The slope-intercept form is:
[tex]y=mx+c[/tex]So first we will find the gradient:
Parallel lines have the same gradient:
[tex]\begin{gathered} g(x)=-2x-6 \\ \text{The gradient from the equation above is -2} \end{gathered}[/tex]So now that we know the gradient of the line as -2, we will then find the equation of the line using the formula below as it passes through (7,4):
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{From (7,4)} \\ x_1=7,y_1=4 \\ y-4=-2(x-7) \\ y-4=-2x+14 \\ y=-2x+14+4 \\ y=-2x+18 \end{gathered}[/tex]2. Find the measure of ZRST.(5x – 4):R(8x + 4)ºST
From the picture we notice that the angles R and Q are the same. Furthermore the interior angle S of the triangle is:
[tex]180-(8x+4)[/tex]Then we have the equation:
[tex]2(5x-4)+180-(8x+4)=180[/tex]Solving for x we have:
[tex]\begin{gathered} 10x-8-8x-4=0 \\ 2x-12=0 \\ x=6 \end{gathered}[/tex]Now we plug the value of x in the expression for the angle RST, then:
[tex]8(6)+4=52[/tex]Therefore the angle RST is 52°.
starting at 00 if you were to go up 7 units and left for you is what coordinates would you end up at what quadrant would you be in
The coordinate is starting from the origin
7 units up and 4 units to the left
My coordinate will be (4, 7)
This is because the up is positive y- axis and the left is postive x - axis as well
X = 4 and y = 7
Joining the two points together will end up in the first quadrant
The answer is (4, 7) and First quadrant
Which of the following equations is the translation 2 units down of the graph of y = Ixl?y = |x - 2|y = |x + 2|y = |xl - 2y = Ixl + 2
Answer:
y = | x | - 2
Explanation:
If we have a function g(x) = f(x) + c, we can say that g(x) is a translation of c units up or down of f(x)
If c is negative, the translation is c units down.
Therefore, the translation of 2 units down of the graph y = | x | is:
y = | x | - 2
Use the inverse relationship between logarithmic and exponential functions to solve the equation for x. Simplify your answer using the rules of logarithms and the change of base formula.ln(x) = −2X=________
using the following property
[tex]e^{b\ln a}=a^b[/tex]We can rewrite our expression by exponentiating both sides:
[tex]\begin{gathered} e^{\ln x}=e^{-2} \\ x^1=e^{-2} \\ x=\frac{1}{e^2} \end{gathered}[/tex]Find an equation of the line that goes through the points (-10,13) and (-4,7). Write your answer in the formY=mx+b
1) In this problem, let's plug those points into the slope formula to get the slope, i.e. the measure of how steep is the line between those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-13}{-4-(-10)}=\frac{-6}{6}=-1[/tex]2) Now, let's find the y-intercept, a.k.a. the linear coefficient "b". To do that we need to plug into the Slope-Intercept Formula one of those points, the slope, and solve it for "b"
[tex]\begin{gathered} (-4,7),m=-1 \\ y=mx+b \\ 7=-4(-1)+b \\ 7=4+b \\ 7-4=b \\ b=3 \end{gathered}[/tex]3) Therefore, the equation of the line is:
[tex]y=-x+3[/tex]Enter the ordered pair for the vertices for (90, (QRST).уQ-RoSRQ=R'=(S'=T=(
Let P(h,k) be the coordinates of a point in the figure. When the figure is rotated 90 degree about the origin in clockwise direction, the new coordinates become P'(k,-h).
Therefore,
Q(1,3)--->Q'(3,-1)
R(3,-3)--->R'(3,-3)
S(0,2)---->S'(2,0)
T(-2,1)---->T'(1,2)
Kim bought new shoes and used a 12% off coupon. The original cost of the shoe is represented as s. The total amount Kim paid for the shoes is represented as s-0.12s= s, which means that _______ of 12% is the same as ___
The difference s - 0.12s is equal to 0.88s. So, the first blank has to be 0.88.
The second blank is "decrease", and the last one is "multiplying by 0.88" because the difference is actually equivalent to 0.88s.
f(x +h)-f(x)For the function defined as follows, find (a) f(x + h), (b) f(x + h) – f(x), and (c)f(x)= 4/x
Given the function:
[tex]f(x)=\frac{4}{x}[/tex]We will find the following:
a) f(x+h)
So, we will substitute with x = x+h
[tex]f(x+h)=\frac{4}{x+h}[/tex]b) f(x+h) - f(x)
[tex]\begin{gathered} f(x+h)-f(x)=\frac{4}{x+h}-\frac{4}{x} \\ \\ f(x+h)-f(x)=\frac{4x-4(x+h)}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{4x-4x-4h}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{-4h}{x(x+h)} \end{gathered}[/tex]c) [f(x+h) - f(x)]/h
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h}{x(x+h)\cdot h} \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-4}{x(x+h)} \end{gathered}[/tex]Line I is parallel to line m. If the measure of >6 is 75^ what is the measure of <4?
