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arsen [322]
3 years ago
13

If (x+2) is a factor of 3x^2+14x+k, what is the value of k?

Mathematics
1 answer:
valkas [14]3 years ago
3 0
If (x+2) is a factor of 3x^2+14x+k, the equation must equal zero when x=-2 so:

3(-2)^2+14(-2)+k=0

12-28+k=0

-16+k=0

k=16
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In the image below, DE || BC. Find the measure of EC. Set up a proportion and solve for the measure. Show your work and label yo
mixer [17]

The missing figure is attached down

Answer:

The measure of EC is 1 foot

Step-by-step explanation:

Let us revise the cases of similarity

  • AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle
  • AA similarity : If two angles of one triangle are equal to the  corresponding angles of the other triangle, then the two triangles  are similar.
  • SSS similarity : If the corresponding sides of the two triangles are  proportional, then the two triangles are similar.
  • SAS similarity : In two triangles, if two sets of corresponding sides  are proportional and the included angles are equal then the two  triangles are similar.  

From the attached figure

∵ DE // BC

∴ ∠ADE ≅ ABC ⇒ corresponding angles

∴ ∠AED ≅ ACB ⇒ corresponding angles

In Δs ADE and ABC

∵ ∠ADE ≅ ABC ⇒ proved

∵ ∠AED ≅ ACB ⇒ proved

∵ ∠A is a common angle in the two triangles

∴ Δ ADE is similar to triangle ABC by AAA postulate

From the results of similarity the corresponding sides of the triangles are proportion

∴ \frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}

∵ AD = 8 feet

∵ DB = 2 feet

∴ AB = AD + DB

∴ AB = 8 + 2 = 10 feet

∵ AE = 4 feet

By using the proportion statement above  \frac{AD}{AB}=\frac{AE}{AC}

∴ \frac{8}{10}=\frac{4}{AC}

By using cross multiplication

∴ 8 × AC = 10 × 4

∴ 8 AC = 40

Divide both sides by 8

∴ AC = 5 feet

∵ AC = AE + EC

∴ 5 = 4 + EC

Subtract 4 from both sides

∴ 1 = EC

∴ The measure of EC is 1 foot

4 0
3 years ago
a milha eh uma unidade usada para medir distancias. ela equivale a cerca de 1,6 quilometros. se cada carro percorrer 240 quilome
Pani-rosa [81]

Classica aplicação de regra de 3:

é dito que: 1 milha = 1,6km

Logo, eis a regra de 3:

  milha           km

     1   --------    1,6

     X  --------   240

1,6X = 240.1

X = 240/1,6

<h3>X = 150milhas</h3><h3 />

Logo 240km equivalem a 150milhas

6 0
3 years ago
What is the inverse function of dx) = 2x - 4?
miss Akunina [59]

Answer:

y = x/2 + 2

Step-by-step explanation:

y = 2x - 4

swap y and x

x = 2y - 4

x + 4 = 2y

x/2 + 2 = y

8 0
3 years ago
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Reagan solved 5.25 ÷ 5 and got 105. What did Reagan do wrong?
horrorfan [7]

Answer:

he forgot to put the decimal point

Step-by-step explanation:

answer is 1.05.

4 0
3 years ago
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Is -7 greater than -4​
antiseptic1488 [7]
No you’re welcome :)
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