The area, in square inches, of the painted face of the brick is; 144 in²
How to find the area of a square with coordinates?The area of a square is given by;
A = L²
where;
L is the length of the side of the square
The sides of a square all have the same length, and as such we just need to find the length of one side.
The length of the side of the square here is the distance between two vertices, which can be calculated as
L = √[(x₂ - x₁)² + (y₂ - y₁)²]
However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;
Horizontal length = (6 + 6) = 12
Thus;
Area = L² = 12² = 144 in²
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Solve one-fourth + two-sixths = ___.
Answer:
7/12
Step-by-step explanation:
Questions 12-14: The box below shows some of the steps of multiplying twopolynomials. Use this picture for the next THREE questions.+8x26x46x2-8x+3x18x3-24x2-64x16+22x2
In the red block will be the product of 6x^2 times +8 so:
[tex]6x^2\cdot8=48x^2[/tex]In the blue block will be the product of -8x and x^2
[tex]x^2\cdot(-8x)=-8x^3[/tex]and in the yellow block will be the product of 2 and 3x so:
[tex]3x\cdot2=6x[/tex]T x 3/4 for t = 8/9
repalce t=8/9
[tex]\begin{gathered} \frac{8}{9}\times\frac{3}{4} \\ \\ \frac{24}{36}=\frac{2}{3} \end{gathered}[/tex]the result is 2/3
After being discounted 10%, a weather radio sells for $62.96. Find the original price. (Round your answer to the nearest cent.)&Enter a number.$
Let the original price be x.
The discount is 10% of original price. So discount is,
[tex]\frac{10}{100}\cdot x=0.1x[/tex]The selling price after 10% discout is,
[tex]x-0.1x=0.9x[/tex]The selling price price is $62.96. So equation is,
[tex]\begin{gathered} 0.9x=62.96 \\ x=\frac{62.96}{0.9} \\ =69.955 \\ \approx69.96 \end{gathered}[/tex]So original price is 69.96.
Answer: 69.96
I went from my house to a playground, 300metres away in 10 minutes. I ran back andreached in 2 minutes. What was my averagespeed?
Average speed= total distance / total time
Distance 1 = 300 meters
Distance 2 = 300 meters (back)
Total distance = 300m+300m = 600 meters
Time 1= 10 minutes
Time 2 = 2 minutes
Total Time = 10min+2min=12 minutes
Average speed= 600 meters / 12 minutes = 50 meters/minute
If lines l, m, and n are parallel,AE is perpendicular to l, AC = 10, CD = 14, andAF = 6, what is the length of DG ? Give your answer as a decimal.
Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .
In triangle ACF by using the properties of Pythagoras Theorem we can say that
AC² = FA² + CF²
Given:
AC = 10 , FA = 6
∴10² = 6² + CF²
or, CF = 8 units.
Now in triangles ΔACF and triangle ΔADG
CF is parallel to DG , therefore the two triangles are similar.
therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.
AC/AD=CF/DG
or, 10/24 = 8 / DG
or, DG = 192 /10
or, DG = 19.2 units
Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.
In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
Hence the length of the side is 19.2 units.
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What are the first five terms of the arithmetic sequence defined explicitly by the formula an=1/8+2/3n
Answer:
D
Step-by-step explanation:
Given the formula of the arithmetic sequence, to find the first 5 terms, you just have to substitute n=1, n=2, n=2, n=4, and n=5.
Then, for the 1st term:
[tex]\begin{gathered} a_n=\frac{1}{8}+\frac{2}{3}n \\ a_1=\frac{1}{8}+\frac{2}{3}(1) \\ a_1=\frac{19}{24} \end{gathered}[/tex]2nd term:
[tex]\begin{gathered} a_2=\frac{1}{8}+\frac{2}{3}(2) \\ a_2=\frac{35}{24} \end{gathered}[/tex]There is no need to find the other 3 because there is no other sequence that has the first two terms as D.
AISD estimates that it will need 280000 in 8 years to replace the computers in the computer labs at their high schools. if AISD establishes a sinking fund by making fixed monthly payments in to an account paying 6% compounded monthly how much should each payment be
The initial amount of money that must be spend to replace the computers is P = $280,000. The period of time expected to replace all the computers is t = 8 years = 96 months. The interest rate is r = 6%.
Then, the monthly payment A is given by the formula:
[tex]\begin{gathered} A=P\frac{r(1+r)^t}{(1+r)^t-1} \\ A=280,000\cdot\frac{0.06\cdot(1+0.06)^{96}}{(1+0.06)^{96}-1} \\ A=\text{ \$16,862.74} \end{gathered}[/tex]A 1. Which of the following is equivalent to 37g - 11g? a. (37 - 11)g b. (37 - 11) +g c.(37 - 11) + g2 d. (37 - 11)9
From 37g - 11g we can factorize g. It yields
[tex]37g-11g=(37-11)g[/tex]Hence, the aswer is a.
12. The PRODUCT of six and a number increased by 2, translates to ? *6 +x+26x + 2O 6-8-2
Call the unknown number x.
The product of six and a number, would be written as 6x.
The product of six and a number increased by 2, would be written as 6x+2.
Find the surface area of a cylinder with a base diameter of 6 in and a height of 9 in. Write your answer in terms of II, and be sure to include the correct unit.
The surface area of a cylinder (S) with radius "r" and height "h" is:
[tex]S=2*\pi *r^2+2*\pi *r*h[/tex]Also, radius = diameter/2
Given:
r = 6/2 = 3 in
h = 9 in
Substitute the values in the equation and find S:
[tex]\begin{gathered} S=2\pi *3^2+2\pi *3*9 \\ S=2\pi *9+2\pi *27 \\ S=18\pi+54\pi \\ S=72\pi\text{ in}^2 \end{gathered}[/tex]Answer: The surface area is 72π in².
#1 An airplane rises at an angle of 14° with the ground. Find, to the nearest 10 feet, the distance it has flown when it has covered a horizontal distance of 1500 feet.
The airplane rises at an angle of 14° with respect to the ground.
You have to find the distances (diagonal) that it frew if it covered a horizontal distance of 1500 feet.
The distance flew by the place with respect to the horizontal ground and the height the plane is at after traveling 1500 feet form a right triangle. Where x represents the hypothenuse of the triangle. To determine its measure, you have to use the trigonometric relations
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypohtenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Given that θ=14° and we know that the adjacent side to the angle measures 1500 feet, using the cosine we can determine the length of x as:
[tex]\begin{gathered} \cos 14=\frac{1500}{x} \\ x\cos 14=1500 \\ x=\frac{1500}{\cos 14} \\ x=1545.92ft \end{gathered}[/tex]The distance flew by the airplane is 1545.92ft
Larry can spend at most $2800 to renovate his home. One roll of wallpaper costs $35, and one can of paint costs $40. He needs at least 20 rolls of wallpaper and at least 30 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.
Answer:
[tex]D[/tex]Explanation:
Here, we want to identify the correct graph and the possible combinations
Let the number of rolls of wallpaper be x and the number of cans of paints be y
The total amount needed is at most $2,800
That means:
[tex]35x\text{ + 40y}\leq\text{ 2,800}[/tex]He needs at least 20 rolls of wallpaper:
[tex]x\text{ }\ge\text{ 20}[/tex]He also needs at least 30 cans of paint:
[tex]y\text{ }\ge\text{ 30}[/tex]Now, we have to plot the graph of the given inequalities on the same axes
We have the image of the plot as follows:
Now, let us select the correct answer choice
The correct answer choice lies within the small triangle (where the three inequalities overlap)
All the points within the small triangle are right answers
The correct answer choice here is thus D
Draw a sketch of f(x)= (x+4)^2-5. Plot the point for the vertex, and label the coordinate as a maximum or minimum, and draw & write the equation for the axis of symmetry.
Answer: The vertex is (-4,-5) and the axis of symmetry is x=-4.
Explanation:
Given:
f(x)=(x+4)^2-5
The graph for the given equation is:
The point for the vertex is at (-4,-5) and it is also the minimum coordinate.
To find the axis of symmetry, we rewrite first the equation y=(x+4)^2-5 in the form y=ax^2 +bx +c.
So,
[tex]\begin{gathered} y=(x+4)^2-5 \\ y=x^2+8x\text{ +16 -5} \\ y=x^2+8x\text{ +1}1 \end{gathered}[/tex]Let:
a=1, b=8, c =11
The formula for the axis of symmetry is:
[tex]x=\frac{-b}{2a}[/tex]We plug in what we know.
[tex]\begin{gathered} x=\frac{-b}{2a} \\ =\frac{-8}{2(1)} \\ =\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The axis of symmetry is x=-4.
