The bisector of the base angles Q and R of an equilateral triangle PQR meet at S. ST and SM are drawn parallel to the sides PQ and PR. Show that QT=TM=MR

Answer & Step-by-step explanation:

[tex]\frac{-t-5}{3}=\frac{t-3}{5}[/tex]

Cross multiply.

[tex]-5t-25=3t-9[/tex]

Subtract -3 on both sides.

[tex]-8t-25=-9[/tex]

Add 25 on both sides.

[tex]-8t=16[/tex]

Divide -8 on both sides.

[tex]t=-2[/tex]

Answer:

Similarity:

In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).

Difference:

The difference between the sine and the cosine graph is the point where they start.

The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.

The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.

Answer:

Step-by-step explanation:

You have to make a table. Do this by taking each of the x values you see there and plug in for x into the equation and solve for y. Then plot the points.

x| -1  |  -2  |   -3   |   -4   |   -5   |

y|                                            

We will plug each x value in, do the math, and come up with y. The first x value is -1:

[tex]y=(-1)^2+6(-1)+10[/tex].  Do the math on that and you should get that y = 5. So one coordinate on this graph is (-1, 5).

At x = -2:

[tex]y=(-2)^2+6(-2)+10[/tex]. Do the math on that and you should get that y = 2. Another coordinate on this graph is (-2, 2).

At x = -3:

[tex]y=(-3)^2+6(-3)+10[/tex]. Do the math on that and you should get that y = 1. A third coordinate on this graph is (-3, 1).

At x = -4:

[tex]y=(-4)^2+6(-4)+10[/tex]. Do the math on that and you should get that y = 2. A fourth coordinate on this graph is (-4, 2).

At x = -5:

[tex]y=(-5)^2+6(-5)+10[/tex]. Do the math on that and you should get that y = 5. A fifth point on that graph is (-5, 5).

Plot all those points and connect the dots. This is a parabola-shaped graph because your equation is a second degree (quadratic).

Answer:

$2388.95

Step-by-step explanation:

The worth of a compound deposit after a period of n years is calculated using the formula:

[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]

[tex]A(2)=2250(1+\frac{0.03}{12})^{12 \times 2}\\\\=2250(1+0.0025)^{24}\\=2250(1.0025)^{24}\\=\$2388.95[/tex]

At maturity, the deposit will be worth $2388.95.

Answer:

-5

Step-by-step explanation:

the slope is -5

Answer:

-5

Step-by-step explanation:

The slope formula used is y=mx+b where m is the slope and b is the y-intercept.

In this case, -2/3 is the y-intercept and -5 is the slope.

Answer:

first tower needs 4

second needs 3

third needs 2

and the fourth needs 1

Total needed triangles for all is 10

Step-by-step explanation:

Answer:

[tex]\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{(\frac{5}{4})^7 }[/tex]

Apply rule : [tex]\sqrt{a} =a^{\frac{1}{2} }[/tex]

[tex]((\frac{5}{4})^7 )^{\frac{1}{2} }[/tex]

Apply rule : [tex](a^b)^c=a^{bc}[/tex]

[tex](\frac{5}{4} )^{7 \times \frac{1}{2} }[/tex]

[tex](\frac{5}{4} )^{\frac{7}{2}[/tex]

Answer:

=

Step-by-step explanation:

1.42 is equal to 1.420. The 0 adds no value since it is after the decimal point so 1.420 is just 1.42, which is equal to itself, 1.42.

Answer:

=

Step-by-step explanation:

When you are looking at decimals, specifically on the right side of the decimal point, the amount of 0's after the last given non-0 digit can be disregarded.

1.420 is the same as 1.42

With this given information:

1.42 ____ 1.420

1.42 ____ 1.42

1.42 = 1.42

= would be your sign.

~

Answer:

$648.00

Step-by-step explanation:

==>Given:

Squared living room of 9m by 9m

Cost of purple carpet per m² = $8.00

==>Required:

Cost of buying carpet to cover the squared living room

==>Solution:

Find the area of the room:

Area of squared room = 9m × 9m = 81m²

Find cost of purple carpet that would cover 81m²:

Let x be the cost of carpet required to cover the room.

