Part 1 - FlooringFor the most part, the floors in Rachel's new house are in good shape. However, there are a couple of rooms that Rachel wants to redo right away. She plans to put new carpet in the family room and living room, and fresh hardwood floors in the foyer and kitchen. She also needs to put a new tile floor in the breakfast nook and mud room. Rachel (with your help) plans to install all the flooring herself, so there are no labor costs. However, she does need to buy the materials.Rachel has already scoped out the local home improvement store and priced out the cost of each material. She found that the carpet she wants will cost $1.80 per square foot, the hardwood flooring will cost $4.50 per square foot, and the tiles will cost $2.30 per square foot.a. How many square feet of carpet does Rachel need?b. How many square feet of hardwood does Rachel need?c. How many square feet of tile does Rachel need?d. How much will the total cost of materials for the re-flooring project be?
Answers
ANSWERS
a. 863.08 ft²
b. 474 ft²
c. 249 ft²
d. $4,259.24
EXPLANATION
Given:
• Rooms with ,carpet,: Family room and living room
,• Rooms with ,hardwood,: kitchen and foyer
,• Rooms with ,tiles,: breakfast nook and mudroom
• Cost ,carpet,: $1.80 per square foot
,• Cost ,hardwood,: $4.50 per square foot
,• Cost ,tiles,: $2.30 per square foot
First, we have to find the area of each of the mentioned rooms,
a. The family room is in the shape of a square whose sides are all 20 feet and a semicircle whose diameter is 20 feet. The area of the family room is the sum of the areas of each of these figures,
[tex]A_{family-room}=(20ft\cdot20ft)+(\frac{1}{2}\cdot\pi\cdot(20ft/2)^2)[/tex]As shown above, the area of the semicircle is half the area of the full circle with the same diameter. Solve,
[tex]A_{family-room}\approx(400ft^2)+(157.08ft^2)=557.08ft^2[/tex]The living room is in the shape of a rectangle with side lengths 15ft and 22ft, but a right triangle is cut out from the corner. The area of the living room is the area of the mentioned rectangle minus the area of the triangle of the corner,
The side lengths of the triangle are 15ft - 9ft = 6ft and 22ft - 14ft = 8ft. The area of the triangle is,
[tex]A_{triangle}=\frac{6ft\cdot8ft}{2}=24ft^2[/tex]So, the area of the living room is,
[tex]A_{living-room}=(22ft\cdot15ft)-24ft^2=330ft^2-24ft^2=306ft^2[/tex]The area that Rachel wants to cover with a new carpet is,
[tex]A_{carpet}=A_{family-room}+A_{living-room}=557.08ft^2+306ft^2=863.08ft^2[/tex]Hence, the area to be covered with carpet is 863.08 ft².
b. The kitchen is a rectangle with dimensions 24 ft and 15 ft, so its area is,
[tex]A_{kitchen}=24ft\cdot15ft=360ft^2[/tex]The foyer is in the shape of a rectangle with dimensions 10ft and 15ft. However, assuming that the stairs won't be covered with hardwood and that they cover that part of the foyer's floor, to find the area we have to subtract the area the stairs occupy in that room.
The rectangle where the stairs are has dimensions 9ft and (10ft - 6ft ) = 4ft. The area of the Foyer is,
[tex]A_{foyer}=(10ft\cdot15ft)-(9ft\cdot4ft)=(150ft^2)-(36ft^2)=114ft^2[/tex]The area Rachel wants to be covered by hardwood is the sum of the two,
[tex]A_{hardwood}=A_{kitchen}+A_{foyer}=360ft^2+114ft^2=474ft^2[/tex]Hence, the area to be covered with hardwood is 474 ft².
c. The mudroom is in the shape of a rectangle with dimensions 15 ft and 7 ft, so its area is,
[tex]A_{mudroom}=15ft\cdot7ft=105ft^2[/tex]The breakfast nook is in the shape of a trapezoid, where the height is 8ft and the lengths of the bases are 24ft and 12ft. Its area is,
[tex]A_{breakfast-nook}=\frac{(12ft+24ft)}{2}\cdot8ft=\frac{36ft}{2}\cdot8ft=18ft\cdot8ft=144ft^2[/tex]The area Rachel wants to cover with tiles is the sum of these two areas,
[tex]A_{tiles}=A_{mudroom}+A_{breakfast-nook}=105ft^2+144ft^2=249ft^2[/tex]Hence, the area to be covered with tiles is 249 ft².
d. Finally, we have to find the cost of flooring with each material,
[tex]Costs=\begin{cases}C_{carpet}=A_{carpet}\cdot p_{carpet}=863.08ft^2\cdot1.80=1,553.54 \\ C_{hardwood}=A_{hardwood}\cdot p_{hardwood}=474ft^2\cdot4.50=2,133 \\ C_{tiles}=A_{tiles}\cdot p_{tiles}=249ft^2\cdot2.30=572.70\end{cases}[/tex]The total cost of the project is the sum of the three,
[tex]C_{project}=C_{carpet}+C_{hardwood}+C_{tiles}=1,553.54+2,133+572.70=4,259.24[/tex]Hence, the total cost of the re-flooring project will be $4,259.24.
Related Questions
A pound of pistachios cost 6.60. and you buy 2.75 pounds
Answers
By performing some simple mathematical operations, we know that the total cost of 2.75 pounds of pistachios is $18.15.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).
So, the total cost will be:
1 pound of pistachios costs $6.60.We purchased 2.75 pounds.Then, the total cost will be:
6.60 × 2.75$18.15
Therefore, by performing some simple mathematical operations, we know that the total cost of 2.75 pounds of pistachios is $18.15.
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Correct question:
A pound of pistachios costs $6.60. and you buy 2.75 pounds. What is the total cost?
Type the correct answer in the box. Use numerals instead of words.The expression x^2 - 12x + 36 factors to (x - )^2
Answers
Explanation: Here we have a factorization problem and the way we solve it depends on the complexity and degree of the equation. We can see our equation is a simple quadratic function so we will use a simple method to solve it.
Step 1: Let's take a look at the illustration bellow
Step 2: As we can see above, we just need to find a way to represent the second term as a sum and the last term as multiplication using the same numbers.
Result: Once we found that this number is -6 so we can represent our factor as
[tex](x-6)^2[/tex]And that is our final answer.
3/4 divided by 2/3 using fractions
Answers
To solve this divition we can write it like:
[tex]\frac{\frac{3}{4}}{\frac{2}{3}}[/tex]So now we can multiplicate the numerator of the first fraction with the denominatior of the second fraction, and put the resould in the numerator of the quationt, ans the same operation for the numeratior with the numerator of the secon fraction and the denominator of the first fraction so:
[tex]\frac{3\cdot3}{4\cdot2}=\frac{9}{8}[/tex]For points K (-6,6) and P (-3,-2), find the following:m:| m:I m:Distance:Equation of a line 1:
Answers
From the question
We are given the points
[tex]K(-6,6),P(-3,-2)[/tex]Finding the slopre, m
Slope is calculated using
[tex]m=\frac{y_{2_{}}-y_1}{x_2-x_1}[/tex]From the given points
[tex]\begin{gathered} x_1=-6,y_1=6 \\ x_2=-3,y_2=-2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} m=\frac{-2-6}{-3-(-6)} \\ m=\frac{-8}{-3+6} \\ m=\frac{-8}{3} \end{gathered}[/tex]Therefore, m = -8/3
The next thing is to find
[tex]\mleft\Vert m\mright?[/tex]A slope parallel to m
For parallel lines, slopes are equal
Therefore,
[tex]\mleft\Vert m=-\frac{8}{3}\mright?[/tex]Next, we are to find
[tex]\perp m[/tex]A slope perpendicular to m
For perpendicular lines, the product of the slopes = -1
Therefore
[tex]\perp m=-\frac{1}{m}[/tex]Hence,
[tex]\begin{gathered} \perp m=-\frac{1}{-\frac{8}{3}} \\ \perp m=\frac{3}{8} \end{gathered}[/tex]Therefore,
[tex]\perp m=\frac{3}{8}[/tex]Next, we are to find the distance KP
Using the formula
[tex]KP=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]This gives
[tex]\begin{gathered} KP=\sqrt[]{(-3-(-6))^2+(-2-6)^2} \\ KP=\sqrt[]{3^2+(-8)^2} \\ KP=\sqrt[]{9+64} \\ KP=\sqrt[]{73} \end{gathered}[/tex]Therefore,
[tex]\text{Distance }=\sqrt[]{73}[/tex]Next, equation of the line
The equation can be calculated using
[tex]\frac{y-y_1}{x-x_1}=m[/tex]By inserting values we have
[tex]\begin{gathered} \frac{y-6}{x-(-6)}=-\frac{8}{3} \\ \frac{y-6}{x+6}=-\frac{8}{3} \\ y-6=\frac{-8}{3}(x+6) \\ y-6=-\frac{8}{3}x-6(\frac{8}{3}) \\ y-6=-\frac{8}{3}x-16 \\ y=-\frac{8}{3}x-16+6 \\ y=-\frac{8}{3}x-10 \end{gathered}[/tex]Therefore the equation is
[tex]y=-\frac{8}{3}x-10[/tex]There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the collection is Rupees 8.50, how many of each are there?
