Here, we want to get the solution to the inequality
To do this, we simply move on to collect like terms
We simply have to bring -4 to the other side
Mathematically, we have this as;
[tex]\begin{gathered} 2x\text{ -4 }\leq\text{ 12} \\ 2x\leq\text{ 12 + 4} \\ 2x\leq\text{ 16} \\ \text{ x }\leq\frac{16}{2} \\ x\leq8 \end{gathered}[/tex]a debt company wants to build a uniquely shaped decks how many square feet of wood will the company need to cover the deck designer below shaped like a regular pentagon a trapezoid the height of the trapezoid is 4.5 ft round your answer to one decimal place to find the area of the Pentagon divided into 5 similar triangles you see if I could the radius at the Pentagon the distance from each vertex Center is 4.25 ft
72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
To find the total wood required we need to add the area of pentagon and area of trapezoid.
Firstly we will draw the 5 similar triangle in the pentagon as shown below:
Lets name one triangle as ABC.
Given, radius of pentagon = 4.25 ft. (Let x)
Now, in triangle ABC,
BD=DC=2.5 ft. (half of the BC)
By applying Pythagoras theorem,
[tex]AB^{2} =AD^{2} +BD^{2} \\AD=\sqrt{AB^{2} -BD^{2} } \\AD=\sqrt{11.81} \\AD=3.44 ft.[/tex]
We know that AD is the height of triangle ABC.
So, Height = AD = 3.44 ft.
Area of triangle ABC = [tex]\frac{1}{2}[/tex] * base * height
=[tex]\frac{1}{2}[/tex] * 5 ft. 3.44 ft. = 8.59 square feet.
Area of pentagon = area of 5 similar triangle
= 5 * area of triangle ABC
= 5 * 8.59 = 42.96 square feet
Area of trapezoid = [tex]\frac{1}{2}[/tex] * (sum of the parallel side) * height
= [tex]\frac{1}{2}[/tex] * (5+8) * 4.5
= [tex]\frac{1}{2}[/tex] * 13 * 4.5 = 29.25 square feet.
Total square feet of wood required = area of pentagon + area of trapezoid
= 42.96 + 29.25 = 72.21 square feet
Rounding to one decimal place 72.21 square feet ≈ 72.2 square feet.
Thus, 72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
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On a certain day the probability of rain is 80% probability of thunder is 3/5 and the probability of both is 2/5. What is the probability that it will rain or thunder?
The probability it will rain or thunder = 100%
Explanation:Probability it will rain = 80%
P(rain) = 4/5 (simplest term in fraction)
Probability of thunder = 3/5
P(thunder) = 3/5
Probability of both rain and thunder = 2/5
P(rain and thunder) = 2/5
We need to find the probability of rain or thinder = P(rain or thunder)
To find the probability of P(rain or thunder), we will apply the formula for the addition rule on any two events:
[tex]P(A\text{ or B\rparen = P\lparen A\rparen +}P(B)\text{ - P\lparen A and B\rparen}[/tex]Applying the formula in our question:
[tex]P(rain\text{ or thunder\rparen = P\lparen rain\rparen + P\lparen thunder\rparen - P\lparen rain and thunder\rparen}[/tex]substitute the values in order to find the probability:
[tex]\begin{gathered} P(rain\text{ or thunder\rparen = }\frac{4}{5}\text{ + }\frac{3}{5}-\text{ }\frac{2}{5} \\ \\ P(rain\text{ or thunder\rparen = }\frac{4\text{ + 3 - 2}}{5} \\ P(rain\text{ or thunder\rparen = }\frac{5}{5} \\ \\ P(rain\text{ or thunder\rparen = 1} \end{gathered}[/tex]In percentage, the probability it will rain or thunder = 100%
Find the slope and y intercept of the line shown below question number 4
The image of the line provided seems to go through the following points:
(0, 4) , (-4, 5), and (4, 3)
Knowing at least two points is essential to calculate the slope via the formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]so, for example if we use the points (0, 4) and (-4, 5) to calculate the slope, we get:
[tex]\text{slope}=\frac{5-4}{-4-0}=-\frac{1}{4}[/tex]Therefore, the slope is -1/4 (negative one fourth)
Notice as well that one of the points we chose is (0, 4) which in fact is the y-intercept of the line (the point at which the line crosses the y-axis ).
so we have al the elements to built the equation of this line:
slope = -1/4
y intercept = 4 for the (0, 4) on the plane
Then the equation could be built using:
y = (-1/4) x + 4
Number 11. Find a quadratic equation with (-2,3) and y intercept of 11
Answer:
[tex]y=2x^2+8x+11[/tex]Explanation:
A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
Given the coordinate (-2, 3), we'll have that;
h = -2
k = 3
Given a y-intercept of 11 and we know that at the y-intercept x = 0.
