We are given a table of values between the number of miles (y) and the number of minutes (x)
A linear function is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two (x, y) pairs from the given table.
Let us choose (10, 1.2) and (30, 3.6)
[tex](x_1,y_1)=(10,1.2)\: \text{and}\: (x_2,y_2)=(30,3.6)[/tex]Let us substitute these points into the above slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.6-1.2}{30-10}=\frac{2.4}{20}=0.12[/tex]So, the slope is 0.12
[tex]y=0.12x+b[/tex]To find the y-intercept (b), choose any one point from the given table
Let us choose (10, 1.2) and substitute it into the above equation
[tex]\begin{gathered} y=0.12x+b \\ 1.2=0.12(10)+b \\ 1.2=1.2+b \\ 1.2-1.2=b \\ 0=b \\ b=0 \end{gathered}[/tex]So, the y-intercept is 0
Therefore, the linear function for the given relationship is
[tex]y=0.12x[/tex]You can find the number of miles (y) Emma rides by substituting the number of minutes (x) into function.
110 Sketch = in standard position. 6 х X ? 1 Drag to show the angle.
We want to draw the angle, theta, in standard position in the unit circle.
We will start off from x = 0 degrees.
First, let's convert the angle (in radians) to degrees. The conversion is shown below:
[tex]\frac{11\pi}{6}\times\frac{180}{\pi}=\frac{11(180)}{6}=330\degree[/tex]We know that 360 degrees is one full circle. So, 330 degree from x = 0 (right side of origin) COUNTERCLOCKWISE to 330 degree will be in the 4th quadrant. Thus,
Solve the system by substitution.5x - 2y + 3z = 6-2x - 4y - 3z = 142 + 6y - 8z = 12yPls see the picture
Given the System of Equations:
[tex]\begin{cases}5x-2y+3z=6 \\ \\ 2x-4y-3z=14 \\ \\ x+6y-8z=12\end{cases}[/tex]You can solve it using the Substitution Method:
1. Solve for "y" from the third equation:
[tex]\begin{gathered} 6y=12-x+8z \\ \\ y=2-\frac{x}{6}+\frac{4z}{3}\text{ (Equation I)} \end{gathered}[/tex]2. Add the first and the second equation:
[tex]\begin{gathered} \begin{cases}5x-2y+3z=6 \\ \\ 2x-4y-3z=14 \\ \end{cases} \\ ---------------- \\ 7x-6y=20\text{ (Equation II)} \end{gathered}[/tex]3. Solve for "y" from Equation I:
[tex]\begin{gathered} -6y=20-7x \\ \\ y=\frac{20}{-6}-\frac{7}{(-6)}x \\ \\ y=-\frac{10}{3}+\frac{7}{6}x\text{ (Equation III)} \end{gathered}[/tex]4. Substitute Equation III into the third equation and simplify:
[tex]\begin{gathered} x+6(-\frac{10}{3}+\frac{7}{6}x)-8z=12 \\ \\ x-\frac{60}{3}+\frac{7}{6}x-8z=12 \\ \\ \frac{13}{6}x-8z=32 \end{gathered}[/tex]5. Substitute Equation I into the second equation and simplify:
[tex]undefined[/tex]Can you help me with this? Also the word at the beginning is what. It is the only thing that got cut off.
To be able to simplify the given expression, let's recall some of the trigonometric identities.