Thus,

1m² = $8.00

81m² = x

cross multiply

1*x = 8.00*81

x = 648

Cost of purple carpet to cover the living room = x = $648.00

Answer:

(B)The GCF of the numbers(28 and 36) in each term in the expression is 4.

(C)The GCF of the variables(a and ab) in each term in the expression is a.

(E)The factored form of the expression is 4a(7+9b)

Step-by-step explanation:

Given the expression: [tex]28a+36ab[/tex]

If we write it as a product, we obtain:

[tex]28a+36ab=4a(7+9b)[/tex]

We can see the following

The correct options are B, C, and E.

Answer:

b c e

Step-by-step explanation:

hope dis helps baes

Answer:

parallelogram

Step-by-step explanation:

Answer:

parallelogram

Step-by-step explanation:

did the test

Answer: perpendicular

Answer:

perpendicular

Step-by-step explanation:

If two lines meet at a right angle they are said to be perpendicular to each other.

Two lines are perpendicular when they intersect at a right angle.

Answer:

7:45

Step-by-step explanation:

2 hours and 15 minutes can also be written as

2:15

if the movie takes 2:15 long and begins at 5:30, add both which is. 5:30+2:15

=7:45

therefore the movie ended at 7 hours and 30 minutes which can also be written as7:45

Answer:

36

Step-by-step explanation:

x+5=y x - Sue age and y - Bill age

x+y=67

---------

x+x+5=67

2x=62

x=31 - Sue age

---------

y=31+5

y=36 - Bill age

Answer:

Bill is 36 years old

Step-by-step explanation:

Let Bill's age be "B" and Sue's age be "S"

Given that Bill is 5 years older than Sue, we can reason that the difference between Bill's and Sue's age must be 5 years, or:

B - S = 5     -----(eq 1)

We are also given that the sum of their ages is 67, or:

B + S = 67 -----(eq 2)

We can solve this system of equations via elimination (by adding the two equations).

(eq 1 ) + (eq2)

(B - S) + (B + S) = 5 + 67

2B = 72

B = 72/2

B = 36 years old

Answer:

No, because one x-value corresponds to two different y-values.

Step-by-step explanation:

Given a function where x represents an input of a particular value, which gives an output for that particular value inputted as defined by the function, if the function is true and valid, a particular value of input should not give us different values of output.

Thus, from the table given, at x = 5, we have y = 3.

Also, at x = 5, we have y = 2.

Here, one x-value is given us two different y-values. This is not true if a function. We cannot regard the table given as representing a function.

Therefore, the answer is:

No, because one x-value corresponds to two different y-values.

Answer:

it is a function because it doesn't have two x coordinates at the same y coordinate.

Answer:

-$0.67

Step-by-step explanation:

If you buy one ticket, the possible outcomes are:

100% chance of spending $1 (buying the ticket)

1 in 5,000 chance of winning $500

3 in 5,000 chance of winning $300

5 in 5,000 chance of winning $30

20 in 5,000 chance of winning $5.

The expected value of the raffle is determined by:

[tex]E(X)=-1+\frac{1}{5,000}*500+\frac{3}{5,000}*300+\frac{5}{5,000}*30+\frac{20}{5,000}*5\\E(X)=-\$0.67[/tex]

The expected value of this raffle if you buy 1 ticket is -$0.67.

Answer:

solution,

<3+<4=180°( linear pair)----> equation (i)

<4+<5=180°( linear pair)------>equation (ii)

From equation (i) and (ii)

<3+<4=<4+<5

<3=<5 (vertically opposite angles)

hope this helps...