Substituting the above values into the vertex form equation and solving for a, we'll have;
[tex]\begin{gathered} 11=a\lbrack0-(-2)\rbrack^2+3 \\ 11=4a+3 \\ 4a=8 \\ a=\frac{8}{4} \\ a=2 \end{gathered}[/tex]Substituting a = 2, h = -2 and k = 3 into the vertex form equation and taking it to standard form, we'll have;
[tex]\begin{gathered} y=2(x+2)^2+3 \\ y=2(x^2+4x+4)+3 \\ y=2x^2+8x+8+3 \\ y=2x^2+8x+11 \end{gathered}[/tex]27,9,3,1,1/3,1/9....Write the sigma notation for the infinite series. ________________
Given
Series,
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},...[/tex]Find
Write the sigma notation for the infinite series.
Explanation
as we see the given series is a geometric series .
here , a = 27
common ratio , r = 9/27 = 1/3
so ,
[tex]\begin{gathered} \sum_{n\mathop{=}1}^{\infty}ar^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(27)(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{-3}(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4} \end{gathered}[/tex]Final Answer
Hence , the sigma notation for the infinite series is
[tex]\sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4}[/tex]7th grade math I'm stuckhelp me fill in the blanks!
ok
item price before tax sales tax price including tax
pillow 8 8 x 0.0725 = 0.58 8 + 0.58 = $8.58
blanket 22 22 x0.0725 = 1.595 22 + 1.595 = $23.595
trash can 14.5 14.5 x 0.0725 = 1.051 14.5 + 0.0725 =$15.55
how do you do how do you point plot on a graph
To point plots on a graph, take the following steps:
1. Identify the x-coordinates and y-coordinates from the variable/data you have. It should be written in this form: (x, y)
2. Label both axes on the graph(x-axis and y-axis). The x-axis is usually on the horizontal line while the y axis is the horizontal line.
3. Start plotting your first 2 points on both axes (usually the numbers on first row). Plot the x value and also plot the y value at the appropriate points
4. Finally, Continue plotting the numbers by pointing each point on the graph (take them in rows)
i need help with math
The following basic properties and characteristics can be used to easily identify parallel lines:
They always are straight lines with equal spacing between them.They are parallel lines.They never cross, no matter how much farther you stretch them in just about any given direction.A transversal line intersecting two parallel lines at two separate positions will form four angles at each point.The statement are given as;
The measurement for the angles for the transversal are-
∠2 = 91° and ∠5 = 89°
Thus,
∠2 = ∠3 = 91° (vertically opposite angles)
The sum ∠3 + ∠5 = 180 (for the parallel lines)
91° + 89° = 180° (supplementary angles).
Thus, two lines are parallel.
The two lines are parallel; True.The measure of ∠7 = 89°; False,Correct; ∠7 = ∠3 = 91°(corresponding angles)
∠3 = ∠6 are same side of interior angles; FalseCorrect; They are opposite side of interior angles.
∠1 is congruent to angle ∠4 because they are vertical angles; True,Thus, the results for the given transversal lines are found.
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find the standard deviation of 3, 7, 4, 6, 5 if necessary, round your answer to the nearest tenth
3, 7, 4, 6, 5
First, find the mean.
Mean = Sum of the values / number of values
Mean = (3+7+4+6+5) /5 = 25/5 = 5
Then, find the variance:
Calculate each value difference from the mean
5-3 = 2
7-5 = 2
5-4= 1
6-5=1
5-5= 0
Square each difference, add them, and divide by the number of values.
Variance : (2^2+2^2+1^2+1^2+0^2 )/ 5 = (4+4+1+1) /5 = 10 /5 = 2
Standard deviation= square root of the variance:
√2 = 1.4
Mobile Cookies delivers packs of cookies which cost $2.60 per package to deliver. The fixed cost to run the delivery truck is $252 per day. If the company charges $5.60 per pack, how many packages must be delivered daily to make a profit of $33?
95 packages must be delivered daily to make a profit of $33.
