System of equations by elimination
2x - 3y = 5
2x + 2y = 10

Answer:

Step-by-step explanation:

We are to show that [tex]\sqrt{3} cosec140^{0} - sec140^{0} = 4\\[/tex]

Proof:

From trigonometry identity;

[tex]cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}[/tex]

[tex]\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\[/tex]

From trigonometry, 2sinAcosA = Sin2A

[tex]= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}[/tex]

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

[tex]\frac{4(sin(420-140)) }{sin280}[/tex]

= [tex]\frac{4sin280}{sin280}\\ = 4 \ Proved![/tex]

Answer:

the answer is graph 1

Answer:

78

Step-by-step explanation:

400-244=156

156/2=78

Answer:

78 years old

Step-by-step explanation:

400 − 2 x = 244

400 − 244 = 2 x

156 = 2 x

so the answer would be 78 years old...

Hope that was helpful.Thank you!!!

Answer:

school b

Step-by-step explanation:

it has more

Answer:

School C

Step-by-step explanation:

It got more than its original amount

Answer:

The expression as a sum of terms is [tex]2\cdot a^{\frac{3}{2} } - 4\cdot a^{-\frac{1}{2} }[/tex].

Step-by-step explanation:

The expression to be rewritten has the following form:

[tex]\sqrt{a} \cdot (2\cdot a^{2}-\frac{4}{a} )[/tex]

A polynomial as a sum of terms consists in a sum of terms of the form [tex]c_{i} \cdot a^{k(i)}[/tex], where [tex]c_{i}[/tex] and [tex]k_{i}[/tex] are the i-th coefficient and exponent. The expression has to be expanded to create the sum of terms:

[tex]a^{\frac{1}{2} }\cdot (2\cdot a^{2} - 4\cdot a^{-1})[/tex]

[tex]2\cdot a^{1 + \frac{1}{2} } - 4\cdot a^{-1+\frac{1}{2} }[/tex]

[tex]2\cdot a^{\frac{3}{2} } - 4\cdot a^{-\frac{1}{2} }[/tex]

The expression as a sum of terms is [tex]2\cdot a^{\frac{3}{2} } - 4\cdot a^{-\frac{1}{2} }[/tex].

Answer:

l = 20 cm

w = 12 cm

Step-by-step explanation:

P = 64 = 2w + 2l

2w = 4 + l

64 = 4 + l  + 2l

64 - 4 = 3l

3l = 60

l = 20 cm

2w = 20 + 4

2w = 24

w = 12 cm

Answer: (2, 6)

Step-by-step explanation:

y - x > -3

x coordinate is 2 and y coordinate is 6

Plug in the x and y coordinates

6 - 2 = 4

4 > -3

Answer:

There are 54 total sweets  

Step-by-step explanation:

Alex: Stephen : Bridget : total

4:          1          :      1       : 4+1+1 = 6

Alex gets 36

36/4 = 9

Multiply each number by 9

Alex: Stephen : Bridget : total

4*9:          1*9   :      1*9    :    6*9

36:               9 :         9     :   54

There are 54 total sweets  

Answer:

[tex]C(m)=0.9m^2+0.25[/tex]

Step-by-step explanation:

The surface area of a cube-shaped box with a side of m feet is given by the function:

[tex]S(m)=6m^2[/tex]

The cost, C, in dollars, of wrapping a box with a surface area of x square feet is given by the function:

[tex]C ( x ) = 0.15 x + 0.25[/tex]

We want to find an explicit expression that models the costs of wrapping a cube-shaped box with a side length of m feet.

In the cost function, C(x), x is the surface area, therefore:

[tex]S(m)=x;$ and$\\C ( S(m) ) = 0.15(6m^2) + 0.25\\C(m)=0.9m^2+0.25[/tex]

To find the cost of wrapping a cube of side length m feet, we use the explicit function:

[tex]C(m)=0.9m^2+0.25[/tex]  

Answer: 60miles/hours

Step-by-step explanation:

From the question, a bus travels the 240 miles from Boston to New York and the bus departs at 11:00 a.m. and arrives in New York at 3:00 p.m. The time taken by the bus is (3:00pm - 11:00am) = 4 hours.

Average speed = Distance/Time

Average speed =240miles/4 hours

Average speed= 60miles/hours

The the average speed of this bus is 60miles/hour.

Answer:

C.

Step-by-step explanation:

If you are distributing, you must distribute the outside to both terms in the inside.

Answer: 2/3xy^-2z

Step-by-step explanation:

18/27 = 2/3

x^2 / x = x

y / y^3 = y^-2

z isn’t changed

Put the variables together after dividing and you get 2/3xy^-2z.

Step-by-step explanation:

do you mean like this?

18x²y/27xy³z =

if yes the answer is like this

18/27 = 2/3

x²/x = x

y/y³ = 1/y²

1/z = 1/z

multiply all and that's the answer

⅔ * x * 1/y² * 1/z =

[tex] \frac{2x}{3 {y}^{2} z} [/tex]

Answer:

6a−14

Step-by-step explanation:

Answer:

[tex]=6a-14[/tex]

Step-by-step explanation:

[tex]3\left(4a-3\right)-\left(6a+5\right)\\\mathrm{Expand}\:3\left(4a-3\right):\quad 12a-9\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\\mathrm{Simplify}\:3\cdot \:4a-3\cdot \:3:\quad 12a-9\\=12a-9\\-\left(6a+5\right):\quad -6a-5\\=12a-9-6a-5\\\mathrm{Simplify}\:12a-9-6a-5:\quad 6a-14\\=6a-14[/tex]

Answer:

Step-by-step explanation:

[tex]12\sqrt{7}\\=31.74901[/tex]

Answer:

Step-by-step explanation:

V = 4/3(π)(3)^3

V= 4/3(27)π

V= 36π

V = 113.1 cm^3

Answer:

[tex]25[/tex]

Step-by-step explanation:

[tex]\frac{5^8 \times 5^{-2}}{5^4}[/tex]

[tex]\frac{5^{8+-2}}{5^4}[/tex]

[tex]\frac{5^{6}}{5^4}[/tex]

[tex]5^{6-4}[/tex]

[tex]5^2[/tex]

[tex]=25[/tex]

Answer:

TV=6 inch

Step-by-step explanation:

If Triangle JKL is similar to Triangle TUV, the following ratio applies.

[tex]\dfrac{JK}{TU}= \dfrac{KL}{UV}=\dfrac{JL}{TV}\\$JK=10in., JL=8in., KL=13in., TU=7.5., UV=9.75\\\dfrac{10}{7.5}= \dfrac{13}{9.75}=\dfrac{8}{TV}\\$Picking any two equal ratios\\ \dfrac{13}{9.75}=\dfrac{8}{TV}\\$Cross multiply\\13*TV=8*9.75\\TV=8*9.75 \div 13\\$TV=6 inch[/tex]

Answer:

The greatest common factor is 5.

15x+10=5(3x+2)

Answer:

m =44

Step-by-step explanation:

1/2 m -3/4 n = 16

Let n =8

1/2 m - 3/4(8) = 16

1/2 m - 6 = 16

Add 6 to each side

1/2 m -6+6 = 16+6

1/2 m = 22

Multiply each side by 2

m = 22*2

m = 44

Answer:c

Step-by-step explanation:

Answer:

40 Minutes.

Step-by-step explanation:

The current time = 4:12 p.M.

Emma's mom will be home from work in 70 minutes.

70 minutes = 1 hour 10 Minutes= 1: 10 Hours

[tex]\left\begin{array}{ccccc}&4&:&12 &p.m.\\+&1&:&10&\\--&--&--&--&--\\&5&:&22&p.m\end{array}\right[/tex]

Therefore, Emma's Mom will get home by 5: 22 p.m.

Emma has gymnastics lessons at 6 : 00 p.M.

To determine how much time Emma will have between the time that her mom gets home from work and the beginning of gymnastics lessons, we simply subtract 5:22 from 6.

[tex]\left\begin{array}{ccccc}&6&:&00 &p.m.\\-&5&:&22&\\--&--&--&--&--\\&00&:&40&\end{array}\right[/tex]

Emma  will have 40 Minutes.

Answer:

38

Step-by-step explanation:

70 mins

​  

=60 mins+10 minutes

=1 hour+10 mins

=1 hour and 10 mins

​  

Hint #22 / 5

\begin{aligned} &4{:}12 + \greenD{1\text{ hour}}=5{:}12\\\\ &5{:}12 +\purpleD{10\text{ minutes}}=5{:}22 \end{aligned}  

​  

4:12+1 hour=5:12

5:12+10 minutes=5:22

​  

Emma's mom will be home at 5{:}22\text{ p.m.}5:22 p.m.5, colon, 22, start text, space, p, point, m, point, end text

How much time will Emma have between 5{:}22\text{ p.m.}5:22 p.m.5, colon, 22, start text, space, p, point, m, point, end text and the beginning of gymnastics lessons at 6{:}00\text{ p.m.}?6:00 p.m.?6, colon, 00, start text, space, p, point, m, point, end text, question mark

Hint #44 / 5

\blueD{8}\text{ mins} + \maroonD{30}\text{ mins} = 38\text{ mins}8 mins+30 mins=38 minsstart color #11accd, 8, end color #11accd, start text, space, m, i, n, s, end text, plus, start color #ca337c, 30, end color #ca337c, start text, space, m, i, n, s, end text, equals, 38, start text, space, m, i, n, s, end text

Hint #55 / 5

Emma will have 38 minutes between the time that her mom gets home from work and the beginning of gymnastics lessons. FROM KHAN ACADEMY THO.