1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
From those identities above, we can replace the numerator and denominator in the given expression with their equivalent value. Thus, the expression becomes:
[tex]\frac{1}{sec^2\theta}[/tex]Now, sec²θ is also just equivalent to 1/cos²θ. So, we can rewrite the expression as:
[tex]1\div\frac{1}{cos^2\theta}[/tex]Then, applying the rules of dividing fractions, the expression becomes:
[tex]1\times cos^2\theta=cos^2\theta[/tex]Therefore, the equivalent expression is cos²θ. (Option 1)
8. Solve the system and write the answer as an ordered triple:x + y - z = 42x + 3y - z = 8x - y = -z
EXPLANATION
First, isolate x for x+y-z=4:
[tex]x=4-y+z[/tex][tex]\mathrm{Substitute\:}x=4-y+z[/tex][tex]\begin{bmatrix}2\left(4-y+z\right)+3y-z=8\\ 4-y+z-y=-z\end{bmatrix}[/tex]Simplifying the equations by applying the distributive property and adding like terms:
[tex]\begin{bmatrix}y+z+8=8\\ -2y+z+4=-z\end{bmatrix}[/tex]Isolate y for y+z+8=8
[tex]y=-z[/tex][tex]\mathrm{Substitute\:}y=-z[/tex][tex]\begin{bmatrix}-2\left(-z\right)+z+4=-z\end{bmatrix}[/tex]Simplify:
[tex]\begin{bmatrix}3z+4=-z\end{bmatrix}[/tex][tex]z=-1[/tex][tex]\mathrm{For\:}y=-z[/tex][tex]\mathrm{Substitute\:}z=-1[/tex][tex]y=-\left(-1\right)[/tex][tex]\mathrm{Simplify}[/tex][tex]y=1[/tex][tex]\mathrm{For\:}x=4-y+z[/tex][tex]\mathrm{Substitute\:}z=-1,\:y=1[/tex][tex]x=4-1-1[/tex][tex]\mathrm{Simplify}[/tex][tex]x=2[/tex][tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex][tex]x=2,\:z=-1,\:y=1[/tex]Expressing as an ordered triple:
[tex](2,1,-1)[/tex]Evaluate ad-bc for the given values of the variable. a=-3,b=-5,c=2,d=9
The given epression is
ad - bc
We would substitute a = - 3, b = 5, c = 2, d = 9 into the above expression. It becomes
[tex]\begin{gathered} (-\text{ 3}\times9)\text{ - (5}\times2) \\ -27\text{ - 10 = - 37} \end{gathered}[/tex]The solution is - 37
On the ACT Math test, the mean score is 20.5 and the standard deviation is 5.5. The scores are normally distributed. Complete the following:Approximately ___% of the students who took the test in April scored 15 and 26.
Answer:
Approximately 68.2% of the students who took the test in April scored 15 and 26
Explanation:
Since the scores are normally distributed, with a mean of 20.5 and a standard deviation of 5.5, this means that from the mean plus 1 standard deviation there is the 34.1% of the scores. Similarly, the percentage of scores from the mean minus 1 standard deviation is 34.1%
Then:
Mean + 1 standard deviation = 20.5 + 5.5 = 26 ⇒ 34.1%
mean - 1 standard deviation = 20.5 - 5.5 = 15 ⇒ 34.1
This total of this range from 15 to 26 is: 34.1% + 34.1% = 68.2%
if the factor is 5 and the product is 35 what is the other factor
Let:
x = The other factor
5*x = 35
Solve for x:
Divide both sides by 5:
5x/5 = 35/5
x = 7
whic fractions haveva least common denominater of 40 1/2 and 3/20 1/4 and 3/ 10 1/8 and 2/5 1/8 and 3 / 15
1/8 and 2/5 is the answer
their LCD is 40
1/2 and 3/20 LCD is 20
1/4 and 3/10 LCD is 20
1/8 and 3/15 LCD is 120
LCD means least common denominator
how do I solve this ? Both sides please !
the equation is:
y=x+3
To find the y- values all we need to do is replace the values of x, so:
x=-3
y=-3+3=0
so for x=-3 y=0
x=-2
y=-2+3=1
so for x=-2 y=1
x=-1
y=-1+3= 2
so for x=-1 y=2
x=0
y=0+3=3
so for x=0 y=3
x=1
y=1+3=4
so for x=1 y=4
x=2
y=2+3=5
so for x=2 y=5
x=3
y=3+3=6
so for x=3 y=6
So the answer is: in this order 0,1,2,3,4,5,6
and the graph you need to see, when the value of x grow (from negative number to positive one) the values of Y also grow, so the rigth answer can be A or C, but also we know all the values of Y we calcu
Hi I need some help with conpleted onl the table topic is quadratic graph
To complete the table, we have to evaluate the terms of the function at different values of x within the range
[tex]-3\le x\le5.[/tex]Now, we are going to evaluate the values:
[tex]x=-3,-2,-1,0,1,2,3,4,5.[/tex]Evaluating
[tex]-x^2[/tex]at the above values, we get:
[tex]-9,-4,-1,0,-1,-4,-9,-16,-25.[/tex]Evaluating
[tex]2x,[/tex]we get:
[tex]-6,-4,-2,0,2,4,6,8,10.[/tex]Evaluating
[tex]3[/tex]at the given values we get 3 because it does not depend on x.
