The difference between two positive numbers is 5 and the square of their sum is 169. find the two numbers.

2^( 2x - 3 ) = 128

2^( 2x - 3 ) = 2^7

2x - 3 = 7

2x = 10

x = 5

Answer:

x = 5

Step-by-step explanation:

[tex]x^{2x-3} +52 = 180\\x^{2x-3} = 180 -52\\x^{2x-3} = 128\\x^{2x-3} = 2^{7} \\2x-3=7\\2x=10\\x=10/5\\x=5[/tex]

Answer:

3520 Yards

Step-by-step explanation:

1 Mile = 1760 Yards

Answer: 3520 yards

Step-by-step explanation:

1 mile = 5280 x 2 = 10,560

2miles = 10,560

in yards = 3520 yards

Answer:

29.89%

Step-by-step explanation:

Step 1: We assume that 435 is 100% since it is our output value.  

Step 2: We next represent the value we seek with [tex]$x$[/tex].  

Step 3: From step 1, it follows that [tex]$100\%=435$[/tex].  

Step 4: In the same vein, [tex]$x\%=130$[/tex].  

Step 5: This gives us a pair of simple equations:  

[tex]100\%=435(1)\\\\x\%=130(2)[/tex]  

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS  (left-hand side) of both equations have the same unit (%); we have  

[tex]$\frac{100\%}{x\%}=\frac{435}{130}$[/tex]  

Step 7: Taking the inverse (or reciprocal) of both sides yields  

[tex]\frac{x\%}{100\%}=\frac{130}{435}\\\\\Rightarrow x=29.89\%[/tex]  

Therefore, [tex]$130$[/tex] is [tex]$29.89\%$[/tex] of [tex]$435$[/tex].

Given:

The figures cylinder, cube, cone, and pyramid.

To find:

The formula of volume for the given figures.

Solution:

Volume of a cylinder is:

[tex]V_1=\pi r^2h[/tex]

Where r is the radius and h is the height.

Volume of a cube is:

[tex]V_2=a^3[/tex]

Where a is side length of cube.

It is also written as:

[tex]V_2=l\times w\times h[/tex]

Where l is length, w is width, h is height and [tex]l=w=h[/tex].

Volume of a cone is:

[tex]V_3=\dfrac{1}{3}\pi r^2h[/tex]

Where r is the radius and h is the height.

Volume of a pyramid is:

[tex]V_4=\dfrac{1}{3}Bh[/tex]

Where B is the base area and h is the height.

Therefore the table of formulae is shown below:

Figure                       Volume formula

Cylinder                   [tex]\pi r^2h[/tex]

Cube                        [tex]l\times w\times h[/tex]

Cone                        [tex]\dfrac{1}{3}\pi r^2h[/tex]

Pyramid                    [tex]\dfrac{1}{3}Bh[/tex]

Answer:

C

Step-by-step explanation:

Use Desmos graphing calculator

Answer:

C. y = 3x + 1

Step-by-step explanation:

The slope can be found by finding two points and the distance in between, which is 3 (rise) over 1 (run). The line passes through the point (0,1), which would be the y-intercept.

Answer:

$182000000000

1.82 * 10^11

Step-by-step explanation:

Given that :

Number of engineers = 2.6 million

Average salary = $70,000

Collective income generated by group of engineers yearly :

This will be on average :

2,600,000 * 70,000 = $182000000000

In scientific notation :

$182000000000 = 182 * 1000000000

182 * 1000000000 = 182 * 10^9

182 = 1.82 * 100 = 1. 82 * 10^2

Hence,

$182000000000 = 1.82 * (10^2 * 10^9)

$182000000000 = 1.82 * 10^11

Answer:

3rd option

Step-by-step explanation:

Using the identities

cot x = [tex]\frac{1}{tanx}[/tex]

csc² x = 1 + cot² x

Given

tanθ = [tex]\sqrt{3}[/tex] , then cotθ = [tex]\frac{1}{\sqrt{3} }[/tex]

csc²θ = 1 + ([tex]\frac{1}{\sqrt{3} }[/tex] )² = 1 + [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

cscθ = ± [tex]\sqrt{\frac{4}{3} }[/tex] = ± [tex]\frac{2}{\sqrt{3} }[/tex]

Since θ is in 3rd quadrant, then cscθ < 0

cscθ = - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = - [tex]\frac{2\sqrt{3} }{3}[/tex]

Answer:

135°

Step-by-step explanation:

The arc length is calculated as

EF = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{?}{360}[/tex]

Given EF = 12π , then

2π × 16 × [tex]\frac{?}{360}[/tex] = 12π ( divide both sides by 2π )

16 × [tex]\frac{?}{360}[/tex] = 6 ( multiply both sides by 360 to clear the fraction )

16 ? = 2160 ( divide both sides by 16 )

? = 135°

Step-by-step explanation:

Remember, math is a language

when you see per think fractions

15.2 miles per hour = 15.2 miles / 1 hour

since this is a fraction, Units can cancel just like numbers

To cancel miles and be left with hours rearrange the fraction

1 hour / 15.2 miles

then multiply by 72 miles

[tex] \frac{1hour}{15.2miles} \times 72miles[/tex]

the miles cancel and youre left with hours!

so youd write and solve 72 / 15.2

Answer:

You can use Protector' but dint have use this method:

Acute. Draw a vertical line connecting the 2 rays of the angle. To determine the number of degrees in an acute angle, connect the 2 rays to form a triangle. Line up the short end of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler.