What is the meaning of profit?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Given that the delivers cost per packets is $2.60 and the cost to run a truck is $252.
Assume that they need deliver x packs of cookies to make a profit of $33.
The total cost to deliver x packs of cookies is $(2.60x + 252).
Given that company charges $5.60 per pack.
The revenue is $5.60x.
The total profit is $(5.60x - (2.60x + 252)) = $(5.60x - 2.60x - 252) = $(3x - 252).
Given that the profit is $33.
Thus 3x - 252 = 33
Add 252 on both sides:
3x = 285
Divide both sides by 3:
x = 95.
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A rare manuscript increased in value 400% over the past 4 years. This was an increase of $1,000. What was the value of the manuscript 4 years ago? What is the value of the manuscript now?The value of the manuscript 4 years ago was $.The manuscript is now worth $
Given
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
To find:
a) What was the value of the manuscript 4 years ago?
b) What is the value of the manuscript now?
Explanation:
It is given that,
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
Then, let x be the value of manuscript 4 years ago.
That implies,
[tex]\begin{gathered} 400\%\times4x=1000+x \\ \frac{400}{100}\times4x=1000+x \\ 16x=1000+x \\ 16x-x=1000 \\ 15x=1000 \\ x=\frac{1000}{15} \\ x=\text{ \$}66.67 \end{gathered}[/tex]And, the value of the manuscript now is,
[tex]\begin{gathered} 4x=4(66.67) \\ =\text{ \$}266.67 \end{gathered}[/tex]Hence, the value of the manuscript is $66.67, and the value off the manuscript now is $266.67.
Which of the following is a quadratic equation that has the roots x = 5 and x = 6?
Answer:
the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]Explanatio
We want to derive the quadratic equation that has the roots x=5 and x=6;
To derive the equation, we have;
[tex](x-5)(x-6)=0[/tex]Expanding;
[tex]\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}[/tex]Therefore, the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]Elisa designed a flower garden in the shape of a square with a side length of 10 feet. She plans to build a walkway along the diagonal. What is the closest measure of the length of the walkway?
A square has all equal sides, then each side has a measure of feet
The diagonal can be found using the following formula:
[tex]d=\sqrt[]{2a}[/tex]Where a represents a side.
Replacing:
[tex]\begin{gathered} d=\sqrt[]{2(10)} \\ d=\sqrt[]{20} \\ d=14.1421 \end{gathered}[/tex]Hence, the closest measure of the walkway length is 14.1421 feet.
Let f(x)=8x+5 and g(x)=6x^2+2x after simplifying (f+g)(x)=
We have to find (f+g)(x), where:
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=6x^2+2x \end{gathered}[/tex]We can write:
[tex](f+g)(x)=f(x)+g(x)=(8x+5)+(6x^2+2x)=6x^2+10x+5[/tex]Answer: (f+g)(x) = 6x^2+10x+5
factor each trinomial. if the trinomial cannot be factored write prime. show ALL work1.) 5x^2+17x+62.) 2x^2+5x-12
In order to determine the factors of the given trinomials, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial:
ax² + bx + c
Replace the values of the coefficients of the given trinomials into the quadratic formula.
1) 5x² + 17x + 6
a = 5, b = 17, c = 6
[tex]\begin{gathered} x=\frac{-17\pm\sqrt[]{17^{2}-4(5)(6)}}{2(5)} \\ x=\frac{-17\pm13}{10} \end{gathered}[/tex]the two solutions for x are:
x1 = (-17-13)/10 = -30/10 = -3
x2 = (-17+13)/10 = -4/10 = -2/5
The factors are given by the following expression:
(x - x1)(x - x2)
Then, you have:
5x² + 17x + 6 = (x - (-3))(x - (-2/5)) = (x + 3)(x + 2/5)
Construct an obtuse angle called ABC. Bisect ABC and call the new angles ABP and PBC. Now bisect the ABP so that there are 3 angles. The measure of angle PBC is 66 degrees. Fe measures of the two smaller angles are equal to 11y and 3x respectively. What are the values of x and y in degrees?
Now,
3x + 11y + 66 = 66x2
3x + 11y + 66 = 132
3x + 11y = 132 - 66
3x + 11y = 66 ...............................(equ 1)
If Angle A is acute and Angle B is obtuse and Angle A is 2X+5 and Angle B is 6X+55, then how many degrees would Angle A be?
