4) What is the slope of the line joining (7, 8) and (17, 13)​

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Answer: [tex] \Rightarrow \sf{\frac{x+3}{x -2}}[/tex]

[tex] \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }[/tex]

[tex] \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}[/tex]

Answer:1017.36[tex]ml^{2}[/tex]

Step-by-step explanation:

Diameter= 36ml

radius=diameter/2

R=36 ÷2

R=18ml

Area=π[tex]r^{2}[/tex]

Area=3.14 x [tex]18^{2}[/tex]

Area=1017.36[tex]ml^{2}[/tex]

Answer:

Step-by-step explanation:

Your answer for TQS is 43.

89 - 46 = 43

Answer:

w= -6

w= 4

Step-by-step explanation:

w= -b sqrt(b^2-4ac)

2a

let

a=1

b=2

c= -24

substitute values~

[tex]==========================================[/tex]

In order to solve this equation for w, we need to factor it.

First, let's think of 2 numbers that multiply to -24 and add to 2.

These numbers are -4 and 6.

Check:

6×(-4)=-24 ✓

6+(-4)=6-4=2✓

Now, factor:

(     ) (    )

That's how it should look like:

(w+   )( w-   )

Now, instead of the blanks, plug in -4 & 6:

(w-4)(w+6)

Now, set each factor equal to 0:

w-4=0

w=4

w+6=0

w=-6

[tex]====================================[/tex]

Nickname:-

The factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.

It is given that the expression [tex]\rm x^2+10x+21[/tex]

It is required to find which expression is the factorization of the given expression, the options are:

a) (x + 3)(x + 7)

b) (x + 4)(x + 6)

c) (x + 6)(x + 15)

d) (x + 7)(x + 14)

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We have an expression:

[tex]\rm x^2+10x+21[/tex]

[tex]\rm x^2+7x+3x+21[/tex]  

Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is [tex]\rm 21x^2[/tex] and the addition is 10x.

[tex]\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)[/tex]or

[tex]\rm (x+3)(x+7)[/tex]

Thus, the factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.

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Answer:

The answer is D : y= −0.15x^2 + 2x + 5.5

Step-by-step explanation:

i got it right on my test

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Quadratic function is in the form y = ax² + bx + c; where a, b and c are constants.

From the table, at point (0, 5.5):

5.5 = a(0)² + b(0) + c          (1)

From the table, at point (1, 7.35):

7.35 = a(1)² + b(1) + c          (2)

From the table, at point (2, 8.9):

8.9 = a(2)² + b(2) + c          (3)

From 1, 2 and 3:

a= -0.15, b = 2, c = 5.5

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

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Answer:

A - 10 feet

D - 5 seconds

Step-by-step explanation:

Insert 12 for r the radius and 1500 for V the volume.

12 = [tex]\sqrt{}\frac{3(1500)}{\pi h}[/tex]

Square both sides

144 = [tex]\frac{4500}{\pi h}[/tex]

Solve 144 = [tex]\frac{4500}{\pi h}[/tex]: h = [tex]\frac{125}{4\pi }[/tex]

h = [tex]\frac{125}{4\pi }[/tex] or 9.9 rounded to the nearest foot,

h = 10

t = [tex]\sqrt\frac{2(200)}{16}[/tex]

t = [tex]\sqrt\frac{400}{16} = 25[/tex]

t = [tex]\sqrt{5^{2} }[/tex]

t = 5

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

The volume of a cylinder is the area of the circle times the hight of the cylinder.

Thus...

3.14*5^2*10=785

The reason it is 5 and not 10 is because it gives you the diameter in the word problem and the equation asks for the radius.

So you know that the radius is always half the diameter and half 10 which gives you 5.

Hope this helps!!!

Answer:

2 semi circles put together

Step-by-step explanation:

just cut the circle in half

Answer:

Step-by-step explanation:

Answer:

y= -x+6

Step-by-step explanation:

G1xG2= -1

G2= -1

-1 = (y-8)

-------

(x+2)

-1 (x+2)=y-8

-x-2=y-8

-y=x+2-8

y= -x+6

Answer:

Step-by-step explanation:

The area of the rhombus is half the product of its diagonals

[tex]area \: of \: rectangle \\= 4 \times area \: of \:identical \: triangle[/tex]

[tex]area \: of \: rectangle =\\ 4 \times area \: of \:identical \: triangle[/tex]

[tex]48 {in}^{2} = 4 \times \frac{1}{2} \times base \times height \\ 48 {in}^{2} = 2 \times base \times height \\ \frac{48}{2} = 8 \times height \\ \frac{ \cancel{48} {}^{ \: \: 24} }{ \cancel{2}} = 8 \times height \\ \frac{24}{8} = height \\ \frac{ \cancel{24} {}^{ \: \: 3} }{ \cancel{8}} = height \: \\ height = x = 3in \: [/tex]

Step-by-step explanation:

Table A represents an arithmetic sequence with a common difference d=+7.5

so for x=4, it's y³+7.5=25+7.5=32.5

for x=5, it's y⁴+7.5=32.5+7.5=40

Table B represents a geometric sequence with a common ratio r=4, so you're essentially multiplying by 4.

for x=4, y⁴=y³×4=160×4=640

for x=5, y⁵=y⁴×4=640×4=2560

Answer:

Step-by-step explanation:

-2(11-12)=-4(1-6x)​ becomes -2(-1) = -4(1 - 6x)

Next, we divide both sides by -2, obtaining -1 = 2(1 - 6x), and then

                                                                        -1 = 2 -12x, or

                                                                         -3 = -12x

Simplifying this result, we get 1 = 4x, or x = 1/4

We conclude that -2(11-12)=-4(1-6x)​ has ONE solution, which is x = 1/4

Answer:

its b trust me i had that one (12,44)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Since FG is congruent to FH, angles FGH and FHG are congruent since angles opposite congruent sides in a triangle are congruent.

