Answer:
y=3x-11
Step-by-step explanation:
In this question, we will use the point slope form:
Which has the equation:
[tex]y-y_1=m(x-x_1)\\subsitute:\\y+5 = 3(x-2) , (y--5=+5)\\y+5=3x-6\\y=3x-11[/tex]
Hope this helps!
please help me......
write in y=mx+b form
Answer:
What?
Step-by-step explanation:
D.
AN ENGLISH EXAM CONSISTS OF TEN ESSAY QYESTIONS. IF A STUDENT MUST CHOOSE 4 OF THE 10 QUESTIONS HOW MANY DIFFERENT SETS OF 4 QUESTIONS ARE AVAILABLE?
Given
Number of questions in an english exam = 10
Find
Number of different sets of 4 questions are available.
Explanation
as we have given that a student must choose 4 of the 10 questions.
so , number of different set of 4 questions are available =
[tex]^{10}C_4[/tex]so ,
[tex]\begin{gathered} ^{10}C_4=\frac{10!}{4!(10-4)!} \\ \\ ^{10}C_4=\frac{10!}{4!6!} \\ \\ ^{10}C_4=\frac{10\times9\times8\times7\times6!}{4\times3\times2\times1\times6!} \\ \\ ^{10}C_4=\frac{5040}{24} \\ \\ ^{10}C_4=210 \end{gathered}[/tex]Final Answer
Hence , the number of different sets of 4 questions are available are 210
A sector has radius 12 and central angle 64°. Find the area of the sector.
We need to find the area of the sector which is given by the next formula:
Area of the sector = ( central angle / total angle ) * area of the circle
First, we need to find the area of the circle:
[tex]\begin{gathered} A_c=\pi\ast r^2 \\ Replacing \\ A_c=\left(12\right)^2\pi \\ A_c=144\pi \end{gathered}[/tex]Now, we can use the formula for the area of the sector
Central angle = 64
The total angle of a circle= 360
Area of the circle = 144π
Replacing using the formula:
Area of the sector = (64/360) * 144π
Area of the sector = 128π/5
Area of the sector = 80.42477
what's the answer
find m<2ifm
The m∠2 is m∠2 = 14°.
What is degree measure?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
As given in the figure,
m ∠WHI = 160°,
m ∠EHI = 104°
m ∠THE = 42°
We have to find the m ∠2
From figure,
m ∠WHI = m ∠WHT + m ∠THE + m ∠EHI
m ∠WHT = m ∠WHI - m ∠THE - m ∠EHI
m ∠WHT = 160° - 42° - 104°
m ∠WHT = 14°
Hence the measure of angle 2 is, m ∠2 = 14°.
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A book was bought for $40 and later sold at profit of 25%. What was the selling price of the book?
Answer:
The book was 50 dollars
Step-by-step explanation:
0.25% x 40 dollars = $10
10 + 40 (the original amount) = $50
Answer:
$50
Step-by-step explanation:
25% of $40 is $10 dollars. so a book sold with 25% profit is $50
Please help me with this I do not understand. I did the steps but am really looking for the answer if you could help.
ANSWER :
The zeros are 1/2 and -5
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=2x^2+9x-5[/tex]The zeros of the function are the values of x when f(x) = 0
[tex]2x^2+9x-5=0[/tex]Using quadratic formula with a = 2, b = 9 and c = -5
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-9\pm\sqrt{9^2-4(2)(-5)}}{2(2)} \\ \\ x=\frac{-9\pm\sqrt{81+40}}{4} \\ \\ x=\frac{-9\pm\sqrt{121}}{4} \\ \\ x=\frac{-9\pm11}{4} \\ \\ x=\frac{-9+11}{4}=\frac{1}{2} \\ \\ x=\frac{-9-11}{4}=-5 \end{gathered}[/tex]Solve the equations and check for extraneous solutions5^3^x + 14 = 78
we have the equation
[tex](5^3)^x+14=78[/tex]Solve for x
[tex]\begin{gathered} (5^3)^x=78-14 \\ (5^3)^x=64 \end{gathered}[/tex]Applying log on both sides
[tex]log((5^3)^x=log(64)[/tex][tex]\begin{gathered} xlog(5^3)^=log(64) \\ x=\frac{log64}{2log5} \end{gathered}[/tex]ſ x - 5y = -9( 4x + 4y = - 12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Given:
[tex]\begin{gathered} x-5y=-9\ldots\ldots(1) \\ 4x+4y=-12\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The given point is (-4,1)
Let's check the ordered pair (-4,1) in the first equation
[tex]\begin{gathered} x-5y=-9 \\ (-4)-5(1)=-9 \\ -4-5=-9 \\ -9=-9 \end{gathered}[/tex]Hence, (-4,1) is a solution of the first equation x-5y=-9.
