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3 years ago

X=3 is a factor of x^3+3x^2-7x+19.

Mathematics

1 answer:

Andrew [12]3 years ago

7 0

Answer:

Step-by-step explanation:

3^3+3(3)^2-7(3)+19

27+27-21+19

54-2

Hope this helps

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Juli2301 [7.4K]

<h3>Answer: 6 ounces</h3>

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

Work Shown:

(6 servings)/(4 oz of sauce) = (8 servings)/(x oz of sauce)

6/4 = 8/x

6*x = 4*8

6x = 32

x = 32/6

x = 5.333 approximately

x = 6 we round up despite 5.333 being closer to 5, than it is to 6.

If we went with 5 ounces, then we wouldn't clear the hurdle needed to serve 8 people.

The section below goes over why this is the case in more detail.

---------

6 servings : 4 ounces

6/4 servings : 4/4 ounces

1.5 servings : 1 ounce

So one ounce of sauce gets us 1.5 servings.

If we multiply both sides by 5, then,

1.5 servings : 1 ounce

5*1.5 servings : 5*1 ounce

7.5 servings : 5 ounces

This shows that 5 ounces of sauce will only produce 7.5 servings, which comes up short compared to 8 servings.

If we multiplied both sides by 6, then

1.5 servings : 1 ounce

6*1.5 servings : 6*1 ounce

9 servings : 6 ounces

This shows that 6 ounces of sauce yields 9 servings. We've gone overboard, but it's better to do that than come up short.

3 0

2 years ago

If the angles are represented in degrees,find both angles: csc(2x+9) =sec(3x+26) Please respond quick

Olenka [21]

Answer:

Before solving the given trigonometric relation change everything to sines and cosines

Step-by-step explanation:

consider the given equation;

$1/sin(2x+9)$ = $1/cos(3x+26)$

Multiplying the above equation on both sides by $cos(3x+26)sin(2x+9)$ then we get,

$cos(3x+26)=sin(2x+9)$

By using identity, $cos a=sin(90-a)$ expand above equation we will get,

$sin(90-(3x+26))=sin(2x+9)$

Then,

$90-3x+26=2x+9$

$x=11$

So the required value of the angle is $11$ degree.

3 0

2 years ago

What is the surface area of a square pyramid with a base side lengths of 10 inches and a slant height of 14 inches

miskamm [114]

You could find the surface area using two different methods, but coming out with the same answer.

Method One: This method involves using an equation that helps finding the surface area for a square pyramid.

The equation: A+(1/2)ps=SA; we should break down what the letters stand for. A=Area of the base; the area of the base is 10×10=100 P= perimeter of the base; 10×4=40 S= Slant height;14

Let's put these values into the equation and find the surface area. 100+(1/2)(40)(14)=100+(20)(14)=100+280=380 The surface area is 380 in².

Method Two: The picture below shows how to lay out the square pyramid so you can find the area of each the shapes, then add them up. There are four triangles and a square.

Triangles: We use the equation (1/2)BH; let's plug the values in. 1/2(10)(14)=1/2(140)=70; there are four triangles, so let's multiply by four to find the area of all four of them triangles together. 70×4=280

Square: It's the side length squared. 10²=100; let's add everything together.

The four triangles+the square= the surface area

280+100=380

So, the surface area is 380 in².