Consider the enlargement of the triangle and use the measurements to calculate the scale factor. 2 triangles have corresponding side lengths of 8 centimeters and 64 centimeters. scale factor =

Answer:

Step-by-step explanation:

4x + y = 8

x + 3y = 8

[tex]Here, \dfrac{a_{1}}{a_{2}}=\dfrac{4}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{1}{3}\\\\\\\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}[/tex]

So, this system of equations is consistent and independent.

-4x + 6y = -2

2x - 3y = 1

[tex]\dfrac{a_{1}}{a_2}}=\dfrac{-4}{2}=\dfrac{-2}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{6}{-3}=\dfrac{-2}{1}\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{-2}{1}\\\\\\\dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}=\dfrac{c_{1}}{c_{2}}[/tex]

So, the system of linear equations are consistent and dependent.

5x -2y = 4

5x - 2y = 6

[tex]\dfrac{a_{1}}{a_{2}}=\dfrac{5}{5}=1\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{-2}{-2}=1\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{4}{6}=\dfrac{2}{3}\\\\\\ \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}} \neq \dfrac{c_{1}}{c_{2}}[/tex]

This system of equations is inconsistent.

Since "a" is on the top and the bottom, you can simplify that

[tex]\frac{a^2b^2}{ac}[/tex]

[tex]\frac{ab^2}{c}[/tex]

The division is one of the four fundamental arithmetic operations. The amount that is needed to be paid by each friend is $74.75.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

As it is given that the total cost of the computer is $299, it is needed to be split between four friends. Therefore, the price will be paid by the four friends equally which can be written as,

[tex]\text{Amount paid by each friend}=\dfrac{\text{Total cost of computer}}{\text{Number of friends}}\\\\\\\text{Amount paid by each friend}=\dfrac{\$299}{4} = \$74.75[/tex]

Thus, the amount that is needed to be paid by each friend is $74.75.

Learn more about Division:

https://brainly.com/question/369266

Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

Eukaryotic cells are larger than prokaryotic cells and have a “true” nucleus, membrane-bound organelles, and rod-shaped chromosomes. The nucleus houses the cell's DNA and directs the synthesis of proteins and ribosomes.

All cells have a plasma membrane, ribosomes, cytoplasm, and DNA. Prokaryotic cells lack a nucleus and membrane-bound structures. Eukaryotic cells have a nucleus and membrane-bound structures called organelles.

So..the answer should be Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

To know more about Cells follow

https://brainly.com/question/13920046

Answer:

Prokaryotes

✔ do not have

a nucleus surrounding their chromosome of DNA.

Prokaryotes are

✔ more

simple cells than eukaryotes.

Prokaryotes have a

✔ cell wall

outside their cell membrane that gives protection and support.

Prokaryotes will often move by a tail-like

✔ flagellum

.

Step-by-step explanation:

Answer:

7/6561

Step-by-step explanation:

nth term = a1 r^(n-1) so

9th term =  7* (1/3)^(9-1)

= 7*(1/3)^8

= 7/6561

Answer:

50²

Step-by-step explanation:

(2×10⁵) ÷ (4×10²)

2 × 100000 ÷ 4 × 100

200000 ÷ 400

= 500

= 50²

as far as I can read that, well, the company has a revenue income of 8250000 and their expenditure on purchases is 49% of that amount, how much is that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{49\% of 8250000}}{\left( \cfrac{49}{100} \right)8250000}\implies 4042500[/tex]

so on saving 2.05% of purchasing expenses or namely 2.05% of 4042500

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{2.05\% of 4042500}}{\left( \cfrac{2.05}{100} \right)4042500}\implies 82871.25[/tex]

so sales must be increased by that much in order to match the 2.05% of 4042500.

Answer:

2

Step-by-step explanation:

Yessir

Let's see

[tex]\\ \bf\bull\rightarrowtail z^2-9[/tex]

[tex]\\ \bf\bull\rightarrowtail z^2-3^2[/tex]

[tex]\\ \bf\bull\rightarrowtail (z+3)(z-3)[/tex]

Answer:

(z+3)(z-3)

Step-by-step explanation:

a^2 - b^2 = (a+b)(a-b) where a = z and b= 3

Answer:

f(9.5) = 558.02.

