Explanation
Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;
[tex]\begin{gathered} lw=35---1 \\ 2(l+w)=24---2 \end{gathered}[/tex]Therefore, we can say
[tex]l=\frac{35}{w}[/tex]We will substitute the above in equation 2
[tex]\begin{gathered} 2(\frac{35}{w}+w)=24 \\ \frac{70}{w}+2w=24 \\ multiply\text{ though by w} \\ 70+2w^2=24w \\ 2w^2-24w+70=0 \\ 2(w^2-12w+35)=0 \\ w^2-7w-5w+35=0 \\ (w-7)-5(w-7)=0 \\ (w-7)(w-5)=0 \\ w=7\text{ or w=5} \end{gathered}[/tex]Since the width must be shorter than the length therefore the width will be 5 inches.
Hence;
[tex]l=\frac{35}{5}=7[/tex]Answers:
The dimensions are:
Length = 7 inches
Width = 5 inches
Can anyone solve this?
The value of x for the given triangle is 2√5 units.
According to the question,
We have the following information:
We have two triangles joint together whose sides are given.
Now, we will use the Pythagoras theorem to find the value of x.
Let's denote the hypotenuse of the triangles with h, perpendicular with p and base with b.
First, we will use it in triangle other than the side x.
[tex]h^{2} =p^{2} +b^{2}[/tex]
[tex]p^{2} =9^{2} -6^{2}[/tex]
[tex]p^{2} =81-36[/tex]
[tex]p^{2} = 45[/tex]
p = √45
p = 3√5 units
Now, the perpendicular of this triangle will be the hypotenuse of another triangle.
[tex]h^{2} =p^{2} +b^{2}[/tex]
[tex]b^{2} =(3\sqrt{5}) ^{2} - 5^{2}[/tex]
[tex]b^{2} = 45-25[/tex]
[tex]b^{2} = 20[/tex]
b = 2√5 units
Hence, the value of x is 2√5 units.
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Determine whether each parabola has a horizontal directrix or vertical directrix 1. (y-3)²= 1/8 (x+1) horizontal or vertical directrix2. (x-2)²=6(y-3) horizontal or vertical directrix 3. (y+4)²=-12(x+2)horizontal or vertical directrix4. (x+3)²= -8(y+2) horizontal or vertical directrix
Answer
1) Horizontal directrix.
2) Vertical directix.
3) Horizontal directix.
4) Vertical directrix.
Explanation
A parabola with a vertical axis will have a horizontal directrix.
A parabola with a horizontal axis will have a vertical directrix.
A parabola with a vertical axis will have a standard equation of the parabola as
(x - h)² = 4p (y - k),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h, k + p).
The directrix is the line y = k - p and it is a vertical directrix.
A parabola with a horizontal axis will have a standard equation of the parabola as
(y - k)² = 4p (x - h),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h + p, k).
The directrix is the line x = h - p and it is a horizontal directrix.
So, for this questions,
1.) (y - 3)² = 1/8 (x + 1)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
2.) (x - 2)²= 6 (y - 3)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
3.) (y + 4)² = -12 (x + 2)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
4.) (x+3)²= -8(y+2)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
Hope this Helps!!!
Suppose that the local sales tax rate is 4% and you purchase a car for $18,000. How much tax is paid? What is the cars total cost?
Solution
Step 1:
Cost = $18000
Tax = 4% of $18000
Step 2
[tex]\begin{gathered} Tax\text{ = 4\% of \$18000} \\ \\ Tax\text{ = }\frac{4}{100}\text{ }\times\text{ \$18000} \\ \\ Tax\text{ paid = \$720} \end{gathered}[/tex]Step 3
[tex][/tex]what is the probability of a student owning a car that is not blue or green round to two decimal places
0.83
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}}[/tex]Step |
Let
[tex]\begin{gathered} \text{favorable outcomes=car that is not blue or gre}en,\text{ so} \\ \text{favorable outcomes=}red\text{ cars+yellow cars+white cars+other} \\ \text{favorable outcomes=}40+29+26+14 \\ \text{favorable outcomes=}109 \end{gathered}[/tex]now, the total outcomes is the total of cars
[tex]\text{total outcomes=40+13+29+26+10+14=132}[/tex]Finally, replace in the equation
[tex]\begin{gathered} P=\frac{favorable\text{ ourcomes}}{\text{total possible outcomes}} \\ p=\frac{109}{132} \\ P=0.83 \end{gathered}[/tex]so, the answer is 0.83
I hope this helps you
What is 3[cos(60)+isin60]*1/2[cos(15)+isin(15)]
1) Let's simplify this expression considering the trigonometric ratios and the complex numbers as well.
