A rectangle with sides 13 cm and 7 cm has the same diagonal as a square. What is the length of the side of the square. Give your answer as a surd.

Answer:

An expression

Step-by-step explanation:

The constant in this case would be 6 because it never changes.

The variable would be x because the value of x can change.

A formula is a mathematical rule, which 6 +x is not.

Therefore, 6+x is an expression.

Answer:

86°

Step-by-step explanation:

b = 29× 2 = 58

d= [180-(86+29)]×2 = 130

a=c=x

a+b+c+d = 360

2x+188= 360

2x= 172

x= 86

a = c = 86°

Answer:

- 24 - 70i

Step-by-step explanation:

Given

([tex]\sqrt{5}[/tex] - 7i)²

= ([tex]\sqrt{5}[/tex] - 7i)([tex]\sqrt{5}[/tex] - 7i)

= 5 - 7[tex]\sqrt{5}[/tex] i - 7[tex]\sqrt{5}[/tex] i + 49i² ( note that i² = - 1 )

= 5 - 14[tex]\sqrt{5}[/tex] i - 49

= - 44 - 14[tex]\sqrt{5}[/tex] i

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

[tex][\sqrt{5} - 7i]^{2}= (\sqrt{5})^{2} - 2*\sqrt{5}*7i + (7i)^{2}\\\\\\= 5 - 14i\sqrt{5}+7^{2}*i^{2}]]= 5 -14i\sqrt{5} +49 * -1\\\\= 5 -14i\sqrt{5} - 49\\\\= -44 - 14i\sqrt{5}[/tex]

Answer:

coordinates of point g is ( -6, 14)

Step-by-step explanation:

The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).

___________________________________________

given point

F(-1, -1) to H(-8, 20)

ratio : 5:2

the coordinates of point g is

(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)

=> (-2 -40/7 , -2+100/7)

=> (-42/7, 98/7)

=>( -6, 14)

Thus ,  coordinates of point g is ( -6, 14)

Answer:

The correct option is;

C) 6554

Step-by-step explanation:

The given data are;

Day,   Amount of change in Bacteria

1,            2

2,          -8

3,           32

4,          -128

Given that the data follows a geometric sequence, we have;

The first term of the series = 2, the common ratio = -4, the sum of a geometric progression is given by the following formula;

[tex]S_n = \dfrac{a \times \left (r^n - 1\right )}{r - 1}[/tex]

Which gives;

[tex]S_7 = \dfrac{2 \times \left ((-4)^7 - 1\right )}{(-4) - 1} = \dfrac{2 \times \left (-16384- 1\right )}{-4 - 1} = \dfrac{2 \times \left (-16385\right )}{-5} = 6554[/tex]

Therefore, the correct option is C) 6554.

Step-by-step explanation:

[tex]\text{Discriminant} =\Delta = b^2-4ac\\

\implies \Delta = 7^2-4(1)(10)=49-40=9\\

\therefore \Delta >0\\[/tex]

Since the discriminant is greater than zero, there are two real solutions.

Also, the solutions are $x=5$ and $x=2$

Answer:

According to an expert your answer is 7.

Step-by-step explanation:

since the unkown number is multiplied by itself what we need to do to get out answer is to work backwards. Thats where we cube root 343 to get 7

Answer:

x = -6; v = 4.

Step-by-step explanation:

–14 = –(-2x + 2)

-14 = 2x - 2

2x - 2 = -14

2x = -12

x = -6.

51 = 7(-1 + 2v) + 2

51 = -7 + 14v + 2

51 = 14v - 5

14v = 56

v = 4.

Hope this helps!

It depends really. If you stay close to the present, then predicting future results isn't too bad. The further you go out, the more unpredictable things get. This is because the points may deviate from the line of best fit (aka regression line) as time wears on. Of course, it also depends on what kind of data we're working with. Some pairs of variables are naturally going to correlate very strongly together. An example would be temperature versus ice cream sales.

A best-fit line shows an association between two variables and can therefore be used to make predictions.

An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.

(see attachment below).

Recall:

Therefore, a best-fit line shows an association between two variables and can therefore be used to make predictions.

An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.

(see attachment below).

Learn more here:

https://brainly.com/question/2396661

Answer:

Step-by-step explanation:

Since we are finding cos A we have

From the question

AC = √96

AB = 14

Substitute the values into the above formula

That's

We have the final answer as

Hope this helps you

Answer:

A.       (-4,8) and (2,-4)

Step-by-step explanation:

Because you already have a value for "y" you can plug in that value of "y" into the next equation and then solve for Y and X

Answer:

1.734

Step-by-step explanation:

Given that:

A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles).