The measure of <4 = 75°
Explanation:Note that:
• <4 and <6 are alternative interior angles
,• Alternative interior angles are equal
Therefore, based on the points given above:
m<4 = m<6 = 75° (Alternative interior angles are equal)
The measure of <4 = 75°
A standard deck of cards has 52 cards. Suppose you decide to play a game using only half of a standard deck. If you draw one card at a time from the half-deck, without replacement, how many different ways can you draw all of the cards? Remember that "without replacement" means that the cards are not returned to the deck after they are chosen. Write your answer in factorial notation.
We are asked to determine in how many ways we can draw all of the cards in half a deck. Since in a deck there are 52 cards, in half a deck there are:
[tex]n=\frac{52}{2}=26[/tex]The number of ways in which the cards can be drawn is equivalent to the number of permutations. And this is equivalent to:
[tex]P=n![/tex]Where "p" is the number of permutations and n! is the factorial of the number of cards in half a deck. Substituting the values we get:
[tex]P=26![/tex]Solving the operations:
[tex]P=403291461126605635584000000[/tex]Thus we determine the number of ways the cards can be drawn.
graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
see the attached figure
Find out the distance, using the sides
Applying the Pythagorean Theorem
c^2=a^2+b^2
a=4-(-5)=4+5=9 units
b=-1-(-3)=-1+3=2 units
c^2=9^2+2^2
c^2=81+4
c^2=85
c=√85
c=9.2 unitswhat is the answer to 2(4y-2)=10
The given equation is expressed as
2(4y-2)=10
Write a system of equation to this real world situation .Number 1
Let be "q" the number of quarters Kiara has and "d" the number of dimes she has.
According to the information given in the exercise, the total number of dimes are quarters Kiara has is 100. Based on this, you can set up the following equation, which will be Equation 1:
[tex]q+d=100[/tex]The total value Kiara has is $19, then knowing that 1 quarter is $0.25 and 1 dime is $0.10, you can set up the Equation 2:
[tex]0.25q+0.10d=19[/tex]Then, the System of equation for this situation is:
[tex]\begin{cases}q+d=100 \\ 0.25q+0.10d=19\end{cases}[/tex]The answer is:
- Equation 1:
[tex]q+d=100[/tex]- Equation 2:
[tex]0.25q+0.10d=19[/tex]A company is designing a steamer for their upcomingThe design of the stream has an area of 12 in^2. If they wantto manufacture a larger version of the sign with an area of147 in^2, what scale factor would they need to use?
Given that the design of the stream has an area of 12 in^2.
We have to find the scale factor if the area of the larger version is 147 in^2.
It is known that the area of a scaled object will be equal to the scale factor squared.
Let the scale factor be x. So,
[tex]\begin{gathered} 12x^2=147 \\ x^2=\frac{147}{12} \\ x^2=12.25 \\ x=\sqrt[]{12.25} \\ x=3.5 \end{gathered}[/tex]So, the scale factor is 3.5.
Given a function f(x)=|7-4x| ,find the objects with an image 11
Given the function f(x) defined as:
[tex]f(x)=|7-4x|[/tex]If the image is 11, the corresponding objects (x-values) are:
[tex]\begin{gathered} |7-4x|=11 \\ 7-4x=11\ldots(1) \\ 7-4x=-11\ldots(2) \end{gathered}[/tex]Solving (1) to find the first object:
[tex]\begin{gathered} 7-4x=11 \\ 7-11=4x \\ -4=4x \\ x=-1 \end{gathered}[/tex]Now, we solve (2) to find the second object:
[tex]\begin{gathered} 7-4x=-11 \\ 7+11=4x \\ 18=4x \\ x=4.5 \end{gathered}[/tex]Answer: -1 and 4.5
What is 32/3 as a proper fraction also I am gay if you don't agree don't help and my name is Oliver
A fraction can be proper or improper.
When a fraction is proper, the numerator is less than the denominator, and therefore, the fraction is less than unity. For example:
[tex]\frac{3}{4}=0.75<1[/tex]When a fraction is improper the numerator is greater than the denominator and therefore the fraction is greater than unity. For example:
[tex]\frac{9}{5}=1.8>1[/tex]So, in this case, you have
[tex]\frac{32}{3}=10.67>1[/tex]Then, as you can see 32/3 is an improper fraction.
To take it to a proper fraction, you can convert this fraction into a mixed number.
A mixed number is made up of an integer part and a proper fraction.
So, you have
[tex]\begin{gathered} \frac{32}{3}=\frac{10\cdot3+2}{3}=\frac{10\cdot3}{3}+\frac{2}{3}=10+\frac{2}{3}=10\frac{2}{3} \\ \text{ Then,} \\ \frac{32}{3}=10\frac{2}{3} \end{gathered}[/tex]Therefore, 32/2 as a proper fraction will be
[tex]10\frac{2}{3}[/tex]A person’s car uses 4 gal of gasoline to travel 156 mi. He has 3 gal of gasoline in the car, and he wants to know how much more gasoline he will need to drive 300 mi. If we assume that the car continues to use gasoline at the same rate, how many more gallons will he need ?
The gallons that the person needs more is 4.7 Gallons.
How to calculate the value?Since the person’s car uses 4 gal of gasoline to travel 156 miles, the mile.per gallon will be:
= 156 / 4
= 39 miles per gallon.
Therefore, to travel for 300 miles, the gallons needed will be:
= 300 / 39
= 7.7 gallons
He has 3 gallons, the gallons left will be:
= 7.7 - 3
= 4.7 Gallons
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Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
SOLUTION
The given expression is:
[tex](x-4)^5[/tex]Using binomial theorem, the function is expanded as follows:
[tex](x-4)^5=x^5+5(x)^4(-4)^+\frac{5(5-1)}{2!}x^3(-4)^2+\frac{5(5-1)(5-2)}{3!}x^2(-4)^3+\frac{5(5-1)(5-2)(5-3)}{4!}x^(-4)^4+(-4)^5[/tex]This gives:
[tex](x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024[/tex]The pascal triangle is shown:
Using pascal triangle the expansion is shown:
[tex]\begin{gathered} (x-4)^5=x^5+5x^4(-4)+10x^3(-4)^2+10x^2(-4)^3+5x(-4)^4+(-4)^5 \\ (x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024 \end{gathered}[/tex]Which expression is equivalent to 3 (m + 2) – 6 (2m + 4)? 15m + 30 15m + 3 - 9m - 18 -9m + 30
To expand and then simplify the expression:
[tex]3(m+2)-6(2m+4)[/tex]We can follow the next steps:
1. Apply the distributive property:
[tex]3m+3\cdot2-12m-6\cdot4=3m+6-12m-24[/tex]Then, we need to algebraically sum the like terms:
[tex]3m-12m+6-24=-9m-18[/tex]Then, the equivalent expression for that given in the question is -9m - 18. It could be also -9(m+2) (using -9 as a common factor).
Solve for y.2y^2 - 10y + 44=(y-7)^2If there is more than one solution, separate them with commas.
Answer:
y=-5,y=1
Step-by-step explanation:
To solve this, we need to solve a quadratic equation, using the bhaskara formula.
Initially, let's place the equation in the standard format. So
[tex]2y^2-10y+44=(y-7)^2[/tex][tex]2y^2-10y+44=y^2-14y+49[/tex][tex]2y^2-y^2-10y+14y+44-49=0[/tex][tex]y^2+4y-5=0[/tex]Now we apply the bhaskara formula:
[tex]y=\frac{-(4)\pm\sqrt{4^2-4\ast1\ast-5}}{2\ast1}[/tex]Then
[tex]y=\frac{-4\pm6}{2}[/tex]So two solutions:
[tex]y^{^{\prime}}=\frac{-4+6}{2}=1,y^{^{\prime}^{\prime}}=\frac{-4-6}{2}=-5[/tex]The solution are y=-5,y=1
There are 25 people who work in an office together. Five of these people are selectedto go together to the same conference in Orlando, Florida. How many ways can theychoose this team of five people to go to the conference?
ANSWER
53,130
EXPLANATION
There are 25 people and 5 have to be chosen from that group, with no specific order,
[tex]_{25}C_5=\frac{25!}{(25-5)!5!}=\frac{25\times24\times23\times22\times21\times20!}{20!\cdot5\times4\times3\times2\times1}=\frac{25\times24\times23\times22\times21}{5\times4\times3\times2\times1}=53,130[/tex]Hence, there are 53,130 ways to choose the five-people team.
If f(x) =(if necessary)?(x-76what is the value of f(3), to the nearest thousandth
The function we have is:
[tex]f(x)=\frac{\sqrt[]{x}-7}{6}[/tex]And we need to find the value of f(3).
To solve this problem and find f(x), we need to substitute x=3 into the given function.
• Substituting x=3 into f(x) to find f(3):
[tex]f(3)=\frac{\sqrt[]{3}-7}{6}[/tex]And now, we start solving the operations.
Since the square root of 3 is equal to 1.732:
[tex]f(3)=\frac{1.732-7}{6}[/tex]Substracting 7:
[tex]f(3)=\frac{-5.268}{6}[/tex]And finally, dividing by 6:
[tex]f(3)=-0.878[/tex]To round to the nearest thousandth we need to round to 3 decimal places, which in this case we already have, thus, the final answer is:
[tex]-0.878[/tex]Got a tutor to help but they got the answer wrong and I need help again!