Finally, to complete the row for f(x) we will add the values we got from each evaluation.
Answer:
Find the net price20% discount on $365 purchase
Step 1: We calculate 20% of $365. For this, we can solve the following rate:
[tex]\begin{gathered} \frac{x}{20\%}=\frac{\text{ \$}365}{100\%} \\ \text{ Multiply by 20\% from both sides} \\ \frac{x}{20\operatorname{\%}}*20\%=\frac{\text{\$}365}{100\operatorname{\%}}*20\% \\ x=\frac{\text{ \$}365*20\%}{100\%} \\ x=\text{ \$}\frac{365*20}{100} \\ x=\text{ \$}\frac{7300}{100} \\ x=\text{ \$}73 \end{gathered}[/tex]Step 2: We calculate the discount.
[tex]\text{ \$}365-\text{ \$}73=\text{ \$}292[/tex]AnswerA 20% discount on a $365 purchase is $292.
A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700 . They are selling shirts with a profit of $7.00 per shirt to earn the remaining money. Part A Create an inequality to represent the minimum number of shirts, n, the band must sell to earn the remaining money. Part B what is the minimum number of shirts the band must sell to earn the remaining money?
Let the number of shirts be x.
The cost of x shirts is $7x.
Determine the inequality for the minimum number of shirts.
[tex]7x+700\ge1150[/tex](B)
Simplify the inequality to obtain the minimum number of shirts.
[tex]\begin{gathered} 7x+700-700\ge1150-700 \\ 7x\ge450 \\ \frac{7x}{7}\ge\frac{450}{7} \\ x\ge64.28 \end{gathered}[/tex]The number of shirts is always a whole number. So the possible value of x is 65.
Thus, minimum number of shirts the band must sell to earn the remaining money is 65.
javier said I have to get atleast an 75 on the test to keep my A in the class if T represents javier's score on the test which inequality matches his statement
T ≥ 75
Explanations:Javier score = T
Since Javier has to score at least 75 to keep his A, it means he has to score 75 and above.
This means that Javier's score (T) must be greater than or equal to 75
This can be represented mathematically as:
T ≥ 75
Check off all of the equations that would give one solution
Solution:
Given the equations:
[tex]\begin{gathered} 5x+10=5x-15 \\ collect\text{ like terms,} \\ 5x-5x=-15-10 \\ 0=-25 \\ thus,\text{ there's no solution.} \end{gathered}[/tex][tex]\begin{gathered} 3x+12=4x-21 \\ collect\text{ like terms,} \\ 3x-4x=-21-12 \\ \Rightarrow-x=-33 \\ divide\text{ both sides by -1,} \\ -\frac{x}{-1}=-\frac{33}{-1} \\ \Rightarrow x=33 \\ thus,\text{ there's a solution} \end{gathered}[/tex][tex]\begin{gathered} 3(x+4)=3x+12 \\ open\text{ parentheses,} \\ 3x+12=3x+12 \\ thus,\text{ there's infinitely many solutions.} \end{gathered}[/tex][tex]\begin{gathered} 5x+10=6x-8 \\ collect\text{ like terms,} \\ 5x-6x=-8-10 \\ \Rightarrow-x=-18 \\ divide\text{ both sides by -1,} \\ -\frac{x}{-1}=-\frac{18}{-1} \\ \Rightarrow x=18 \\ thus,\text{ there's a solution.} \end{gathered}[/tex][tex]\begin{gathered} 2(3x-4)=6x-8 \\ open\text{ parentheses,} \\ 6x-8=6x-8 \\ thus,\text{ there's infinitely many solutions.} \end{gathered}[/tex][tex]\begin{gathered} 6x-8=2(3x-3) \\ open\text{ parentheses,} \\ 6x-8=6x-6 \\ collect\text{ like terms,} \\ 6x-6x=-6+8 \\ 0=2 \\ thus,\text{ there's no solution.} \end{gathered}[/tex]Hence, the equations that would give one solution are:I need help please it says find the area of each shaded sector. Round to the nearest hundredth place.
