ABCD is a square. Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark. What is the measure of angle BAC? 30° 45° 60° 90

Answer:

a) [tex]a_n=3\,n-11[/tex]

b) [tex]a_{20}=49[/tex]

c) term number 17 is the one that gives a value of 40

Step-by-step explanation:

a)

The sequence seems to be arithmetic, and with common difference d = 3.

Notice that when you add 3 units to the first term (-80, you get :

-8 + 3 = -5

and then -5 + 3 = -2 which is the third term.

Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:

[tex]a_n=a_1+(n-1)\,d[/tex]

That in our case would give:

[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]

b)

Therefore, the term number 20 can be calculated from it:

[tex]a_{20}=3\,(20)-11=60-11=49[/tex]

c) in order to find which term renders 20, we use the general form we found in step a):

[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]

so term number 17 is the one that renders a value of 40

Answer:

a) 0

b) 1

c) 0

Step-by-step explanation:

These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.

Answer:

  0.20, 0.36 seconds

Step-by-step explanation:

We have already seen that the equation for y(t) can be written as ...

  y(t) = √29·sin(4πt +arctan(5/2))

The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...

  4πt +arctan(5/2) = 7π/6 or 11π/6

  t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds

and

  t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds

The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.

Answer:

h=3√3 cm

Step-by-step explanation:

An equilateral triangle has 3 Equal sides

The height of an equilateral triangle with side a =a√3/2

That is,

h=a√3/2

Where,

h=height of the equilateral triangle

a=side length

From the triangle given,

a=6cm

Therefore,

h=6√3/2

=3√3

h=3√3 cm

Answer:

40

Step-by-step explanation:

We know there are 16 oz in a pound

We can use ratios

15             x

-----  = ----------

6 oz       16 oz

Using cross products

15 * 16 = 6x

240 = 6x

divide by 6

240/6 = 6x/6

40 =x

Answer:

x = [ -b +- sqr root (b^2 - 4ac)] / 2a

a = 1

b = -5

c = -2

x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1

x = [5 +- sqr root (25 + 8)] / 2

x1 =  5.3723

x2 =-0.37228

Step-by-step explanation:

Exact solution for the give quadratic equation are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

Quadratic equation of the form [tex]ax^2+bx+c=0[/tex]

For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .

Quadratic formula

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Given equation is [tex]x^2-5x-2=0[/tex]

The value of a=1, b= -5  and c=-2

Substitute all the values in the formula.

To find out exact solutions , we need to simplify the final answer.

Exact solutions are without any decimals.

[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]

Exact solutions are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

Learn more information about 'Quadratic formula ' here

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Answer:

2<F(x)<5

Step-by-step explanation:

We can guess that it come between 2 and 5 given the pattern that we see in the table, but there’s no reason we can’t solve it to be sure.

F(x)=3 (Times the square root of 1.5-1)+2

3(square root of .5)+2

3(0.7)+2

2.12+2

4.12

So, yes, it is between 2 and 5

2<F(x)<5

Answer:

3 degrees F

Step-by-step explanation:

if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.

i hope this helped?

Answer:

D) Van: 7, Bus: 20

Step-by-step explanation:

Add the amount of students together (455 students in total)

Then I added the amount of buses and vans together (5 Vans and 21 Buses)

Then I plugged in each answer

5 x 7 = 35

455 - 35 = 420

420 / 21 = 20

Answer:

[tex]p = \frac{1}{2}[/tex]

[tex]q = 5[/tex]

[tex]h^{-1}(h(3)) = 3[/tex]

Step-by-step explanation:

Given

[tex]h(x) = px - \frac{5}{2}[/tex]

[tex]h^{-1}(x) = q + 2x[/tex]

Solving for p and q

Replace h(x) with y in [tex]h(x) = px - \frac{5}{2}[/tex]

[tex]y = px - \frac{5}{2}[/tex]

Swap the position of y and d

[tex]x = py - \frac{5}{2}[/tex]

Make y the subject of formula

[tex]py = x + \frac{5}{2}[/tex]

Divide through by p

[tex]y = \frac{x}{p} + \frac{5}{2p}[/tex]

Now, we've solved for the inverse of h(x);

Replace y with [tex]h^{-1}(x)[/tex]

[tex]h^{-1}(x) = \frac{x}{p} + \frac{5}{2p}[/tex]

Compare this with [tex]h^{-1}(x) = q + 2x[/tex]

We have that

[tex]\frac{x}{p} + \frac{5}{2p} = q + 2x[/tex]

By direct comparison

[tex]\frac{x}{p} = 2x[/tex] --- Equation 1

[tex]\frac{5}{2p} = q[/tex]  --- Equation 2

Solving equation 1

[tex]\frac{x}{p} = 2x[/tex]