Step-by-step explanation:

Because it is an exponential function, it can be written: y = (a)(b)^x

Now substitute in the two known points:

72 = (a)(b)^7.5 and

2 = (a)(b)^4 : => since 2 = (a)(b)^2 divide the left side by 2 and the right by (a)(b)^2

72/2 =[(a)(b)^7.5]/[(a)(b)^4]: => the (a) cancels out and b becomes b^(7.5–4)

36 = b^3.5: => To isolate b take the 3.5 root of both sides

{3.5 root}(36) = {3.5 root}(b^3.5)

2.783927 = b

Now to solve for a

2 = (a)(b)^4 => 2 = (a)(2.783927)^4 => 2 = (a)(60.066375) divide both sides by 60.066375 0.0332965 = a

Equation: y = (0.0332965)(2.783927)^x

Now plug in 9.5 for x

(0.0332965)(2.783927)^9.5 = 558.0178525 = 558.02

The amount of fabric needed to cover 8 blocks is 192cm.

In order to determine the amount of fabric needed, the total surface area of the rectangular prism has to be determined. The total surface area of the rectangular prism is the sum of the areas its faces.

Total surface area of a rectangular prism = 2 (lw + wh + lh)

where:

2 x [(4 x 1/2) + (1/2 x 2) + (4 x2)] = 24cm

Fabric needed fo 8 blocks = 24 x 8 = 192cm

To learn more about rectangular prisms, please check: https://brainly.com/question/8890358

Answer:

The amount of fabric needed to cover 8 blocks is 192cm.

How much fabric is needed to cover 8 blocks?

In order to determine the amount of fabric needed, the total surface area of the rectangular prism has to be determined. The total surface area of the rectangular prism is the sum of the areas its faces.

Total surface area of a rectangular prism = 2 (lw + wh + lh)

where:

l = length

w = width

h = height

2 x [(4 x 1/2) + (1/2 x 2) + (4 x2)] = 24cm

Fabric needed fo 8 blocks = 24 x 8 = 192cm

Step-by-step explanation:

Answer:549.81

Step-by-step explanation:because that is thhe answer you get

Answer:

$549.81

Step-by-step explanation:

Price

Money in hand

Money needed

Answer:

[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]

Step-by-step explanation:

[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Learn more about scale factors here :

https://brainly.com/question/8765466

Answer:

514 square feet

Step-by-step explanation:

2(7×4+4×5+5×7)+2(10×8+8×6+10×6)

=2*83 +2*188

=166+376

=542 square feet

7*4=28

542-28=514 square feet

Answer:

640ft

Step-by-step explanation:

7ft×4ft×5ft = 160

10ft×8ft×6ft=480

Add them together

480+160=640 so the answer is 640ft

The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.

If two solids, A and B, are given and have corresponding dimensions as a and b respectively, we would have the following:

Surface area of solid A/Surface area of solid B = a²/b²

Volume of solid A/Volume of solid B = a³/b³

Given that solid A and solid B are similar, and:

Find their corresponding dimensions, a and b:

Surface area of solid A/Surface area of solid B = a²/b²

Substitute

675/432 = a²/b²

√(675/432) = a/b

1.25 = a/b

Scale factor of Solid A to Solid B is 1.25.

Multiply 1.25 by 960 to get the volume of solid A.

Volume of solid A = 960 × 1.25 = 1,200 m³.

Learn more about area and volume of similar shapes on:

https://brainly.com/question/12580764

Answer:

The answers are A, B, C, and probably F

Step-by-step explanation:

Volume is how much space an object takes up, while surface area is how much space is on the surface of the object. In option A, we are measuring how much gas can fit in a tank, so volume is used. B and C are also dealing with filling a container. Options D, E, and G are measuring the surface area because they are asking how much of something is needed to cover the surface of a car, barn, and gift. In option F, assuming that the jewelry is pure gold, not just a metal with a gold coating, volume is used.

Hope this helps!