Answers
We will have the following:
*First:
**We stablish that x will represent the number of 20 paise coins.
**We stablish that y will represent the number of 25 paise coins.
Second: From this we will then have:
[tex]x+y=38[/tex]&
[tex]20x+25y=850[/tex][This 850 is due to the fact that 8.50 Rupees are equal to 850 paise].
*Third: We solve for either x or y in the first equation:
[tex]x=38-y[/tex]Now, we replace this in the second equation and solve for y:
[tex]20(38-y)+25y=850\Rightarrow760-20y+25y=850[/tex][tex]\Rightarrow5y=90\Rightarrow y=18[/tex]So, we have that there are 18 25 paise coins.
Now, using this we solve for x in the first equation:
[tex]x+18=38\Rightarrow x=20[/tex]So, we have that there are 20 20 pais coins.
A boy at an amusement park has 65 ride tickets. Each ride on the roller coaster costs 7 tickets. After riding the roller coaster as many times as he can, how many tickets will the boy have left?
Answers
ANSWER
[tex]32\text{ tickets}[/tex]EXPLANATION
The group consists of 4 friends and each friend has 12 tickets.
Each friend uses 4 tickets to ride the roller coaster.
To find the number of tickets each friend has after the ride, subtract the number of tickets used for the ride from the number of tickets each friend had initially.
That is:
[tex]\begin{gathered} \Rightarrow12-4 \\ 8 \end{gathered}[/tex]Now, to find the number of tickets the group has, multiply the number of friends in the group by the number of tickets left:
[tex]\begin{gathered} 4\cdot8 \\ 32\text{ tickets} \end{gathered}[/tex]Hi can someone please give a full explanation on how to solve this problem? I’ll give Brainliest
Answers
Answer:
C is correct.
Step-by-step explanation:
The area of the rectangle is 10 × 6, or 60 square meters.
The area of the triangle is 1/2 × 7 × 6, or 21 square meters.
So the area of the shaded region is the area of the rectangle minus the area of the triangle. That area is 60 - 21, or 39 square meters. C is correct.
In ΔIJK, k = 53 cm, j = 66 cm and ∠J=64°. Find all possible values of ∠K, to the nearest 10th of a degree.
Answers
The value of ∠K is 46.2° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side i = 68.91521 cm
Side j = 66 cm
Side k = 53 cm
Angle ∠I = 69.8°
Angle ∠J = 64°
Angle ∠K = 46.2°
∠K= sin⁻¹(k·sin(J)/j)
=sin⁻¹(53.(sin 64°)/66)
=46.2°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠K is 46.2°.
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f(x) = {(7,3), (5,3), (9,8).(11,4)}g(x) = {(5, 7),(3,5), (7,9), (9,11)}a) f-1(x)b) g-1(x)
Answers
Given the coordinates of the function;
f(x) = {(7,3), (5,3), (9,8).(11,4)}
The inverse of any coordinate points is gotten by changing the y coordinate valuewith the x coordinate values i.e y = x
f-1(x) = {(3,7), (3,5), (8,9), (4,11)
You can see that the x coordinates has been swapped with the y coordinates.
Similarly;
g-1(x) = {(7, 5),(5,3), (9,7), (11,9)}
Latoya cut a circle into & equal sections and arranged the pieces to form a shape resembling a parallelogram. So in of
Answers
Based on the diagram, the base length of the new shape is half the circumference of the circle as indicated by 1/2C.
which of the following is most likely to represent a fixed rate, secured debit?A- Student loanB- Credit CardC- Loan from a friend D- dealer-finaced auto loan
Answers
D because financing has a fixed rate
a friend's loan has no rate
the credit card varies the rate while you are using it
The student loan has no financing
The park near Amber's house has a path around its perimeter 3 that is mile long. Amber's goal is to walk 4.5 miles a day. If 4 Amber reaches her daily goal, how many times will Amber walk around the park?
Answers
We know that
• The path is 3 miles long.
,• Amber's goal is 4.5 miles a day.
To find the number of times she will walk around the park, we have to divide.
[tex]\frac{4.5}{3}=1.5[/tex]Hence, Amber will walk around 1 entire lap and a half.Find the area of a rectangle that is 3 3 over 4 inches long by 2 1 fourth inches wide. ANS.( Use mixed number) _______. in squared
Answers
Let's begin by listing out the given information:
[tex]\begin{gathered} Length(l)=3\frac{3}{4} \\ Width(w)=2\frac{1}{4} \\ Area=l\cdot w \\ Area=3\frac{3}{4}\cdot2\frac{1}{4} \\ Area=\frac{15}{4}\cdot\frac{9}{4}=\frac{15\cdot9}{4\cdot4} \\ Area=\frac{135}{16}=8\frac{7}{16} \\ Area=8\frac{7}{16}in^2 \\ \\ \therefore Area=8\frac{7}{16}in^2 \end{gathered}[/tex]The total number of photos on Hannah's camera is a linear function of how long she was in Rome. She already had 44 photos on her camera when she arrived in Rome. Then she took 24 photos each day for 6 days. What is the initial value of the linear function that represents this situation? 24 photos 44 photos 6 days o days per day
Answers
she already had 44 photos
She took 24 photos each day for 6 days.
The function is:
y= 44+24x
where y is the total number of photos and x is the number of days.
The initial value is when x=0
y= 44+24(0) =44
The initial value is 44.
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5 questions if you guess randomly on each question?A. 0.9936B. 0.2C. 0.0264D. 0.0003
Answers
If there are 10 questions with 5 answer choices, then first we need to find out the probability of getting the first questions randomly correct.
Therefore, that is:
[tex]\begin{gathered} Probability\text{ of getting 1 answer correct= }\frac{1}{5} \\ \\ Then\text{ if we need to get the second question correct it is:} \\ \frac{1}{5}(first\text{ question\rparen x }\frac{1}{5}=\text{ \lparen}\frac{1}{5})^2 \\ \\ And\text{ for the other questions applies the same. Therefore, if we need 5 correct answers, then:} \\ \frac{1}{5}\text{ x }\frac{1}{5}x\frac{1}{5\frac{}{}}x\frac{1}{5}x\text{ }\frac{1}{5}=\text{ \lparen}\frac{1}{5})^5\text{ = }\frac{1}{3125}=\text{ 0.0003} \end{gathered}[/tex]The answer is D. 0.0003
A regular polygon with 9 sides (a nonagon) has a perimeter of 72 inches. What is the area of this polygon? Provide mathematical evidence.
Answers
The perimeter of the regular nonagon is 72 inches, the length of each side can be determined as,
[tex]\begin{gathered} P=9s \\ 72=9s \\ s=8\text{ inches} \end{gathered}[/tex]The diagram can be drawn as,
The value of apopthem a can be determined as, where n is the number of sides,
[tex]\begin{gathered} a=\frac{s}{2\tan (\frac{180^{\circ}}{n})} \\ =\frac{8}{2\tan20^{\circ}} \\ =10.98\text{ in} \end{gathered}[/tex]The area can be determined as,
[tex]\begin{gathered} A=\frac{P\times a}{2} \\ =\frac{72\text{ inches}\times10.98\text{ inches}}{2} \\ =395.63in^2 \end{gathered}[/tex]Thus, the required area of the polygon is 395.63 square inches.
Find the area of quadrilateral ABCD. Round the area to the nearest whole number, if necessary.у| A(-5,4)4B(0, 3)22F(-2,1)-226 xTC(4, -1)-4E(2, -3)D(4, -5)6The area issquare units.
Answers
We have a quadrilateral ABCD and we want to calculate the area.
We can divide it in three areas (two triangles and one rectangle) and then add the surfaces.
As it is rotated 45 degrees, we can define a "new unit" that is the diagonal of a square of 1 by 1 unit, in the scale of the graph.
