help with this math ​

Answer:

x = 28

Step-by-step explanation:

By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28

Answer:

£ 2121.8

Step-by-step explanation:

The formula to find the compound interest is :

[tex]A=P(1+\frac{R}{100} )^n[/tex]

Here,

A = Amount ⇒ ?

P ⇒ Principal ⇒ £2000

R ⇒ Interest rate ⇒ 3%

n ⇒ Time  ⇒ 2 years

Let us find now.

[tex]A=P(1+\frac{R}{100} )^n[/tex]

[tex]A=2000(1+\frac{3}{100} )^2[/tex]

[tex]A=2000(1+0.03 )^2[/tex]

[tex]A=2000(1.03 )^2[/tex]

[tex]A=2000*1.0609[/tex]

[tex]A=2121.8[/tex]

Therefore, there will be £ 2121.8 in the bank account after 2 years.

Answer:

y = 6l + 43

Step-by-step explanation:

y=mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers

b = 43

The slope is you purchase one pair of laces, it increases by 6 each time

m = 6

The y coordinate will represent the total cost spent

y

The x coordinate will represent the total number of laces purchase and we are told that the variable is l

x = l

combine:

y = 6l + 43

Answer:

wouldn't be 4.5 or something close too that maybe 5 or 5.5

Step-by-step explanation:

I got you I think

Answer:

no solutions

Step-by-step explanation:

Since the two terms have the same base, we are able to use the rule for subtracting logarithms:

[tex]log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )[/tex]

Therefore, the equation can be written as:

[tex]log_{6}(\frac{x-6}{x+4} )=2[/tex]

By using the definition of a logarithm we can say that:

[tex]\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}[/tex]

When plugging this solution in, you find that the term [tex]log_{6}(x-6)[/tex] has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so [tex]-\frac{30}{7}[/tex] is not a valid solution. This means that there are no solutions.

Answer:

Step-by-step explanation:

a)

the area of the field :

= 250 × 150

= 37 500 ft²

……………………

b)

→ the number of bags needed :

37 500 ÷ 1 000

= 37.5

Then he needs 38 bag

→ The cost :

= 38 × 54.00

= 2 052

The amount that the beneficiaries of his life insurance would receive would be $30000.

The total amount of insurance is 40000

percentage  needed by beneficiaries on this amount = 75%

Hence 75% * 40000

= $30000

Therefore it can be concluded that the amount that the beneficiaries would require on 75% is $30000.

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The year, where the number of cars sold exceed 46,000 is 13496

The equation of the function is given as:

y = 4x + 2

When the sales exceed 46000;

It means that y > 46000

So, we have:

4x + 2 > 46000

Subtract 2 from both sides

4x > 45998

Divide both sides by 4

x > 11499.5

The year is then calculated as:

Year = 1996 + x

So, we have:

Year > 1996 + 11499.5

Evaluate

Year > 13495.5

Approximate

y > 13496

Hence; the year, where the number of cars sold exceed 46,000 is 13496

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The number of customers served in the ice cream shop in June, July and August are 125, 25 and 250 customers respectively

let

Total = June + July + August

400 = x + (x- 100) + 2x

400 = x + x - 100 + 2x

400 = 4x - 100

400 + 100 = 4x

500 = 4x

x = 500/4

x = 125

So,

June = x

= 125 customers

July = x - 100

125 - 100

= 25 customers

August = 2x

= 2(125)

= 250 customers

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Answer:

4th one is correct

Step-by-step explanation:

it perfectly matches all the given condition

Answer:

5/1

Step-by-step explanation:

sin P = 24/26

cos P = 10/26

tan P = 24/10

sin Q = 10/26

cos Q = 24/26

tan Q = 10/24

you have the first part right. using Soh Cah Toa is the best way to find the trig function when given a labeled triangle.

remember the hypotenuse is the longest side and always across from the 90 degree angle.

The expression is assumed here as it's unclear looking

If it's P=(P_o)ln0.015t then the below solution of Part B is correct else they may vary.

#a

#b

As per our assumed equation

It's.

Simplify

Initial amount of account is not given so you have to solve the above equation after putting known P_o

#3

Hence it's less than 3 and greater than 2

Answer:

[tex]x=a \cos t \implies \dfrac{dx}{dt}=-a \sin t[/tex]

[tex]y= a \sin t \implies \dfrac{dy}{dt}=a \cos t[/tex]

Using the chain rule:

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & =\dfrac{dy}{dt} \times \dfrac{dt}{dx}\\\\& = a \cos t \times \dfrac{1}{-a \sin t}\\\\& = \dfrac{a \cos t}{-a \sin t}\\\\& = - \dfrac{\cos t}{\sin t}\\\\& = - \cot t\end{aligned}[/tex]

Answer:

C. 225°.

Step-by-step explanation:

1) according to the condition minor arc is 135°;

2) the measure of the major arc can be calculated as

360°-135°=225°.

