A rectangle measures 2(3x - 1) cm by (2x + 3) cm. If its perimeter is 98 cm what are the dimensions of this rectangle?​

Answer: 15

Step-by-step explanation:

Pythagorean theorem: c^2 = a^2 + b^2 where c is hypotenuse, a and b are legs.



In this problem:

a = 20

c = 25

b - ?

b^2 = c^2 - a^2

b^2 = 25^2 - 20^2

b^2 = 625 - 400

b^2 = 225

b = sqrt(225)

b = 15

I assume the given expression is

[tex]\sqrt x \sqrt[4]{x}[/tex]

We can write each root as a rational power of x, then add the exponents:

[tex]\sqrt x \sqrt[4]{x} = x^{\frac12} x^{\frac14} = x^{\frac12 + \frac14} = x^{\frac34}[/tex]

Then putting it back into radical form, we have

[tex]\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}[/tex]

The equation that can be used to determine the distance from school to his aunt's house is x = 29 miles / 10.What equation can be used to represent the total distance travelled? Total miles rode = 10(miles ridden to school) + (10 x miles rode to his aunt's house from school) 44 miles = (10 x 1.5) + (10 × x)44 miles = 15 miles +  10x What equation that can be used to determine distance rode from school to her aunt's house? Given this equation : 44 miles = 15 miles +  10x, take the following steps: Combine similar terms: 44 miles - 15 miles = 10x 29 miles = 10x Divide both sides by 10 x = 29 miles / 10 

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

Speed of Carmen = 40km/h

and speed of Carmella = 60km/h

Step-by-step explanation:

Let the speed of Carmen = x km/h

Carmella speed will be (x + 20)km/h

Distance = 120 km

Time between Carmen and Carmella = 1 hour

[tex] \sf Time= \frac{distance}{speed} [/tex]

Let the time taken by Carmen be T1

and Carmella be T2

[tex] \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} [/tex]

As there is 1 hour difference so

[tex] \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}[/tex]

We have not considered 60 as it will become negative value and negative value is not possible in distance

Speed of Carmen = 40km/h

Speed of Carmella = 40 + 20 = 60km/h

Answer:

last option, {x|x≠13}

Step-by-step explanation:

(f of g)(x) means f(x) x g(x):

(x + 7) x (1 / x - 13) = (x + 7) / (x - 13)

domain is all possible x values which is the denominator, x - 13

x - 13 = 0

Interval notation: (−∞,13)∪(13,∞) this means x does not equal 13

Answer:

B. AA similarity postulate

Answer:

Your net pay is

[tex]$1410[/tex]

Step-by-step explanation:

All we have to do is add the deductions and then subtract them from what your earn.

[tex]1600 - (110 + 66 + 14) = \\ 1600 - 190 = 1410[/tex]

Answer:

3.5.

Step-by-step explanation:

Y = kx   where k is the slope of the line

k = y/x

The slope 3/5/1 = 3.5

y/x = 3.5.

We have to double 5 and add 1 to get the same result.

5 + 5 + 1 = 11

We can also double 6 and subtract 1 to get the same result.

6 + 6 - 1 = 11

Hope this will helpful.

Answer:

They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more. Thus, 5 + 6 = 11. Practice solving other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.

The probabilities of cases 1, 2, 3, and 4 will be 1/3, 5/36, 1/6, and 1/4 respectively.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

The probability is given as

P = Favorable event / Total event

1.  The probability that you get a white chip from a box with 1 black chip, 1 white chip, and 1 red chip will be

P = 1/3

2.  The probability that you get an 8 when you are rolling a number cube will be  

P = 5/36

3.  From a letter cube (A, B, C, D, E, and F), Then the probability that a B is on top when you roll the cube will be

P = 1/6

4.  Mila and 3 other applicants apply for a job. Then the probability that Mila gets hired will be

P = 1/4

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Answer:

x = 10.5

Step-by-step explanation:

Intersecting chord theorem : If two chords intersect within a circle then the product of the measures of the segemnts made up of the chords are equal to each other.
For more reference to this, kindly view the attatched image.

Applying this theorem we would create an equation which would be 2 × x = 7 × 3

We then solve for x

2 × x = 7 × 3

==> simplify both sides

2x = 21

==> divide both sides by 2

x = 10.5

The distance that would be covered after t seconds = 1.5t meters

The speed of the race=distance/time =1.5m/s

The time given = t seconds

The distance (d) = ?

From the formula of speed = distance/time, make distance the subject of formula,

distance (d) = speed×time

= 1.5×t

= 1.5t meters

Therefore, the distance covered is 1.5t meters after t seconds.

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Answer:

1.47 is larger

Step-by-step explanation:

the reason why it's larger is bc the negative sign shows it's below zero

If the measure of the angle is 2π/3 the correct option will be tan∅=-√3.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

It is given in the question that:-

The measure of the angle is = [tex]\dfrac{2\pi}{3}[/tex]

We can also write the angle as = [tex]\dfrac{2\times 180}{3}=120[/tex]

Now from the options, the only value which satisfies this angle is tan∅=-√3.