Step 1
State the formula for the area of a sector of a circle
[tex]A=\frac{\theta}{360}\times\pi\times r^2[/tex]Step 2
Find the value of θ.
[tex]m\angle WZV=\theta=180-108=72^{o^{}}(sum\text{ of angles on a straight line is }180^o)[/tex]r=wz= 5.3km
Step 3
Find the area of the shaded part.
[tex]\begin{gathered} A=\frac{72}{360}\times\pi\times(5.3)^2 \\ A=\frac{1}{5}\times\pi\times28.09 \\ A=\frac{2809}{500}(\pi)km^2 \end{gathered}[/tex]Since there are 2 of such shaded sectors, they both will have the same area. Therefore the total area of the shaded sectors will be;
[tex]\begin{gathered} \frac{2809}{500}(\pi)km^2\times2 \\ =35.29893506 \\ \approx35.30km^2 \end{gathered}[/tex]Answer; The area of the shaded sector approximately to the nearest hundredth is = 35.30km²
Espen
Deandre deposits $500 into an account that pays simple interest at a rate of 4% per year. How much Interest will he be paid in the first 2 years?
sd
Х
5
?
The Interest I paid on a deposited amount (principal) at a certain certain rate r over a period of time t is;
[tex]I=\frac{prt}{100}[/tex][tex]\begin{gathered} p=\text{ \$500} \\ r=4\text{ \%} \\ t=2\text{years} \end{gathered}[/tex][tex]\begin{gathered} I=\frac{500\times4\times2}{100} \\ I=40 \end{gathered}[/tex]Hence, the interest paid after the first two years is $40
The physics department of a college has 5 male professors, 7 female professors. 16male teaching assistants and 9 female teaching assistants. If a person is selected atrandom from the group, find the probability that the selected person is a teachingassistant or a female.
32/37
Explanation:male professors = 5
female professors = 7
male teaching assistants = 16
female teaching assistants = 9
Total = 5 + 7 + 16 + 9
Total = 37
[tex]\begin{gathered} N(T.A\text{ or F) = N(T.A) + N(F) -N(T.A and F)} \\ T.A\text{ = teach i}ng\text{ assistant} \\ F\text{ = female} \end{gathered}[/tex][tex]\begin{gathered} N\text{ (T.A) }=\text{ }16\text{ + 9 = 25} \\ N(F)\text{ = 7 +9 = 1}6 \\ N(T.A\text{ and F) = }9 \\ N(T.A\text{ or F) = 25 + 16 - }9 \\ N(T.A\text{ or F) }=\text{ 3}2 \end{gathered}[/tex][tex]\begin{gathered} \text{Probability of teach i}ng\text{ assistant or a female = }\frac{N(T.A\text{ or F)}}{\text{Total}} \\ \text{Probability of teach i}ng\text{ assistant or a female =}\frac{32}{37} \end{gathered}[/tex]Find the missing length of the solid figure.3 m3 m8 m
Let's begin by identifying key information given to us:
We have the total length of the side = 8 m
We have the length of 2 out of the 3 sides:
What is the solution of the system of equations? y=-3x-14y+5=3(x+3)
y=-3x-14 (a)
y+5=3(x+3) (b)
First, express both equations in the form: ax+by = c
3x+y = -14 (a)
y+5 = 3x+9
-3x +y = 9-5
-3x+y = 4 (b)
Now we have the system:
3x+y = -14 (a)
-3x+y = 4 (b)
Add both equations to eliminate x:
3x+y = -14 (a)
+
-3x+y = 4 (b)
__________
2y = -10
y= -10/2
y=-5
Then replace y on any initial equation and solve for x:
y=-3x-14
-5 = -3x-14
3x = -14+5
3x = -9
x=-9/3
x= -3
Solution: (x,y) = (-3,-5)
a cookie cake is cut into 8 equal slices Damon is 1/8 of the cake shaunita eats 1/2 of the cake and Michael least two slices how many slices remain
1 - (1/8) - (1/2) - 2(1/8)
1 - (5/8) = 3/8
Only 3/8 of the cake remain or 3 slices.
