What is the vertex of the graph of f(x) = |x + 5| – 6?

(–6, –5)
(–6, 5)
(–5, –6)
(5, –6)

Final answer:

The correct formula for the surface area of a triangular prism is SA = 2B + Ph, where B is the area of one triangular base, P is the perimeter of this base, and h is the height of the prism.

Explanation:

To find the surface area of a triangular prism, we don't use any of the formulas mentioned for the area of a triangle or volume. The correct formula is one that combines the area of the base triangles and the rectangles formed by the sides of the prism. In this case, the correct formula is SA = 2B + Ph, where B represents the area of one of the triangular bases, P is the perimeter of the triangular base, and h is the height of the prism that is perpendicular to the bases.

Let's clarify the correct formula with an example: Imagine a triangular prism with a triangular base having sides of lengths 3m, 4m, and 5m, and a height of 6m. To find the base area B, you'd use the formula for the area of a triangle, which is B = bh/2, where b is the base and h is the height of the triangle. The perimeter P would simply be the sum of the sides of the triangular base. The surface area would then be calculated by plugging these values into the SA = 2B + Ph formula.

they need to equal 180 degrees

180-72 = 108 degrees

Answer: 108, 108, and 72 degrees

Step-by-step explanation:

Angle A = 72

Angle B = Angle D

Angle C = 72 (Since it is congruent to Angle A)

Angle D = Angle B

Since Angle A and C are congruent, so are angles B and D. Now you would have to subtract 72 from 180.

180 - 72 = 108

Angle A = 72

Angle B = 108

Angle C = 72

Angle D = 108

First we calculate the volume of the foundation:

Volume (V) = 20 ft * 12 ft * 4 in (1 ft / 12 in)

V = 80 ft^3

Since the cost is in cubic yard (yard^3) so convert:

V = 80 ft^3 * (1 yard^3 / 27 ft^3) = 2.963 yard^3

So the total cost is:

cost = ($125 / yard^3) * 2.963 yard^3

cost = $370.37

Answer:

$370.37.

Step-by-step explanation:

We have been given that a general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 12 feet and 4 inches thick.

First of all, we will convert the given dimensions of foundation in yards.

[tex]\text{3 feet}=\text{1 yard}[/tex]

[tex]20\text{ feet}=\frac{20}{3}\text{ yards}[/tex]

[tex]12\text{ feet}=\frac{12}{3}\text{ yards}[/tex]

[tex]\text{36 inches}=\text{1 yard}[/tex]

[tex]\text{4 inches}=\frac{4}{36}\text{ yards}=\frac{1}{9}\text{ yards}[/tex]

Since the foundation of building is in form of cuboid, so volume of foundation will be the product of 3 sides.

[tex]\text{Volume of foundation}=\frac{20}{3}\text{ yards}\times \frac{12}{3}\text{ yards}\times \frac{1}{9}\text{ yards}[/tex]

[tex]\text{Volume of foundation}=\frac{20\times 12\times 1}{3\times 3 \times 9}\text{ yards}^3[/tex]

[tex]\text{Volume of foundation}=\frac{240}{81}\text{ yards}^3[/tex]

[tex]\text{Volume of foundation}=2.962962962962963\text{ yards}^3[/tex]

Since the local home supply store sells concrete for $125 per cubic yard, so the cost of the concrete for the foundation will be the volume of foundation times $125.

[tex]\text{The cost of the concrete for the foundation}=2.962962962962963\text{ yards}^3\times \frac{\$125}{\text{ yards}^3}[/tex]

[tex]\text{The cost of the concrete for the foundation}=\$370.37037\approx \$370.37[/tex]

Therefore, the cost of the concrete for the foundation is $370.37.

Answer: A) all real numbers

Step-by-step explanation: I got it right on my quiz I’m also FLVS.

The ordered  pair which can be removed so that resulting graph represent a function is:

                               (1,3)

Function--

A function is a relation in which each of the element of first set is mapped to a single element of the other set.

i.e. no element is mapped to two elements i.e. there is a single image for each pre-image.