Divide both sides by x

[tex]\frac{1}{p} = 2[/tex]

Take inverse of both sides

[tex]p = \frac{1}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex] in equation 2

[tex]\frac{5}{2 * \frac{1}{2}} = q[/tex]

[tex]\frac{5}{1} = q[/tex]

[tex]5 = q[/tex]

[tex]q = 5[/tex]

Hence, the values of p and q are:[tex]p = \frac{1}{2}[/tex];  [tex]q = 5[/tex]

Solving for [tex]h^{-1}(h(3))[/tex]

First, we'll solve for h(3) using [tex]h(x) = px - \frac{5}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex];  and [tex]x = 3[/tex]

[tex]h(3) = \frac{1}{2} * 3 - \frac{5}{2}[/tex]  

[tex]h(3) = \frac{3}{2} - \frac{5}{2}[/tex]

[tex]h(3) = \frac{3 - 5}{2}[/tex]

[tex]h(3) = \frac{-2}{2}[/tex]

[tex]h(3) = -1[/tex]

So; [tex]h^{-1}(h(3))[/tex] becomes

[tex]h^{-1}(-1)[/tex]

Solving for [tex]h^{-1}(-1)[/tex] using [tex]h^{-1}(x) = q + 2x[/tex]

Substitute [tex]q = 5[/tex] and [tex]x = -1[/tex]

[tex]h^{-1}(x) = q + 2x[/tex] becomes

[tex]h^{-1}(-1) = 5 + 2 * -1[/tex]

[tex]h^{-1}(-1) = 5 - 2[/tex]

[tex]h^{-1}(-1) = 3[/tex]

Hence;

[tex]h^{-1}(h(3)) = 3[/tex]

Answer:

7x-1

Step-by-step explanation:

i did the test

Answer:

7x-1

Step-by-step explanation:

correct answer on edge

Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.  

Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g

Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:

She has 158 dollars.

Step-by-step explanation:

This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.

Thus, Taylor has 158  dollars left now.

Answer:

The carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100

Step-by-step explanation:

Let x be the no. of dining chairs and y be the no. of rocking chair

Time taken by carpenter to make 1 dining chair = 1 hour

Time taken by carpenter to make x dining chairs = x hours

Time taken by carpenter to make 1 rocking chair = 2 hour

Time taken by carpenter to make y rocking chairs = 2y hours

He only has 40 hours available to work on the chairs.

[tex]\Rightarrow x+2y \leq 40[/tex]

He has enough wood to make 30 chairs.

[tex]\Rightarrow x+y\leq30[/tex]

He makes $60 profit on a dining chair and $90 profit on a rocking chair.

So, profit =60x+90y

Plot the equations on graph

Refer the attached figure

Coordinates of feasible region

(0,20),(20,10) and (30,0)

Profit =60x+90y

At(0,20)

Profit = 1800

At(20,10)

Profit = 1200+900=2100

At(30,0)

Profit=900

So,the carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100

Answer:

see file attached

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).

Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80                              .                  .                 .    1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68               .                 .                  .        2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

0.65x + 0.65y = 52            .                  .               .        3)

Subtract equation 3 from 2 and solve for y:

0.25y = 16

y = 16/0.25 = 64

y = 64 pints

Put y = 64 in equation 1:

x + 64 = 80

x = 80 - 64 = 16

x = 16 pints

Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.

Answer:

B

Step-by-step explanation:

Because this equation is just a normal greater than symbol, it has to be a dotted line.

This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)

Than you shade the region with the larger number vaules, since it is greater than.

Answer:

A. AB

Step-by-step explanation:

Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.

What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.

m < A = 59°

m < C = 57°

m < C = 180 - (59+57) (sum of angles in a triangle)

m < C = 64°

The smallest angle out of the three angles is angle C = 57°.

The side opposite it, is side AB.

Side AB is the shortest side of ∆ABC.

Therefore, AB should be parallel to the ground.

The

side

of the musical instrument that should be parallel to the ground if the

dimensions

are as given is side AB, which is option A.

Given that:

Jordon will play a

triangle

in his school’s music program.

When playing, the shortest side

is hanging down,

parallel

to the ground.

From the figure:

m∠A = 59°

m∠C = 57°

By the

angle sum

property,

m∠A + m∠B + m∠C = 180°

59° + m∠B + 57° = 180°

m∠B + 116° = 180°

m∠B = 180° - 116°

        = 64°

The

shortest side

will be the side that is opposite to the smallest angle.

So, the smallest side is the side opposite to C.

So, the side is AB.

Hence, the side is AB, which is option A.

Learn more about

Triangles

here :

https://brainly.com/question/2773823

#SPJ6

Approximate what the value of [tex]7/15[/tex] is by using calculator.