[tex]\begin{gathered} 3\left[\cos \left(60^{\circ \:}\right)+i\sin \left(60^{\circ \:}\right)\right]\frac{1}{2}\left[\cos \left(15^{\circ \:}\right)+i\sin \left(15^{\circ \:}\right)\right] \\ Convert\:to\:radians: \\ 3\left[\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right]\frac{1}{2}\left[\cos \left(\frac{\pi }{12}\right)+i\sin \left(\frac{\pi }{12}\right)\right] \\ \quad \cos \left(x\right)+i\sin \left(x\right)=e^{ix} \\ 3\times\frac{1}{2}\lbrack\left[e^{i\frac{\pi}{3}}\right]\left[e^{i\frac{\pi}{12}}\right] \\ \frac{3\left(-1\right)^{\frac{5}{12}}}{2} \\ \end{gathered}[/tex]We have transitioned that to work with radians for convenience and used one identity. Note that we could have written our final answer in a radical form.
using the digits -9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution in quadrant 2. Tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
Okay, here we have this:
Considering the provided information and options, we are going to find the requested numbers, so we obtain the following:
So first we will choose two values for x and y that meet the given tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
For our case we will take x=-1 and y=1, then we can write the following two equations:
1x+3y=2 -> 1(-1)+3(1)=2 -> -1+3=2 -> 2=2
y=7x+8 -> 1=7(-1)+8 -> 1=-7+8 -> 1=1
Poss Combine like terms to create an equivalent expression. Skill 4 3 2 m 5 m т 5 5 Over Introl Subs Quiz 80% Take Com
Collecting like terms =>
[tex]\begin{gathered} (\frac{2m}{5}-\frac{3m}{5})\text{- }\frac{4}{5} \\ we\text{ can simplify the terms with m coefficient} \\ \frac{2}{5}m\text{ -}\frac{3}{5}m \\ =\text{ find the lowest common multiple of the denominator} \\ =\text{ lowest common multiple of 5 and 5 is 5} \\ =\text{ }\frac{2m\text{ - 3m}}{5} \\ \Rightarrow\text{ }\frac{-m}{5} \\ \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Then we will obtain} \\ \frac{-m}{5}\text{ -}\frac{4}{5} \end{gathered}[/tex]We may decide to further simplify the expression or leave the answer as it is shown above,
On simplification we will need to get the lowest common multiple of the denominator which is 5
[tex]\frac{-m}{5}\text{ -}\frac{4}{5}\Rightarrow\text{ }\frac{-m\text{ - 4}}{5}[/tex]Find the inverse function of F(x)=2 arccos xF^-1(x)=
Given the inverse function
[tex]f(x)\text{ = 2arccosx}[/tex]A function g is the inverse of f if for y = f(x) , x = g(y)
[tex]\begin{gathered} y\text{ = 2arccosx} \\ \arccos x\text{ = }\frac{y}{2} \\ \arccos a\text{ = b} \\ a=\cos (b) \end{gathered}[/tex][tex]\begin{gathered} x=\text{ cos(}\frac{y}{2}) \\ \text{substitute y = x} \\ y=\cos (\frac{x}{2}) \end{gathered}[/tex]Hence the correct answer is Option B
Reduce to the lowest terms by canceling -14/9 times -3/7
Answer:
2/3
Explanation:
Given the below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}[/tex]We can see from the above that 9 is divisible by 3 and that 14 is divisible by 7, let's go ahead and reduce to the lowest term as shown below;
[tex]\frac{-14}{9}\times\frac{(-3)}{7}=\frac{-2}{3}\times\frac{(-1)}{1}=\frac{2}{3}[/tex]Find the value of b.a=5 and c = 10A.9.5B.10C.9D.8.7Please can you explain.
1) Assuming this is a right triangle, we can find the missing leg by making use of the Pythagorean Theorem.
2) Thus, we can write out this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ (10)^2=5^2+b^2 \\ \\ 100=25+b^2 \\ \\ b^2=100-25 \\ \\ b=\sqrt{75} \\ \\ b\approx8.7 \end{gathered}[/tex]Note that the hypotenuse (the largest side) is always on the left side. And that this is an approximation rounded off to the nearest tenth.
