Work out the length of BC .

Answer:

4x +16 the slope is 4 because its parallel to the other equation

The solution is: the equation of the line that is parallel to the line

y - 1 = 4(x + 3) and passes through the point (4, 32) is y = 4x + 16.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have,

When two lines are parallel, their slope stays the same. thus we have y = 4x (so far)

Then use the point (4, 32) to plug in the coordinates to y = 4x + b

y = 4x + b (because y-intercept changes)

32 = 4(4) + b

32 = 16 + b

b = 32 - 16

b = 16

now, we get,

the y-intercept is 16 and the equation of the line that passes through the point (4,32) and is parallel to the line y = 4x + 13 is y = 4x + 16.

Hence, The solution is: the equation of the line that is parallel to the line

y - 1 = 4(x + 3) and passes through the point (4, 32) is y = 4x + 16.

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Answer:

40

Step-by-step explanation:

To solve this, we can create an equation that represents this situation. Since Christopher score 7 more than twice what Mathew scored, the equation will be:

C = 2M + 7

(Variables are representative of the first letter of each name)

Seeing as Christopher scored 87, we can put that into the equation and solve for M.

So, the equation will be:

87 = 2M + 7

Subtract 7 from both sides in order to isolate variable M on the right side.

80 = 2M

Now solve for M, which is 40 (divide both sides by 2).

Solution,

Principal (P)=$4.62

Rate(R)=7%

Time(T)=2 years

Interest (I)=?

Now,

Interest=P*T*R/100

= 4.62*7*2/100

=64.68/100

=$0.6468

Hope it helps

Good luck on your assignment

Answer:

Step-by-step explanation:

[tex]principal(p) = 4.62 \\ rate(r) = 7 \\ time(t) = 2[/tex]

[tex]simple \: \: \: \: = \frac{prt}{100} \\ interest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{4.62 \times 7 \times 2}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.6468 \\ [/tex]

Answer:

250 girls in the school and 370 students all total

Step-by-step explanation:

250 girls are in the school and 390 total students in the school.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The ratio of boys to girls in a school is 12:25

Let, No. of boys in the school = 12x

No. of girls in the school = 25x

Total students in the school = 12x+25x = 39x

Given, there are 120 boys

So, 12x = 120

x = 10

No. of girls in the school = 25x = 25(10)

No. of girls in the school = 250

Total students in the school = 39x = 39(10)

Total students in the school = 390

Hence, 250 girls are in the school and 390 total students in the school.

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Answer:

r = 7/(9sinθ - cosθ)

to rectangular form is:

y = (1/9)x + 7/9

Step-by-step explanation:

Given that

r = 7/(9sinθ - cosθ)

Consider the following polar-to-rectangular equivalents.

x² + y² = r²

x/r = cosθ

y/r = sinθ

So

r = 7/(9sinθ - cosθ)

Can be written as

r = 7/(9y/r - x/r)

r = 7/(1/r)(9y - x)

Multiplying through by (1/r)

1 = 7/(9y - x)

Multiplying through by (9y - x)

9y - x = 7

9y = x + 7

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

And this is the answer

Answer:

y = (1/9)x + 7/9

Step-by-step explanation:

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

Divide both sides by 9

y = x/9 + 7/9

y = (1/9)x + 7/9

The area of a triangle is 1/2 x base x height.

The base is 2 , the height is 4.

Area = 1/2 x 2 x 4 = 4 square cm.

The area of a square is s^2

S is the length of a side, which is 2

Area = 2^2 = 4 square cm

Both shapes have an area of 4 square cm

Answer: 4.5.

Step-by-step explanation for the triangle:

A = 1/2 ⋅ b ⋅ h  A = 1/2 ⋅ 3 ⋅ 3  A= 4.5

                       OR

Step-by-step explanation for the square:

A = a^2 = 2^2 = 4 = 4.5

Answer:

Step-by-step explanation:

to calculate mean add all the entries in a week ,then divide by 7(the number of days)

i give you hint

mean for week 1=(52+65+...   +60)/7

Answer: 136 sq. m.

Step-by-step explanation:

Area = (base x height ) / 2

= (17x16)/2

= 272/2 = 136

Answer:

The first pair.

