The rectangular frame is made from 5 straight pieces of metal.
6 m
8 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.

Answer: The measurement of ∠EFG is equal to 70°.

Step-by-step explanation:

Two interior angles who are always opposite to an exterior angle sums to that exterior angle. So we would start as the following:

(6x - 10) + 38 = 7x + 18

In order to find m∠EFG, we must first isolate x. In order to do that, we first add like terms together on both sides.

(6x - 10) + 38 = 7x + 18

6x + 28 = 7x + 18

We then substract 18 on both sides.

6x + 10 = 7x

We finally substract 6x from both sides in order to have the value of x.

x = 10

Now that we know the value of x, we substitute it in our the equation in order to find m∠EFG.

m∠EFG = 6x + 10

m∠EFG = 6(10) + 10

m∠EFG = 60 + 10

m∠EFG = 70

Answer:

50°

Step-by-step explanation:

( 7x + 18 )° = ( 6x - 10 )° + 38°

7x + 18 = 6x - 10 + 38

7x - 6x = 28 - 18

x = 10

m∠EFG = 6(10) - 10

m∠EFG = 50°

Answer:

2ax − 6ay + bx − 3

Step-by-step explanation:

The expression is not factorable with rational numbers

Answer:

Step-by-step explanation:

2a(x - 3y) + b(x - 3y)

Answer:

(f ∘ g) (3) = 22

Step-by-step explanation:

f( x + 3x - 5; g (x) = x² ∴ g ( 3 ) = 3² = 9

( f ∘ g ) ( 3 ) = f(g(3)) = f ( 9 ) =  3 · 9 - 5 = 27 - 5 = 22 [Ans]

Answer:

this means it shows half as a fraction turned into a decimal

Step-by-step explanation:

1/2=fraction form

0.5=decimal form

50%=percent form

half=word form

Answer:

see explanation

Step-by-step explanation:

substitute the values of x in the table into g(x)

Using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

g(- 2) = [tex]4^{-2}[/tex] = [tex]\frac{1}{4^{2} }[/tex] = [tex]\frac{1}{16}[/tex]

g(- 1) = [tex]4^{-1}[/tex] = [tex]\frac{1}{4}[/tex]

g(0) = [tex]4^{0}[/tex] = 1

g(1) = [tex]4^{1}[/tex] = 4

g(2) = 4² = 16

Answer:

64, -64, -64

-27, 27, 27

Step-by-step explanation:

If x = 4,

x³ = 4³ = 64

-x³ = -4³ = -64

(-x)³ = (-4)³ = -64

If x = -3,

x³ = -3³ = -27

-x³ = -(-3)³ = 27

(-x)³ = (-(-3))³ = 27

Answer:

5

Step-by-step explanation:

14x - 8x = 30

5x = 30

x = 6

..........

Answer:

solution

14x=8x+30

collect like terms

30=8x-14x

30= -6x

divide by -6x

30/-6 = -6x/-6

X= –5

Answer:

4.5927 x 10^-2 ?

Step-by-step explanation:

Answer:

1st: $50 2nd: $250 3rd: $85

Answer: 1/4

Given : On average, Carson spends about 26% of his allowance each month on candy and soft drinks.  

To Find : When creating a circle graph of what Carson does with his money, which of the following fractions would be the best to represent how much he spends on food?

If these are your Choices:

A) 1/4

B) 1/3

C) 3/4

D) 1/2

Solution:

To Convert fraction into % multiply by 100  

(1/4) * 100 = 25 %

(1/3) * 100  = 33.33 %

(3/4) * 100 = 75 %

(1/2) * 100 = 50 %

Therefore 1/4 fraction best represent how much he spends on food

Answer:

Step-by-step explanation:

A= W*L

A= 31/3*21/4

A=10.3*5.25

A=54.075cm^2

Answer:

7 1/2in^2

Step-by-step explanation:

LxW=A

2 1/4 x 3 1/3 = A

A = 7 1/2

Answer:

Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.

Step-by-step explanation:

Find the z-scores by subtracting the score they got by the mean and then dividing by the standard deivation of their respective exams.

