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3 years ago

Are the expressions 8a2 - 4b + 7a2 and 5(3a2 - 2b) + 6b equivalent? Explain your reasoning.

Mathematics

1 answer:

77julia77 [94]3 years ago

7 0

Answer:

Yes, The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent

Step-by-step explanation:

To answer the question you must simplify each expression, then compare them to find if they are equivalent or not

∵ The 1st expression = 8a² - 4b + 7a²

→ Add the like terms

∴ The 1st expression = (8a² + 7a²) - 4b

∴ The 1st expression = 15a² - 4b

∵ The 2nd expression = 5(3a² - 2b) + 6b

→ Multiply the bracket by 5

∴ The 2nd expression = 5(3a²) - 5(2b) + 6b

∴ The 2nd expression = 15a² - 10b + 6b

→ Add the like terms

∵ The 2nd expression = 15a² + (-10b + 6b)

∴ The 2nd expression = 15a² + -4b

→ Remember (+)(-) = (-)

∴ The 2nd expression = 15a² - 4b

∵ The 1st expression = The 2nd expression

∴ The two expressions are equivalent

∴ The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent

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Water is leaking out of an inverted conical tank at a rate of 6800.0 cubic centimeters per min at the same time that water is be

m_a_m_a [10]

Answer:

6.82 $mt^3/min$

Step-by-step explanation:

By congruence of triangles, the radius r of the cone base when its height is 1 meter satisfies the relation

r/1 = 2.5/6

(See picture attached)

So, r = 0.4166 meters when the water is 1 meter high.

The volume of a cone with radius of the base = R is given by

$V=\frac{\pi R^2h}{3}$

So, the volume of water when it is 1 meter high is

$V=\frac{\pi* 0.(4166)^2}{3}=0.1817\;mt^3$

One minute later, the height of the water is 1 meter + 30 centimeters = 1.30 mt

The radius now satisfies

r/1.3 = 2.5/6

and now the radius of the base is

r = 0.5416 mt

and the new volume of water is $0.3071\;mt^3$

So, the water is raising at a speed of

0.3071-0.1871 = 0.12 $mt^3/min$

This speed equals the difference between the water being pumped and the water leaking,

So,

0.12 = Speed of water being pumped -6.8

and

Speed of water being pumped = 6.8+0.12 = 6.82 $mt^3/min$

8 0

3 years ago

Can someone please tell me the answer on this.

marishachu [46]

Answer: x = 31

Step-By-Step:

To Find x:

$\left(2x+20\right)+\left(x+10\right)+\left(2x-5\right)=180$ (Angle Sum Property Of Triangles)

(Remove the brackets)

$2x+20+x+10+2x-5=18$

(Group Accordingly)

$2x+x+2x+20+10-5=180$

= $5x+20+10-5=180$

= $5x\:+\:25$ $=180$

= $5x= 180 - 25$

= $5x = 155$

= $x=\frac{155}{5}$

= $31$

Therefore x = 31

So,

Angle A = x + 10 = 31 + 10 = 41

Angle B = 2*x + 20 = 2*31 + 20 = 82

Angle C = 2*x - 5 = 62 - 5 = 57

5 0

3 years ago

Passes through (1,4) and is parallel to the line y=2x-3

Novay_Z [31]

Answer:

y = 2x + 2

Step-by-step explanation:

Slope = 2

y-intercept: 4 - (2)(1) = 2

3 0

3 years ago

Home Depot wants to buy a new line of fertilizers. Manufacturer A offers a 22/19 chain discount. Manufacturer B offers a 25/14 c

Temka [501]

Answer: A is 36.82%. B is 35.5%

Step-by-step explanation: For manufacturer A 22/19 chian discount simply means 22% discount followed by 19% discount.

Therefore we have 100-22= 78 and 100-19=81.

The final price would be 0.78*0.81=0.6318

Therefore discount would be

1 - 0.6318=0.3682

Hence, percentage discount would be 0.3682*100%=36.82%.

For manufacturer B 25/14 chian discount means 25% discount followed by 14% discount. So we have 100-25=75% and 100-14= 86%

Final price would be 0.86*.75=0.645.

Discount= 1 - 0.645= 0.355.

Percentage discount would be 0.355*100%=35.5%.

3 0

3 years ago

Rafeeq bought a field in the form of a quadrilateral (ABCD)whose sides taken in order are respectively equal to 192m, 576m,228m,

Valentin [98]

Answer:

a. 85974 m²

b. 17,194,800 AED

c. 18,450 AED

Step-by-step explanation:

The sides of the quadrilateral are given as follows;

AB = 192 m

BC = 576 m

CD = 228 m

DA = 480 m

Length of a diagonal AC = 672 m

a. We note that the area of the quadrilateral consists of the area of the two triangles (ΔABC and ΔACD) formed on opposite sides of the diagonal

The semi-perimeter, s₁, of ΔABC is found as follows;

s₁ = (AB + BC + AC)/2 = (192 + 576 + 672)/2 = 1440/2 = 720

The area, A₁, of ΔABC is given as follows;

$Area\, of \, \Delta ABC = \sqrt{s_1\cdot (s_1 - AB)\cdot (s_1-BC)\cdot (s_1 - AC)}$

$Area\, of \, \Delta ABC = \sqrt{720 \times (720 - 192)\times (720-576)\times (720 - 672)}$

$Area\, of \, \Delta ABC = \sqrt{720 \times 528 \times 144 \times 48}$ = 6912·√(55) m²

Similarly, area, A₂, of ΔACD is given as follows;

$Area\, of \, \Delta ACD= \sqrt{s_2\cdot (s_2 - AC)\cdot (s_2-CD)\cdot (s_2 - DA)}$

The semi-perimeter, s₂, of ΔABC is found as follows;

s₂ = (AC + CD + D)/2 = (672 + 228 + 480)/2 = 690 m

We therefore have;

$Area\, of \, \Delta ACD = \sqrt{690 \times (690 - 672)\times (690 -228)\times (690 - 480)}$

$Area\, of \, \Delta ACD = \sqrt{690 \times 18\times 462\times 210} = \sqrt{1204988400} = 1260\cdot \sqrt{759} \ m^2$

Therefore, the area of the quadrilateral ABCD = A₁ + A₂ = 6912×√(55) + 1260·√(759) = 85973.71 m² ≈ 85974 m² to the nearest meter square

b. Whereby the cost of 1 meter square land = 200 AED, we have;

Total cost of the land = 200 × 85974 = 17,194,800 AED

c. Whereby the cost of fencing 1 m = 12.50 AED, we have;

Total perimeter of the land = 576 + 192 + 480 + 228 = 1,476 m

The total cost of the fencing the land = 12.5 × 1476 = 18,450 AED

4 0

3 years ago