=802

Chicago to Houston=1067

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:

Step-by-step explanation:

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