Here in the graph we have ordered pairs as:

(-5,-3)  (-4,-4)  (-2,2)  (1,-2)  (1,3)  (2,1)  (5,-4)

Hence, we see that element " 1 " is mapped two different elements

1 is mapped to -2  ( since, we have ordered pair (1,-2) )

and 1 is mapped to 3 ( since, we have ordered pair (1,3) )

If we  remove the ordered pair (1,3) then the resulting graph will be a graph of a function.

Answer:

[tex]y-1= \frac{4}{5} (x+2)[/tex]  

Step-by-step explanation:

Using point-slope intercept form:

The equation of line is given by:

[tex]y-y_1 = m(x-x_1)[/tex]              .....[1]

where,

m is the slope of the line and [tex](x_1, y_1)[/tex] is the point on the line.

As per the statement:

A line with slope 4/5 that contains the points (-2,1)

⇒m = [tex]\frac{4}{5}[/tex] and [tex](x_1, y_1)=(-2, 1)[/tex]

Substitute these values in [1] we have;

[tex]y-1= \frac{4}{5} (x+2)[/tex]  

Therefore, [tex]y-1= \frac{4}{5} (x+2)[/tex]  is the point slope form of a line with slope 4/5 that contains the points (-2,1).

We have that the statement  If four points are collinear, they are also coplanar is

True

From the Question we are told that

four points are collinear

Collinear

This occurs when three or more lines lines on the same plane or line

While

Coplanar is when simply means on the same plane

Therefore

If four points are collinear, they are also coplanar

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80 * 1/4 = 80 /4 = 20

80-20= 60

 she has 60 dollars saved still

To determine the radius and circumference of a circle with an area of 153.86 square inches, one must first divide the area by 3.14 to solve for r², then take the square root to find the radius, and finally use the radius to calculate the circumference. The radius is approximately 7.00 inches, and the circumference is approximately 43.96 inches.

To find the radius and circumference of a circle with an area of 153.86 square inches, we first use the formula for the area of a circle, which is A = πr². Given that A is 153.86 and π is approximately 3.14, we can rearrange the formula to solve for the radius (r) as follows:

Performing the calculations, we get:

Therefore, the radius of the circle is approximately 7.00 inches, and the circumference is approximately 43.96 inches.

To find the radius from the area of a circle, use the formula r = sqrt(A/pi), with A = 153.86 sq inches and pi as 3.14. Once the radius is determined, calculate the circumference with the formula C = 2*pi*r. Both values should respect the significant figures.

The student is asking for help finding the radius and circumference of a circle given its area using 3.14 for pi. To find the radius, we start with the area formula for a circle, which is A = πr². Given the area A as 153.86 square inches, and using 3.14 for π, the radius r can be found by rearranging the formula to r = √(A/π). Plugging the numbers in, we get r = √(153.86/3.14), which we then calculate.

Once we have the radius, we can find the circumference C of the circle using the formula C = 2πr. Now that we know the radius, we plug the value into this formula to get the circumference.

Both radius and circumference should be calculated carefully, keeping in mind significant figures. The radius should then be used to calculate the circumference, which will be limited by the same degree of precision.

The value of 1.580 hectoliters in decilitres will be 1580.

Unit conversion is the process of changing a quantity's measurement between different units, usually using multiplicative conversion factors.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given that the fluids have a value of 1.580 hectoliters.

The value of hectoliters in deciliters will be converted as below,

1 hectoliters = 1000 deciliters

1.580 hectoliters = 1.580 x 1000 deciliters

1.580 hectoliters = 1580 deciliters

Therefore, the value of 1.580 hectoliters in decilitres will be 1580.

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Option: C is the correct answer.

              C.)  F(x)= x

We know that a linear parent function is a function whose graph is a straight line passing through the origin and the equation of such a function is given by:

                                y=F(x)=x

Since, it is the simplest form of the equation of all the linear functions that are known to us and hence known as the parent linear function.

Answer:

its -5 not five

Step-by-step explanation:

volume = l x w x h

 to increase volume by 3 you would have  3*l*w*h

so 3*l*w*h= l*2*w* x *h  ( x is the scale factor)

cancel out the l w and h on both sides

3 = 2x 

Divide both sides by 2   

 x = 3/2 = 1.5

 the height should increase by a factor of 1.5

Answer:

3/2 or 3 over 2

Step-by-step explanation:

A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box.

They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.

If they decide to double the width to create the family-sized box, by what factor must they increase the height?

Odyssey Question