[tex]7/15\approx0.47[/tex].

And now just multiply by 100 to get percentage.

[tex]100\cdot0.47=\boxed{47\%}[/tex].

Hope this helps.

Answer:

24%

Step-by-step explanation:

7\15 x 100

simplify and get=140\3

dived140\3=48\2

simplify 48\2=24%

Answer:

39 units²

Step-by-step explanation:

The figure is composed of a rectangle VEDR and Δ RMV

Area of rectangle = VE × ED = 5 × 6 = 30 units²

Area of Δ = 0.5 × RV × perpendicular from M to RV

                = 0.5 × 6 × 3 = 9 units²

Thus

Area of polygon = 30 + 9 = 39 units²

Answer: 40%.

Step-by-step explanation:

From the table : Total Seniors = 2+3= 5

Number of male seniors = 2

If a student is selected at random find the probability the student is a male given that it's a senior:

P(Male | senior)[tex]=\dfrac{\text{Number of male seniors}}{\text{Total seniors}}[/tex]

[tex]=\dfrac{2}{5}[/tex]

In percent, [tex]\dfrac{2}{5}\times100=40\%[/tex]

Hence, the probability the student is a male given that it's a senior.  =40%.

The probability of the student is a male senior is 7%.

Given, here from the 2- way table the total no. students will be 30.

We have to find out the probability of the student select at random, student is a  senior male .

We know that, the probability of an event E, will be

[tex]P(E)=\dfrac{No.\ of \ favaurable\ outcomes}{Total\ outcomes}[/tex]

Now,

[tex]P( Senior\ male)= \dfrac{2}{30} \\\\P( Senior\ male)=0.06\\[/tex]

Representing it in percentage as,

[tex]P( Senior\ male)=0.06666\times100\%\\P( Senior\ male=6.66\%[/tex]

Hence the nearest whole percent will be 7%.

Thus probability of the student is a male senior is 7%.

For more details on probability follow the link:

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Answer:

The table D represents the function that will have the greatest y-values for very large values of x.

Step-by-step explanation:

The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.

The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.

The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.

The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.

Answer:

D

Step-by-step explanation:

BIGBRAIN

Answer:

see below

Step-by-step explanation:

We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.

f(x) = x² + 3x - 2

= (x² + 3x + 9/4) - 9/4 - 2

= (x + 1.5)² - 4.25

The vertex is (-1.5, -4.25).

Answer:

(a) 56 ways

(b) 6 ways

(c) 56 ways

Step-by-step explanation:

Given:

candidates: 6 mail, 1 female

number to hire : 3

a) In how many different ways can choose new employees?

use the combination formula to choose r to hire out of n candidates

C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways

b) In how many different ways can choose a single male candidate?

6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways

c) In how many different ways can choose at least one male candidate?

To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.

Since there are only two females, there is no way to choose 3 female candidates.

In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.

Answer:

T1he values for x and y of the equations is y = 11, and x = -19/5.

Step-by-step explanation:

To solve this question, we need to rearrange the expression:

5x+4y=25 - (5x+2y=3)

Look, if we subtract one equation to the other, then:

5x+4y=25 [1]

-(5x+2y=3) [2]

Which is the same as:

5x+4y=25

-5x-2y=-3

Subtract them:

5x+4y=25

-5x-2y=-3

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

      2y =22

y = 22/2 = 11

Then, y = 11.

To find x, we can substitute y in either equation [1] or [2].

Let us use [1]

5x+4y=25

5x+4(11)=25

5x+44=25

5x=25-44

5x=-19

x = -19/5

Then, the values for x and y of the equations is y = 11, and x = -19/5.

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Step-by-step explanation:

The strategy is to translate B to E then reflect about the x-axis (y=0)

From B to E, the process is

(x,y) -> (x-4, y-1)

Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Answer:

Step-by-step explanation:

Please check ones more because this might be incorrect.

The area is in square meters...Let's change it

Square 48= 48*48 =2304

2304 divided by 4( 4 since the formula for the area of a sqaure is s*s and square has 4 sides)

2304 divided by 4 = 576

The formula for area of a square is S*S(side times side)

Let's apply the formula here.

so, 576 times 576

331776 square meters

Hope this is right and helps! :)

( This just my point of view. Please check this onces again)

Answer:

the answer is 64

Step-by-step explanation:

khan

Answer:

[tex]f(x) =\sqrt[3]{x}[/tex]

Step-by-step explanation:

Hello!

Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:

[tex]g(x) = \sqrt[3]{x-5}+7[/tex]

To have the the parent function, we must find the parent one, let's call it by f(x).

[tex]f(x) =\sqrt[3]{x}[/tex]

This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.

Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.

Answer:

5 units to the right and 7 units up (B on edge)

Step-by-step explanation: