As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]A Distance Run (km) B Distance Run (km) 0 1 1 1 | 2 | 4 | 7 7 088 9 1 1|224 5 5 8 1 2 3 2 3 3 6 8 9 2 3 5 5 6 7 8 9 2 1 1 3 6 | 7 3 03 4 4 15 310 What is the DIFFERENCE in the ranges of the 2 sets of data?Type your answer without a label.
The range of a data set is said to be the difference between the highest value and the lowest value in the given set of data.
To find the difference in the ranges of the 2 sets of data, find the range of data set A, find the range of data set B, then subtract the range of A from B.
Thus, we have:
For data A:
Minimun data value = 08
Maximum data value = 35
Range of data set A = 35 - 08 = 27
For data set B:
Minimum data value = 01
Maximum data value = 30
Range of data set B = 30 - 01 = 29
Difference in the ranges = Range of set B - Range of set A = 29 - 27 = 2
Therefore, the difference in the ranges of the sets of data is 2
ANSWER:
2
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
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!!!
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
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 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
The product of 10 over 22 and 14 over 5 is equivalent to which of the following
Given
Product means multiplication
[tex]\frac{10}{21}\times\frac{14}{5}[/tex][tex]\begin{gathered} \frac{10}{21}\times\frac{14}{5}=\frac{140}{105} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{140\div5}{105\div5}=\frac{28}{21} \\ \\ \frac{28\div7}{21\div7}=\frac{4}{3} \\ \\ \frac{4}{3}=1\frac{1}{3} \end{gathered}[/tex]The final answer
[tex]\frac{10}{21}\times\frac{14}{5}=1\frac{1}{3}[/tex]one week a student exercise 3 hours at school and another 2/3 of an hour at home. If 1/4 of the student's total exercise came from playing soccer,how munch time did the students spend playing soccer that week? Enter your answer in hours ; do not include units in your answer.Enter your answer as a fraction in simplest terms using the / as the fraction bar
it is given that,
student exercise 3 hours at school,.
and 2/3 hours at home,
let he do exercise for total 'x' hours,
also,
1/4 of the student's total exercise came from playing soccer
so, exercise came from soccer is , x/4
now sum the hours,
3 + 2/3 + x/4 = x
11/3 = x - x/4
3x/4 = 11/3
[tex]x=\frac{11\times4}{3\times3}[/tex]x = 44/9 hours,
so, the time spend on soccer is,
x/4 =
[tex]\begin{gathered} \frac{\frac{44}{9}}{4} \\ =\frac{44}{36} \end{gathered}[/tex][tex]=\frac{11}{9}[/tex]thus, the answer is
time spend on soccer is, 11/9
The function f is defined by the following rule.f(x) = 3x-3Complete the function table.хf(x)- 4-30145
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.
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]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.
In right triangle ABC, angle c is a right angle and sin A= sin B. What is m
which
In plane trigonometry, the sine theorem or also known as the law of sines is a ratio between the lengths of the sides of a triangle and the sines of their corresponding opposite angles.
it is
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex]According to the question Sin A=Sin B, so
[tex]a=b[/tex]wich means that this right traingle has two equal sides
if the two sides of a right triangle have the same length, then, they form the same angle with the hypotenuse
also, the question says that C=90 °
we know the sum of the internal angles on a triangle must be 180 °,then
[tex]\begin{gathered} A+B+C=180 \\ A=B \\ 2A+C=180 \\ A=\frac{180-C}{2} \\ A=\frac{90}{2} \\ A=45\text{ \degree} \\ B=45\text{\degree} \end{gathered}[/tex]so the answer is B)45 °
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]Each vertex of a quadrilateral is dilated by a factor of 1/2 about the point P (-3,7). What will be the effect on the perimeter of the resulting figure.
Note that the perimeter of any quadrilateral is the sum of its sides.
[tex]P=\sum ^n_{i\mathop=1}a_i[/tex]So it is always proportional to the length of any side,
[tex]P\propto a_i[/tex]Note that the dilation either stretches of compresses the sides.
For the factor 1/2, each side of the quadrilateral will get multiplied by 1/2, which simply means that the sides will get halved.
So the new perimeter is given by,
[tex]P^{\prime}=\sum ^n_{i=1}(\frac{1}{2}a_i)=\frac{1}{2}\sum ^n_{i=1}(a_i)=\frac{1}{2}P[/tex]Thus, the perimeter will also get halved due to the dilation.
Therefore, option A is the correct choice.
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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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]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
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
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;
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]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]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 the given conditions to write an equation for each line in the point-slope form and slope-intercept form (-3,2) with slope -6
Explanation
the slope-intercept form of a line has the form:
[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]when given the slope and a point of the line we can use the slope-point formula, it says.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ (x_1,y_1)\text{ is a point of the line} \end{gathered}[/tex]so
Step 1
a)Let
[tex]\begin{gathered} slope=\text{ -6} \\ point\text{ \lparen -3,2\rparen} \end{gathered}[/tex]b) now, replace and solve for y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-2=-6(x-(-3)) \\ y-2=-6(x+3) \\ y-2=-6x-18 \\ add\text{ 2 in both sides} \\ y-2+2=-6x-18+2 \\ y=-6x-16 \end{gathered}[/tex]so, the equation of the line is
[tex]y=-6x-16[/tex]I hope this helps you
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]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]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.
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]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
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]