The fitted regression is Time = −7.126 + .0214 Distance

Based on a sample size n = 20

And an Estimated standard error of the slope = 0.0053

the critical value for a right-tailed test to see if the slope is positive, using ∝ = 0.05 can be computed as follows:

Let's determine the degree of freedom df = n - 1

the degree of freedom df = 20 - 2

the degree of freedom df =  18

At the level of significance ∝ = 0.05 and degree of freedom df =  18

For a right tailed test t, the critical value from the t table is :

[tex]t_{0.05, 18} =[/tex] 1.734

Answer:

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

[tex]A (n) = a ({r})^{n - 1} [/tex]

where

a is the first term

r is the common ratio

n is the number of terms

To find the eighth term we must first find the first term

4th term = 108

common ratio = 3

That's

[tex]A(4) = a ({r})^{4 - 1} [/tex]

[tex]108 = a ({3})^{3} [/tex]

[tex]27a = 108[/tex]

Divide both sides by 27

For the eighth term

[tex]A(8) = 4 ({3})^{8 - 1} [/tex]

[tex]A(8) = 4({3})^{7} [/tex]

The final answer is

Hope this helps you

Answer:

$1.60 a crate

Step-by-step explanation:

t= 95.94/(6x20)

(6x20)= 60

95.94/60

$1.60

Answer:

Step-by-step explanation:

i) Cost per box = cost of a crate ÷ Number of boxes in the crate

b = 95.94 ÷ 6

b = $ 15.99

ii) Cost per tile = Cost per box ÷ Number of tiles in a box

 t = b ÷ 20

 t = 15.99 ÷20

t = $ 0.7995

Answer:

The answer is below

Step-by-step explanation:

To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.

Volume = length × width × height.

Firstly 1 feet (1') = 12 inches (12"),

For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet

Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³

For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet

Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³

The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³

Answer:

7000 (7 thousand)

700 (7 hundred)

20 (2 tens)

2 (2 units)

Step-by-step explanation:

what is the relationship between the values of the given digits?

1. The 7s in 7,700

2. The 2's in 522

From the knowledge of place values;

7,700 could be broken down thus :

7000 + 700 + 0 + 0

The first 7 depicts thousands as it has 3 trailing digits (7000)

The second 7 depicts hundred as it has 2 trailing digits (700)

522 could be broken down thus :

500 + 20 + 2

From 522

The first '2' has one trailing digit = tens

The ending / last digit ia always = Unit value

Answer:

C) $20.80

Step-by-step explanation:

1 kg of cooking oil = $6.5

1 packet of cooking oil =2/5 kg

If 1 kg of cooking oil = $6.5

2/5kg of cooking oil = $X

Cross Multiply

1kg × $X = 2/5kg × $6.5

$X = 13/5

$X = 2.6

Hence 2/5kg of oil cost $2.6

Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6

The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:

1 packet of oil = $2.6

8 packets of oil =

$2.5 × 8

= $20.80

Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80

One example is that you're given blueprints and you want to find out how large the object is in real life, rather than just on paper. The scale factor will help find those real life measurements. Let's say a house on paper is 2 inches long, and also let's say the scale factor is labeled "1 inch = 20 feet". This means the real life house is 2*20 = 40 feet long.

You could think of it as 1 inch = 20 feet, so 2 inches = 40 feet (multiply both sides by 2).

Scale factors are also used in maps. Look at the bottom corner of any map and it will show you how each distance on paper corresponds to a real life distance (in miles or kilometers maybe). Usually it shows a checkered "ruler" of sorts.

Answer:

  everyday living

Step-by-step explanation:

Scale factors are involved in virtually every aspect of the logistics of everyday life. Scale factors of number of units, price per unit, and tax rate are applied to every shopping experience. Scale factors of miles per gallon, or daily rate, or number of travelers are applied to most travel experiences. Scale factors of number of people and/or serving size are applied to food planning--even when ordering pizza.

Scale factors are involved in virtually every aspect of engineering, from specifying or estimating a job, to scheduling, material choice, purchase, and application. Sometimes, these are "rules of thumb", and sometimes they are based on careful calculation.

Much of modern technology is based on the observation that computing power doubles every 2 years or so--a scale factor consistently seen for more than 50 years. This has informed systems planning in many different industries.

