How many hours are in a year?

Answer: 1.)

A. 30in^2

B. 18cm^2

C. 130yd^2

2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2

3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.

4.) From the Pythagorean Theorem we know:

hypotenuse^2 = side^2 + side^2

hypotenuse^2 = 36 + 36

hypotenuse = square root (72)

hypotenuse = 8.48528... feet

5.) a. 5

b. √128

c. √221

Area of triangle are  [tex]30inches^{2}[/tex] in part(a),

[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)

What is Triangle?

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

What is area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

According to questions, we have the following

In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches

In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters

In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards

We have to find the area of each triangle with the given heights and bases.

Now, Area of triangle in part a

[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]

[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]

[tex]=30inches^{2}[/tex]

Area of triangle in part b

[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]

[tex]=18[/tex] [tex]centimerters^{2}[/tex]

Area of triangle in part c

[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]

[tex]=130[/tex] [tex]yards^{2}[/tex]

Hence, we can conclude that area of triangle are  [tex]30inches^{2}[/tex] in part(a),

[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)

Learn more about area of triangle  here:

https://brainly.com/question/19305981?referrer=searchResults

#SPJ2

( x + 6 )^2 = 6 or ( x + 6 )^2 = 6

Solution:

x = -6 + √6, x = -6 - √6

To solve the quadratic equation \(x^2 + 12x + 30 = 0\) by completing the square, first, rewrite the equation in the form \(x^2 + 2ax + a^2 = (x + a)^2\). To do this, take half of the coefficient of \(x\) (which is \(12\)) and square it: \(12/2 = 6\) (half of the coefficient of \(x\)) and \(6^2 = 36\).

Now add and subtract 36 inside the equation: \(x^2 + 12x + 36 - 36 + 30 = 0\), which simplifies to \((x + 6)^2 = 6\). This is the completed square form.

To solve for \(x\), take the square root of both sides:[tex]\(x + 6 = \pm \sqrt{6}\). Then solve for \(x\): \(x = -6 + \sqrt{6}\) and \(x = -6 - \sqrt{6}\). These are the two solutions for \(x\).[/tex]

Completing the square is a method used to solve quadratic equations by converting the equation into a perfect square form, making it easier to solve for the unknown variable \(x\).

Answer:

(2x+3)(x+2)

Step-by-step explanation:

i hope this helps

1 1/3 + 1 1/6

 add the 1 +1 = 2

add 1/3 + 1/6 ( find common denominator, which in this case is 6)

 so 1/3 becomes 2/6

2/6 + 1/6 = 3/6 which reduces to 1/2

 they ate  2 1/2 pints total

The average rate of change from x = –4 to x = 1 is 3.

To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.

A.  We have two lines:  y = 4-x   and   y = 8-x^-1

Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when

4-x = 8-x^-1

This is where the two lines will cross and that is the common point that satisfies both equations.

B.  4-x = 8-x^-1

 x         4-x      8-x^-1

______________

-3          7        8.33

-2          6        8.5

-1          5        9

 0          4        -

 1          3        7

 2          2        7.5

 3          1        7.67

The table shows that none of the x values from -3 to 3 is the solution because in no case does

4-x = 8-x^-1

To find the solution we need to rearrange the equation to find for x:

4-x = 8-x^-1

Multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

Therefore there are two points that satisfies the equation.

Find y:  

x=-4.236

y = 4-x  = 4 – (-4.236) = 8.236

y = 8-x^-1 =  8-(-4.236)^-1 = 8.236

x=0.236

 y = 4-x  = 4 – (0.236) = 3.764

y = 8-x^-1 =  8-(0.236)^-1 = 3.764

Thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

C.  To solve graphically the equation 4-x = 8-x^-1

We would graph both lines: y = 4-x  and   y = 8-x^-1

The point on the graph where the lines cross is the solution to the system of equations.

Just graph the points on part B on a cartesian coordinate system and extend the two lines.  The solution is, as stated, the point where the two lines cross on the graph.

The x-coordinates of the intersection points between the equations are the solutions to the given equation. Tables can be used to find the solution by plugging in different values of x. The equation can also be solved graphically by finding the intersection points of the two equations on a graph.

Part A:

The x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. To find the intersection points, we set the two equations equal to each other and solve for x.

Part B:

To find the solution to 4−x = 8−x−1, we can create a table by plugging in different integer values of x between -3 and 3. Substitute each value of x into the equation and solve for y. The values of x and y that make the equation true are the solutions.