3) Thus, the answer is:
[tex]D.\:8.7[/tex]for the literal equation x^2+m=y, express x in terms of y and m
We have the equation of y as a function of x:
[tex]y(x)=x^2+m[/tex]To find x(y) we just need to solve for x, first by subtracting m from both sides
[tex]y-m=x^2[/tex]Now, we just have to take the square root on both sides
Taking the square root of a number it's actually raising it to the 1/2 power:
[tex]\sqrt[]{a}=a^{\frac{1}{2}}[/tex]Now, when we proceed to raise the square root of a number to two, we can arrange it like this:
[tex](a^{\frac{1}{2}})^2=a^{\frac{2}{2}}=a^1=a[/tex]When we take the square root of a number that is raised to two the result will be the number without any power, like this:
[tex]\sqrt[]{a^2}=a[/tex]Then:
[tex]\sqrt[]{x^2}=x=\sqrt[]{y-m}[/tex]Simplify the inequality. Graph it, write it in interval notation, and then inequality notation. Write your answer in interval notation.3x+2<−4 or 3x+3>27Clear All Draw: Line segments interval inequality
given the inequality
[tex]3x+2<−4\text{ }or\text{ }3x+3>27[/tex]then
[tex]3x<−4-2\text{ }or\text{ }3x>27-3[/tex][tex]3x<−6\text{ }or\text{ }3x>24[/tex][tex]x<−2\text{ }or\text{ }x>8[/tex]Graph:
notice the empty circle because the ineqaulity does not have equal symbol
interval:
[tex]\left(-\infty \:,\:-2\right)\cup \left(8,\:\infty \:\right)[/tex]inequality:
[tex]x<-2\text{ }or\text{ }x>8[/tex]kris is buying 165 square feet to turf to put on the floor of his square garage. which measurement is closest to the side length of each side of the garage?A 83 ftB 41 ftC 13 ftD 12ft
SOLUTION
Kris is buying 165 square feet to turf to put on the floor of his square garage.
which measurement is closest to the side length of each side of the garage?
Area of the square = Length x Length
165 = L X L
L^2 = 165
square root both sides, we have :
L = 12. 845
L = 13 feet ............... OPTION C
Three people share 4/5 of a lasagna. What fraction of the lasagna does each person eat?
4/15
1) Since 3 people share 4/5 of a lasagna we can write:
[tex]\frac{\frac{4}{5}}{3}=\frac{4}{5}\times\frac{1}{3}=\frac{4}{15}[/tex]Remember that when dividing a fraction we must multiply the dividend (4/5) by the reciprocate of the divisor (3).
2) So each one ate 4/15 of a whole lasagna.
Two chords intersect with the measures shown in the drawing. What is the value of x? 0 4 -2 2
it is given that
the length of cords segments are
8 , 2x , 5x , 5
we know that when two chords intersect
the multiplication of the segments of the one chord will be equal the other chord
so,
[tex]8\times5=2x\times5x[/tex][tex]\begin{gathered} 40=10x^2 \\ x^2=4 \\ x=2 \end{gathered}[/tex]thus, the answer is x = 2
need help with math
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]Sam wants to cover a gift box with paper the top of the box is 8in wide and 15in long the box is 12in tall what is the minimum amount of paper Sam will need to cover the entire box?
In order to find the amount of paper that will be needed, we need to calculate the surface area of this rectangular prism.
The faces of this figure are:
- 2 rectangles with dimensions 8 in and 15 in,
- 2 rectangles with dimensions 15 in and 12 in,
- 2 rectangles with dimensions 12 in and 8 in.
Calculating the area of each rectangle, we have:
[tex]\begin{gathered} A_1=8\cdot15=120 \\ A_2=15\cdot12=180 \\ A_3=12\cdot8=96 \end{gathered}[/tex]Now, the surface area is:
[tex]\begin{gathered} S=2A_1+2A_2+2A_3 \\ S=240+360+192 \\ S=792\text{ in}^2 \end{gathered}[/tex]So the amount of paper needed is 792 in².
The local water slides have 40 employees,of which 95% are temporary.How many temporary employees are there?
Mul,tiply the number of employees by the percentage in decimal form (divided by 100)
40 x (95/100) = 40 x 0.95 = 38 employees
A small town has two local high schools. High School A currently has 900 studentsand is projected to grow by 50 students each year. High School B currently has 500students and is projected to grow by 100 students each year. Let A represent thenumber of students in High School A in t years, and let B represent the number ofstudents in High School B after t years. Graph each function and determine whichhigh school is projected to have more students in 4 years.so i accidentally disconnected from my tutor and i am not sure if this graph is right or wrong. can you help me?
Answer:
High school A will have 200 more students than High school B.
Graphing the two equations;
Explanation:
Given that High School A currently has 900 students and is projected to grow by 50 students each year.
If t represent number of years, A represent the number of students in High School A in t years, and B represent the number of students in High School B after t years.
[tex]A=900+50t[/tex]High School B currently has 500 students and is projected to grow by 100 students each year.
[tex]B=500+100t[/tex]The number of student each high school is projected to have in 4 years is;
[tex]\begin{gathered} A=900+50(4)=900+200 \\ A=1100 \\ \\ B=500+100(4)=500+400 \\ B=900 \end{gathered}[/tex]Therefore, high school A will have 200 more students than High school B.
Graphing the two equations;
the radius of a circle is 15 what is the length of an arc that subtends an angle of Pi radians
The arc length of a circle is calculated by the formula
[tex]s=\theta\cdot r[/tex]replace the values of the angle and the radius into the formula
[tex]\begin{gathered} s=\pi\cdot15 \\ s=15\pi \end{gathered}[/tex]the arc length of the arc that subtends an angle of pi is 15pi.
Find the slope of the line that passes through (4, 3) and (9, 10). Simplify your answer and write it as a proper fraction, improper fraction
Answer:
Slope = 7/5
Explanation:
The slope of a line that passes through the points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) by (4, 3) and (x2, y2) by (9, 10), we get that the slope of the line is equal to:
[tex]m=\frac{10-3}{9-4}=\frac{7}{5}[/tex]Therefore, the slope is equal to 7/5
Solve for y. y - 10 = 7 - X
We are given the following expression:
[tex]y-10=7-x[/tex]To solve for "y" we will add 10 to both sides:
[tex]y-10+10=7-x+10[/tex]Adding like terms:
[tex]y=17-x[/tex]Which of the triangles does not have the same base length as the others?A)CD)7
Look at the graphs and measure the bases of each triangle:
A. 4 units
B. 4 units
C. 5 units
D. 4 units
Answer: triangle C
The center of a circle is at (8,-8). One point on the circle is at (8, -3). What is thearea of the circle? (Use 3.14 for pi.)A 15.7 unitsB 64 units?C 78.5 units?D 200.96 units2
The center of a circle is at (8,-8). One point on the circle is at (8, -3). Then the radius of the circle is -3 - (-8) = -3 + 8 = 5 units.
The area of a circle is computed as follows:
A = πr²
Replacing with π = 3.14 and r = 5:
A = 3.14(5)²
A = 3.14(25)
A = 78.5 units²
3 Check your notes! A container is shaped like a rectangular prism and has a volume of 72 cubic feet. Give two different sets of measurements that could be the dimensions of the container. Answers: a feet X feet x a feet feet X feet X feet >
Explanation:
The volume of the container = 72 cubic ft
The container is a rectangular prism.
The formula for volume of rectangular prism:
[tex]\text{Volume = length }\times\text{ width }\times\text{ height}[/tex]To get the posssible values of the containers dimention, we will find the factors of 72. Since the volume is a product of the dimensions
[tex]\begin{gathered} 72\text{ = 3 }\times\text{ 24} \\ 72\text{ = 3 }\times\text{ 4 }\times\text{ 6} \\ \text{The possible dimensions can be:} \\ 3\text{ ft }\times\text{ 4ft }\times\text{ 6ft} \end{gathered}[/tex][tex]\begin{gathered} 72\text{ = }2\text{ }\times\text{ 36} \\ 72\text{ = 2 }\times4\text{ }\times\text{ 9} \\ \text{The possible dimensions:} \\ 9ft\text{ }\times\text{ 4ft }\times\text{ 2ft} \end{gathered}[/tex]David is running a fried chicken stand at fall music festivals. He sells fried chicken legs for $4 each and fried chicken tenders for $8/ cup. A festival costs $60 for a vendor license and supply costs are $1 for each chicken leg and $2 for each cup of tenders. David wants to make profit of more than $300 but he only has $110 to spend on costs ahead of time. Create a total profit and a cost equation to model the situation with x = # of chicken legs and y = # cups of tenders.