My question is to create a graph with a constant of proportionality of 1 1/4.
The general graph of equation is:
[tex]y=kx[/tex]Where k is proportionality then:
k is:
[tex]\begin{gathered} k=1\frac{1}{4} \\ k=\frac{4+1}{4} \\ k=\frac{5}{4} \end{gathered}[/tex]So graph of equation is :
[tex]\begin{gathered} y=kx \\ y=\frac{5}{4}x \end{gathered}[/tex]so graph is:
Maria buys lunch every work day. She always eats at the same restaurant and spends no more than $5.25 for lunch. She has created a budget in which she has allowed herself $1700 for the year to buy lunches during her five-day work week. Assume Maria spends the maximum she allows for each lunch. Write an equation to determine how much of her budget, in dollars, remains unspent at the end of a particular week of the year? Include definitions of the variables you used. B = 26.25n- 1700, where B is her budget balance and n is the number of complete weeks of work O B= 1700 - 26,25n, where B is her budget balance and n is the number of complete weeks of work O B = 1700 - 5.25n, where B is her budget balance and n is the number of complete weeks of work O B = 5.25n - 1700, where B is her budget balance and n is the number of complete weeks of work
Let's begin by listing out the information given to us:
Maria spends $5.25 for every lunch;
Maria has 5 lunches every week (five-day work week) = 5 * ($5.25) = $26.25
Maria's budget = $1700
n = the number of complete weeks of work
Budget balance = Maria's Budget - (26.25 * the number of weeks)
B = 1700 - 26.25n
A 19-foot lader is placed against a vertical wall of a building with the bottom of the ladder on level ground 5 feet from the base of the building how high up the wall does the ladder reach
Answer
The ladder reaches a height of 18.33 feet on the wall.
Explanation
The sketch of the ladder and wall is shown below
Noting that the ladder is slanting and is 19 feet long and 5 feet from the base of the wall on the level ground.
Let the height of the ladder on the wall be H feet.
We can see that this setup forms a right angle triangle
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 question,
a = H
b = 5 feet
hyp = 19 feet
a² + b² = (hyp)²
H² + 5² = 19²
H² + 25 = 361
H² = 361 - 25
H² = 336
H = √336
H = 18.33 feet to the nearest hundredth!
Hope this Helps!!!
Graph the quadrilateral with vertices (0, 4), (5, 8), (10, -7), and (-3, -7).
Answer:
Explanation:
From the figure above, we see that the vertices are labelled as follows;
A(0, 4), B(5, 8), C(10, -7), and D(-3, -7).
it takes an older computer 4 times as long to send out a company's email as it does in newer computer working together it takes the two computers 5 minutes to send out an email how long will it take the newer computer to send out the email on its own ?
We have a problem where we have to relate the capacities of an old and a new computer.
We will call C1 the capacity of the old computer and C2 the capacity of the new computer.
We define the capacity as the inverse of the time it takes to complete the task T:
[tex]\begin{gathered} C_1=\frac{T}{t_1_{}} \\ C_2=\frac{T}{t_2} \end{gathered}[/tex]That means that the less time it takes to complete the task, the higher the capacity is.