Hello there I hope you are having an great day :)

X + 10 = Y if you are trying to work out Y it would equal y  =  x  +  10

If you are trying to work out X it would equal x  =  y  −  10

Hopefully that helps You :)

Answer:

10t+3

Step-by-step explanation:

Answer:

10t+3

Step-by-step explanation:

Answer:

Q 5.9

Step-by-step explanation:

Que el dinero gastado por Juan sea x

Deja que el dinero gastado por Carolina sea y

Si el dinero total gastado es Q 15

Luego;

x + y = 15 ------- (1)

De la segunda oración;

y = x + 3,2 -------- (2)

Sustituyendo (2) en (1)

x + x + 3,2 = 15

2x + 3,2 = 15

2x = 15 - 3,2

2x = 11,8

x = 5,9

x = Q 5.9

Por lo tanto Juan gastó Q 5.9

Answer:

I = PRT where I is the interest, P is the principal deposited/borrowed, R is the rate as a decimal (take the number & divide by 100), and T is time in years.

Answer:

4 x 3 = 12

2 x 3 = 6

12 + 6 = 18 cubic cm

Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:bjgnjfvnifcb

Answer:

392.5cm³

Step-by-step explanation:

height of broth in can used= 17-12

= 5cm

Amt. of broth used= πr²h

= 3.14×5²×5

= 392.5cm³

Answer:

e.

Step-by-step explanation:

Answer:

x = 16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x + (3x - 4) = 5 - (-7 - 3x)

Step 2: Solve for x

Answer:

5,250 minutes

Step-by-step explanation:

0.5 cubic Centimeter = 0.0005 liter

So, 4.5 liters = 4,500 cubic Centimeter

Time required for 0.5 cubic Centimeter = 35 seconds

So, we can calculate the total time required by using following formula

Total time required = (Time required for 0.5 cubic Centimeter × 2 ) × 4,500 cubic Centimeter

So, Total time required = (35 seconds ×2 ) × 4,500

= 70 × 4,500

= 315,000 seconds

= 5,250 minutes

Answer:

The answer is below

Step-by-step explanation:

A geometric sequence is a sequence such that each term after the first is found by multiplying the previous one by a fixed number (common ratio). It is given by:

[tex]a_n=ar^{n-1}\\\\n=1,2,3,\ .\ .\ .[/tex]

where a is the first term, r is the common ratio.

From the question, the first term is 14 (at n = 1). a₁ = 14

After 30 minutes (n = 2), the population is 28. a₂ = 28

After 1 hour (n = 3), the population is 56. a₃ = 56

Common ratio (r) = a₃/a₂ = a₂/a₁ = 56 / 28 = 28/14 = 2

a) This sequence is represented as:

[tex]a_n=14(2)^{n-1}[/tex]

b) After 4 hours, that is n = 9:

[tex]a_9=14(2)^{9-1}=14(2)^8=3584[/tex]

Answer:

2

Step-by-step explanation:

3x+15=21 (the opposite side of parallelogram is equal)

3x=21-15

3x=6

x=6/3

so x=2

AD=2

Answer:

C

Step-by-step explanation:

Answer:

The answer my friend is B.

Answer:

[tex]\frac{1}{12}[/tex] or 1:12

Step-by-step explanation:

There are 11 teachers : 132 students

Because ratios are just another way of writing fractions, by putting this into a fraction we get:

[tex]\frac{11}{132}[/tex]

Dividing both the numerator and denominator (top and bottom) by 11, we get:

[tex]\frac{1}{12}[/tex]

Thus, the ratio is [tex]\frac{1}{12}[/tex], or 1:12

Answer: I think 100,000

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

plug in a=3 for a

I belive you meant 99- 7 * a^2

so 99- 7 * (3)^2 = 36

The value of the expression  99 - 7a² for a = 3 is 36.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given expression is 99 - 7a².

Substitute a = 3 into the given expression:

99 - 7 (3)²

= 99 - 7×9

= 99 - 63

= 36

Hence, the value of the expression  99 - 7a² for a = 3 is 36.

Learn more about algebraic expressions here:

https://brainly.com/question/953809

#SPJ6

Answer:

B is the answer

Step-by-step explanation:

Answer:

[tex]d.\ 0.33 + 0.64 – (0.90)(0.33) = 0.673[/tex]

Step-by-step explanation:

Given

[tex]P(Baseball) = 33\%[/tex]

[tex]P(Baseball\ n\ Football) = 90\%[/tex]

[tex]P(Football) = 64\%[/tex]

Required

[tex]P(Baseball\ or\ Football)[/tex]

This is calculated as:

[tex]P(Baseball\ or\ Football) =P(Baseball) + P(Football) -P(Baseball\ n\ Football)[/tex]

[tex]P(Baseball\ or\ Football) = 0.33 + 0.64 - (0.90)(0.33)[/tex]

[tex]P(Baseball\ or\ Football) = 0.33 + 0.64 - 0.297[/tex]

[tex]P(Baseball\ or\ Football) = 0.673[/tex]