Angle A is 35° and Angle B is 145°
Supplementary angles are angles that give 180° when added together
Angle A and Angle B are supplementary angles such that
∠A + ∠B = 180°
Given that ∠A is acute angle and ∠B is obtuse angle
also , ∠A = 2x+5 and ∠B = 6x+55
using supplementary angle property ,
2x+5 + 6x+55 = 180
solving for x ,
8x + 60 = 180
x = 15
8x = 180 - 60
8x = 120
∠A = 2x+5
substituting value of x
∠A = 2(15)+ 5 = 30+5
∠A = 35°
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A student has 42 coins worth a total of $5.90. Each coin is either a nickel (five cents) or a quarter (twenty-five cents). If x is the number of nickels, then x can be determined from the equation---
Given
no. of coins = 42
worth of coins = $5.90
Find
number of nickels
Explanation
The number of quaters is 42 - x
0.05x + 0.25(42 - x) = 5.9
-0.2x + 10.5 = 5.9
-0.2x = -4.6
x = 23
Final Answer
Number of Nickels, x = 23
Part A in. (a) For the following figure, the value of x is 45° 8 in. 459 B 45
Answer
The value of x = 8 in.
y = 8√2 = 11.31 in.
For the second question,
x = 8.3 units
Explanation
Isoscelles triangles have two of their sides being of the same lengths and those two sides are the ones whose base angles are the same.
From the image, we can see that two angles of the triangle have the same measures, hence, we can easily conclude that
x = 8 inches.
To find y, we will use pythagoras theorem.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this triangle,
hyp = y
a = 8 in
b = x = 8 in
a² + b² = (hyp)²
8² + 8² = y²
64 + 64 = y²
y² = 128
Take the square roots of both sides
√(y²) = √128
y = 8√2 = 11.31 in
For the other question.
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For that triangle,
Hyp = 11 units
Opp = ?
Adj = x
θ = 41°
We can then use trignometrical identities to solve this
CAH allows us to say
Cos 41° = (Adj/Hyp)
Cos 41° = (x/11)
x = 11 Cos 41°
x = 11 (0.7547)
x = 8.3 units
Hope this Helps!!!
Write the given fraction in simplest form 25/27
Notice that:
[tex]\begin{gathered} 25=5\cdot5, \\ 27=3\cdot3\cdot3. \end{gathered}[/tex]Then 25 and 27 have no common factors.
Since the denominator and the numerator have no common factors, then the given fraction is in its simplest form.
Answer: 25/27.
[tex]\frac{25}{27}\text{.}[/tex]The number of McDonald's restaurants worldwide in 2014 was 36.258. In 2009, there were 32,737 McDonald's restau- rants worldwide. Let y be the number of McDonald's res- taurants in the year, where r = O represents the year 2009 (Source: McDonald's Corporation) a. Write a linear equation that models the growth in the number of McDonald's restaurants worldwide in terms of the year x. [Hinr. The line must pass through the points (0.32.737) and (5.30,258).]b. use this equation to predict the number of McDonald's restaurants worldwide in 2016.
a) y = 704.2x + 32737
b) There are 37,666 McDonald's restaurants in 2016
Explanations:The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope, and is given by the formula: } \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]For the line passing through the points (0, 32737) and (5, 36258)
x₁ = 0, y₁ = 32737, x₂ = 5, y₂ = 36258
Substituting the values into the equations above:
[tex]\begin{gathered} \text{m = }\frac{36258-32737}{5-0} \\ \text{m = }\frac{3521}{5} \\ m\text{ = }704.2 \\ y\text{ - 32737 = 704.2}(x\text{ - 0)} \\ y\text{ - 32737 = 7}04.2x \\ y\text{ = 7}04.2x\text{ + 32737} \\ \end{gathered}[/tex]b) In 2016, x = 7
substitute x = 7 into the equation
[tex]\begin{gathered} y\text{ = 704.2(7) + 32737} \\ y\text{ = }4929.4+32737 \\ y\text{ = }37666.4 \end{gathered}[/tex]There are 37,666 McDonald's restaurants in 2016
suppose the odds against winning the lottery are 59,000,000 to 1. What is the probability of the event of winning the lottery given those odds? P(E) = __________
The odds against winning the lottery is 59,000,000 : 1
Thus,
Not winning bets = 59,000,000
Winning bets = 1
Total bets = 59,000,000 + 1 = 59,000,001
Thus,
The probability of winning = 1/59,000,001
Answer[tex]P(E)=\frac{1}{59,000,001}[/tex]Fill in the missing number to complete the pattern.18, 12, ,0
using Ap formula,
[tex]\begin{gathered} a+(n-1)d \\ a=18 \\ d=12-18=-6 \\ 18+(3-1)-6 \\ 18-12=6 \end{gathered}[/tex]The missing term = 6
tell whether the red line segment is the height or Stan height.