STATEMENT:
SOLUTION:
ANSWER:
Which of the following sets is a finite set of rational numbers
The correct option is the third one.
In set notation, '...' indicates that the set is infinite. With this we can discard option 1 and 4.
If we look option 2, they're all irrational numbers.
Thus, the correct option is the third one.
Write a compound inequality for the graph shown below.Use x for your variable.++-10-9-8-7 -6 -5 4-3-2-1002 3 4 5 6 7 8 9 10 xDand口口>DorOSONO?X
The question said we should write a compound inequality of the given graph.
We are also asked to use x as the variable.
From the graph, we can see that both end values are shaded dots, which means x is inclusive of those two values.
Since:
x ≥ -5
and
x ≤ 6
Therefore, the compound inequality of the given graph is:
-5 ≤ x ≤ 6.
A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents. In this situation, which quantities do you think can vary (change)? Which might be fixed (stay the same)?
Let's begin by listing out the given information:
total number of members = 75
printing charge = $2 per shirt
colour print for each shirt = $50 fee for each color to be printed on the shirts
Let the number of t-shirts be represented as n
Let the number of colors on the shirts be represented as x
Let the total cost of the order be represented as C
Every member must have a t-shirt means
total number of members * printing charge + (colour print for each shirt * number of colors on the shirts) = total cost of the order
75 * 2 + 50 * x = C
150 + 50x = C
C = 50x + 150
The number of colors on the shirts (x) can vary change; if the number of colors used increases, the cost of the order increases & if the number decreases, the cost of the order decreases
The printing company charges is fixed as every member is to get a shirt
The isotope Sr-85 is used in bone scans. It has a half-life of 64.9 days. If you start with a10-mg Sample, how much would be remaining after 50 days? Round to the nearest hundredth.
The formula for the half life is as follows:
[tex]N(t)=N_0\mleft(\frac{1}{2}\mright)^{\frac{t}{(t_{_{_{1)}}}}}[/tex]where N(t) is the final amount, N₀ is the initial amount, t is the time that passed, and t2 is the half-life.
The following are the given values in the problem:
[tex]\begin{gathered} N_0=10 \\ t=50 \\ t2=64.9_{} \end{gathered}[/tex]Substitute the values into the equation.
[tex]N(50)=10\mleft(\frac{1}{2}\mright)^{\frac{50}{64.9}}[/tex]Simplify the right side of the equation. Divide 50 by 64.9 and then raise 1/2 by the obtained quotient. And finally, multiply the obtained value by 10.
[tex]\begin{gathered} N(50)\approx10\mleft(\frac{1}{2}\mright)^{0.7704160247} \\ \approx10(0.5862483959) \\ \approx5.862483959 \end{gathered}[/tex]Therefore, after 50 days, it will become approximately 5.86 mg.
10. Do the ratios -2:1,-4: 2 and - 6:3 represent a proportional relationship? O No, the ratios do not represent a proportional relationship because, when graphed, the line passes through the origin but is not straight. No, the ratios do not represent a proportional relationship because, when graphed, the line is not straight, and it does pass through the origin. Yes, the ratios represent a proportional relationship because, when graphed, the line passes through the origin and is a straight line. No, the ratios do not represent a proportional relationship because, when graphed, the line is straight, but it does not pass through the origin.
Solution
For this case we have the following proportions:
-2:1 = -2
-4:2 = -2
-6:3 = -2
If we plot the relationship we got something like this
And then we can conclude that the answer is:
Yes the ratios represent a proportional relationship because when graphed the line passes through the origin and is a straight line
estimate the answer the amount of money rick spends on gasoline in a year if the average amount he spends per month is $140.87.chose the correct estimate below a: $16,800b:$168 c:2,520d: $1,680
Given data:
The given amount of money spend in a month is $140.87.
The expression for the given statement is,
[tex]1\text{ month =\$140.87}[/tex]Multiply the above expression by 12 on both sides.
[tex]\begin{gathered} 12(1\text{ month))=12(\$140.87)} \\ 1\text{ year=\$1690.44} \end{gathered}[/tex]Thus, the amount Rick spends in a year is $1690.44.
I need help finding an answer to a math question. I just need to know how to solve it. The question is:A gallon of water weighs 8.34 pounds. The Patel family has a round, 12-foot diameter, above-ground pool. How much weight is added to the pool when it is filled with 3,110 gallons of water?
We know a gallon of water weighs 8.34 pounds.
If 3,110 gallos of water are used to fill the Patel family's pool, then the water weighs:
8.34 * 3,110 = 25,937.4 pounds.
Answer: 25,937.4 pounds of water are added to the pool