Now, let's check (-4,1) in the second equation.
[tex]\begin{gathered} 4x+4y=-12 \\ 4(-4)+4(1)=-12 \\ -16+4=-12 \\ -12=-12 \end{gathered}[/tex]So, (-4,1) is a solution of the second equation 4x+4y=-12.
Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.
Exercise #99) g(x) = x3 + x f(x) = 2x-3 - 3 Find (gof)(x)
Given two functions f(x) and g(x), its composition will be:
[tex](g\circ f)=g(f(x))[/tex]It is read g compound f or simply said to g we are going to fill it with f. So, you have
[tex]\begin{gathered} (g\circ f)=g(f(x)) \\ (g\circ f)=(2x-3)^3+(2x-3) \end{gathered}[/tex]To expand the binomial, apply the binomial formula to the cube, that is:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]So, you have
[tex]\begin{gathered} (g\circ f)=(2x-3)^3+(2x-3) \\ (g\circ f)=(2x)^3-3(2x)^2(3)+3(2x)(3)^2-(3)^3+(2x-3) \\ (g\circ f)=2^3x^3-3(2^2x^2)(3)+3(2x)9-27+(2x-3) \\ (g\circ f)=8x^3-3(4x^2)(3)+54x-27+(2x-3) \\ (g\circ f)=8x^3-36x^2+54x-27+2x-3 \end{gathered}[/tex]Finally, operate similar terms
[tex](g\circ f)=8x^3-36x^2+56x-30[/tex]find the greatest common factor of 615 and 570.
Given the numbers:
[tex]615\text{ and 570}[/tex]Let's find their greatest common factor:
Step 1: Let's determine the factors of the numbers.
a.) 570
The factors of 570 are: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
b.) 615
The factors of 615 are: 1, 3, 5, 15, 41, 123, 205, 615
Their common factors are: 1, 3, 5, 15
But the greatest among all factors is 15.
Therefore, their greatest common factor (GCF) is 15.
find 3 consecutive odd integers when the sum of the first and third integer is 26
Let's call the first odd number x.
The next odd number will be x + 2, and the last one will be x + 4.
If the sum of the first number and the last one is 26, we have that:
[tex]\begin{gathered} x+x+4=26 \\ 2x+4=26 \\ 2x=22 \\ x=\frac{22}{2}=11 \end{gathered}[/tex]So the numbers are:
[tex]\begin{gathered} x\to11 \\ x+2\to13 \\ x+4\to15 \end{gathered}[/tex]11, 13 and 15.
Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. P(h) =P. e-0.00012h In this function, Po is the air pressure at the surface of the Earth, and his the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 65% of the air pressure at the surface of the Earth?
A. 0.65 m
B. 5416.7 m
C. 3587.4 m
D. 3589.9 m
3589.9 m is the height at which air pressure equals 65% of the air pressure at the surface of the Earth
How to find the height at which air pressure equals 65% of P₀?
Given: the function P(h) =P₀ e^(-0.00012h)
When air pressure equals 65% of the air pressure at the surface of the Earth. That means P = 0.65P₀
Substitute P = 0.65P₀ into the function:
P(h) = P₀ e^(-0.00012h)
0.65P₀ = P₀ e^(-0.00012h)
Dividing both sides by P₀ gives:
0.65 = e^(-0.00012h)
Take ln of both sides (ln is the inverse of e):
ln 0.65 = -0.00012h
h = ln 0.65/ (-0.00012)
h = 3589.9 m
Therefore, the height at which air pressure equal 65% of the air pressure at the surface of the Earth is 3589.9 m. Option D is the answer
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16 oz harbor peanut butter for 2.49 or a 64 oz jar of peanut butter for 6.99 round everything up to the nearest cent or hundreth. yes mam
We have to find the "better buy" between two options:
1) 16 oz jar for $2.49
2) 64 oz jar for $6.99
We can compare this two options with the unit price of each one. The unit price will be expressed in "$ per oz" or "$/oz". The option with the smaller unit price is the "better buy".
We can calculate the unit price as teh quotient between the price and the weight of each option.
Unit price for Option 1:
[tex]u_1=\frac{2.49\text{ \$}}{16\text{ oz}}\approx0.16\frac{\$}{oz}_{}[/tex]Unit price for Option 2:
[tex]u_2=\frac{6.99\text{ \$}}{64\text{ oz}}\approx0.11\frac{\$}{oz}[/tex]As the Option 2 (64 oz jar) has a smaller unit price, the better buy is the 64 oz jar for $6.99.
Answer: the better buy is the 64 oz jar for $6.99.