Answer:

Step-by-step explanation:

Recall the logic quantifiers [tex]\forall, \exists[/tex] which means for all/for every and exists.

a) This means that for every student in D that is a computer science this implies that the student is not an engineering student. So for a student s in D such that C(s) then  E(s) is false. This is symboled by

[tex]\forall s \in D C(s) \implies \neg E(s)[/tex]

b) By saying "some computer science students" this means that there exists some studenst that study computer science and are also math majors. This is symboled by

[tex]\exists s \in D C(s)\land M(s) [/tex]

Answer:D

Step-by-step explanation:

Answer:-7n-21-8-64n

-71n-29

Step-by-step explanation:

Answer: -71n - 29

Step-by-step explanation:

-7n - 21 -8 - 64n

Collect like terms:

-7n - 64n -21 - 8

=========================================================

Work Shown:

We see that one of the legs is unknown. We'll call this 'a'.

The other leg is b = 2, which becomes b^2 = 4

The hypotenuse (always opposite the 90 degree angle) is c = sqrt(58). This turns into c^2 = 58 when you square both sides.

---------

Use the pythagorean theorem to get

a^2+b^2 = c^2

a^2+4 = 58

a^2 = 58-4

a^2 = 54

a = sqrt(54)

a = sqrt(9*6)

a = sqrt(9)*sqrt(6)

a = 3*sqrt(6)

The third side in simplest radical form is x=3[tex]\sqrt{6}[/tex]

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios, metric relationships, or the Pythagorean Theorem.

For solving this question, you need to apply the Pythagorean Theorem that says: (hypotenuse)²= (leg1)²+(leg2)².  

The question gives:

Applying the Pythagorean Theorem, you have:

([tex]\sqrt{58}[/tex])² = 2²+ x²

58=4+x²

x²=58-4

x²=54

x=[tex]\sqrt{54}[/tex]

x=[tex]\sqrt{2*3^3}[/tex]

x=[tex]\sqrt{2*3^2*3}[/tex]

x=3[tex]\sqrt{2*3}[/tex]

x=3[tex]\sqrt{6}[/tex]

Learn more about the Pythagorean theorem here:

brainly.com/question/11528638

#SPJ6

Answer:

50 percent

Step-by-step explanation:

Answer: there is a 50% chance

Step-by-step explanation:

there are three numbers less than four on a number cube. 3/6 is equivalent to 1/2

Answer:

[tex]9\; \rm m[/tex].

Step-by-step explanation:

Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with [tex]\rm 12\; m[/tex]. The three labelled lines in this diagram will form a right triangle.

Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:

[tex](\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2[/tex].

In this particular right triangle:

[tex](\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2[/tex].

[tex](\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2[/tex].

Therefore, the height of this ridge would be [tex]\sqrt{81}\; \rm m = 9\; \rm m[/tex]. (Note the unit.)

[tex]answer \\ b = 15 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

The measure of angle b is 15 degrees and this can be determined by using the properties of the isosceles triangle.

Given :

The following steps can be used in order to determine the measure of angle b:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

[tex]\angle Q + \angle P + \angle R = 180[/tex]

[tex]\angle Q + 2\angle R = 180[/tex]

[tex]2\angle R = 180-60[/tex]

[tex]\angle R = 60^\circ[/tex]

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

[tex]\angle P + \angle S + \angle R = 180[/tex]

[tex]\angle S + 2\angle R = 180[/tex]

[tex]2\angle R = 180-90[/tex]

[tex]\angle R = 45^\circ[/tex]

Step 4 - Now, the measure of angle b is calculated as:

[tex]\angle b = 60-45[/tex]

[tex]\angle b = 15^\circ[/tex]

The measure of angle b is 15 degrees.

For more information, refer to the link given below:

https://brainly.com/question/7915845

Step-by-step explanation:

milk container

a room spray

coke can

Answer:

Pipes

Cold drink cans

Water tanks

Battery

Gas cylinder

Candle

Test tube

Beaker

Fire extinguisher

Answer:

Yes

Step-by-step explanation:

Yes because there is only 1 y value per x value.

Answer:

yes

Step-by-step explanation:

There is a one to one correspondence and this will pass the vertical line test