We have seen the isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use information to the right to help the measure of angles 1, 2, 3, 4, and 5.

In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:

where:

v2: final speed of the car = 2.8 m/s

v1: initial speed of the car = 1 m/s

Δt: time interval = 12 s

You replace the previoues values into th formula for the acceleration:

Next, you the Newton's second law to find the mass of the car. You proceed as follow;

where:

m: mass of the car = ?

a: acceleration of the car = 0.15m/s²

F: force exerted on the car by the man = 127.5N

You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:

Hence, the mass of the car is 850kg

The value of the expression 0.3(1/4 - 1) + 0.35 is 0.125

The expression is

0.3(1/4 - 1) + 0.35

The expression is defined as the sentence with a minimum of two variables and at least one math operation.

Here the expression is

0.3 (1/4 - 1) + 0.35

First do the arithmetic operation in the bracket

0.3(1/4 - 1) + 0.35 = 0.3 × -0.75 + 0.35

In next step do the multiplication

0.3 × -0.75 + 0.35 = -0.225 + 0.35

Do the addition of the numbers

-0.225 + 0.35 = 0.125

Hence, the value of the expression 0.3(1/4 - 1) + 0.35 is 0.125

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Hence the product of 3/3 and 12 is not greater than the product of 3/2 and 12.

So timmy is not correct

We are given the following proportions:

The second proportion is equivalent to:

Now, we substitute the value of "z":

Now, we multiply both sides by 30:

Solving the operation we get:

Now, since we have the value of "y" we can use the first proportion to get the value of "x":

This is equivalent to:

Now, we substitute the value of "y":

Now, we multiply both sides by 9:

Solving the operations:

Therefore, the value of "x" is 3.

1. At age 65 when you retire, you have (future value) $202,531.69 from the IRA.

2. The total interest earned on the monthly investment of $95 at 6.25% for 40 years is $156,931.69.

The future value, which represents the compounded value of the monthly investments, can be computed using the FV formula or an online finance calculator as follows:

Number of years = 40 (65 - 25)

N (# of periods) = 480 months (40 x 12)

I/Y (Interest per year) = 6.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $95

Results:

Future Value (FV) = $202,531.69

Sum of all periodic payments = $45,600 ($95 x 480 months)

Total Interest = $156,931.69

Thus, the future value of the monthly investment is $202,531.69 with an interest of $156,931.69.

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Let's say that the vertex is the following red point:

Then, its reflection across y-axis would be the blue point:

If we observe the coordinates, we will have that:

(5, 3) is transformed into (-5, 3). This is going to happen no matter the coordinate:

The zeros of a quadratic function are the points where the graph cuts the x axis.

If one zero is - 3, it means that

x = - 3

x + 3 = 0

Thus, one of the factors is (x + 3)

If another zero is - 13, it means that

x = - 13

x + 13 = 0

Thus, one of the factors is (x + 13)

Thus, the quadratic function would be

(x + 3)(x + 13)

We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have

x * x + x * 13 + 3 * x + 3 * 13

x^2 + 13x + 3x + 39

x^2 + 16x + 39

Thus, the quadratic function is

f(x) = x^2 + 16x + 39

A)

For this tringle we can turn the figure like this:

now we have two right triangles and we can calulate the base of the first triangle with the sin law

the angle b is going to be:

Now the base is going to be:

and the base of the secon triangle is going to be:

And the area of the triangles is going to be:

so in total the area is going to be:

B)

the procedure is similar, first we turn the tiangle like this:

the angle a is going to be:

the angle b is going to be:

now the base is going to be:

and the base of the other triangle will be:

And the area of the triangles will be:

And the total area will be:

Solution

- We are asked to find the complement of rolling a 5 or 6 given a cube numbered 1 - 6.

- The complement of an event is defined as every other event asides the event in context.

- Other than rolling a 5 or 6, we can also roll a 1, 2, 3, or 4. This constitutes the complement of rolling 5 or 6.

Final Answer

The complement of rolling a 5 or 6 is:

{Rolling a 1, 2, 3, or 4} (OPTION B)

Calculate the division as shown below

Therefore, the quotient is 16 and the remainder is 5

Problem: Find 8 3/4 ÷ 1 2/7. Write the answer in the simplest form.​

Solution:

this is equivalent to:

Now, we do cross multiplication:

then, the correct answer would be:

To solve the exercise you can use the rule of three, like this

Therefore, Curt and Melanie should use 0.45 quarts of yellow paint to make seafoam green paint.

As shown at the graph, we need to find x and y

The angles (x+1) and (2y+1) are vertical

so, x + 1 = 2y + 1

so,

x = 2y eq.(1)

And the sum of the angles (x+1) , (3x + 4y) and (71 - 3y) are 180

So,

(x+1) + (3x + 4y) + (71-3y) = 180

x + 1 + 3x + 4y + 71 - 3y = 180

4x + y = 180 - 1 - 71

4x + y = 108

Substitute with x from eq (1) with 2y

4 * 2y + y = 108

8y + y = 108

9y = 108

y = 108/9 = 12

x = 2y = 2 * 12 = 24

So, x = 24 and y = 12

Note:

Corresponding agles are angles on corresponding (the same) side of the two lines intersected by the transversal

Alternate angles are angles on the opposite sides of the transversal

We have to solve the equation:

The steps are:

1. Original equation

2. Distributive property

3. Substraction property of equality

4. Addition property of equality

5. Combine all terms

6. Division property of equality

7. Solution

The composition of the function, (g o h)(0) = 0.

To find the composition of a function, first, find the value of the inner function by plugging in the given value of x. The output of the inner function would now be used as the input to evaluate the outer function.

We are given the following:

g(x) = 5x

h(x) = √x

To find the composition of the function, (g o h)(0), first, find h(0). To find h(0), substitute x = 0 into the inner function, h(x) = √x:

h(0) = √0

h(0) = 0

Find (g o h)(0) by substituting x = 0 into g(x) = 5x:

(g o h)(0) = 5(0)

(g o h)(0) = 0

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SOLUTION

Let us use a diagram to illustrate the information, we have

Now, from the diagram, let the length of the uniform strip of floor around the rug be x, So, this means the length and width of the rug is

Now, since she can afford to buy a rug of 264 square feet for carpeting, this means that the area of the rug is 264, hence we have that

Solving for x, we have

Dividing through by 4 we have

So from our calculation, we go for x = 3, because 20 is large look at this

length cannot be negative, so we go for x = 3.

Hence the dimensions of the rug becomes

So the dimension of the rug should be 22 x 12 feet

We want to picture the inequalities

and

First, we consider the lines y= -x -3 and and y=(4/5) x +5 . Since the first line has a negative slope, this means that its graph should go downwards as x increases and since the other line has a positive slope, this means that its graph should go upwards as x increases. This leads to the following picture

Now, the expression

means that the y coordinate of the line should be below the red line. Also, the expression

means tha the y coordinate should be above the blue line. If we combine both conditions, we find the following region

so we should look for a point that lies in this region

We are given the points (-1,9), (-6,2), (9,-9) and (-8,-5).

We see that the yellow region is located where the x coordinate is always negative. So, this means that we discard (9,-9).

so we should test the other points. Since -8 is the furthest to the left, let us calculate the value of each line at x=-8.

so, in this case the first expression is accomplished since -5 < 5. And

However note that -5 < 1.4, and it should be greater than -1.4 to be in the yellow region. So we discard the point (-8,-5) .

We can check , iusing the graph, that the lines cross at the point (-40/9, 13/9) which is about (-4.44, 1.44). This means that for the point to be on the yellow region, it should be on the left of -4.44. Since the only point that we are given that fulfills this condition is (-6, 2), this should be our answer. We check that

and

so, the point (-6,2) is in the yellow region

We would begin by determining the slope of the line given;

To determine the slope, we would have to express the equation of the line in slope-intercept form as follows;

Therefore, we need to make y the subject of the equation as shown below;

The equation in slope-intercept form appears as shown above. Note that the slope is given as the coefficient of x.

Note alo that the slope of a line perpendicular to this one would be a "negative inverse" of the one given.

If the slope of this line is

Then, the inverse would be

The negative of the inverse therefore is;

The answer therefore is option D

We have the following: system of equations:

A: 3c=d-8

B: c=4d+8

To eliminate variable d first, if we want to use elimination method, we need to have variable d in both equations with the same coefficient but with different signs.

As in equation B, the coefficient of d is 4, then we need to have in equation A a coefficient of -4 for variable d.

Then the answer is we need to multiply equation A by -4.

In a x-y coordinate plane of you moves to the right it increase the value of x and if you moves vertically it increases the value of y.

The ordered pair is (x,y)

Hello there. To solve this question, we have to remember some properties about polar curves and determining maximum and minimum values.

In this case, we have the function in terms of the angle θ:

We want to determine its minimum and maximum values on the closed interval:

We graph the function as follows:

Notice on the interval, it has a maximum value of 0.

We can determine its minimum value using derivatives, as follows:

Setting it equal to zero, we obtain

Taking its second derivative, we obtain

And notice that when calculating it on this point, we get

A positive value, hence it is a minimum point of the function.

Its minimum value is then given by

Of course we cannot determine that 0 is a maximum value of this function using derivatives because it is a local maxima on a certain interval, and derivatives can only gives us this value when the slope of the tangent line is equal to zero.

Two lines that parallel, their slopes are equals.

L1 and L2 are parallel only if the slopes of the lines are s1 and s12 are identical

therefore the correct answer is A. slope m = slope (n) since they say that two slopes the same

The percentage change can be found below

Since the percentage is negative, this means there is a 60% decrease.

1) Note that we need to find a perpendicular line. Perpendicular lines have reciprocal and opposite slopes. So we know that the slope we need is -3

2) We also know that it must pass through (-2,-6), so let's plug the slope -3 the point (-2,-6) so that we can find the linear coefficient:

A direct variation between two variables "x" and "y" is given by the following formula:

y = kx

We can rewrite the given expression 8y-7x=0 to get an equation of the form y = kx like this:

8y - 7x = 0

8y - 7x + 7x = 0 + 7x

8y = 7x

8y/8 = 7x/8

y = 7/8x

The number that is being multiplied by x should be the constant of variation k, then in this case, the constant of variation equals 7/8

Answer:

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

Explanation:

Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as

m∠ECB = 180 - 140

m∠ECB = 40

Then, the interior sum of the angles of a triangle is equal to 180 degrees, so

m∠ECB + m∠EBC + m∠BEC = 180

40 + m∠EBC + m∠BEC = 180

However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows

40 + m∠EBC + m∠EBC = 180

40 + 2m∠EBC = 180

40 + 2m∠EBC - 40 = 180 - 40

2m∠EBC = 140

m∠EBC = 140/2

m∠EBC = 70

Then, the measure of ∠ABE is equal to

∠ABE = 180 - m∠EBC

∠ABE = 180 - 70

∠ABE = 110

Therefore, we can answer it as follows

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

Given the graph of the function:

The graph will be shifted 3 units and to the right 2 units

So, the new vertex will be the point ( 2, 3 )

The new function will be:

So, we will adjust the slider on the following values:

We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.

The expression used to calculate the amount compounded monthly is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.

The expression used to calculate the amount compounded continuously is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.

With the two expressions we can calculated the final amount on both situations, this is done below:

The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.

The number of gallons that the large fishbowl holds would be = 47,925 gallons.

The fishbowls are containers that can be used to transport liquid substance such as water and food products such as fish. This can be measured in Liters, millilitres or in gallons.

The quantity of water the small fishbowl can take = 225 gallons.

The quantity of water the large fish bowl can take = 213(225 gallons)

That is, 213 × 225= 47,925 gallons.

Therefore, the quantity of water that the large fishbowl can hold is 47,925 gallons.

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