Answer:

- 17° C

Step-by-step explanation:

the temperature falls at 3° per hour

midnight → 5.00 am is 5 hours , then

5 × - 3 = - 15 ← falls 15° in the 5 hours

temperature at 5..00 am = - 2 - 15 = - 17° C

Answer:

-17

Step-by-step explanation:

as it is falling by three so at 5am it will reach -17

Answer:

a = 9    b = 9    c = 18

Step-by-step explanation:

a+b = c

a+ b + c = 36        but we know   a+b = c   sub that in

  c    + c = 36

       c = 18             now  a + b = c    and a and b are the same

                                   so  a and b are = 9

Answer:

a is 9

b is 9

c is 18

Step-by-step explanation:

Let's list the information provided

a + b =c

a + b + c = 36

a=b

Knowing that a=b we can replace b with a in the equations

a+a is the same as 2a since a is being doubled

2a=c

Knowing this we can replace c with 2a

2a+2a=36

Now solve for a

[tex]2a+2a=36\\4a=36\\\frac{4a}{4} =\frac{36}{4} \\a=9[/tex]

Now let's sub this value of a into the equations to see what the other values are

a=b

9=b

2a=c

2(9)=c

18=c

Answer:

B. Subtract 2x

D. Add 6

Step-by-step explanation:

To solve this problem, isolate it by the term of x from one side of the equation.

First, add by 6 from both sides.

[tex]\sf{8x-6+6=2x+24+6}[/tex]

Solve.

Add.

24+6=30

Rewrite the problem down.

[tex]\sf{8x=2x+30}[/tex]

You have to subtract by 2x from both sides.

[tex]\sf{8x-2x=2x+30-2x}[/tex]

Solve.

8x-2x=6x

Rewrite the problem down.

6x=30

Then, you divide by 6 from both sides.

6x/6=30/6

Solve.

Divide the numbers goes from left to right.

30/6=5

x=5

Therefore, the solution is x=5, which is our answer.

In the correct answer is B and D.

I hope this helps you! Let me know if my answer is wrong or not.

The Critical z-values are -1.96 and 1.96 option second is correct.

It is given that the teachers were allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes.

It is required to find the critical z-values.

It is defined as the area region enclosed by the standard normal curve or bell curve. It gives an idea about every variable, and what value of probability the variables acquire.

We are assuming the data given below:

x = 3.5

[tex]\mu =3.3[/tex]

[tex]\sigma = 0.6[/tex]

n = 40

We know the formula for the Z score:

[tex]\rm Z = \frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]\rm Z = \frac{3.5-3.3}{\frac{0.6}{\sqrt{40} } }[/tex]

Z = 2.10

The area under the normal distribution curve:

P(Z= 2.10)  = 0.9821   ( from the z table)

We have null hypothesis H0: in the two groups, the level of job satisfaction is the same ie. with no difference.

H1: There is a significant difference in levels of job satisfaction.

The above hypothesis defined that the test is two-tailed which means there will be two rejection regions.

The critical z-values are:

-1.96 and 1.96  (from the critical value calculator at a 5% significance level with two-tailed)

Thus, the Critical z-values are -1.96 and 1.96 option second is correct.

Learn more about the critical value here:

https://brainly.com/question/13686040

Answer:X = 13

Step-by-step explanation:

An exterior angle is equal to the sum of the two opposite interior angle

⇒95=4x+3 + 3x+ 1

95=4x + 3x + 3 + 1

95=7x + 4

95-4=7x

91=7x

91/7=x

13=x

This implies that X= 13

Answer:

A formula is a method that has been proven to work when solving specific types of problems.

Step-by-step explanation:

Answer:

Three digit number to be divisible by 5 , the last digit should be 5 or 0

_ _ _5

Two remaining places can be filled in 4×3=12

_ _ _0

Two remaining places can be filled in 3×3=9 (0 cannot be filled in the first place, it will become 2 digit number).

Total =12+9=21

Answer:

-180√3

Step-by-step explanation:

3√10 x - 6√30

= 3x-6 x -√10 x √30

= -18 x√300

= -18 x 10√3

= -180√3

Answer:

∠ YZX ≈ 19.7°

Step-by-step explanation:

using the sine ratio in the right triangle.

sin YZX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{XY}{YZ}[/tex] = [tex]\frac{7.5}{22.3}[/tex] , then

∠ YZX = [tex]sin^{-1}[/tex] ( [tex]\frac{7.5}{22.3}[/tex] ) ≈ 19.7° ( to 3 significant figures )