This new unit, the diagonal that we will call "d", by the Pythagorean theorem, has a value of:
[tex]d=\sqrt{2}[/tex]We will start then with the triangle ABF. It has a side BF that has a value of 2 diagonals (2d) and a side FA that has a value of 3 diagonals (3d). The area of a triangle is half the multiplication of this two sides, so we have:
[tex]\frac{\bar{BF}\cdot\bar{FA}}{2}=\frac{2d\cdot3d}{2}=3d^2=3(\sqrt{2})^2=3\cdot2=6[/tex]The second triangle is CED. We repeat the process and we have:
[tex]\frac{\bar{CE}\cdot\bar{ED}}{2}=\frac{2d\cdot2d}{2}=2d^2=2\cdot2=4[/tex]The rectangle BCEF has an area of:
[tex]\bar{BF}\cdot\bar{EF}=2d\cdot4d=8d^2=8\cdot2=16[/tex]Now we have the three areas. If we add them we get the area of ABCD:
[tex]6+4+16=26[/tex]The quadrilateral ABCD has an area of 26 units^2.
For the function h(x) defined below . Find the function f(x) and g(x)
Answers
ANSWER:
1st option.
[tex]f\left(x\right)=x^3\text{ and }g\left(x\right)=\frac{x+2}{x}[/tex]STEP-BY-STEP EXPLANATION:
We have the following composite function obtained from two functions:
[tex]h(x)=\:\left(f\circ g\right)\left(x\right)=\left(\frac{x+2}{x}\right)^3[/tex]We can determine the functions as follows:
[tex]\begin{gathered} \left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right) \\ \\ f\left(g\left(x\right)\right)=\left(\frac{x+2}{x}\right)^3 \\ \\ g(x)=\frac{x+2}{x},\text{ therefore} \\ \\ f(x)=x^3 \end{gathered}[/tex]Therefore, the correct answer is the 1st option.
graph a piecewise function with 3 equations and sketch a graph
Answers
Solution:
Given:
[tex]h(x)=\begin{cases}2x,x\le-2 \\ x^2-1,-2A piecewise function is a function that is defined by different formulas or functions for each given interval.It is a function in which more than one formula is used to define the output over different pieces of the domain.
The function h(x) given has three outputs for three different domains.
[tex]\begin{gathered} \text{The first is a linear function;} \\ h(x)=2x \\ \\ \text{The second is a quadratic function;} \\ h(x)=x^2-1 \\ \\ \text{The third is a linear function;} \\ h(x)=x-3 \end{gathered}[/tex]Therefore, the graph using a graph plotter (desmos) is as shown below;
And each diagram below, right, the 2 number on the sides of the acts that are multiplied together to get the top number of the x, but added together to get the bottom number of the x.
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-34 = x*y
15 = x +y
17 and -2
__________________________
_____________
9 = x*y
6 = x +y
_
y=2/3 × + 4. use this equation to find y for the following values of x. x=0
Answers
a) for x = 0
y = (2/3) x 0 + 4
y = 0 + 4
y = 4
b) x = 3
y = (2/3) x 3 + 4
y = 6/3 + 4
y = 2 + 4
y = 6
c) x = 9
y = (2/3) x 9 + 4
y = 18/3 + 4
y = 6 + 4
y = 10
d) x = -9
y = (2/3) x (-9) + 4
y = -18/3 + 4
y = - 6 + 4
y = -2
e) x = 10
y = (2/3) x 10 + 4
y = 20/3 + 4
y = 32/3
f) x = 1/2
[tex]\begin{gathered} y\text{ = }\frac{2}{3}\text{ x }\frac{1}{2}\text{ + 4} \\ y\text{ = }\frac{1}{3}\text{ + 4} \\ y\text{ = }\frac{1\text{ + 12}}{3} \\ y\text{ = }\frac{13}{3} \end{gathered}[/tex]make an equation to find the area of rectangle. move number and symbols to the line
Answers
We know that the multiplication of both sides of the rectangle is the area of it.
In this case
Area: 6 x 8 = 48i don't know how to identify the domain and range of the graph
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The domain is the set of all possible values for x. All x values ( horizontal axis) that are going to be used
Domain = (-4,-1,0,4)
The range is the set of all possible y-values . All the y-values (vertical axis) that are used.