 [tex]tan\dfrac{2\pi}{3}=tan \dfrac{2\times 180}{3}=tan(120)=-\sqrt{3}[/tex]

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Answer:

x alpha 1/y

: Introducing a constant k

x = k/y

where x = 7, y= 6

7 = k / 6

Cross Multiply

K ( constant) = 42

Answer: k = 42

Step-by-step explanation:

Formula = [tex]y = \frac{k}{x}[/tex]

plug in values:

6 = [tex]\frac{k}{7}[/tex]

multiply both sides by 7

k = 42

Answer: 88 units²

Step-by-step explanation: Alright, this ones is easy. Ok, so we know we have a right triangle so, therefore, we can find the missing sides required using trigoneomeric functions. If you dont know what these are here, take a look:

sinФ= opposite/hypotenuese

cosФ= adjancent over hypotneuse

tanФ= opposite/adjecent.

angle is 34

In this case the opp (opposite would be the base of the trinagle, the adj would be 16 units, and the hyportneuse would be "we dont know"

From here, we can set up this equation to find the area->

Now we know the base and height of the triangle, so using the formula 1/2*B*H for the area we get 88 units². Thank you!

The Area of Triangle is 86.272 unit².

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Perpendicular = 16

Using Trigonometry

tan 34 = P / B

0.674 = 16/ B

B= 10.784

So, Area of Triangle = 1/2 x b x h

                                 = 1/2 x 16 x 10.784

                                 = 86.272 unit²

Hence, the Area of Triangle is 86.272 unit².

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Answer:

C and J

Step-by-step explanation:

Answer:AA , BB , and CC are parallel to MN.

Step-by-step explanation:

Answer:

a = 13.24 m

Step-by-step explanation:

Finding ∠A :

Applying the Law of Sines :

Answer:

  13.2 m

Step-by-step explanation:

The Law of Sines can be used to solve a triangle when angles and one side are known.

__

The angles of a triangle total 180°, so the missing angle A is ...

  ∠A = 180° -48° -54° = 78°

The Law of Sines tells us ...

  a/sin(A) = b/sin(B)

  a/sin(78°) = (10.0 m)/sin(48°)

__

Multiplying by sin(78°), we find ...

  a = sin(78°)/sin(48°)×(10.0 m) ≈ 0.978148/0.743145×(10.0 m)

  a = 13.1623 m

The length of side 'a' is approximately 13.2 meters.

Answer:

8/12

Step-by-step explanation:

Answer:

Down below

Step-by-step explanation:

First one:  Sixth root of B.  Second one:  Fourth root of X to the Z power.  Third one:  Square root of nine to the third power.  Fourth one:  M root of M to the P power.  Fifth one:  Square root of J to the two plus x power.

Sorry if this is wrong.  I'm almost positive this is correct.  The only one I'm not sure about is the third one and maybe the last one.  Since there's no two there I'm not sure if it would still be called the square root.

Answer:

6 medians.

Step-by-step explanation:

because the medians of 5 and 7 is 6.

Answer:

864 ft^2

Step-by-step explanation:

Surface area equation is the same as the one used in the other problem; S=(1/2)lP + B

one side is 20 x 14 = 280

another side is 12x14 = 168

another side is 16x14 = 224

the triangle bases are A=(1/2)bh

(1/2)12 x 16 = 96

2(96) = 192

Add all sides together 192 + 224 + 280 + 168 = 864

Answer:

2nd row

Step-by-step explanation:

The y-intercept corresponds to the ordered pair having an x-value of 0. The second row of the table has an x-value of 0, and y-value of 2. Therefore, the y-intercept is (0, 2).

Abraham Lincoln, in his autobiography, kept his portrayal of his life very: A. neutral.

An autobiography can be described as the account of the of an individual which is authored by the individual whose life is being narrated.

For Abraham Lincoln, the manner in which he described himself sounded quite neutral in the autobiography he authored.

We can conclude that Lincoln kept his portrayal of his life very: A. neutral.

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Answer:

30 days.

Step-by-step explanation:

27 ÷ 0.9 = 30.

Answer:

in 30 days she will reach 27 miles.

Step-by-step explanation:

27 miles / 0.9 miles = 30 days

Answer:

C & D

Step-by-step explanation:

x^2+6x+7=0

Delta=b^2-4ac=6^2-(4*1*7)=36-28=8

X=((-b)+-(delta)^(1/2))/2

X=((-6)+-(2^(3/2)))/2

[tex]x1 = - 3 - \sqrt{2} \\ x2 = - 3 + \sqrt{2} [/tex]

The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of triangle ABC, hence:

18 ft² = (1/2) * 3 * h

h = 12 ft

Let x represent the height of triangle EFG, hence:

x/12 = 2/3

x = 8 feet

Area of EFG = (1/2) * 2 * 8 = 8 ft²

The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².

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