Thank you :)

[tex]\pink{ \rule{1pt}{90000000pt}}\color{blue}{ \rule{1pt}{90000000pt}}\color{yellow}{ \rule{1pt}{90000000pt}}\purple{ \rule{1pt}{90000000pt}} \green{\rule{1pt}{90000000pt}}

[/tex]

Answer:

-3(x+1)² + 2

Step-by-step explanation:

-3(x+1)² + 2 because the +2 indicates the y value of the turning point and the turning point is a maximum meaning the coefficient must be negative leaving this answer

Answer:

See below

Step-by-step explanation:

4.33 = 3.83 * (1.13)       .13 is decimal for 13%  

You have to maintain a minimum level of financial responsibility when transporting any type of hazardous material in intrastate commerce Option A is correct.

Interstate commerce refers to any transaction or movement of goods, services, or money over state lines.

You operate a motor carrier for hire. When shipping any quantity of hazardous material in intrastate trade, A mandates that you maintain a minimum degree of financial accountability.

Hence option A is correct.

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Answer: A is correct

Step-by-step explanation:

The approximation of the circumference of the ride is 138 feet to the nearest foot

The given parameters are:

The radius is calculated using:

[tex]r = \sqrt{(x - a)^2 + (y -b)^2}[/tex]

So, we have:

[tex]r = \sqrt{(16 - 0)^2 + (15.1 -0)^2}[/tex]

Evaluate

r = √484.01

Evaluate the square root

r = 22.0

The circumference is calculated using

C = 2πr

So, we have:

C = 2π * 22.0

Evaluate

C = 138

Hence, the approximation of the circumference of the ride to the nearest foot is 138 feet

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An equation is formed of two equal expressions. The value of x and y is 17 and 20, respectively. Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Solving the first equation for y,

4x - 3y = 8

-3y = 8 - 4x

y = (8-4x)/(-3)

Solving the second equation for y,

5x - 4y = 5

-4y = 5 - 5x

y = (5 - 5x)/(-4)

Equate the value of y,

y = y

(8-4x)/(-3) = (5 - 5x)/(-4)

-32 + 16x = -15 + 15x

16x - 15x = -15 + 32

x = 17

Substitute the value of x in any one of the equation,

4x - 3y = 8

4(17) - 3y = 8

68 - 3y = 8

-3y = -60

y = 20

Hence, the value of x and y is 17 and 20, respectively. Thus, the correct option is D.

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Answer:

Step-by-step explanation:

a)  Sum of nine and two ⇒ 9 + 2

Four multiplied by (9+2) :  

       4* (9+2)

[tex]b) \dfrac{(18-6)}{4}[/tex]

[tex]c) \dfrac{45}{3*(3+2)}[/tex]

2) a) Multiply the sum of five and eight by 6

   b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?

3) a) 7*(8-3)

      Multiply the difference of eight and three by 7.

Hey there !

Answer:

Step-by-step explanation:

In this question we are given with an expression that is -2mn + n - 3m , value of m as -3 , value of n as -2 . And we are asked to evaluate the expression .

Solution : -

For solving such types of expression in which we are provided with values of variables we need to substitute value of variable ( in given equation m and n ) and solve them .

Expression :

[tex] \longmapsto \: \qquad \: \rm{- 2mn + n - 3mn}[/tex]

Substituting value of m and n :

[tex] \longmapsto \: \qquad \: - 2( - 3)( - 2) + ( - 2) - 3( - 3)[/tex]

Simplifying it :

[tex]\longmapsto \: \qquad \: - 2(6) - 2 + 9[/tex]

Multiplying -2 and 6 :

[tex]\longmapsto \: \qquad \: - 12 - 2 + 9[/tex]

Adding -12 and -2 :

[tex]\longmapsto \: \qquad \: - 14 + 9[/tex]

Solving -14 and 9 :

[tex]\longmapsto \: \qquad \: \underline{ \blue{\boxed{\frak{- 5}}}} \quad \bigstar[/tex]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to evaluate the expression

[tex]\star~\mathrm{-2mn+n-3m}~\star[/tex]

for

[tex]\star~\mathrm{m=-3}~\star[/tex]

[tex]\star~\mathrm{n=-2}~\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, let's compute...

//\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\

                               Evaluating the expression

Since the value of m is -3, we should substitute -3 for m:

[tex]\star~\mathrm{-2(-3)n+n-3(-3)}[/tex]

Since the value of n is -2, we should substitute -2 for n:

[tex]\star~\mathrm{-2(-3)(-2)+(-2)-3(-3)}[/tex]

Simplify!