Range = (-5)
A) 9- (-22) - 13B) 9 - (-22) = -13A football team gained 9yards on one play andthen lost 22 yards on thenext. Write a sum ofintegers to find theoverall change in fieldposition-9- (-22) = -13D) None of the above
Answers
The sum of integers should be written like:
9 + (-22) = -13
because the are asking in fact for a SUM of integers
The two integers are 9 and -22
when added you get:
9 + (-22) = 9 - 22 = -13
ANYONE HELP ME WITH THE AREA OF THE FLOOR PLAN FOR THE OFFICE
NEED CLEAR EXPLAINATION AND ANSWER.
Answers
The area of the floor plan for the office is 2200 m².
We are given a diagram. The diagram shows the floor plan of an office. The height of the office is 50 meters. The length of the floor of the office is 55 meters. The width of the floor of the office is 40 meters. We need to find the area of the floor of the office.
The shape of the floor of the office is a rectangle. The area of a rectangle is calculated as the product of its length and width. Let the area of the floor of the office be represented by the variable "A".
A = 55*40
A = 2200
Hence, the area of the floor of the office is 2200 m².
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given: s is the midpoint of QR , QR , PS and angle RSP and angle QSP are right angles prove PR is congruent to PQ
Answers
∆RSP ≈ ∆QSP through SAS congruency theorem. PR is congruent to PQ.
Given that,
S being the midpoint of QR
SR = QS (∵ midpoint)
PS = PS (common side/reflexive property)
Two right triangles are congruent due to
∵ PS ≅ PS (SAS congruency)
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle contained between the sides of one triangle are equal to the second triangle's two sides and angle between its sides correspond to the first triangle's.
QS ≅ PS
Thus, ∆RSP ≈ ∆QSP through SAS congruency.
While PQ = PR (by CPCT).
Hence, proved.
Therefore, ∆RSP ≈ ∆QSP through SAS congruency theorem. PR is congruent to PQ.
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Caleb's recipe calls for 4.4 cups of an ingredient. His measuring bowl only has measurements marked in liters. Caleb knows that one cup is approximately 240 milliliters. Determine the number of liters of that ingredient that Caleb needs for his recipe.
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If f(x) = 2x^3 + 10x^2 + 18x + 10 and x + 1 is a factor of f(x), then find all of the zeros of f(x) algebraically
Answers
Given the polynomial:
[tex]f(x)=2x^3+10x^2+18x+10[/tex]We know that (x + 1) is a factor of f(x). We divide f(x) by (x + 1):
Then:
[tex]f(x)=(x+1)(2x^2+8x+10)=2(x+1)(x^2+4x+5)[/tex]For the quadratic term, we solve the following equation:
[tex]x^2+4x+5=0[/tex]Using the general solution for quadratic equations:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt{4^2-4\cdot1\cdot5}}{2\cdot1}=\frac{-4\pm\sqrt{16-20}}{2}=\frac{-4\pm\sqrt{4}}{2} \\ \\ \therefore x=-2\pm i \end{gathered}[/tex]The zeros of f(x) are:
[tex]\begin{gathered} x_1=-1 \\ \\ x_2=-2-i \\ \\ x_3=-2+i \end{gathered}[/tex]ABC and BCD are identical triangles. The overlapping area is 19cm . Find the area ofthe shaded figure.
Answers
The area of the shaded figure is 45 [tex]cm^{2}[/tex]
It is given that ABC and BCD are identical triangles and the overlapping area is 19[tex]cm^{2}[/tex]
Now, to evaluate the area of the shaded figure, we will calculate the area of the two triangles ABC and BCD, then we will subtract the overlapping area from it.
So, by evaluating the figure, it comes out that the length of the triangle is 4 units and 1 unit is 2cm.
So, Height of the triangle = 4 * 2 cm = 8 cm
And the base of the triangle is 3 units, then,
Base of the triangle = 3* 2 cm = 6 cm
The area of the triangle = 1/2 * base* height
Area of triangle ABC = [tex]\frac{1}{2} *8*6 = 24cm^{2}[/tex]
The area of both the triangles = area(ABC) +area(BCD)
Since two the triangles are identical, their areas are also identical,
So, the Area of both the triangles = 2*area(ABC) = 2*24 = 64[tex]cm^{2}[/tex]
Now, The area of the shaded figure = area(ABC) +area(BCD) - overlapping area.
The area of the shaded figure = 64 - 19 = 45 [tex]cm^{2}[/tex]
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Z + 24 = -33one step equation
Answers
We solve as follows:
[tex]z=-57[/tex]We operate like terms after substracting 24 from each side of the function.