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3 years ago

Explain how the expression 19√2+2√8 can be simplified using the distributive property.

Mathematics

1 answer:

Ilya [14]3 years ago

3 0

Answer:

23√2

Step-by-step explanation:

1. Simplify √8 to 2√2

19√2 +2* 2√2

2. Simplify 2*2√2 to 4√2

19√2 + 4√2

3. Simplify

23√2

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In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

sinθ = opposite/hypotenuse Soh

cosθ = adjacent/hypotenuse Cah

tanθ = opposite/adjacent Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the hypotenuse. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the adjacent side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has hypotenuse and adjacent: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = $d*\frac{41ft}{d}$ Multiply both sides by "d"

dcos77° = 41 ft

dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°

d = 41 ft / cos77° Input into calculator

d = 182.261874....... ft Unrounded answer

d ≈ 182 ft Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

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3 years ago

Kate made an 85 on her English test. Her grade on the English test was 37 points less than twice the grade on her Science test.

Irina18 [472]

The grade of her sci test was 61. First I add 37 to 85, the sum being 122. Then if you divide it in half, you get the quotien and final answer of 61

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3 years ago

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What is the answer is it a Yes or No HELP!!! This is at test and I only need help on this problem

allsm [11]

Answer:

Yes

Step-by-step explanation:

y is said to be a function of x. where x is the independent variable and y is the dependent variable. The height of the stacks is y and the number of cups in the stack is x, so yes, we can say that the height of the stack is a function of the number of cups in the stack.

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2 years ago

Bengus the expert blacksmith forged 16 swords from copper, 25 swords from iron, and 20 swords from mythril.

Sidana [21]

You will get 61 swords

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3 years ago

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un rectangulo tiene 28 cm de perimetro y unos de sus lados mide 4 cm ¿cuantos cuadrados de 2 cm por lado se mecesitan para armar

seraphim [82]

Answer:

10 cuadrados

Step-by-step explanation:

Si uno de los lados de rectangulo es de 4cm entonces el lado parallelo tambien es de 4cm. Eso nos da 8cm del perimetro y nos quedan los otros dos lados que tienen la misma medida. Entonces dividimos el resto del perimetro por 2.

28 - 8 = 20cm

20cm / 2cm = 10cm

Ahora que tenemos todas las medidas podemos multiplicar el largo por el ancho para calcular el area del rectangulo

10cm * 4cm = 40 $cm^{2}$

el cuadrado de 2cm tendra un area de

2cm * 2cm = 4 $cm^{2}$

Ahora simplemente dividimos el area del rectangulo por el area del cuadrado para saber cuantos cuadrados necesitamos para armar ese rectangulo

40 $cm^{2}$ / 4 $cm^{2}$ = 10 cuadrados

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2 years ago