Good luck on your assignment

Answer:

the answer is line RQ and line OP

Answer:

c

Step-by-step explanation:

Answer:the answer is 90

Step-by-step explanation:

Answer:

Children = 200

Adults = 190

Step-by-step explanation:

Children = x

Adults = y

x + y = 390

x = 390 - y..............(1)

20x + 35y = 10650

Substituting

20(390-y) + 35y = 10650

y = 190

x = 390 - 190 = 200

Answer:

Step-by-step explanation:

Number of children = c

Number of adults = a

Total people = 390

a + c = 390 ------------------ (I)

Admission fee for 'c' children = 20 * c = 20c

Admission fee for 'a' adult = 35 * a = 35a

Total amount = $ 10650

35a + 20c = 10650 -------------(II)

Multiply equation (I) by (-20)

(I)*(-20)  -20a - 20c = - 7800

(II)           35a + 20c = 10650    { Now add and so 'c' will be eliminated}

              15a            = 2850

a = 2850/15

a =  190

Plug in a = 190 in equation (I)

190 + c = 390

          c =  390 - 190

c = 200

Number of children = 200

Number of adults = 190

Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

Answer:

Step-by-step explanation:

Given that:

First Option (Leasing)

250x - y + 4000 = 0

Expressing the equation in the Slope-Intercept Form y=mx+b, we have:

y=250x+4000

Second Option (Financing)

$400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400).

First, we determine the slope of the line joining (0,400) and (10,4400)

[tex]Slope, m= \dfrac{4400-400}{10-0}= \dfrac{4000}{10}=400[/tex]

We have:

y=400x+b

When y=400, x=0

400=400(0)+b

b=400

Therefore, the Slope-Intercept Form of the second option is:

y=400x+400

Significance

Part B

We notice from the graph that after 24 months, the cost for leasing and financing becomes the same ($10,000). Therefore, a consumer will be better off financing since the downpayment for leasing is higher.

i.e

Answer:

[tex] \frac{3a}{a-2} [/tex]

Step-by-step explanation:

[tex] \frac{2a - 7}{a}*\frac{3a^2}{2a^2 - 11a + 14} [/tex]

Factorise [tex] 2a^2 - 11a + 14} [/tex]

[tex]\frac{2a - 7}{a}*\frac{3a^2}{(2a - 7)(a - 2)}[/tex]

[tex] 2a - 7 [/tex] cancels  2a - 7

[tex] \frac{1}{a}*\frac{3a^2}{(1))(a - 2)} [/tex]

[tex] \frac{1(3a^2)}{a(a-2)} [/tex]

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

"a" cancels "a"

[tex] \frac{3a}{a-2} [/tex]

Thus,

[tex] \frac{2a - 7}{a}*\frac{3a^2}{2a^2 - 11a + 14} [/tex] = [tex] \frac{3a}{a-2} [/tex]

Answer:

Step-by-step explanation:

diameter = 18 inches

radius = r = 18/2 = 9 in

Volume of cylinder = 405π/2

[tex]\pi r^{2}h = \frac{405}{2}\pi \\\\\\\pi * 9 * 9* h =\frac{405}{2}\pi \\\\\\h =\frac{405}{2*9*9*\pi }*\pi \\\\\\h=\frac{5}{2}[/tex]

h = 2.5 inches

Answer:

Slope  = -3

Step-by-step explanation:

(3 , 5)   ; (4, 2)

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{2-5}{4-3}\\\\=\frac{-3}{1}\\\\=-3[/tex]

Answer:

T1=0

T2=2

T3=6

T4=12

T50=2450

59 is not a term in the sequence

Step-by-step explanation:

Tn=n(n-1)

182=n2 - n

0=n2 - n - 182

0=n2-14n+13n-182

0=n(n-14)+13(n-14)

0=(n-14) (n+13)

Since n cannot be negative n is not equal to -13

Therefore,

n=14

Answer: 11

Step-by-step explanation:

The stem is the 10s place and leaf is the ones

Answer:

Correct answer option A.

Step-by-step explanation:

We need to figure out the graph of

[tex]y= log_3(x + 2)[/tex]

First of all, let us discuss graph of:

[tex]y=log_3x[/tex]

[tex]y=log_31 = 0[/tex] ([tex]\because[/tex] log of 1 is always 0 irrespective of the base)

i.e. point (1, 0) lies on the graph.

i.e. [tex]x\rightarrow 1 \Rightarrow y\rightarrow -\infty[/tex]

[tex]y =log_33 = 1[/tex] i.e. point (3, 1)  lies on the graph

Graph of logarithmic function is always increasing.

Now, let us consider the graph of [tex]y= log_3(x + 2)[/tex]

Please refer to attached graph as well.

Correct answer option A.

The correct option is A, just got it right (: