What is the measure of the unknown angle in the base of this pyramid? A) 25° OB) 40° OC) 55° OD) 70°

We have

Answer: A.

The value of b is 18.

Here, we are given a triangle as shown in the figure above.

RS = RU

ST = b + 72

and TU = 5b

In triangle TRU, by Pythagoras theorem, we get-

(TU)² = (TR)² + (RU)²

⇒ (5b)² = (TR)² + (RU)²

(TR)² = (5b)² - (RU)²

Similarly, in triangle STR, we will get-

(TR)² = (b + 72)² - (SR)²

Equating the two equations, we get-

(5b)² - (RU)² = (b + 72)² - (SR)²

Since RS = RU,

(5b)² - (RS)² = (b + 72)² - (SR)²

25b² = b² + 72² + 2(72)b

24b² = 5,184 + 144b

b² = 216 + 6b

b² - 6b -216 = 0

Solving this quadratic equation will give us 2 values for b

b = 18 or b = -12

Since length of the side cannot be negative, the value of b will be 18.

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3/5 of the students are girls-

1-3/5 = 2/5

2/5 of the students are boys

1/3 of the girls have blonde hair.

So, multiply, the number of girls that have blonde hair (1/3) by the number of girls (3/5)

1/3 * 3/5 = 3 /15 = 1/5

of all students, 1/5 are girls with blonde hair.

For the boys;

1/2 of the boys have brown hair. of all students 2/5 are boys

2/5 * 1/2 = 2/10 = 1/5

Of all students 1/5 are boys with brown hair

Given the Quadratic Polynomial:

You need to factor it using the Grouping Method.

You can identify that it has this form:

Notice that, in this case:

In order to rewrite it in a form that then you can apply the Grouping Method, you need to find two numbers whose product is the value of "c" and whose sum is the value of "b".

Notice that:

Therefore, you can set up that:

Hence, the answer is: Second option.

If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.

We are required to find the cost after all the rebates and envelopes provided.

The cost can be calculated as under:

Cost=109.99-10.00+0.35+0.41

=$100.75

Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

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Answer:

m∠FGE=52.5 degrees

Explanation:

Angle FGE is formed by the intersection of two secants (BG and GD).

The intercepted arcs are BD and FE.

Therefore:

Substitute the given values:

The student's survey of nine student with regards to the number of first cousins they have gives the standard deviation of the data as the option;

The standard deviation gives a measure of the variability or dispersion of a set of data.

The survey is with regards to a data obtained from a sample of the population (the first nine response),

The standard deviation of a sample is given by the formula;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } }} [/tex]

Where;

n = The data count = 9

[tex] \displaystyle{ \bar x = \frac{6+2+7+8+8+8+5+10+10}{9 } = \frac{64}{9} }[/tex]

Which gives;

[tex]\displaystyle{ \sum (x_{i} - \bar x)} [/tex]

(6-64/9)+(2-64/9)+(7-64/9)+(8-64/9)+(8-64/9)+(8-64/9)+(5-64/9)+(10-64/9)+(10-64/9) = 50.888889

Therefore;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } } = \sqrt{\frac{50.888889}{8}} \approx 2.52 } [/tex]

The standard deviation of the data is therefore;

2.52 first cousins

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The function notation f(-5) has a value of -6

Functions are graphs, ordered pairs, relations, tables and equations that are used to relate independent and dependent variables

The function notation is given as

f(-5)

Also, we have the graphs to be f(x) and g(x)

This is represented by

So, we use the blue curve i.e. f(x)

On the blue curve, we have

f(-5) = -6

Hence, the value of the function is -6

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(6) A function is increasing when the y-value increases as the x-value increases.

The domain is the set of allowable x-values

The following graphs increases over their entire domain:

B, E, I, J, N, G

(7) A function is said to be decreasing when the y-value decreases as the x-values increase.

The following graphs decreases over their entire domain:

A, F

Given the equation:

The slope-intercept form will be as follows:

3a. What error did Han make?

He didn't divide 10 by 4

3b. What are the x- and y-intercepts of the line?

First, we will find the y-intercept

so, put x = 0

y = 5 - 0 = 5

So, the point of y-intercept is (0, 5)

Second, we will find the x-intercept

So, put y = 0

So,

So, the point of the x-intercept is (2, 0)

Answer:

A the answer is a

Step-by-step explanation:

it's corn a beautiful thing for me it has the juice

The savings plan balance (future value), after 4 years with an APR of 4% and monthly payments of ​$100, is $5,213.28.