[tex]\star\mathrm{6(-2)-2+9}[/tex]

Simplify more!

[tex]\star\mathrm{-12-2+9}[/tex]

[tex]\star~\mathrm{-14+9}[/tex]

[tex]\boxed{\mathrm{-5}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

The residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

The regression equation is given as:

y = 0.141x + 0.842

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.141 * 13.8 + 0.842 = 2.78

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 16.7 + 0.842 = 3.20

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 0.7 + 0.842 = 0.94

y = 0.141 * 21.9 + 0.842 = 3.93

y = 0.141 * 15.5 + 0.842 = 3.03

y = 0.141 * 9.2 + 0.842 = 2.14

y = 0.141 * 19.5 + 0.842 = 3.59

y = 0.141 * 16.7 + 0.842 = 3.20

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

Residual = 1.42 - 2.78 = -1.36

Residual = 3.7 - 3.38 = 0.32

Residual = 3.21 - 3.20 = 0.01

Residual = 4 - 3.38 = 0.62

Residual = 1.11 - 0.94 = 0.17

Residual = 3.69 - 3.93 = -0.24

Residual = 3.92 - 3.03 = 0.89

Residual = 2.23 - 2.14 = 0.09

Residual = 3.77 - 3.59 = 0.18

Residual = 2.5 - 3.20 = -0.7

Hence, the residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

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The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base,

then its volume is:

V = B x  h

where h is the height of that prism and B is the area of the base of that prism.

Given:

Base side length =14 and 10 units

Height=8 units

Diameter=5 units

The volume of the shaded region is;

Expression =  1-( half 14)(10)(8) - π(2.52)(8)

Expression = 1-(7) (10)(8) - π(2.52)(8)

Expression = 1- (560)- 63.33

Expression = -559-63.33

Expression = -622.33

Hence, The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).

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answer: A

the first one

Answer:

Let Musa's mark be = m

Emmanuel's mark be = e

Faith's mark be = f

m = e + 7

e = 25

m = 25 + 7 = 32

f = 1/4 m + e

f = (1/4 × 32) + 25

f = 8 + 25

f = 33

Answer:

3 ways

Step-by-step explanation:

2×3=6. That is how you do it

Answer:

-8

Step-by-step explanation:

Solving for r means that we need to isolate r from the expression.

[tex] \frac{ - 8}{r + 6} = 4[/tex]

Multiply both sides by (r +6) to 'get rid' of the fraction:

-8= 4(r +6)

Expand:

-8= 4r +4(6)

-8= 4r +24

Minus 24 on both sides:

4r= -8 -24

4r= -32

Divide both sides by 4:

r= -32 ÷4

r= -8

Additional:

For a similar question on solving for a variable:

Answer:

r = -8

Step-by-step explanation:

-8/(r + 6) = 4
          -8 = 4(r + 6)
          -8 = 4r + 24
        -32 = 4r
          -8 = r

Answer:

Step-by-step explanation:

You can use this information to "guess" at the answers without doing any "work."

__

The missing angle is the complement of the marked acute angle in the right triangle, so is ...

  C = 90° -65° = 25°

This angle is opposite the side of length 8.9 cm. The next-smallest angle is 65°, which is more than double the smallest angle. Hence the side opposite 65° will not be either of 3.8 or 9.8.

Of the two remaining measures, the longer one, 21.1, will be the hypotenuse, BC. The shorter of those, 19.1, will be the long side, AC.

Our solution is ...

__

The mnemonic SOH CAH TOA reminds you of the relations between trig functions and right triangle sides. Here, we're given an angle and the length of its adjacent side. We are asked for the opposite side and for the hypotenuse. This suggests useful relations might be ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Solving the first of these for the hypotenuse gives ...

  hypotenuse = adjacent/cos(65°)

  BC = 8.9 cm/cos(65°) ≈ 21.059 cm ≈ 21.1 cm

Solving the second relation above for the opposite side gives ...

  opposite = adjacent×tan(65°)

  AC = 8.9 cm×tan(65°) ≈ 19.086 cm ≈ 19.1 cm

As above, the missing angle is the complement of the given one:

  C = 90° -65° = 25°

Then the quantitative solution is ...

_____

Additional comment

If AC were 9.8 cm, the angle at B would be about 48°. That is, the two acute angles in the triangle would be very nearly equal.

We know that the side ratios in a 30°-60°-90° right triangle are 1 : √3 : 2. This triangle has a larger angle greater than 60°, so its longer side will be more than √3 times the short side. That means a length of 9.8 cm is way too short.