50% of the tickets sold an amusement park or a discount tickets at the park sold 94 tickets to know how many discount tickets did it sell
we have that
50%=50/100=0.50
Multiply the total tickets sold by the factor of 0.50
so
94*0.50=47 tickets
the answer is 47 ticketsI don't have a diagram, but here's the key info:
There is a sector of a circle:
The radius is 5.2
The arc length is 6π
You are not given the angle of the sector
Find the area of the sector, and give your answer in terms of pi I got 49π, let me know if I'm right ty. I've attached my working out
Answer:
Area of sector is 15.6π========================
Let the central angle be α.
Arc length equations = 2πr × α/360, if α in degreess = 2πr × α/2π = αr, if α in radiansWe have s = 6π and r = 5.2Find the central angles = αr6π = 5.2αα = 6π/5.2Area of sectorA = r²α/2, when α in radiansSubstitute the value of αA = 5.2² × 6π/5.2 × 1/2 = 5.2 × 3π = 15.6πNote: You could get it more easily if considered 360° = 2π in your calculations.
Answer:
[tex]\dfrac{78}{5} \pi = 15.6 \pi[/tex]
Step-by-step explanation:
Given values:
Radius (r) = 5.2Arc length = 6πAs the arc length is given in terms of pi, use the formulas where the angle is measured in radians.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the given values into the arc length formula to calculate the central angle (in radians):
[tex]\implies 6\pi=5.2\; \theta[/tex]
[tex]\implies \theta=\dfrac{6\pi}{5.2}[/tex]
[tex]\implies \theta=\dfrac{15}{13}\pi[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Area of a sector of a circle}\\\\Area of a sector = $\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the radius and the found angle into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area of the sector}&=\dfrac{1}{2}(5.2)^2 \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{1}{2}(27.04) \left(\dfrac{15}{13}\pi\right)\\\\&=(13.52) \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{78}{5}\pi \\\\&=15.6 \pi\end{aligned}[/tex]
Vivian has $535 in her stavings account and she has to pay $5.00 each month for her cell phone Reza has $145 and he saves $25 each month for his job walking the dogs at this rate when will they had the same amount of money and how much will they have
Answer: $456
Step-by-step explanation: They will both have the same amount of money at 7 months
Question
Solve for x.
5(x−225)=−5.2
Enter your answer as a decimal or simplified mixed number in the box.
x =
Answer:
x=223.96
Step-by-step explanation:
Answer as a decimal: x=223.96
Answer as a fraction: x= 223 24/25
Let's solve this equation step-by-step!
5(x−225)=−5.2
Step 1: Simplify both sides of the equation.
5(x−225)=−5.2
(5)(x)+(5)(−225)=−5.2 (Distribute)
5x+−1125=−5.2
5x−1125=−5.2
Step 2: Add 1125 to both sides.
5x−1125+1125=−5.2+1125
5x=1119.8
Step 3: Divide both sides by 5.
5x/5=1119.8/5
x=223.96
What ratio is equal to 4:18?
Answer:
2:9
or
8:32
There are many
Answer: 8:36 or 12:54
Step-by-step explanation:
All you have to do is multiply both by 2, so 4 times 2 is 8 and 18 x 2 is 36, and the answer is 8:36.
I need know the answer and how to write out my answer as well
5 . 3
6 I 3 1 . 8
- 3 0
1 8
- 1 8
0
Therefore, the answer is 5.3
On a snow day, Robert created two snowmen in his backyard. Snowman A was built to a height of 33 inches and Snowman B was built to a height of 45 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 6 inches per hour and Snowman B's height decreased by 9 inches per hour. Let AA represent the height of Snowman A tt hours after sunrise and let BB represent the height of Snowman B tt hours after sunrise. Graph each function and determine which Snowman is taller after 3 hours.
Nate and his family plan to take a 2,438 mile cross-country trip this summer.if they drive 85 miles each day ,how many days will they be driving? explain your answer
28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .
What is division ?Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.
Calculationspeed = 85miles / day
distance = 2438
time = 2438 / 85 = 28.68235294117647 days
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find area and perimeter
Answer:
Area: 20cm^2
perimeter: 20cm
(4*2) + (4*3) =
8 + 12 = 20cm^2
use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.
We are given the following expression:
[tex]\log a-3\log b+4\log c[/tex]we are asked to simplify this expression. To do that we will first use the following property:
[tex]a\log b=\log ^{}b^a[/tex]we will apply this to the second and third terms, like this:
[tex]\log a-\log b^3+\log c^4[/tex]Now we will use the following property:
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]we will use this property for the first and second terms:
[tex]\log (\frac{a}{b^3})+\log c^4[/tex]Now we will use the following property:
[tex]\log a+\log b=\log ab[/tex]We will use the property in the last two terms, like this:
[tex]\log (\frac{ac^4}{b^3})[/tex]And thus, we have simplified the logarithmic expression into one single logarithm
Brian drove from Houston to New York, then to Chicago, then back to Houston. How far did he drive altogether?
