A 20ft ladder leans against a house. The bottom of the ladder is 8 feet from the base of the house. To the nearest foot, how high above the ground is the top of the ladder?

Answer:

Minimum: y=-106. Maximum: infinite

Step-by-step explanation:

The function described is a parabola, written in the form:

[tex]f(x)=ax^2 +bx+c[/tex]

with:

[tex]a=2\\b=28\\c=-8[/tex]

First of all, we notice that the parabola is upward, because the sign of the coefficient of the second-order term (a) is positive (in fact, a=2). Therefore, it has a minimum value of y. The x corresponding to the vertex of the parabola is given by:

[tex]x_v=-\frac{b}{2a}=-\frac{28}{2\cdot 2}=-7[/tex]

And substituting into f(x), we find the minimum value of y:

[tex]f(-7)=2(-7)^2+28(-7)-8=98-196-8=-106[/tex]

While the parabola has no maximum value, since it goes to infinite as x becomes larger.

Final answer:

The edge length of a cube with a volume of 1/27 cubic units is 1/3 unit, as it's the cube root of the volume.

Explanation:

To find the edge length of a cube when the volume is 1/27:

Volume is equal to edge length to the third power.

Convert meters into centimeters.

Calculate the density by dividing mass by volume.

The question is to find the edge length of the cube if the volume is 1/27 cubic units. To find the edge length, we need to take the cube root of the volume, because the volume of a cube is equal to the cube of one of its edges (V = L3, where V is the volume and L is the edge length). Since the volume is 1/27, the edge length would be the cube root of 1/27, which is 1/3. Therefore, the edge length of the cube is 1/3 unit.

Answer:

.

Step-by-step explanation:

If we have a parallelogram and a triangle with the same base and height, the area of the parallelogram will be exactly twice the area of the triangle. This can be expressed as:

[tex]\[ A_{\text{parallelogram}} = 2 \times A_{\text{triangle}} \][/tex]

The area of a parallelogram is twice the area of a triangle that has the same base and height.

To understand the relationship between the area of a parallelogram and the area of a triangle with the same base and height, we can start by recalling the formulas for the area of each shape.

The area [tex]\( A \)[/tex] of a triangle with base[tex]\( b \)[/tex] and height [tex]\( h \)[/tex] is given by the formula:

[tex]\[ A_{\text{triangle}} = \frac{1}{2} \times b \times h \][/tex]

The area [tex]\( A \)[/tex] of a parallelogram with the same base [tex]\( b \)[/tex] and height [tex]\( h \)[/tex] is given by the formula:

[tex]\[ A_{\text{parallelogram}} = b \times h \][/tex]

From these formulas, we can see that the area of a parallelogram is the full rectangle formed by the base and height, while the area of a triangle is half of that rectangle (since a triangle is essentially half of a parallelogram with the same base and height).

Answer:

Discs, Congruent, Parallel

Step-by-step explanation:

On APEX

To find Paul and Luis's ages, the ratio 2:3 is translated to 2x and 3x, and with the sum of their ages being 35 years, we solve the equation to find x = 7. Therefore, Paul is 14 years old and Luis is 21 years old.

The question involves finding the ages of Paul and Luis given that the ratio of their ages is 2:3 and the sum of their ages is 35 years. To solve this, let's denote Paul's age as 2x and Luis's age as 3x, where x is a common multiplier. The equation based on the sum of their ages will then be:

2x + 3x = 35

Solving this equation, we combine like terms:

5x = 35

Now, divide both sides by 5 to find the value of x:

x = 35 / 5

x = 7

So, Paul's age is 2x which is 2 * 7 = 14 years, and Luis's age is 3x which is 3 * 7 = 21 years.

(0,1) (2,-2) (4,-5) are the answers

y+2=1(x=2) you have to use the formula y-y1=m(x-x1) hope this helps :)

The equation of a line passing through points (-2, -2) and (2, 2) is y = x.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, a line that passes through the points (-2, -2) and (2, 2).

So, the slope of the line is (y₂ - y₁)/(x₂ - x₁).

= (2 + 2)/(2 + 2).

= 4/4.

= 1.

Equation of a line in point-slope form is y - y₁ = m(x - x₁).

y + 2 = 1.(x + 2).

y + 2 = x + 2.

y = x.

learn more about slopes and lines here :

https://brainly.com/question/14511992

#SPJ2

Answer:

Step-by-step explanation:

Given that Mr. Green teaches band, choir and math.

Total students = 57

Students who learn band A = 25

Students who learn math alone =9

From venn diagram we see that

band alone 11 

choir alone 17 

band and choir alone 4 

band and math alone 7 

math and choir alone 6 

band choir and math 3 

math alone 9 from 11+4+10+6+17 + M = 57 

so 

2 classes = 4+7+6 = 17

17 students take exactly two classes with Mr. Green

Answer:

y = 21x

Step-by-step explanation:

12x for the almonds

9x for the walnuts

12x + 9x is:

21x total

So, the formula should be:

y = 21x

Final answer:

The equation is Total nuts = 24 nuts per bag * x bags.

Explanation:

To find the total number of nuts needed to fill the snack bags the company sells, we need to calculate the sum of almonds and walnuts in each bag and then multiply that by the number of snack bags sold (represented by x).

Each snack bag contains:

The total number of nuts per bag is:

15 almonds + 9 walnuts = 24 nuts per bag

Thus, if x represents the number of snack bags sold, the equation to find the total number of nuts required is:

Total nuts = 24 nuts per bag * x bags

Answer:

Infinitely Many Solutions

Step-by-step explanation:

All they did was DOUBLE the bottom equation and wrote the new equation above it. This is what is considered dependency. Whenever we have infinitely many solutions, we have a dependent system of equations.

I am joyous to assist you anytime.

Based on the graph, the coordinates of the vertex are at (0, -1), and since the parabola opens upwards, the vertex is a minimum.

Therefore, the correct answer is A:

(0,-1) ; minimum

The image shows a parabola opening upwards on a coordinate plane. The vertex of a parabola is the highest or lowest point on the graph, depending on whether the parabola opens downward or upward, respectively.

Here's a detailed explanation for identifying the vertex and determining if it is a maximum or minimum:

Step 1: Identify the Vertex

The vertex of a parabola in the form [tex]\(y = ax^2 + bx + c\)[/tex] can be found using the vertex formula [tex]\(x = -\frac{b}{2a}\)[/tex] for the x-coordinate and then substituting that back into the equation for y to find the y-coordinate. However, in this case, we can directly observe the vertex from the graph. It's the point where the parabola changes direction.

Step 2: Read the Coordinates from the Graph

From the graph, we can see that the vertex is at the origin of the parabola's turning point. It appears to be at (0, -1) by looking at where the axis of symmetry of the parabola intersects the y-axis.

Step 3: Determine Maximum or Minimum

Since the parabola opens upwards, as indicated by the shape of the graph, the vertex represents the minimum point of the parabola. If the parabola were to open downwards, the vertex would represent the maximum point.

Given is the shape of a triangle with base = 7 feet and height = 4 feet.

We know the formula for area of triangle is given as follows :-

[tex] Area\; of\; Triangle=\frac{1}{2} *(Base)*(Height) \\\\
Area = \frac{1}{2} (7)(4) \\\\
Area = \frac{28}{2} \\\\
Area = 14 \;squared \;feet [/tex]

So, the area of a blade is 14 squared feet.

There are four blades on wind mill. Then area of all four blades would be 4 times 14.

Hence, total area of all four blades = 4 x 14 = 56 squared feet.

The total area of the four windmill blades, each with a base of 7 feet and a height of 4 feet, is 56 square feet.

The question involves calculating the total area of windmill blades, each shaped as a triangle. To find the area of a single blade, we use the formula for the area of a triangle, which is (base x height) / 2. For a blade with a base of 7 feet and a height of 4 feet, the area of one blade is:

Area = (7 ft x 4 ft) / 2 = 28 ft² / 2 = 14 ft²

Since there are four blades on the windmill, the total area of the blades can be calculated by multiplying the area of one blade by the number of blades:

Total area = 14 ft2 x 4 = 56 ft²

Answer:

25.5÷3=8.5

answer is 8.5....

Answer: C 8.5

Step-by-step explanation:

We can use the formula:

time = (number of revolutions) / (rate of revolution)

Substituting the given values, we get:

time = 25.5 / 3

time = 8.5

Therefore, the Carousel will take 8.5 minutes to spin 25.5 times.

The answer is option C.