Use the figure shown. Find the slope of the line.
у
4
3
C(-2,2)
B(-4, 2)
2
1
A(-2, 1)
-7-6-5-4-3-2
OY
X
The slope is

Answer:

m<PQT= 94°

Step-by-step explanation:

If line QS bisect <PQR

m<PQS = m < SQR

7x-6= 4x+15

7x-4x= 15+6

3x= 21

X= 21/3

X= 7

m<PQS= 7x-6

m<PQS= 7(7)-6

m<PQS= 49-6

m<PQS= 43°

m<PQS= m<SQR

<mSQR=43°

m<PQR= m<PQS + m < SQR

m<PQR=43+43

m<PQR= 86°

BUT

m<PQR= m<TQW

m<PQT= m<RQW

m<PQR+m<TQW +m<PQT+ m<RQW

= 360°

Let m<TQW= x

86+86+x+x= 360

2x+172= 360

2x= 188

X= 94°

m<PQT= 94°

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.

Answer:

Step-by-step explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

  U = {1, 2, 3, 4, 5, 10, 11, 12}

  A' = U - A = {10, 11, 12}

  A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.

Answer:

Mean is obtained by adding of all of the term values by the number of terms in a given set of data. Mean is also called "average".

Median on the other hand is the arrangement of numerical data in chronological order from least to greatest and finding the middle number from that arranged set of data.

Answer:

D) 84cm

Step-by-step explanation:

Square area = √(441cm²) = 21 cm

perimeter = 4*21 = 84 cm

Given that

To Find

Formula

Solution

→ Volume = πr²h

Using π as 3.14

→ 3.14 × 10 × 10 × 20 = Volume

→ 314 × 20 = Volume

→ 6280 inches² is the holding capacity of the container.

Answer:

6280

Step-by-step explanation:

this is correct on khan academy

Answer:

(a) (f o g)(x) =  x^2 - 15x + 54

(b) (g o f)(x) = x^2 + 3x - 9

(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d) (g o g)(x) = x - 18

Step-by-step explanation:

f(x) = x^2 + 3x

g(x) = x - 9

(a)

(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)

(f o g)(x) = x^2 - 18x + 81 + 3x - 27

(f o g)(x) = x^2 - 15x + 54

(b)

(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9

(c)

(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)

(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x

(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d)

(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18

Answer:

[tex]\Large \boxed{\mathrm{100\pi \ cm^2 }}[/tex]

Step-by-step explanation:

[tex]\displaystyle area \ of \ circle \ = \ \pi (\frac{diameter}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( \frac{20}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( 10 )^2[/tex]

[tex]\displaystyle A \ = \ 100\pi[/tex]

Answer:

Step-by-step explanation:

The question above means that how many numbers can divide 2003 with a remainder of 23

That means all the numbers are less than 2003

The number of numbers that have this property are only

Hope this helps you

Answer:

z=-3

Step-by-step explanation:

1:open the brackets.

2:take 21 to the other side to be subtracted by 42

3:you get a -z but you can take it to the other side to get a +z but -21 divide to get the answer

42=-7(z-3)

-7(z-3)=42

-7z+21=42

-7z=42-21

-7z=21

therefore,

z=21\-7

that is, -21\7=-3

Answer:

600 numbers

Step-by-step explanation:

For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.

However, 0 cannot be used as the first digit, because it would make a 5-digit number.

Therefore

there are 5 choices for the first digit (exclude 0)

there are 5 choices for the first digit (include 0)

there are 4 choices for the first digit

there are 3 choices for the first digit

there are 2 choices for the first digit

there are 1 choices for the first digit

for a total of 5*5*4*3*2*1 = 600 numbers

Answer:

x=150°

Step-by-step explanation:

Using the vertical angle theorem, you can infer that AEC and DEB are in fact the same angle, 20°, and the same goes for FED and CEG, both 130°.

So, x spans AEC and CEG so is 20° + 130° = 150°

Answer:

X = 14,700

Step-by-step explanation:

you can use a calculator to get the x.

X=3816371/(27×63)

Answer:

50%

Step-by-step explanation:

its 50% it will land on head and 50% it will land on tails since there is only two sides on a coin

Answer:

1/2 or .5

p(1/2)

Step-by-step explanation:

its simple, there are 2 sides to a coin, so there are 2 possible outcomes. and the question asks what is the probability of the coin landing on one or in other wrds, its asking what is te probilitity of one of the two heads to be up. SO the probility is 1/2

Answer:

[tex]-5\sqrt{7}[/tex]

Step-by-step explanation:

2√28 - 3√63

4√7 - 9√7

- 5√7

Answer:

- 5√7

Step-by-step explanation:

Answer:

m∠C = 102°

Step-by-step explanation:

This is is a cyclic quadrilateral

• The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral

• Note that m∠B is Opposite the exterior angle m∠CDA

Hence,

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

• m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

• Another external angle we need to find is m∠DAB

m∠DAB = m∠DA + m∠AB

We know that m∠DA = 84°, therefore,

m∠DAB = 84° + 120°

m∠DAB = 204°

• The final step is to solve for m∠C

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Answer:

B The graft of h is the graft of g vertically shifted up 3 units

Answer:

(3.5,4)

x coordinate =

[tex] \frac{5 + 2}{2} [/tex]

= 3.5

y coordinate =

[tex] \frac{ - 1 + 9}{2} [/tex]

= 4

midpoint = (3.5,4)

Answer:

(  3.5,4)

Step-by-step explanation:

To find the midpoint

Add the x coordinates together and divide by 2

(5+2)/2 = 7/2 = 3.5

Add the y coordinates together and divide by 2

(9+-1)/2 = 8/2 = 4

( 3.5,4)

Answer:

Every choice is not equivalent to 4✖️38.

Step-by-step explanation:

4✖️38=152

A. 54✖️4=216

B. 12✖️18=216

C. 72✖️3=216

D. 12✖️72=864

Every choice is not equivalent to 4✖️38.

Answer: Vertically shifting it by 3

The transformation of a function is horizontally shrink by a factor of 3 .

Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.

How do you horizontally shrink  by a factor of 3 ?

Learn more about Transformation on :

brainly.com/question/10644134

#SPJ2

Answer:

A

Step-by-step explanation:

First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:

[tex]\tan(x)=opp/adj[/tex]

The opposite side is 20 while the adjacent side is 14.

Plug in the numbers. Use a calculator:

[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]

Edits: Improved Answer. Removed Wrong Answer.

Answer:

55

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan x = 20/14

Taking the inverse tan of each side

tan ^-1 tan x = tan ^ -1 (20/14)

x =55.0079798

To the nearest degree

x = 55

Question 1:

Price per milliliter

Small $4.50 / 250ml

Medium $9.95 / 500 ml

Large $16.95 / 1000 ml

Question 2:

$9.95 / 500 ml > $4.50 / 250ml > $16.95 / 1000 ml

Question 3 - 4:

$4.50 / 250ml = ($4.50 * 6) / (250ml * 6 ) = $27 / 1500ml = 0.018

$9.95 / 500 ml = ($9.95 * 3) / (500 ml * 3) = $29.85 / 1500ml = 0.019

$16.95 / 1000 ml = ($16.95 * 3) / (1000 ml * 3) = $50.85 / 1500ml = 0.0339

( Use the first one for question 3 and the second for question 4)

$4.50 / 250ml would be the cheapest way to get 1500ml.

$9.95 / 500ml would be the most expensive way to get 1500ml.

I hope this helps you! Tell me if I'm wrong!

Hello, because of the geometric sequence we can say that:

[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]

So there is no real root, so the function does not cut the x axis.

Thank you

For the given quadratic function, the x-axis is not cut by the function because there is no true root.

To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.

As per provided data in question,

α = b/a = c/b

c/a = (c × b)/(a × b) = (c/b) (b/a) = α²

For the equation,

ax² + bx + c = 0

x² + b/a(x) + c/a = 0

⇒ x² + ax + α² =0

Δ = b² - 4 ac = α² - 4α²

Δ = -3α² < 0, which means that no real root is there.

To know more about quadratic functions:

https://brainly.com/question/27958964

#SPJ2

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

Answer:

[tex]\huge \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]

Distribute negative sign.

[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]

Combine like terms.

[tex]0xe^2 +0x-1[/tex]

[tex]0-1=-1[/tex]

C, because we multiply the exponents to get the answer.

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex](a^{m}b^{n}) ^{p}[/tex] = [tex]a^{mp}[/tex] × [tex]a^{np}[/tex]

Thus

[tex](7^{2}5^{6})^4[/tex]

= [tex]7^{2.4}[/tex] × [tex]5^{6.4}[/tex]

= [tex]7^{8}[/tex] × [tex]5^{24}[/tex] → C

Hello, please consider the following.

[tex]x^2 + 10x + 25 = 8\\\\\text{\bf We can notice that } x^2+10x+25=(x+5)^2 \text{ so}\\\\x^2 + 10x + 25 = (x+5)^2=8\\\\\text{\bf We take the root.}\\\\x+5=\pm\sqrt{8}\\\\\text{\bf We subtract 5}\\\\\boxed{x=-5-\sqrt{8}} \ \ or \ \ x=-5+\sqrt{8}[/tex]

In the box, you can find the smallest solution.

Thank you.

Answer:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b) x = 24

(c) y = 17; z = 51

Step-by-step explanation:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b)

15/45 = 8/x

1/3 = 8/x

x = 3 * 8

x = 24

(c)

a^2 + b^2 = c^2

x^2 + 45^2 = z^2

24^2 + 45^2 = z^2

576 + 2025 = z^2

z^2 = 2601

z = 51

15/45 = y/z

1/3 = y/51

3y = 51

y = 17

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Answer:

r = 1

Step-by-step explanation:

2πr = x

πr² = y

x = 2y

2πr = 2πr²

r = 1