Equation in slope intercept form is written as
y = mx + b
If slope m = 1/3 and y-intecept b = 3
Equation form using the information above is
[tex]y\text{ =}\frac{1}{3}x\text{ + 3}[/tex]Point slope form using the point (3, 4)
simply use the formula
y - y₁ = m( x- x₁ )
[tex]y\text{ -4=}\frac{1}{3}(x-3)[/tex]
What is the value of the expression below when z=7 and w=10
Given that z = 7 and w = 10 then the expression 7z + 10w
substituting the values of z and w into tye expression
= 7(7) + 10 (10)
= 49 + 100
= 149
Jeff decides to lease a $35,000 vehicle for 4 years. It is estimated that the car will be resold in two years at a price of$17,955. If the annual interest is 3%, what is the financing fee?$44.89O $87.50$66.19$151.30
Fred's car van travel 368 miles on one tank of gas. His has tank holds 16 gallons what is the unit rate for mules per gallon
16 gallons is needed for 368miles
Therefore
1 gallon is needed for 368/16 = 23miles
Hence the rate for miles per gallon is
Enter in the coordinates for each point in the graph below.Quezon 2Not yetansweredPoints out of16.00H.c.5FlagquestionE.5-1990GD
ANSWER:
A. (-7,2)
B (-5, -2)
C (-3, 5)
D (-2, -7)
E (2, 3)
F (3,3)
G (5,-6)
H (6, 6)
i just need a tutor to tell me if my answers are correct or wrong
Given the expression below,
from this part ,find the estimated y-intercept .Round your answer to the three decimal places.
y - incercept = 371.4
60% of the
students take the
bus. If there were
120 students on the
busses, how many
total students are
there?
Answer:
168
Step-by-step explanation:
60%=120
40% of 120
10%12
10%12
10%12
10%12
12×4=48
120+48=168
For the function N(t) = 4t + 5] + 3. evaluate N(2).
Answer:
Explanation:
Putting in x = 2 in the function gives
[tex]N(2)=4|2+5|+3[/tex][tex]N(2)=31[/tex]which is our answer!
What point is a solution to the linear inequality y > 4x -3?
Answer:
(0,-3 )and (0.75,0)
Step-by-step explanation:
y=4x_3
Hi I need help with a couple of questions. It's math algebra
The equation above is the formula of the speed (s) in terms of the distance (d) and the time (t).
For the distance 132 mi
With a speed of 8 miles per hour it takes the next hours:
[tex]\begin{gathered} \\ \text{Solve t:} \\ s\cdot t=d \\ t=\frac{d}{s} \\ \\ t=\frac{132mi}{8\frac{mi}{h}}=16.5h \end{gathered}[/tex]With a speed of 12 miles per hour it takes the next hours:
[tex]t=\frac{132mi}{12\frac{mi}{h}}=11h[/tex]Then, the possible number of hours that take to the kayaker to travel 132 miles is between 11 and 16.5
Find the length of the third side. If necessary, write in simplest radical form.DV895
In order to solve the missing side for a right triangle, we can use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]then, we rewrite the expression for on of the sides different from the hypotenuse
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]replace with the values
[tex]\begin{gathered} a=\sqrt[]{(\sqrt[]{89})^2-5^2} \\ a=\sqrt[]{89-25} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]A local health clinic surveys its patients about their water drinking habits it found data is normally distributed the mean amount of water consumed daily is 62 ounces and the standard deviation is 5.2how much water in ounces do approximately 95% of the patients drink each day
The approximate amount of water consumed by 95% of the patients will be given as a range which can be gotten by
[tex]P=x\pm2S[/tex]Where
P = Amount of water.
x = mean
S = Standard Deviation
Therefore,
The lower limit is
[tex]\begin{gathered} x-2s \\ =62-2(5.2) \\ =62-10.4 \\ =51.6\text{ ounces} \end{gathered}[/tex]The upper limit is
[tex]\begin{gathered} x+2s \\ =62+2(5.2) \\ =62+10.4 \\ =72.4\text{ ounces} \end{gathered}[/tex]Therefore, the amount of water that 95% of the patients drink approximately is 51.6 ounces to 72.4 ounces.
1) P(A) = 0.6 P(B) = 0.45 P(A and B) = ? O 0.35 0.65 O 0.75 O 0.27
We are given the following probabilities:
[tex]\begin{gathered} P(A)=0.6 \\ P(B)=0.45 \end{gathered}[/tex]We are to find P(A and B), to do that we will use the following relationship:
[tex]P(\text{AandB)=P(A) x P(B)}[/tex]Replacing we get:
[tex]P(AandB)=0.6\times0.45[/tex]Solving the operations:
[tex]P(\text{AandB)}=0.27[/tex]Therefore, the probability of A and B is 0.27.
Jan is trying to fix her circular window and needs to know how much space it takes up. It has a diameter of 10 inches.
ANSWER
The area is 78.54 in²
EXPLANATION
We need to find the area of this circle. The area of a circle with radius r is:
[tex]A=\pi r^2[/tex]The diameter of a circle is twice the radius, so if the diameter is 10 inches, then the radius is 5 inches:
[tex]A=\pi\cdot5^2=25\pi=78.54in^2[/tex]This answer is rounded to the nearest hundredth.
Simplify this expression. Assume that x is nonzero.– 11.7X<-11.x?(Type exponential notation with positive exponents.)
If two numbers have the same base ( the number below the exponent) then the multiplication of the two of them is the number with the same base but with the sum of its exponents (rule of exponents)
[tex]x^{-11}\cdot x^7=x^{-11+7}=x^{-4}[/tex]On the other hand, if a number is to the power a negative number, it means that it is the reciprocal elevated to the number, in this case
[tex]x^{-4}=(\frac{1}{x})^4[/tex]Nina deposited $20.59 in her checking account. Later that week, she wrote a checkfor one-third the amount in the account, and then another check for $9.74. If shehad $108.60 left in her account, how much did she have to begin with.
1) Reading carefully, we can do it step by step.
2) She had deposited $20.59 and wrote a check, since she wrote a check we can understand that as a debit so we can write out the following:
[tex]\begin{gathered} 20.59-\frac{20.59}{3}= \\ 20.59-6.86 \\ 13.7 \end{gathered}[/tex]Note that we rounded off to the nearest hundredth.
2.2) So now, she wrote another check, i.e. -$9.74
[tex]\begin{gathered} \$13.7-\$9.74 \\ \$4 \\ 108.60 \\ 108.60+\mleft(20.59-6.86-9.74\mright)=112.59 \end{gathered}[/tex]Millie Gaines 4% by selling her cycle for 6644.80 rupees find a cp for cycle
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
bike price = 644.80 rupees
gain = 4% = 0.04
cp = cost price = ?
Step 02:
cost price = bike price - bike price*gain
= 644.80 rupees - 644.80 rupees * 0.04
= 644.80 rupees - 25.729 rupees
= 619 rupees
The answer is:
The cost price is 619 rupees.
what is x? how would i find the value of
Given the Right Triangle ABC, you know that:
[tex]\begin{gathered} AB=29 \\ BC=9 \end{gathered}[/tex]In order to find the measure of the angle "x", you need to use the following Inverse Trigonometry Function:
[tex]\theta=sin^{-1}(\frac{opposite}{hypotenuse})[/tex]In this case, you can identify that:
[tex]\begin{gathered} \theta=x \\ opposite=BC=9 \\ hypotenuse=AB=29 \end{gathered}[/tex]Therefore, when you substitute values and evaluate, you get:
[tex]x=sin^{-1}(\frac{9}{29})[/tex][tex]x\approx18\text{\degree}[/tex]Hence, the answer is:
[tex]x\approx18\text{\degree}[/tex]evaluate 2x + y when x = 15 and y = 4
Given the following expressions:
[tex]\text{ 2x + y}[/tex]With x = 15 and y = 4, let's evaluate by substituting the values to the respective variables.
We get,
[tex]\text{ 2x + y}[/tex][tex]\text{ 2(15) + (4)}[/tex][tex]\text{ 30 + 4}[/tex][tex]\text{ = 34}[/tex]Therefore, 2x + y when x = 15 and y = 4 is 34.
Find the value of 2[3(x2 – 5) + 5y] when x = 9 and y = 3.
Answer
The value of the expression is 486
Step-by-step explanation
Given the expression
2[3(x^2 - 5) + 5y]
To solve this, we will be applying the PEMDAS rule
Where x = 9 and y = 3
Step 1: solve the smaller parenthesis first
2[3(9^2 - 5) + 5*3]
2 [ 3(81 - 5) + 15]
2 [ 3(76) + 15]
2 [ 228 + 15]
Solve the larger parenthesis
2 [ 243] = 486
Hence, the value of the expression is 486
Lisa's rectangular living room is 20 feet wide. If the length is 5 feet less than twice the width, what is the area of her living room?
1) Let's gather all the data
Width: 20'
Length: 2w-5
2) Now we can plug that into the formula for the are of a rectangle, like this
[tex]\begin{gathered} A=wl \\ A=20\cdot(2(20)-5) \\ A=20\cdot(40-5) \\ A=20\cdot35 \\ A=700ft^2 \end{gathered}[/tex]Notice that we have plugged into that the width w=20. Therefore the area of the living room is 700ft²
explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
1) There are some ways to solve a quadratic equation. We can solve it using the Quadratic Formula, Graphing it or via Newton's Identities, or even factoring
The most common way is via Quadratic Formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}[/tex]Which a, b, and c are the coefficients of a Quadratic Equation, say:
x²+6x+9, a= 1, b=6, and c=9.
[tex]x=\frac{-6\pm\sqrt[]{6^2-4(1)(9)}}{2(1)}=x_1=x_2=-3[/tex]Note that in this case, both roots were equal to -3
2) We can always expect two roots. When the Quadratic Formula yields just one answer then we can call it double root, or 1 root with multiplicity 2, actually there are two roots with the same value.
3) Thus the answer is:
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
Write an Equation: Gary worked for 20 hours tutoring students at the library. He uses $35 to pay for gas on his way home. If he has $60 left after paying for gas, how much money, x, in dollars, was Gary paid per hour?
Answer:4.75 in us dollars it will be 5.31
Step-by-step explanation:
first you divide 95 by 20 witch will give you 4.75 and if you want to check that answer you do 4.75 times 20 and it will give 95
Answer question number 18. The question is in the image.
18.
Given:
[tex]g(x)=3sin2x[/tex]Required:
We need to graph the function and find the transformation from the parent function.
Explanation:
The given equation is of the form.
[tex]g(x)=Asin(Bx+C)[/tex]where A =3, B=2, and C=0.
We know that A is amplitude.
[tex]Amplitude=3[/tex][tex]Period=\frac{2\pi}{|B|}[/tex]Substitute B=2 in the equation,
[tex]Period=\frac{2\pi}{|2|}[/tex][tex]Period=\pi[/tex]Recall that the amplitude of a function is the amount by which the graph of the function travels above and below its midline.
The distance between the maximum point and midline is 3.
The time interval between two waves is known as a Period
The time interval between two waves is pi.
The graph of the function.
[tex]The\text{ parent function is f\lparen x\rparen=sinx.}[/tex]Recall that the amplitude stretches or compresses the graph vertically.
Here we have amplitude =3. it is a positive value.
The parent function stretches vertically by 3 units.
Recall that the period stretches or compresses the graph horizontally.
Here we have the period is pi.
The parent function compresses horizontally by pi.
Final answer:
[tex]Amplitude=3[/tex][tex]Period=\pi[/tex]The transformation is stretched vertically by 3 units and compressed horizontally by pi.
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.A. (4, 1)B. (16, -2)C. (6, -3)D. (8, -1)
The coordinates of the point which partitions a directed line segment AB at the ratio a:b from A(x1, y1) to B(x2, y2) is computed as follows:
[tex](x,y)=(x_1+\frac{a}{a+b}(x_2-x_1),y_1+\frac{a}{a+b}(y_2-y_1_{}))[/tex]In this case, the segment goes from R(-2, 4) to S(18, -6), and the partition ratio is 3:7. Substituting into the above formula, we get:
[tex]\begin{gathered} (x,y)=(-2+\frac{3}{3+7}(18-(-2)),4+\frac{3}{3+7}(-6-4)) \\ (x,y)=(-2+\frac{3}{10}\cdot20,4+\frac{3}{10}(-10)) \\ (x,y)=(4,1) \end{gathered}[/tex]2. Perform cach of the following calculations using a single multiplication. Do not round your final answers.(a) Decrease 160 by 10% (b) Decrease 450 by 6%(c) Decrease 122,000 by 12%(d) Decrease $1,820 by 3%(c) Decrease $12,500 by 15%(f) Decrease $4.50 by 8%
We have the following:
(a) Decrease 160 by 10%
[tex]160\cdot(\frac{100-10}{100})=144[/tex](b) Decrease 450 by 6%
[tex]450\cdot(\frac{100-6}{100})=423[/tex](c) Decrease 122,000 by 12%
[tex]122000\cdot(\frac{100-12}{100})=107360[/tex](d) Decrease $1,820 by 3%
[tex]\begin{gathered} 1820\cdot(\frac{100-3}{100})=1765.4 \\ \end{gathered}[/tex](e) Decrease $12,500 by 15%
[tex]12500\cdot(\frac{100-15}{100})=10625[/tex](f) Decrease $4.50 by 8%
[tex]4.5\cdot(\frac{100-8}{100})=4.14[/tex]The sum of two numbers is 20. The difference between three times the first rumber and twice the second is 40. Find the two numbers.
Let the first number is x and second number is y.
According to given conditions:
The sum of two numbers is 20.
[tex]x+y=20[/tex]And The difference between three times the first rumber and twice the second is 40.
[tex]3x-2y=40[/tex]Now multiply equation 1 with 2 and add in second eqution;
[tex]\begin{gathered} 2(x+y)+(3x-2y)=2(20)+40 \\ 2x+2y+3x-2y=40+40 \\ 5x=80 \\ x=16 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 16+y=20 \\ y=4 \end{gathered}[/tex]So the first number is x=16 and second number is y=4.
According to given co
X= 7 4. Find the equation of a line passing through (5, -6) perpendicular (b) 3x + 5y = (d) 7x - 12y (f) x = 7 (a) 2x + y = 12 (c) x + 3y = 8 (e) 2y = 5 Find the equation of the line connecting the points of intersect (a) S x + y = 4 S 3x - y = 12 (b) Sy= and 2x=6 = -6 X=
Given data:
The first set of equations are x+y=4, and x=6.
The second set of equations are 3x-y=12 and y=-6.
The point of intersection of first set of te equations is,
6+y=4
y=-2
The first point is (6, -2).
The point of intersection of second set of te equations is,
3x-(-6)=12
3x+6=12
3x=6
x=2
The second point is (2, -6).
The equation of the line passing through (6, -2) and (2, -6) is,
[tex]\begin{gathered} y-(-2)=\frac{-6-(-2)}{2-6}(x-6) \\ y+2=\frac{-6+2}{-4}(x-6) \\ y+2=x-6 \\ y=x-8 \end{gathered}[/tex]Thus, the required equation of the line is y=x-8.
What is the minimum? Where is the function increasing? Where is the function decreasing?
As given by the question
There are given that the graph.
Now,
The minimum value of the given graph is shown below:
[tex](2,\text{ -1)}[/tex]Solve the system by graphing. (If there is no solution, enter NO SOLUTION.)x + 2y < 6y < x − 5
From the problem, we have the inequalities :
[tex]\begin{gathered} x+2y<6 \\ yNote that the boundary line is dashed if the symbols are < or >.Let's graph first the first inequality :
[tex]\begin{gathered} x+2y<6 \\ \text{Change the symbol into ''=''} \\ x+2y=6 \\ \text{Solve for the intercepts} \\ \text{when x = 0} \\ 0+2y=6 \\ y=\frac{6}{2}=3 \\ \\ \text{when y = 0} \\ x+2(0)=6 \\ x=6 \end{gathered}[/tex]Plot the points (0, 3) and (6, 0)
The region will pass through the origin if (0, 0) satisfies the inequality.
Test for (0, 0)
[tex]\begin{gathered} x+2y<6\text{ } \\ 0+0<6 \\ 0<6 \\ \text{TRUE!} \end{gathered}[/tex]Since it is true, the region will pass through the origin.
The graph will be :
Next is to graph the second inequality :
[tex]\begin{gathered} yPlot the points (0, -5) and (5, 0)Check again origin (0, 0) to the inequality :
[tex]\begin{gathered} ySince it is false, the region will not pass through the origin.Tha graph will be :
The solution to the system is the overlapping region between the two inequalities.