SOLUTION
From the question,
Chicken legs cost $1, but the selling price is $4
Chicken tender cost $2 per cup, but the selling price is $8
Now, a festival costs $60 and David has only $110 to spend.
Also number of chicken legs sold is represented as x and
number of chicken tenders sold is represented as y.
Hence the cost equation becomes
[tex]\begin{gathered} x\times1\text{ dollar for chicken legs + y}\times2\text{ dollars for chicken tender + 60 }\leq110 \\ x+2y+60\leq110 \end{gathered}[/tex]Note that profit = sales - cost
So we have to subtract the cost from the sales.
Now, David wants to make sales more than $300.
Hence the sales equation becomes
[tex]\begin{gathered} x\times4\text{ dollars for chicken legs + y}\times8\text{ }\times\text{dollars for chicken tender }\ge300 \\ 4x+8y\ge300 \end{gathered}[/tex]So, we will subtract the cost equation from the sales equation to get the profit equation. This becomes
[tex]\begin{gathered} 4x+8y-(x+2y+60)\ge300 \\ 4x+8y-x-2y-60\ge300 \\ 4x-x+8y-2y\ge300+60 \\ 3x+6y\ge360 \end{gathered}[/tex]Hence, the cost and profit equation is
[tex]\begin{gathered} 60+x+2y\leq110 \\ 3x+6y\ge360 \end{gathered}[/tex]But what we have as a correct choice in the answers is the cost and sales equation, which is
[tex]\begin{gathered} 60+x+2y\leq110 \\ 4x+8y\ge300 \end{gathered}[/tex]Yasmin has some identical rectangular tiles.
Each tile is L’cm by W'cm.
Using 9 of her tiles, Yasmin makes rectangle ABCD, shown in the diagram below.
Diagram NOT
accurately drawn
The area of ABCD is 1620 cm²
Work out the value of L and the value of W.
B
Diagram NOT
accurately drawn
The dimensions L and W, considering the area of the rectangle, are given as follows:
L = 6.1 cm.W = 4.9 cm.How to obtain the area of a rectangle?The area of a rectangle of dimensions L and W is given by the multiplication of these dimensions, as follows:
Considering the image shown at the end of the answer, with the composition of the smaller rectangles, the dimensions of the large rectangle are given as follows:
Width: 5W = 4L.Length: L + W.Hence the expression for the area of the rectangle is given as follows:
5W(L + W) = 1620.
From the width relation, we have that:
5W = 4L
W = 0.8L.
Hence the length is obtained as follows:
5W(L + W) = 1620.
5 x 0.8L(L + 0.8L) = 1620
7.2L³ = 1620
L = (1620/7.2)^(1/3) -> cubic root
L = 6.1 cm.
W = 0.8L = 0.8 x 6.1 = 4.9 cm.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Use inverse trig ratios to find the angle measures sinX = 0,259 [ Choose ] Cosx = 0,743 [ Choose ] < tanX = 4 [Choose < sinX = 4/7 [ Choose
ANSWER:
[tex]\begin{gathered} x=15.01\text{\degree} \\ x=42.01\text{\degree} \\ x=75.96\text{\degree} \\ x=34.85\text{\degree} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We calculate the value of the angles for each point as follows:
[tex]\begin{gathered} \sin x=0.259\rightarrow x=\arcsin 0.259\rightarrow x=15.01\text{\degree} \\ \cos x=0.743\rightarrow x=\arccos 0.753\rightarrow x=42.01\text{\degree} \\ \tan x=4\rightarrow x=\arctan 4\rightarrow x=75.96\text{\degree} \\ \sin x=\frac{4}{7}\rightarrow x=\arcsin \frac{4}{7}\rightarrow x=34.85\text{\degree} \end{gathered}[/tex]The function f is defined by the following rule.f(x) = 3x-3Complete the function table.хf(x)- 4-30145
find a set of parametric equations for the rectangular equation
We have for the fisrt equation that
[tex]\begin{gathered} t\text{ = 2 -x } \\ x\text{ = 2 - t = -t + 2} \end{gathered}[/tex]Now knowing this we are going to replace in the second equation
[tex]\begin{gathered} y\text{ = 8x - 6} \\ y\text{ = 8(-t + 2) - 6 = -8t +16 -6} \\ y\text{ = -8t +10} \end{gathered}[/tex]So the answer is the fourth option.