Therefore, the vertex is (-4,-5) and the axis of symmetry is x=-4.
Kyle is a secretory. She earns $12.38 per hout. She worked 2 hours last week. What is her straight fine pay
Answer:
Her pay is;
[tex]\text{ \$24.7}6[/tex]Explanation:
Given that;
She earns $12.38 per hour
and She worked 2 hours last week.
Her pay can be calculated as;
[tex]\text{Total pay}=Rate\times time[/tex]Substituting the given values;
[tex]\begin{gathered} \text{Pay}=\text{ \$12.38}\times2 \\ \text{Pay}=\text{ \$24.76} \end{gathered}[/tex]Her pay is;
[tex]\text{ \$24.7}6[/tex]Given: triangle ABC is an equilateral triangle. L, M, and N are the midpoints of AC, CB, and AB respectively. Prove: LMNB is a rhombus
Given:
∆ABC is an equilateral triangle, hence, all the three sides have the same length.
L, M, N are the midpoints of AC, CB, and AB. Hence, for instance, the distance between segment CM and MB are equal, by definition of midpoint.
Prove: LMNB is a rhombus.
Statement → Proof
1. ∆ABC is an equilateral triangle. → Given
2. Segment AB ≅ Segment AC ≅ Segment BC → Definition of an Equilateral Triangle
3. 1/2AB ≅ 1/2AC ≅ 1/2BC → Division Property of Equality
4. M and L are midpoints of BC and AC respectively. → Given
5. 1/2AB = Segment ML. → Midpoint Theorem
6. 1/2BC = Segment MB → Definition of Midpoint
7. Segment ML = Segment MB → Transitive Property of Equality using Statement 5 and 6
8. L and N are midpoints of AC and AB respectively. → Given
9. 1/2BC = Segment LN → Midpoint Theorem
10. 1/2AB = Segment BN → Definition of Midpoint
11. Segment LN = Segment BN → Transitive Property of Equality using Statement 9 and 10
12. Segment ML = Segment BN → Transitive Property of Equality using Statement 5 and 10
11. Segment MB = Segment LN → Transitive Property of Equality using Statement 6 and 9
13. Segment LN = Segment BN = Segment ML = Segment MB → Substitution Property of Equality using Statement 11 and 12
14. LMNB is a rhombus. → Definition of a rhombus.
One of the properties of a rhombus is that all 4 sides are equal in length.
Solve theses equations by elimination y= 3/2x -10 and -2x -4y =-8
SOLUTION
We want to solve the question with elimination method
[tex]\begin{gathered} y=\frac{3}{2}x-10.\text{ . . . . . . equation 1} \\ -2x-4y=-8\text{ . . . . . . . equation 2} \\ multiply\text{ equation 1 by 2, so as to remove the fraction } \\ 2\times y=(2\times\frac{3}{2}x)-(2\times10) \\ 2y=3x-20 \\ re-arranging\text{ we have } \\ -3x+2y=-20 \end{gathered}[/tex]So our paired equation becomes
[tex]\begin{gathered} -3x+2y=-20 \\ -2x-4y=-8 \end{gathered}[/tex]To eliminate y, multiply the upper equation by 4 and the lower by 2, we have
[tex]\begin{gathered} 4(-3x+2y=-20) \\ 2(-2x-4y=-8) \\ -12x+8y=-80 \\ -4x-8y=-16 \\ we\text{ have } \\ (-12x-4x)+(8y-8y)+(-80-16) \\ -16x+0=-96 \\ -16x=-96 \\ x=\frac{-96}{-16} \\ x=6 \end{gathered}[/tex]So put x for 6 into the second equation, we have
[tex]\begin{gathered} -2x-4y=-8 \\ -2(6)-4y=-8 \\ -12-4y=-8 \\ -4y=-8+12 \\ -4y=4 \\ y=\frac{4}{-4} \\ y=-1 \end{gathered}[/tex]Hence x = 6 and y = -1
The graph is shown below
Hence the point of intersection is (6, -1)
According to the complex conjugates theorem, if -3+i is a root of a function what else is a root?
To have an understanding of the question, we need to understand what the complex conjugates theorem is.
