For the remaining questions, show your work.
6. Solve each of the following equations.
a. - 5 = -3 + a
b.Зc + 2 = -22

Answer:

x = 35.0

Step-by-step explanation:

the height is 26√3 since the left one is a 30-60-90 triangle

so to find x

cos(39) = x/26√3

or, x = 26√3×cos(39)

or, x = 35.0

Answered by GAUTHMATH

Answer:

[tex](a)\ Ratio = 13.5 : 4[/tex]

(b) The height of the smaller bucket is 10.7

Step-by-step explanation:

Given

[tex]V_L = 13\frac{1}{2}[/tex]

[tex]V_S = 4[/tex]

[tex]H_L = 36cm[/tex]

Solving (a): The ratios

This is represented as:

[tex]Ratio = V_L : V_S[/tex]

So, we have:

[tex]Ratio = 13\frac{1}{2} : 4[/tex]

Express as decimal

[tex]Ratio = 13.5 : 4[/tex]

Solving (b): The height of the smaller bucket

The ratio of the heights is:

[tex]Ratio = H_L : H_S[/tex]

So, we have:

[tex]13.5 : 4 = H_L : H_S[/tex]

Substitute known value

[tex]13.5 : 4 = 36 : H_S[/tex]

Express as fraction

[tex]4/13.5 = H_S/36[/tex]

Multiply by 36

[tex]36 * 4/13.5 = H_S[/tex]

[tex]10.7 = H_S[/tex]

[tex]H_S = 10.7[/tex]

Answer:

6

Step-by-step explanation:

how often is that question posted here ?

this means that we need to find the value of x, so that the functional (result) value is 7.

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

Answer:

11

Step-by-step explanation:

To calculate the mean you add all the numbers and divide by the number of numbers. There are 4 numbers in this set so we will divide by 4.

Let x be the unknown number,

(10+4+7+x)/4=8(mean)

To solve for x, we first mutliply both sides by 4.

To simplify the left side we can add 10+4+7 and get 21 where now our equation is 21+x=32. Subtract 21 on both sides and you will get 11 which is our answer.

Plug-in 11 and solve for the mean to verify where we do indeed get 8 as the mean.

Answer:

17.6 mi

Step-by-step explanation:

I know you are using Windows 10 OS or something because of the cortana thingie and task bar option, and you can do Windows Key + Shift + S to take a screenshot.

This gives much better quality than a third party device and lets us evade the terrible pixel green line rippley thingies that form. Plus it is more efficient and faster.

Circumference formula is Diameter * Pi.

I assume the 5.6 mi. is the diameter since the line segment is going completely through the circle.

Pi is something of the lines of 3.141592653 blah blah blah and goes on forever, but the point is, we take it to be 3.14 when doing circle stuff so we don't die from old age trying to figure out a question of a 1 x 1 circle.

So 5.6 * 3.14 is 17.584 which is your answer.

It says to round to the nearest tenth though, so you round and get

17.6 since the 5 in 17.584 is the tenths place, the 8 is the hundredths place, the 4 is the thousandths place and so on and so forth.

(The "  *  " symbol represents multiplication and is in use all the time when going to higher levels of education.)

Your answer is -6.

Hope my answer is helpful to you. Stay blessed .

[tex]\\ \large\sf\longmapsto {27}^{x} = {9}^{x - 3} \\ \\ \large\sf\longmapsto ( {3}^{3} ) {}^{x} = ({3}^{2} ) {}^{x - 3} \\ \\ \large\sf\longmapsto 3 {}^{3x} = 3 {}^{2(x - 3)} \\ \\ \large\sf\longmapsto {3}^{3x} = 3 {}^{2x - 6} \\ \\ \large\sf\longmapsto 3x = 2x - 6 \\ \\ \large\sf\longmapsto 3x - 2x = - 6 \\ \\ \large\sf\longmapsto x = - 6[/tex]

Answer: x+2y+6=0

Option 3

Explanation:

y = (-x-6)/2

2y = -x-6

x+2y+6=0

Must click thanks and mark brainliest

Answer:

Step-by-step explanation:

Answer:

[tex]-\frac{3p^8}{4q^3}[/tex]

Step-by-step explanation:

One is given the following expression,

[tex]\frac{15p^-^4q^-^6}{-20p^-^1^2q^-^3}[/tex]

Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

Now bring all of the terms with a negative exponent to the numerator. Multiply the exponents by (-1), then add them to the exponents of the like term in the numerator. Simplify the resulting exponents

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

[tex]\frac{3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^)}{-4}[/tex]

[tex]\frac{3p^-^4^+^1^2q^-^6^+^3}{-4}[/tex]

[tex]\frac{3p^8q^-^3}{-4}[/tex]

Rewrite the fraction such that there are no negative exponents. Remember the rule, when bringing a number from the numerator to the denominator and back, multiply the exponent of the number by (-1). One can only switch numbers between the numerator and the denominator when all operations are multiplication or division.

[tex]\frac{3p^8q^-^3}{-4}[/tex]

[tex]-\frac{3p^8}{4q^3}[/tex]

Answer:

9

Step-by-step explanation:

See the picture for steps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{1}{4} (38 -14) + \dfrac{3^3}{9}}[/tex]

[tex]\mathsf{38-14=\bf 24}[/tex]

[tex]\mathsf{= \ \dfrac{1}{4} (24)+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{\dfrac{1}{4}(24)= \bf 6}[/tex]

[tex]\mathsf{= \ 6+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]

[tex]\mathsf{= \ 6+\dfrac{27}{9}}[/tex]

[tex]\mathsf{\dfrac{27}{9}}\\\mathsf{= 27\div9}\\\mathsf{= \bf 3}[/tex]

[tex]\mathsf{= \ 6 + 3}[/tex]

[tex]\mathsf{= \bf 9}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[ (10)(x^3)(y^2) / (5)(x^-3)(y^4) ]^-3

[ (2)(x^3)(y^2) / (x^-3)(y^4) ]^-3

[ (2)(x^6)(y^2) / (y^4) }^-3

[ (2)(x^6)(y^-2) ]^-3

(2^-3)(x^-18)(y^6)

---Not simplified (contains negative exponents)

(1/8)(x^-18)(y^6)

---Fully simplified

(y^6) / (8)(x^18)

Hope this helps!

Answer:

AC² + BD² = 2[AB² + BC²]

Step-by-step explanation:

Let the parallelogram be ABCD with sides AB, BC, CD and AD. It also has diagonals AC and BD.

Since the diagonals are perpendicular and bisect each other at their mid-point, and P is the point of intersection of the diagonals, we have that AP = AC/2, PC = AC/2, PB = BD/2 and PD = BD/2.

Since APB forms a right angled triangles with length of sides AP, PB and AB where AB is the hypotenuse side, using Pythagoras' theorem, we have

AB² = AP² + PB²

Since AP = AC/2 and PB = BD/2, we have

AB² = (AC/2)² + (BD/2)²

AB² = AC²/4 + BD²/4   (1)

Also, BPC forms a right angled triangles with length of sides BP, PC and BC where BC is the hypotenuse side, using Pythagoras' theorem, we have

BC² = BP² + PC²

Since PC = AC/2 and PB = BD/2, we have

BC² = (AC/2)² + (BD/2)²

BC² = AC²/4 + BD²/4   (2)

Adding equations (1) and (2), we have

AB² = AC²/4 + BD²/4   (1)

+

BC² = AC²/4 + BD²/4   (2)

AB² + BC² = AC²/4 + BD²/4 +  AC²/4 + BD²/4

AB² + BC² = AC²/2 + BD²/2

Multiplying through by 2, we have

2[AB² + BC²] = AC² + BD²

So, AC² + BD² = 2[AB² + BC²]  which proves our expression.

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then

[tex]3^{-2}[/tex] = [tex]\frac{1}{3^2}[/tex] = [tex]\frac{1}{9}[/tex]

Answer:

c = 85 yd

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

c² = 77² + 36² = 5929 + 1296 = 7225 ( take square root of both sides )

c = [tex]\sqrt{7225}[/tex] = 85

Answer:

[tex]85yd[/tex]

Step-by-step explanation:

According to PYTHAGORAS Theorem,

[tex] {c}^{2} = {77}^{2} + {36}^{2} \\ {c}^{2} = 5929 + 1296 \\ {c}^{2} = 7225 \\ c = \sqrt{7225} \\ c= 85yd[/tex]

Answer:

The inequality is -3<x<3

Step-by-step explanation:

(-3,3)

Answer:

the school band

Step-by-step explanation:

the band, the band has a percentage of 53.85...,which is (14/26)x100, and the choir has 35.71% which is (5/14)x100

Answer:

"97" is the appropriate answer.

Step-by-step explanation:

Given:

Number of trees,

= 485

Orchards of trees,

= 5

The number of trees in each orchard will be:

= [tex]\frac{Number \ of \ trees}{Orchards \ of \ trees}[/tex]

= [tex]\frac{485}{5}[/tex]

= [tex]97[/tex]

Answer:

again it has a ratio

Step-by-step explanation:

follow this steps.

firstly look at the side and you got the ratio 24/16

secondly write 42/? and multiply by 24/16

the answer is ?*24=42*16 and divide it by 8 and write again ?*3=42*2 and finally the answer is ?=28

Answer:

h=17.3 A=173

Step-by-step explanation:

Calculator

Answer:

height = 17.3 mm

area = 173 mm²

Step-by-step explanation:

all three sides are of the same length (20 mm).

so, the height actually splits the baseline in half

(2 × 10 mm) while hitting it at a 90 degree angle.

so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.

c² = a² + b²

20² = 10² + height²

400 = 100 + height²

300 = height²

height = 17.3 mm

the area of the main triangle is baseline (20) times height divided by 2.

so,

At = 20×17.3/2 = 10×17.3 = 173 mm²

Answer:

7x and 2x. 3x^2 and -7x^2.