Answer:

Step-by-step explanation:

We will get m when we multiply (m/2)*(2/3) &  m *(-3/2)

[tex]\frac{m}{2}*\frac{2}{3}+m*\frac{-3}{2}=\frac{m}{3}-\frac{3m}{2}\\\\\\=m(\frac{1}{3}-\frac{3}{2})\\\\\\=m(\frac{2}{6}-\frac{9}{6})\\\\\\=\frac{-7}{6}m[/tex]

Coefficient of m = -7/6

Answer:

The highest power of the equation is 2, since the equation is y = 4x^2 - 1. That means that the graph is a parabola. And because the 4 is positive, the parabola curves into a smile.

You can use the Math is Fun Function and Calculator to graph the parabola.

Hope this helps!

Answer:

The monthly growth rate is 3.5%.

Step-by-step explanation:

The exponential growth function is given as follows:

[tex]y=a(1+r)^{x}[/tex]

Here,

y = final value

a = initial value

r = growth rate

x = time taken

The provided expression for the monthly growth of membership in the new drama club at a school is:

[tex]f(x) = 12\cdot(1.035)^{x}[/tex]

Comparing this function with the exponential growth function:

[tex]a(1+r)^{x}=12(1.035)^{x}\\\\a(1+r)^{x}=12(1+0.035)^{x}[/tex]

Then value of r is 0.035 or 3.5%.

Thus, the monthly growth rate is 3.5%.

Answer:

1. (x+9)^2 = 89

2. (Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Step-by-step explanation:

x^2 - 6 = 2 - 18x

1) rewrite the equation by completing the square

x^2 - 6 = 2 - 18x

x^2 + 18x = 2+6

x^2 + 18x = 8

Find the half of the coefficient of x and square it

18x

Half=9

Square half=(9)^2

=81

Add 81 to both sides

x^2 + 18x = 8

x^2 + 18x + 81 = 8 + 81

x^2 + 18x + 81 = 89

(x+9)^2 = 89

Check:

(x+9)(x+9)=89

x^2 + 9x + 9x + 81=89

x^2 + 18x +81 =89

2) (x+9)^2 = 89

√(x+9)^2 = √89

x+9=√89

x=√89 - 9

It can be rewritten as

x= -9 ± √89

(Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Answer:

-1

Step-by-step explanation:

The formula for finding a slope is: m = (change in y)/(change in x)

Find the change in each value

Y: 9 - 6 = 3

X: -3 - 0 = -3

Input the values

m = 3/-3

m = -1

I would start this problem by setting up a table.

In the left column, we will have our x values

and in the right column, we have our y values.

Put our first ordered pair on the top and second on bottom.

We can see the y values go from 6 to 9 so change in y is 3.

The x values go from 0 to -3 so change in x is -3.

The slope is equal to the rate of change or change in y / change in x.

So our slope is 3/-3 of -1.

Answer:

The capacity of the container is 2546.78 cm³.

Step-by-step explanation:

The volume of the frustum of a cone is:

[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]

The information provided is:

r = 16/2 = 8 cm

R = 24/2 = 12 cm

h = 8 cm

Compute the capacity of the container as follows:

[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]

            [tex]=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78[/tex]

Thus, the capacity of the container is 2546.78 cm³.

Answer:

Matrix multiplication is associative: ( A B ) C = A ( B C ) \displaystyle \left(AB\right)C=A\left(BC\right) (AB)C=A(BC).

Matrix multiplication is distributive: C(A+B)=CA+CB,(A+B)C=AC+BC. C ( A + B ) = C A + C B , ( A + B ) C = A C +

Answer:

2.35 x 10^11

Step-by-step explanation:

The formula for finding the nth term in a geometric sequence is ar^n-1.

a = 3, r = 23, and n = 9:

3(23)^9-1 = 3(23)^8 = 2.35 x 10^11.

Answer:

12.9%

Step-by-step explanation:

Answer:

0.129%

Step-by-step explanation:

Just add the percent sign

Answer:

2184 different combinations

Step-by-step explanation:

To find how many different combinations are possible, multiply all of the values:

3 * 13 * 7 * 4 * 2 = 2184 different combinations

Answer:

2,184 different skateboards.

Step-by-step explanation:

You would have to multiply

3 x 13 x 7 x 4 x 2 = 2184

If it helps you then please mark it as brainliest!

Answer:

x = 8.4

y = -2

Step-by-step explanation:

Step 1: Sub y=-2 into y=5x + 40

-2 = 5x + 40

Step 2: Solve for 'x'

-2 = 5x +40

-42 = 5x

x = 42/5

x = 8.4

Step 3: Solve for 'y'

y is given in the question, y=-2