In a simpler form, what the complex conjugate theorem is saying is that perhaps, we have a Polynomial N with a complex root x + yi, then the complex conjugate of x + yi which in this case is x -yi is also a root of the polynomial N
Applying this to the question at hand;
x = -3 and y = 1
We find the conjugate of the above by negating y( turning it to a negative number)
So its conjugate will be -3 -i
Summarily; According to the complex conjugates theorem, if -3+i is a root of a function , -3 - i is also a root of the function
Find area under standard normal curve between -1.69 and 0.84
Required:
We need to find the area under the standard normal curve between -1.69 and 0.84
Explanation:
We need to find P(-1.69
P-value form z-table is
[tex]P(x<-1.69)=0.045514[/tex][tex]P(x<0.84)=0.79955[/tex]We know that
[tex]P(-1.69Substitute know values.[tex]P(-1.69Final answer:0.7540 is the area under the standard normal curve between -1.69 and 0.84.
Solve the proportions 28/35=8/r
ANSWER
r = 10
EXPLANATION
To solve for r first we have to put r in the numerator. To do that, we have to multiply both sides of the proportion by r:
[tex]\begin{gathered} \frac{28}{35}\cdot r=\frac{8}{r}\cdot r \\ \frac{28}{35}r=8 \end{gathered}[/tex]Now, we have to multiply both sides by 35:
[tex]\begin{gathered} \frac{28}{35}r\cdot35=8\cdot35 \\ 28r=280 \end{gathered}[/tex]And finally divide both sides by 28:
[tex]\begin{gathered} \frac{28r}{28}=\frac{280}{28} \\ r=10 \end{gathered}[/tex]Please help:What is the mean of the data set?108, 305, 252, 113, 191Enter your answer in the box. __
Solution
- The formula for finding the mean of a dataset is
[tex]\begin{gathered} \bar{x}=\sum_{i=1}^n\frac{x_i}{n}=\frac{x_1+x_2+x_3+x__4+...+x_n}{n} \\ where, \\ x_i=\text{ The individual data points} \\ n=\text{ The number of data points in the data set} \\ \bar{x}=\text{ The mean} \end{gathered}[/tex]- The dataset given is:
108, 305, 252, 113, 191
- Thus, we can infer that:
[tex]\begin{gathered} x_1=108,x_2=305,x_3=252,x_4=113,x_5=191 \\ \\ \text{ The number of datapoints is }n=5 \end{gathered}[/tex]- Now, we can proceed to find the mean of the dataset as follows:
[tex]\begin{gathered} \bar{x}=\frac{108+305+252+113+191}{5} \\ \\ \therefore\bar{x}=193.8 \end{gathered}[/tex]Final Answer
The mean of the dataset is 193.8
7. Which digital construction tool would help youdetermine whether point C or point D is the midpoint ofsegment AB?A. Angle bisectorB. Perpendicular bisectorC. Perpendicular lineD. Parallel line
The digital construction tool that would help determine wherer point C or point D is the midpoint of segment AB would be a Perpendicular Bisector. [Option B]
Since a bisector would divide the segment in two identical parts and the perpendicular line would mark the exact point in which the segment is being divided.
5) . Write theequation of a line in slope-intercept form.
Explanation
Given the two points
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(-1,1) \end{gathered}[/tex]The rise and run of the line is given as;
[tex]m=\frac{\text{rise}}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-4}{-1-(-2)}=-\frac{3}{1}=-3^{}_{}[/tex]Recall, the equation of a line in slope-intercept form is given as;
[tex]y=mx+c[/tex]Since we know the value of m, we can find the value of c by using one of the points above.
When x=-2, y= 4. Therefore;
[tex]\begin{gathered} 4=-3(-2)+c \\ 4=6+c \\ c=4-6 \\ c=-2 \end{gathered}[/tex]We then insert m and c into the slope-intercept equation.
Answer:
[tex]y=-3x-2[/tex]Find the area of this figure.Triangle: Rectangle: Half circle: Total area:
To determine the area of the figure given we need to divide the composite figure into figures in which we know how to find the area. We divide the figure into a triangle, a rectangle and a circle.