The slant height is the height that can be found using the height of the pyramid and the half length from the center of one of the sides to the center of the pyramid, this would be the hypotenuse.
The red line in this case represents the height of the pyramid.
Which shows another way to write 6*3? A.3 + 3 + 3 + 3 + 3 + 3 B.3 × 3 × 3 × 3 × 3 × 3 C.6 × 6 × 6 D.6 + 6 + 6
Another way to write the given expression 6×3 is by use of addition operator 6+6+6 .
We know that multiplying a number by another number is another way of adding the number that many times.
If we multiply a with n it can be written as
a × n = a + a + a + a +.... n terms
Similarly we can use the same formula for 6×3.
6×3 = 6+6+6
Addition can be defined and carried out using abstractions known as numbers, such as integers, real numbers, and complex numbers, in addition to counting things.
Addition is a part of the arithmetic branch of mathematics. In algebra, a different area of mathematics, addition can also be performed on abstract objects like vectors, matrices, subspaces, and subgroups.
The words, addends, or summands collectively refer to the quantities or components that must be combined to make a whole number; this terminology also includes the summing of multiple terms. This needs to be differentiated from multiple factors.
Hence the given expression can be written as 6+6+6 .
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Which expression represents the area of the remainingpaper shape in square centimeters?O (x-7)(x-9)O (3x-2)(3x-8)O (3r-4)(3x +4)O (9x - 1)(x+16)
A square corner of 16 cm² is removed from a square paper with an area of 9X squared, square centimeters. which expression represents the area of the remaining paper shape in the square centimeters?
we have taht
Find out the difference
9x^2-16
apply difference of squares
9x^2-16=(3x-4)(3x+4)
answer is
(3x-4)(3x+4)
(08.01 LC)Find the area of a circle with a diameter of 20 inches. Use 3.14 for pi.(1 point)
The area of a circle can be calculated using the following formula:
[tex]A=\pi r^2[/tex]Where
A represents the area
r represents the radius of the circle
π is the number pi, you have to use 3.14 for the calculatins
You have to calculate the area of a circle that has a diameter of 20 inches. The radius of a circle is half the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{20}{2} \\ r=10in \end{gathered}[/tex]The area of the circle can be determined as follows:
[tex]\begin{gathered} A=3.14\cdot10^2 \\ A=314in^2 \end{gathered}[/tex]The area of the circle is 314in²
Which of the following is an equation of a line parallel to the equaticy = 4x+12O A. y=-x-2y4O B. y = -4x – 2O c. y = 4x-2O O D. y=-x-2
Given
The equation of the line is,
[tex]y=4x+1[/tex]To find the equation of the line parallel to y=4x+1.
Explanation:
It is given that,
The equation of the line is,
[tex]y=4x+1[/tex]Since two parallel lines have same slope.
Then,
The slope of the line parallel to y=4x+1 is, 4.
Therefore, the equation of the line parallel to y=4x+1 is of the form,
[tex]y=4x+k[/tex]Hence, the equation of the line parallel to y=4x+1 is c) y=4x-2.
Find the volume of a pyramid with a square base, where the side length of the base is10 m and the height of the pyramid is 7.2 m. Round your answer to the nearesttenth of a cubic meter.
hello
to find the volume of the figure, we need to know the formula of a pyramid with a square base
once we know that, we can proceed to simply substitute the values into the equation
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\times l^2\times h \\ l=\text{side length} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} l=10m \\ h=7.2m \end{gathered}[/tex][tex]\begin{gathered} \text{volume}=\frac{1}{3}\times10^2\times7.2 \\ \text{volume}=\frac{100\times7.2}{3} \\ \text{volume}=240m^3 \end{gathered}[/tex]the volume of the figure is 240m^3
the figure below has a point marked with a large dot.first rotate the figure 90 degrees counterclockwise about the origin.then give the coordinates of the Mark point in the original figure in the final figure.
When we do a 90 degree counterclockwise rotation about the origin, a point moves from ( x,y) to ( -y,x)
Using the point with the blue dot
It is originally at (2,-3)
It will move to (3,2)