The future value is the compounded amount of monthly payments after four years of monthly savings.

The future value can be computed using an online finance calculator.

N (# of periods) = 48 months (4 x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

Future Value (FV) = $5,213.28

Sum of all periodic payments = $4,800 ($100 x 48)

Total Interest = $413.28

Thus, in 4 years, the savings plan will have a future value of $5,213.28.

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ANSWER

EXPLANATION

Step 1: Given that:

Step 2: Expand the limit

Hence,

A store Mark's down toys by 15% in january. how much does each toy cost during january? use p for price in December

__________________________

P

Answer:mark has 1 liter, lisa has an impossible -1 liter

Step-by-step explanation:

lets take m as slope

x1=4 y1=13 x2=5 y2=16

so we get the slope as 3.

so the answer is 3.

as this is a vertical line, the slope is undefined

The volume of a cone is given by

Diameter = 34 in

radius = 34/2 = 17 in

Height = 17in

The annual payment is $73416.96

[tex]- Total \ cost \ of \ the \ land $=\$ 225 \times 4700$$$=\$ 1057500$$Down payment $=0.25 \times 1057500$$$=\$ 264375$$so, loan amount $=\$ 1057500-264375$$$=\$ 793125$$[/tex]

[tex]Present \ value,\ $P V=P M T\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]$$$P r=793125, r=0.0675 \text {, }$$$t=20$ years, $n=1$$$\therefore \quad P M T=\frac{P v}{\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]}$$$$=\frac{793125}{\left[\frac{1-\left(1+\frac{0.0675}{1}\right)^{-20}}{\left(\frac{0.0675}{1}\right)}\right]}$$$=73416.96$\\So, Annual payment $=\$ 73416.96$[/tex]

A down payment is the first down payment when buying an expensive good/service, such as a car or house. It is usually paid in cash or equivalent at the time of the transaction. Then some kind of loan is needed to finance the rest of the payment. The biggest advantage of a down payment is that it reduces the amount of the loan you need. If you borrow less, you pay less interest.

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The number of toothpicks that the jumbo box hold is 6760.

From the information, there are 250 toothpicks in a regular-size box and jumbo-size box is made by tripling the length, width, and height of the regular box.

Therefore, the number of toothpicks will be illustrated by multiplying the value by the change. This will be:

= 250 × 3 × 3 × 3

= 6750

This was because the dimensions were tripled

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From the diagram, we can see that CL bisects angle JCN. This means that CL divides the angle JCN into 2 equal halves. It means that

angle JCN = angle JCL + angle LCN

Given that angle JCN = 8r - 2 and angle LCN = 3r + 15, it means that

8r - 2 = angle JCL + 3r + 15

Since angle JCL = angle LCN, then

8r - 2 = 3r + 15 + 3r + 15

8r - 2 = 6r + 30

8r - 6r = 30 + 2

2r = 32

r = 32/2

r = 16

angle JCL = 3r + 15 = 3 * 16 + 15

angle JCL = 48 + 15

angle JCL = 63 degrees

Given,

Total money needed = 225

Money already Marie has = 85

Marie per day Income = 20

Let it take x days for Marie to have enough money to buy the prom dress.

We can say:

Total Money = Money Marie already has + per day income

Using the given information, we can craft an inequality shown below:

This means "85 already have plus 20 per day will need to be atleast 225".

Now, we can do algebra and solve for x. Steps are shown below:

Thus, Marie needs 7 days more to have enough money to buy the prom dress.

The general equation of line with passing points (a, b) and slope m is :

y = m(x - a) + b

In the given question :

A line goes through the point (2,1)

Passing point (a, b) = (2, 1)

a slope of 2

Slope : m = 2

Substitute these value in the general equation of line :

y = m( x - a ) + b

y = 2 ( x - 2) + 1

y = 2x - 4 + 1

y = 2x - 3

y = 2x - 3

A)

To plot on the graph :

We have one coordinate ( 2, 1)

Find one more coordinate

Substitute x = 1 in the equation os line :

y = 2x - 3

y = 2(1) - 3

y = ( - 1 )

So, (x, y) = ( 1, -1)

Plot the coordinates ( 2, 1) & ( 1, - 1)

y- intercept is the point on the line where x = o

Substitute x = 0 in the given equation of line :

y = 2x - 3

y = 2( 0 ) - 3

y = ( -3 )

Y -intercept : y = ( -3) , (x, y) = ( 0, -3)

In the graph y -intercept is :

The purple point in the graph represent the y -intercept.