Xiaoyu:

z = [tex]\frac{27 - 18}{6}[/tex] = 1.5

Emily:

z = [tex]\frac{720 - 500}{100}[/tex] = 2.2

______

Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.

Answer:

B)120º

Step-by-step explanation:

70+50=x

120=x

Sum of two interior angles=exterior angle

[tex]\\ \sf\longmapsto 50+70=x[/tex]

[tex]\\ \sf\longmapsto x=120[/tex]

Option B

Answer:

45 miles in 3 days

Step-by-step explanation:

if she drives 3 miles an hour for 5 hours a day that would be 3x5=15

15x3 days=45 miles in 3 days

Answer:

no, it is incorrect it is 1-100 the value

Step-by-step explanation:

0.006×10= 0.06

0.006×100=0.6

Answer:

Every point of a number line is assumed to correspond to a real number, and every real number to a point. The integers are often shown as specially-marked points evenly spaced on the line.

Answer:

Answer 1 is 4:2 or also write as 2:1.

[tex]\large\underline{\sf{Solution-}}[/tex]

Given function is

[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]

Now,

[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]

We know,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]

So,

[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]

So, from graph we concluded that cosx > 0 in the following intervals.

[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]

So, if we generalized this we get

[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]

Hence,

Domain of the function is

[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]

[tex]\textsf{More to know :-} \\[/tex]

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]

Answer:

7!!

Step-by-step explanation:

nth number is 83 hope you understand my answer thanks

Answer: 3n^2 + 8

Step-by-step explanation:

an^2 + bn + c

It is a quadratic sequence

11, 20, 35, 56, 83

 +8 +15 +21 +27

    +6   +6   +6

a + b + c

4a + 2b + c

9a + 3b + c

4a + 2b + c - a + b + c = 20 - 11

4a + 2b + c - a + b + c = 9

3a + b = 9

9a + 3b + c - 4a + 2b + c = 35 - 20

5a + b = 15

-2a = -6

a = -6/-2

a = 3

Substitute to find the values of b & c

For b

5(3) + b = 15

15 + b = 15

b = 15 - 15

b = 0

For c

9(3) + 3(0) + c = 35

27 + c = 35

c = 35 - 27

c = 8

3n^2 + 0n + 8

3n^2 + 8

Answer:

Any number in the form of p/q where p and q are integers and q is not equal to 0 is a rational number.

So, 323.2685109 is IRRATIONAL number.

Answer:

If you mean percent, its 350%

Answer:

1134

Step-by-step explanation:

1134/63=18

The upper bound means the highest number that you can round up to the nearest unit, in this case meters. So the upper bound for the distance of 100 meters is 100.4 meters.

Answer:

bye

Step-by-step explanation:

Answer:

88 trucks

Step-by-step explanation:

Ratio of cars : vehicles = 5:13

Hence, the ratio of trucks : vehicles = 8:13

143/13 = 11

If the number of vehicles is 143,

we have to multiply both sides of the ratio by 11:

8*11 : 13* 11

88 : 143

Hence, there are 88 trucks for every 143 vehicles.

Hope this answers your question... Have a wonderful time ahead at Brainly!

Answer:

12

Step-by-step explanation:

the answer is just 12.

Answer:

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )

Step-by-step explanation:

let me write the standard form of a quadratic equation

[tex]a {x}^{2} + bx + c[/tex]

Now let me rewrite the original equation

[tex]3 {x}^{2} + 18x + 32[/tex]

Now we use this simple formula to find the vertex (h, k)

[tex]x = h = - \frac{b}{2a} \\ = - \frac{18}{2(3)} = - \frac{18}{6} = - 3 \\ h = - 3[/tex]

substitute -3 for x back into our original equation to solve for y our k value of our vertex

[tex]y = 3 ({ - 3})^{2} + 18( - 3) + 32 \\ = 3(9) - 54 + 32 \\ = 27 + 32 - 54 \\ = 59 - 54 \\ k = 5[/tex]

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )

Answer:

1/4

Step-by-step explanation:

Slope = (change in the y-values)/(change in the x-values)

Slope = (4 - 2)/(1 - (-7) )

Slope =  (4 - 2)/(1 + 7)

Slope = 2/8

Slope = 1/4