Answer: 20%

Step-by-step explanation: Add all the marbles together:5 + 8 + 6 +11= 30

Find the probability of orange: 6/30

Now divide 6 by 30= .2

Turn .2 into a decimal: 20%

The number of sides of a polygon with interior angles of  134° and 156° and each of the remaining angles as 151° is 12 sides.

The sum of the exterior angles of a polygon is 360°. For regular polygons the exterior angles are the same (congruent).

Therefore,

Interior angle  + exterior angle = 180°

Therefore,

156 + x = 180

x = 180 - 156

x = 24°

134 + y = 180

y = 180 - 134

y = 46°

180 - 151 = z

z = 29°

sum of exterior angle = 360 degrees.

Therefore,

360 - 46 - 24 = 290°

Then,

290 / 29 = 10

The number of sides = 10 + 2 = 12 sides

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Answer:

-1

Step-by-step explanat

yes

Answer:

38.5 in²

Step-by-step explanation:

Area of circle= πr², where r is the radius

Substitute the value of the radius into the formula above:

Area of circle

= π(3.5)²

= 12.25π

= 38.5 in² (3 s.f.)

Answer:

height : 150 feet

Step-by-step explanation:

[tex]\sf \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

using tan rule:

[tex]\hookrightarrow \sf tan(62)= \dfrac{b}{80}[/tex]

[tex]\hookrightarrow \sf b = tan(62)*80[/tex]

[tex]\hookrightarrow \sf b =150.46 \ feet[/tex]

Answer:

[tex]\approx 150 \: ft[/tex]

Step-by-step explanation:

recall sohcahtoa

here,

To find:

since we are given the value of adjacent side and need to figure out the opposite side , we will work with tan function,

So,

[tex] \tan( {62}^{ \circ} ) = \dfrac{h}{80} [/tex]

[tex] \implies \: h = 80\tan( {62}^{ \circ} ) [/tex]

using calculator,we acquire

[tex] \implies \: h \approx 150 \: ft[/tex]

hence, the height of the building is approximately 150ft

59.99 - 59.99 x saving rate = 42.89

with saving rate = r%

59.99 - 59.99 x r% = 42.89

so 59,99 ( 1 - r%) = 42.89

1 - r% = 42.89 : 59.99

1 - r% = 0,7150

r% = 1 - 0,7150

r = 28,5%

Answer:

2008

Step-by-step explanation:

when she is 12 (4 years after 2004) her dad will be 36, which is 3 x 12, therefore, in 2008 he will be able to say this.

Answer:

  2008

Step-by-step explanation:

The difference in their ages is ...

  4m -m = 3m = 3(8) = 24 . . . years (Marika was 8 in 2004)

__

Marika's age when the father was 3 times her age was ...

  3m -m = 2m = 24 . . . years

  m = 12 . . . . . Marika was 12 when her father was 3 times her age

That is 12 -8 = 4 years from 2004, so it will be true in 2008.

Step-by-step explanation:

law of sine :

a/sinA = b/sinB = c/sinC

with the sides and correlating angles being always opposite to each other.

we are dealing with a right-angled triangle here.

the train track is the Hypotenuse (the side opposite of the 90° angle) : 1600 ft.

the horizontal level "connection" from beginning to the end of the track is one leg, and the elevation difference at the end of the track is the second leg.

the 2 legs enclose a 90° angle, as the elevation goes straight up from the horizontal level.

so, we have

1600/sin(90) = elevation difference / sin(1.6)

sin(90) = 1

1600 = elevation difference / sin(1.6)

elevation difference = 1600 × sin(1.6) =

= 1600 × 0.027921639... =

= 44.67462196... ft

≈ 44.7 ft

Answer:

Below in bold.

Step-by-step explanation:

8 18 30 44

the differences are 10 12 14 .etc

1.1.1  Next 2 terms are  44+ 16 = 60 and 60+ 18= 78.

1.1.2  8 =  1^2 + 7

       18 = 2^2 + 14

       30 = 3^2 + 21

       44 = 4^2 + 38

So the nth term = n^2 + 7n.

1.1.3 n^2 + 7n = 330

n^2 + 7n - 330 = 0

(n +  22)(n - 15) = 0

n =  -22, 15

As  the term sequence must be positive the answer is 15.

A rectangular prism with a height of 6 centimeters would have a volume of 138 cubic centimeters.

Given the following data:

Base area = 23 [tex]cm^2[/tex]

Height = 6 centimeters.

Mathematically, the volume of a rectangular prism is given by this formula:

[tex]V = B \times H[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]V = 23 \times 6[/tex]

V = 138 cubic centimeters.

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