Step-by-step explanation:

3 corresponding parts must be congruent for two triangles to be congruent. The first pair has 3 congruence markings; two angles and one side are congruent. Additionally, they are congruent by the ASA postulate because two angles and the included side are congruent.

Answer:

Including the princpal and two counselors, only 40 students will be able to attend each meeting.

If the principal and two counselors dont attend, then 41 students can attend with one of their parents.

Answer:

I think that the answer is C

Answer: D. h(x) = 3x - 6

Step-by-step explanation:

edge2021

Answer:

11

Step-by-step explanation:

14-3 = 11

you have 14 apples and you eat 3 of them. wow! now you have 11 apples!

Answer:

1. 0.7

2. 0.25

3. -0.3

4. 0.125

5. 0.23

6. 0.64

7. -0.6

Step-by-step explanation:

First divided those fractions, then you got those repeating decimals.

Answer:

1.) 0.7

2.) 0.25

3.) -0.3

4.)0.125

5.)0.233 (bar on top of threes)

6.)0.63 (bar on top of 6 and 3)

7.)-0.6

Step-by-step explanation:

1.) 7 divided by 10

2.)1 divided by 4

3.) -3 divided by 10

4.)1 divided by 8

5.)7 divided by 30

6.)7 divided by 11

7.)-3 divided by 5

Answer:

63

Step-by-step explanation:

w(x) = 2x³ + 3x

Put x as 3.

w(3) = 2(3)³ + 3(3)

Solve for the power.

w(3) = 2(27) + 3(3)

Multiply the terms.

w(3) = 54 + 9

Add both the terms.

w(3) = 63

Answer:

I hope it helps :)

Step-by-step explanation:

[tex]w(x) = 2x^3+ 3x\\w(3)\\w(3) = 2(3)^3 +3(3)\\w(3) = 2(27) +9\\w(3) = 54+9\\w(3) =63[/tex]

Answer:

$180

Step-by-step explanation:

First, you have to calculate the amount that Olivia would have paid at the end of the loan which would be the result of multiplying her monthly payment for the number of payments:

Total payment= $308*(12*5)

Total payment= $308*60

Total payment= $18,480

Then, you have to calculate the amount that Garrett would have paid at the end of the loan:

Total payment= $311*(12*5)

Total payment= $311*60

Total payment= $18,660

Now, you have to calculate the difference in the amount Olivia and Garrett would have paid:

$18,660-$18,480= $180

According to this, an $18,000 loan will cost Garrett $180 more than Olivia.

Answer:

2/3, 7/10, 11/15 and 4/5

Step-by-step explanation:

2/3=0.66

7/10=0.7

11/15=0.73

4/5=0.8

Answer:

3. 10m

4. 14m

Step-by-step explanation:

Angle inequality rule: A triangle can only form if it's 2 shortest sides add up to have MORE length than it's longer side.

1. 23 m

2. 4m

3. 10m

4. 14m

5. 7m

1 doesn't follow the angle inequality rule.

2 doesn't follow the angle inequality rule.

3 can be the third side.

4 can be the third side

5 doesn't follow the angle inequality rule.

Answer: W= 40cm

Step-by-step explanation:

16*10

A=160

160/4

=40

Answer: w=40

Step-by-step explanation:

Answer:

[tex](x^{-3} )^{2}[/tex]

[tex]x^6 x^{-12}[/tex]

Step-by-step explanation:

[tex](x^{3} x^{-6} )^{2}[/tex] is the expression given to be solved.

First of all let us have a look at 3 formulas:

[tex]1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}[/tex]

Both the formula can be applied to the expression([tex](x^{3} x^{-6} )^{2}[/tex]) during the first step while solving it.

Applying formula (1):

[tex](x^{3} x^{-6} )^{2}[/tex]

Comparing the terms of [tex](x^{3} x^{-6} )[/tex] with [tex]p^a \times p^b[/tex]

[tex]p=x, a =3, b=-6[/tex]

[tex]\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}[/tex]

So, [tex](x^{3} x^{-6} )^{2}[/tex] is reduced to [tex](x^{-3} )^{2}[/tex]

Applying formula (2):

Comparing the terms of [tex](x^{3} x^{-6} )^{2}[/tex] with [tex](p^a \times q^b)^c[/tex]

[tex]p=q=x, a =3, b=-6, c=2[/tex]

[tex]\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}[/tex]

So, [tex](x^{3} x^{-6} )^{2}[/tex] is reduced to [tex]x^6 x^{-12}[/tex].