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
[tex]A=\frac{1}{2}(6)(6)=\frac{36}{2}=18[/tex]The area of the rectangle is given by:
[tex]A=lw[/tex]where l is the length and w is the width. For this triangle the length is 9 and the width is 6 then we have:
[tex]A=(9)(6)=54[/tex]The area of a circle is given by:
[tex]A=\pi r^2[/tex]where r is the radius of the circle. The circle shown has a diameter of 6; we know that the radius is half the diameter, then the radius is 3. Plugging the radius, we have:
[tex]A=(3.14)(3)^2=28.26[/tex]Now we add the areas of each figure, therefore we have:
[tex]18+54+28.26=100.26[/tex]Can someone pls help me with my homework I have to go to sleep so pls be fast
Okay, here we have this:
Let's calculate the slope (using the points: (2, 58.5) and (4, 107.5)):
m=(107.5-58.5)/(4-2)=49/2=24.5
Finally we obtain that the slope is 24.5, so this means that option III is incorrect.
And considering that the y intercept represents the value of y when x equals 0 (0 tickets sold), If a person does not buy any ticket, they should not pay anything, this means that the option IV isn't right.
So, finally we are only left with option I and II let's check them:
Replacing in function:
Total value = (number of tickets * cost per ticket) + service charge
2 Tickets:
58.5=(2*24.5)+9.5
58.5=49+9.5
58.5=58.5
4 Tickets:
107.5=(4*24.5)+9.5
107.5=98+9.5
107.5=107.5
8 Tickets:
205.5=(8*24.5)+9.5
205.5=196+9.5
205.5=205.5
12 Tickets:
303.5=(12*24.5)+9.5
303.5=294+9.5
303.5=303.5
20 Tickets:
499.5=(20*24.5)+9.5
499.5=490+9.5
499.5=499.5
Finally we obtain that the correct answer is the option A. Statements I and III.
A car rental company charges a $85 initial fee and $45 dollars a day to rent a car. Write an equation representing the cost, y, of renting the car for x days. (y= mx + b)
The given equation, y = mx + b is the slope intercept form of a linear equation where
m represents slope
b represents y intercept
The slope represents the rate of change of the values of y with respect to x. The values of y in this case represents the cost of renting the car while x represents the number of days for which the car is rented. Therefore,
slope, m = $45
The y intercept is the value of y when x is zero. We can see that the initial fee is $85. This means that even if the car is rented for zero days, the initial fee of $85 must be charged, Thus, y intercept is 85
Therefore, the equation representing the cost, y, of renting the car for x days is
y = 45x + 85
a financial advisor estimates that a company's profits follow the equation.
The equation that represent the profit is given by:
[tex]y=1000\cdot2^x[/tex]So in 3 years there are 36 months so the equation will be:
[tex]\begin{gathered} y=1000\cdot2^{36} \\ y=68^{},719,476,736,000 \end{gathered}[/tex]So is option A) it don't have sence because the profits are to great.
I need help with my math. I am working on linear equations. I don’t understand what I am doing and I am struggling on my homework. C/-9 + 6 = 14
Given:
[tex]\frac{C}{-9}+6=14[/tex]Solve this equation to find the value of C,
[tex]\begin{gathered} \frac{C}{-9}+6=14 \\ \text{Subtract 6 from both sides} \\ \frac{C}{-9}+6-6=14-6 \\ \frac{C}{-9}=8 \\ Multiply\text{ both sides by -9} \\ \frac{C}{-9}(-9)=8(-9) \\ C=-72 \end{gathered}[/tex]Answer: C= -72
Determine if the expression -w is a polynomial or not. If it is a polynomial, state thetype and degree of the polynomial.The given expression representsJa polynomial. The polynomial is aand has a degree of
SOLUTION
We want to show if the expression -w is a polynomial or not
-w can also be written as
[tex]-1(w^1)[/tex]Since it has one term, and the power or exponent is not negative number or fraction, it is a polynomial.
Since it has one term, it is a monomial
So it is a polynomial called a monomial.
Since it has an exponent or power of 1
It is a polynomial of degree 1
Please help me help help me please help help me out
1) We can find the inverse function, by following some steps. So let's start with swapping the variables this way:
[tex]\begin{gathered} f(x)=\sqrt[3]{x-1}+4 \\ y=\sqrt[3]{x-1}+4 \end{gathered}[/tex]2) Now let's isolate that x variable getting rid of that cubic root:
[tex]\begin{gathered} x=\sqrt[3]{y-1}+4 \\ x-4=\sqrt[3]{y-1} \\ (x-4)^3=(\sqrt[3]{y-1})^3 \\ (x-4)^3=y-1 \\ y=(x-4)^3+1 \end{gathered}[/tex]Note that when we isolate the y on the left we had to adjust the sign dividing it by -1, to get y, not -y.