We know that the capacity of the new computer is 4 times the capacity of the old computer:
[tex]C_2=4\cdot C_1[/tex]If the computers work together they add their capacity, so we have:
[tex]C_1+C_2=\frac{T}{t_3}[/tex]We know that the time it takes for the two computers is 5 minutes, so we can write:
[tex]\begin{gathered} C_1+C_2=\frac{T}{t_3}=\frac{T}{5} \\ \frac{C_2}{4}+C_2=\frac{T}{5}_{}_{} \\ \frac{5}{4}C_2=\frac{T}{5} \\ C_2=\frac{T}{5}\cdot\frac{4}{5} \\ C_2=\frac{T}{\frac{25}{4}}=\frac{T}{t_2} \\ t_2=\frac{25}{4}=6.25 \end{gathered}[/tex]We then know that the time it takes for the new computer to complete the task on its ownis 6.25 minutes.
Answer: 6.25 minutes.
[tex]y = x {}^{2} + 8x + 16[/tex]what is the vertex
Answer:
Vertex: (-4, 0)
Axis of Symmetry: x = -4
Maximum Value: Does Not Exist
Minimum Value: y = 0
Explanation:
The vertex form of an equation is
[tex]y=a(x-h)^2+k[/tex]where the coordinates of the vertex are
[tex]V=(h,k)[/tex]Tofind the vertex of the parabola, we first convert the equation to the vertex form.
An air traffic controller works at the top of a 150-foottower. From that point she measures the angle ofdepression to a plane at point S of 40°. Shemeasures the angle of depression to a second planeat point R of 70°.150feetSRWhich is closest to the distance between the twoplanes?44 ft0 73 ft
Okay, here we have this:
We need to find the approximate distance between the two planes, let's do it:
Considering that we have right triangles we can use the pythagorean theorem.
For the measurement from the base of the tower to point S (x) we obtain:
[tex]\begin{gathered} \tan \text{ (90-}40)=\frac{x}{150} \\ \text{tan}(50)\cdot150=x \\ x=178.76 \end{gathered}[/tex]For the measurement from the base of the tower to point R (z) we obtain:
[tex]\begin{gathered} \tan \text{ (90-7}0)=\frac{z}{150} \\ \tan (20)\cdot150=z \\ z=54.59 \end{gathered}[/tex]Now, to calculate the distance between the planes we are going to subtract the distance from each point to the base of the control tower:
Distance between the planes=178.76-54.59=124.17≈124.
Finally we obtain that the correct answer is the third option.
Gwen can read 2 7/9 pages of a book in a minute. If she read 4 5/6 minutes, how much would she have read?
The rate of reading has been given as
[tex]\begin{gathered} 2\frac{7}{9}\text{ pages =1minute} \\ \text{If 1 minute is 2}\frac{7}{9},\text{ then it means any amount of time greater than 1 minute would simply be } \\ \text{Number of pages per minute times the number of minutes given} \\ \text{That is, 2 minutes would be 2}\frac{7}{9}\times2.\text{ And so on}\ldots \\ \text{Therefore, 4}\frac{5}{6}\min utes\text{ would be;} \\ 4\frac{5}{6}\min =2\frac{7}{9}\times4\frac{5}{6}pages \\ 4\frac{5}{6}\min =\frac{25}{9}\times\frac{29}{6}\text{pages} \\ 4\frac{5}{6}\min =\frac{725}{54}pages \\ 4\frac{5}{6}\min =13\frac{23}{54}pages \\ \end{gathered}[/tex]The results shows that she would read 13 23/54 pages in the time given
Mrs Hernandez has 12 girls and 13 boys and our second grade class 2nd grade class if she chooses one student at random, what is the probability that the student is a girl the answer would be 12/25 right?
Sketch the figure described. Two lines that do not intersect, and a third line that intersects each of them.
We want to sketch a figure that describe the statement;
"Two lines that do not intersect, and a third line that intersects each of them."
Two lines that cannot intercept are parallel.
And a third line that intersects each of them. will cut through both lines.
Above is a typical sketch of "Two lines that do not intersect, and a third line that intersects each of them."
Line one and two do not intercect while line 3 intersect both line 1 and 2.