So, the answers can be:

[tex](x^{-3} )^{2}[/tex]

[tex]x^6 x^{-12}[/tex]

Answer:

b d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total surface area of a cone [tex]S[/tex] = [tex]\pi r^{2}+\pi rl\\[/tex]

Since the diagram is half of a cone, its surface area will be [tex]S = \frac{\pi r^{2} +\pi rl}{2}[/tex]

r = radius of the cone

l = slant height

From the diagram diameter of the cone = 16m;

r = 16/2 = 8m

l = 17m

[tex]S = \frac{\pi (8)^{2} +\pi (8)(17)}{2}\\S = \frac{64\pi + 136\pi }{2} \\S = 32\pi + 68\pi \\S = 100\pi cm^{2}[/tex]

Answer:

y=8x+6

Step-by-step explanation:

m=slope

c=y-intercept

y=mx+c

y=8x+6

Answer:

y=8x+6

Step-by-step explanation:

Step-by-step explanation:

2x + 3 = x + 1

x + 3 = 1

x = -2

Answer:

x= -2

Step-by-step explanation:

2x+3=x+1

   -3     -3

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

2x = x - 2

-x    -x

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

x= - 2

Answer: The no. is 8

Step-by-step explanation:

Let the no. be x

6x - 1 = 47

6x = 48

x = 8

Answer:

let the certain number be x

6 × x - 1= 47

6x - 1 = 47

6x = 47 + 1

6x = 48

x = 48/6

x = 8

Answer:

7.2

Step-by-step explanation:

The radius of the circle is 14.

The length of the chord is 12.

Half the length of the chord and radius form a right angled triangle as shown in the diagram below.

We need to find one of the sides of the triangle, d in the diagram.

Using Pythagoras rule:

[tex]14^2 = 12^2 + d^2\\\\196 = 144 + d^2\\\\d^2 = 196 - 144 = 52\\\\d = \sqrt{52} = 7.2[/tex]

The distance between the chord and the center of the circle is 7.2

Answer: 4sqrt10

Step-by-step explanation: The Chord is 12 so half the chord is 6 so the base is 6 and the radius is the hypotenuse, which is 14. and the distance is the missing leg.

so 14^2=6^2+x^2

196=36+x^2

sqrt160=x

4sqrt10=x

Answer:

-13

Step-by-step explanation:

(5+1)²-(11+3²)÷4

(6)-14^2 divided by 4

36-14^2/4

13-196/4

13-49

-13

Answer & Step-by-step explanation:

(5 + 1)² - (11 + 3²) ÷ 4

Following the rules of order of operation, the first thing we have to do is the operations in the parentheses ().

(6)² - (11 + 3²) ÷ 4

Next, solve for your exponents.

36 - (11 + 9) ÷ 4

Next, do the operations in the parentheses ().

36 - (20) ÷ 4

Now, divide -20 by 4.

36 - 5

Subtract 5 from 36.

31

So, your final answer to this equation is 31.

Answer to the question:

2.9m

Answer: H' = (-4, 4)

Step-by-step explanation:

H = (-4, -4)

reflect across y = -2:

H is 2 units below y = -2 so when reflected it will be 2 units above y = -2

--> the x-coordinate doesn't change    the new y-coordinate is: 0

H' = (-4, 0)

reflect across y = 2:

H' is 2 units below y = 2 so when reflected it will be 2 units above y = 2

--> the x-coordinate doesn't change    the new y-coordinate is: 4

H'' = (-4, 4)

Answer:

1) 229 Teens

2) (12,-2)

Answer:

Is the time in the graph drawn?

Step-by-step explanation:

The value of the given expression √121 + ∛125 would be 16 which is determined by the square root and cube root properties.

Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.

The expression below which is given in the question

⇒ √121 + ∛125

Here 11×11 = 121 and 5×5×5 = 125

⇒ √(11×11) + ∛(5×5×5)

By the square root and cube root properties to get

⇒ 11 + 5

Apply the addition operation,

⇒ 16

Thus, the value of the given expression √121 + ∛125 would be 16.

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