Houston to NY= 1608
NY to Chicago=802
Chicago to Houston=1067
If x squared minus 6x plus 7 equal k(2x-3) has real equal roots find the possible values of K
We will have the following:
[tex]\begin{gathered} x^2-6x+7=k(2x-3)\Rightarrow x^2-6x+7=2kx-3k \\ \\ \Rightarrow x^2-6x-2kx+7+3k=0 \end{gathered}[/tex]Now, we want to operate like terms and take to "solve for x" using the quadratic expression, that is:
[tex]\Rightarrow x^2+(-6-2k)x+(7+3k)=0\Rightarrow x=\frac{-(-6-2k)\pm\sqrt{(-6-2k)^2-4(1)(7+3k)}}{2(1)}[/tex]No, in order to determine the possible real values for "k" we have to analyze the value under the root, so:
[tex]\begin{gathered} \sqrt{(-6-2k)^2-4(1)(7+3k)}\Rightarrow(-6-2k)^2-4(1)(7+3k)\ge0 \\ \\ \Rightarrow36+24k+4k^2-28-12k\ge0\Rightarrow8+12k+4k^2\ge0 \end{gathered}[/tex]Now, we will have to use the quadratic expression again to determine the values for "k" that make the inequality true, that is:
[tex]\begin{gathered} k=\frac{-(12)\pm\sqrt{(12)^2-4(4)(8)}}{2(4)} \\ \\ \Rightarrow k\leq-2 \\ \\ and \\ \\ \Rightarrow k\ge-1 \end{gathered}[/tex]So, the values for which the inequality and thus the expression under the root are true are then given by:
[tex]k\leq-2\wedge x\ge-1[/tex]In other notation:
[tex](-\infty,2]\cup[-1,\infty)[/tex]What is the result when the number 8 is increased by 25%?
Answer:
Step-by-step explanation:
Ok1
1. Put percent into numbers
25/100*8=
200/100=
2
2. Add
There was a increase of 2 dollars from 8$
8$+2$=
10$
Answer: 10$
Answer:10
note: please tell me if I'm wrong
Your bank account has -$21 in it and you deposit $6 per day. How much money is in your account after 4 days?
So the original amount of money in the bank account is given by a negative number: -$21. If you deposit $6 per day during four days then the total amount of money deposited by the fourth day is:
[tex]4\cdot\text{\$}6=\text{\$}24[/tex]The total amount of money in the account is given by adding the deposited money to the original amount:
[tex]-\text{\$}21+\text{\$}24=\text{\$}3[/tex]Then the answer is $3.
Suppose the cost per ton y to build an oil platform of x thousand tons is approximately by:What is the cost per ton for x=300?
The cost per ton of x = 300 is 318.18
To solve this, we need to reaplce x in the function:
[tex]\begin{gathered} \begin{cases}f(x)=\frac{262,500}{x+525} \\ x=300\end{cases} \\ f(300)=\frac{262,500}{300+525}=\frac{262,500}{825} \\ f(300)\approx318.18 \end{gathered}[/tex]And then we get the anser
You flip a coin and then spin this spinner. a) Determine whether these events are Independent or Dependent. Write I on D b) Find the probability that the coin lands tails-up and the spinner Yands on a I Write as a reduced fraction (numerator/denominator). 1
SOLUTION
Dependent events influence the probability of other events or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.
PART A
Since the flip of a coin would not affect the spin of the spinner, therefore these events are independent events.
The answer is 'I'
PART B
To find the probability that the coin lands tails-up and the spinner lands on 1, we would need to find the probability of getting a tail, then we find the probability of getting a 1
Therefore,
[tex]\text{Probaility}=\frac{no\text{ of favourable outcomes}}{\text{Total possible outcomes}}[/tex]When we flip a coin, the favourable outcome for a tail is 1 since a tail can only occur once in one flip. The total possible outcomes are 2, since we can have either a tail or head occurring in one flip.
Then,
[tex]Pr(\text{Tail)}=\frac{1}{2}[/tex]When we spin the spinner, the favourable outcome for one is 1, since we have only one slot for one on the spinner. The total possible outcome is 4 since we have 4 different number
slots on the spinner.
Then,
[tex]Pr(1)=\frac{1}{4}[/tex]To get the probability of getting a tail, then we find the probability of getting a 1 we multiply the probability of getting a one on the spinner and a tail on the flip.
[tex]undefined[/tex]7. A box contains bags of nails. Each
bag has 24 nails. There are 960 nails
in the box. How many bags are in
the box?
40 bags of 24 nails in the box
Answer:
Step-by-step explanation:
you divide 960 by 24 and you will have 40 so you will have 40 nails. :0