Step-by-step explanation:

7x and 2x both have x. 3x^2 and -7x^2 both have x^2.

Answer:

i. 12cm

ii. 16.5cm

Step-by-step explanation:

The side lengths on an equilateral triangle are all equal to each other. So if one side is given we can find the perimeter of the triangle by multiplying one of the sides by 3.

4*3=12

5.5*3=16.5

Answer:

1.02secs

Step-by-step explanation:

Using the equation of motion

v = u+at

Since the ball moves upward then:

a = -g

Substitute into the formula

v = u-gt

Given the following

Initial velocity u = 10m/s

Final velocity v = 0m/s (on the ground)

g = 9.8m/s²

Required

Time t

Substitute the given values into the formula

0 = 10-9.8t

-9.8t = -10

t = 10/9.8

t = 1.02secs

Hence your opponent have 1.02secs

Answer:

c ≥ 600

p ≥ 5000

Step-by-step explanation:

Let :

credit score = c

Cost of car, p

To qualify :

Credit score must be atleast 600 ;

c ≥ 600

Cost of car must be atleast 5000

p ≥ 5000

Step-by-step explanation:

something is missing here.

it is not clear, what exactly is 27 km. only the side of the orange triangle ? or the whole distance to the 90 degree angle ?

but in both cases that is not enough. we need some information about the split ratio of the orange side and the white side. it some angles in the graphic.

otherwise I can simply keep the given sides with their lengths but freely move the line between the orange and white triangles. there are infinite many solutions.

is it meant to be an isoceles triangle (2 equal sides) ? it certainly does not look like it, but that would be the only case where the given information can lead to a solution.

under that assumption the baseline of the white triangle is also 27 km.

the first side is 9km.

the second side we get via Pythagoras :

27² = 9² + x²

729 = 81 + x²

648 = x²

x = 25.46 km

now, since this is a right-angled triangle we can (especially to calculate the area) also consider the two sides enclosing the 90 degree angle as baseline and height.

the area of a triangle is baseline×height/2

area = 9×25.46/2 = 114.55 km²

Answer:

B. 3ˣ + 8x + 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3ˣ + 10x

g(x) = 2x - 4

Step 2: Find

Answer:

3^x+8x+4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4

(f- g)(x)=3^x + 10x  - (2x - 4)

Distribute the minus sign

(f- g)(x)=3^x + 10x  - 2x + 4

Combine like terms

         3^x+8x+4

Answer:

3/2

Step-by-step explanation:

Let it be

C (5;4) , A (2;1) ; B(7;6)

Suppose that C divide the line AB in ratio m/n from point A (AC is m, CB is n)

Use the formula xc=(m*xb+n*xa)/ (m+n)

5=(m*7+2n)/(m+n)

5m+5n= 7m+2n

2m=3n

m/n=3/2

Answer:

Step-by-step explanation:

-2/3(1)-1 = -2/3 - 1 = - 5/3

Answ

Step-by-step explanation:

-2/2 =-1 nha

The required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

The formula for calculating the volume of the conical lid's is expressed as

[tex]V = \frac{1}{3} \pi r^2h[/tex] where:

r is the radius

h is the height

v is the volume

Given the following

r = x

If the conical lid’s height is 2 centimeters less than the radius, x, then;

h = x - 2

V = 25π cm³

Substitute the given values into the formula as shown:

[tex]25 \pi = \frac{1}{3} \pi x^2 (x-2)\\3(25) = x^2(x-2)\\Expand\\75=x^3-2x^2\\Swap\\x^3-2x^2 = 75\\Equate \ to \ zero\\x^3-2x^2 - 75 = 0[/tex]

Hence the required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

Answer:

25%

Step-by-step explanation:

1 dozen = 12

3 out of 12

3/12

Simplify

1/4

Multiply top and bottom by 25 to get a denominator of 100

25/100

25%

Answer:

First, subtract

7

from each side of the inequality to isolate the

x

term while keeping the inequality balanced:

1

4

x

+

7

−

7

>

0

−

7

1

4

x

+

0

>

−

7

1

4

x

>

−

7

Now, multiply each side of the inequality by

4

to solve for

x

while keeping the inequality balanced:

4

×

1

4

x

>

4

×

−

7

4

4

x

>

−

28

1

x

>

−

28

x

>

−

28

Answer:

1/2 < x < 7/2

Step-by-step explanation:

First, simplify then put everything on one side: 16x -4x^2 -7 > 0

Then use the quadratic formula to factor and find out x.

For a quadratic equation in the form of ax^2 + bx + c = 0, use this formula:

X (1,2) = (-b ± √(b^2 -4ac))/2a

(The X (1,2) part means that there are 2 solutions for x)

In this case, a is -4, b is 16, and c is -7. By using this formula, you get that x=1/2, x=7/2

Answer:

1 : 45

Step-by-step explanation:

Given

Rs 20 and 900 ( divide both by 20 )

= 1 : 45