Part C:

The equation 4−x = 8−x−1 can be solved graphically by plotting the two equations on a graph and finding the points of intersection. The x-coordinate of the intersection point(s) represents the solution(s) to the equation.

2/3x = 4/15 =

 x = 4/15 / 2/3 =   4/15 x 3/2 = 12/30 = 2/5

x = 2/5

all i know is x=25 its hard for me to explain.

Step-by-step explanation:

[tex]x + 2y \leq 4[/tex]

To graph this inequality we replace <= symbol with = sign

[tex]x + 2y =4[/tex]

subtract x on both sides

[tex]2y =-x+4[/tex]

divide both sides by 2

[tex]y= \frac{-1}{2} x +2[/tex]

Graph the equation using a table

LEts assume some number for x  and find out y

x                           [tex]y= \frac{-1}{2} x +2[/tex]

-2                           3

0                             2

2                             1

Now graph the equation using points (-2,3)  (0,2)(2,1)

use solid line for graphing

Now use test point (0,0) for shading

[tex]x + 2y \leq 4[/tex]

[tex]0 + 2(0) \leq 4[/tex]

[tex]0 \leq 4[/tex]     true

So  we shade the region that contains (0,0)

the graph is attached below

A critical value is the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:

critical value zα/2 at 98% confidence level = 2.326

Answer: 2.326

Answer:

2.33

Step-by-step explanation:

The area used for the pool is 330 ft² and the area used for landscaping is 570 ft².

1. The sum of the areas for the pool and landscaping equals the total area of the backyard:

[tex]\[ P + L = 900 \][/tex]

2. The area for landscaping is 240 ft² more than the area for the pool:

[tex]\[ L = P + 240 \][/tex]

Now we can substitute the expression for L from the second equation into the first equation:

[tex]\[ P + (P + 240) = 900 \][/tex]

Combining like terms gives us:

[tex]\[ 2P + 240 = 900 \][/tex]

Subtract 240 from both sides to isolate the term with P:

[tex]\[ 2P = 900 - 240 \] \[ 2P = 660 \][/tex]

Divide both sides by 2 to solve for P:

[tex]\[ P = \frac{660}{2} \] \[ P = 330 \][/tex]

Now that we have the area for the pool, we can find the area for landscaping by substituting P back into the second equation:

[tex]\[ L = 330 + 240 \] \[ L = 570 \][/tex]

Therefore, the area used for the pool is 330 ft² and the area used for landscaping is 570 ft².

Answer:

84 is the score that you Russell needs on the next test to achieve an average of at least 80.

Step-by-step explanation:

Russell's test scores are:  70,74,87 and 85

Average of the test scores = A = 80

Let thescore needed to achieve an average of 80 be x

Average = [tex]\frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]

[tex]A=\frac{70+74+87+85+x}{5}[/tex]

[tex]80=\frac{70+74+87+85+x}{5}[/tex]

[tex]70+74+87+85+x=400[/tex]

[tex]x=400-(70+74+87+85)=84[/tex]

84 is the score that you Russell needs on the next test to achieve an average of at least 80.

15 /3 = 5. so each 1/5 is $5

5*5 = 25

 so the game costs $25

Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.

Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.

https://brainly.com/question/12079637

#SPJ12

Answer:

12

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=Prt[/tex]

where

I represents simple interest

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]

[tex]I=Prt[/tex]

Solve for P

[tex]P=I/(rt)[/tex]

substitute the values

[tex]P=40/(0.10*5)=\$80[/tex]

therefore

the answer is

[tex]\$80[/tex]

Answer:

C) Amplitude = 2 feet; period = 24 hours; midline: y = 3

Step-by-step explanation:

above

A quadratic equation is one in which the highest exponent of a variable is 2. We can solve this problem by expanding each choices then find which has highest exponent equal to 2.

y(y + 4)(y - 6) = 0           ---> By expansion we get y^3, therefore highest exponent is 3.

z2 + 2 = 3z(z2 - 1)          ---> By expansion we get z^3, therefore highest exponent is 3.

(2x - 3)(4x + 5) = 10x     ---> By expansion we get x^2, therefore highest exponent is 2.

(3b)(5b – 7)(b + 8) = 0    ---> By expansion we get b^3, therefore highest exponent is 3.

The answer to this problem is therefore:

(2x - 3)(4x + 5) = 10x