B)

The general form of the equation of line in the form of slope intercept form :

y = mx + b

The equation of line y = 2x - 3

On compare with the general equation of slope intercept form we have : m - 2, b = (-3)

So, equation of line in the slope intercept form is : y = 2x - 3

y = 2x - 3

Answer : A) ( x, y) = (0, -3)

B) y = 2x - 3

The measure of angle c is 72.15.

What is angle sum property for a triangle?

Angle sum property of triangle states that The measure of all interior angles of a triangle is [tex]180^{o}[/tex] that is sum of all 3 interior angle is 180

We are given a Δ[tex]ABC[/tex]

Measure of interior angles of ABC is 180.

Hence the equation can be given as,

∠A+∠B+∠C=180

48.36+59.49+∠C=180

107.85+∠C=180

∠C=72.15

Hence the measure of ∠C is 72.15

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Answer:72.15

Step-by-step explanation:

Gigi, this is the solution to the problem:

This is the information provided to us:

Plan A : $ 6 per month + $ 2 per movie wathced

Plan B : $ 16 per month + $ 1 per movie watched

Step 1: Let's calculate the number of movies that would make the two plans to have an equal monthly payment, as follows:

Let x to represent the number of movies watched by Jonathan

Plan A = Plan B

6 + 2x = 16 + 1x

Like terms:

2x - x = 16 - 6

x = 10

If Jonathan watches 10 movies per month the two plans will have an equal monthly cost

Step 2: Let's graph the functions that represent each plan, this way:

Solution

Step-by-step explanation:

we have:

Part 1) Find the x-intercepts of the parabola and write them as ordered pairs

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

For x=4 and x=-2 the equation is equal to zero

therefore

The x-intercepts are the points (-2,0) and (4,0)

Part 2) Write the equation y=(x-4)(x+2) in standard form

The quadratic equation in standard form is equal to

applying distributive property

where a = 1, b = -2, c = -8

Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex

we know that

the x-value of the vertex is -b/2a

we have

where a = 1, b = -2, c = -8

substitute

x = -b/2a = -2/2(1) = 1

therefore

The x-coordinate of the vertex is 1

Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.

we have

For x=1

substitute and solve for y

therefore

The y-coordinate of the vertex is -9

The coordinate of the vertex is the point (1,-9)

Answer:  (10,5) or (14,3) are two possible answers.

Infinitely many answers are possible. Pick one to write as the final answer to your teacher.

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

Explanation:

Focus on the points B(1,4) and C(5,2)

More specifically, focus on the x coordinates 1 and 5. To go from B to C, we move to the right 4 units since 1+4 = 5

We also move down 2 units since we go from y = 4 to y = 2

In short, the translation motion is "right 4, down 2". We can further abbreviate this into the vector notation <4, -2>. This translation vector only applies going from B to C.

The vector notation <4,-2> is the same as writing [tex](x,y) \to (x+4,y-2)[/tex] but the first method is much faster to write out since it avoids needing to write x or y.

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

Now if we want to construct a similar triangle A'B'C', we will use that vector to scale it up or down. Let's scale it up and double each coordinate.

<4, -2> doubles to <8,-4>

So instead of "right 4, down 2" we now follow the path "right 8, down 4". Take notice how both motions involve the same slope.

Start at B'(2,9) and move right 8 and down 4 to arrive at C'(10,5)

See figure 1 below.

This is one possible answer out of infinitely many. This is because we can change the scale factor to any nonnegative real number we want.

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

Another example:

Instead of doubling the coordinates of the translation vector, let's triple them.

<4,-2> triples to <12,-6>

Then start at B'(2,9) and move right 12 and down 6 to arrive at C'(14,3) which is another possible answer out of infinitely many.

See figure 2 below.

Pick whichever of (10,5) or (14,3) is your favorite to get the final answer, assuming your teacher wants you to write one (x,y) location only. Or pick some other scale factor (other than 2 or 3) and follow the same idea to get some other possible location of point C'.

Answer:

C' = (10, 5)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.

Step-by-step explanation:

If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.

Therefore, to maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.

Given vertices of triangle ABC:

Given vertex of triangle A'B'C':

If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8).  If the triangle is then translated 1 unit up, B' = (2, 9), which matches the given coordinate of point B'.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x, 2y + 1)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5), 2(2) + 1) = (10, 5)

Answer:

7,680 beetles

Explanation:

The function that gives the beetle population after x weeks is given below:

To determine the beetle population after 56 days, first convert 56 days to weeks.

Thus, the beetle population will be:

There will be 7,680 beetles after 56 days.