Given the equation of a line in Point-Slope Form:
[tex]y+2=-7(x-4)[/tex]You need to rewrite it in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you have to solve for "y":
1. Apply the Distributive Property on the right side of the equation. Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then:
[tex]y+2=(-7)(x)+(-7)(-4)[/tex][tex]y+2=-7x+28[/tex]2. Apply the Subtraction Property of Equality by subtracting 2 from both sides of the equation:
[tex]y+2-(2)=-7x+28-(2)[/tex][tex]y=-7x+26[/tex]Hence, the answer is:
[tex]y=-7x+26[/tex]The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
50 X 5 X 3
answer divide
by 36
Evaluate f(2) and f(2.1) and use the results to approximate f '(2). (Round your answer to one decimal place.)f(x) = x(9 − x)f '(2) ≈
Given a function f(x) = x(9 - x).
We need to find the value of f(2) and f(2.1) and use them to approximate the value of f'(2).
The value of f(2) is calculated below:
[tex]\begin{gathered} f(2)=2(9-2) \\ =2(7) \\ =14 \end{gathered}[/tex]The value of the f(2.1) is calculated as follows:
[tex]\begin{gathered} f(2.1)=2.1(9-2.1) \\ =2.1(6.9) \\ =14.49 \end{gathered}[/tex]Now, by the definition of f'(x), we know that
[tex]f^{\prime}(x)=\frac{f(x+\Delta x)-f(x)}{(x+\Delta x)-x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]For the given condition, x = 2, and delta x = 0.1. So, the value of f'(2) is
[tex]\begin{gathered} f^{\prime}(2)=\frac{f(2+0.1)-f(2)}{0.1} \\ =\frac{f(2.1)-f(2)}{0.1} \\ =\frac{14.49-14}{0.1} \\ =\frac{0.49}{0.1} \\ =4.9 \end{gathered}[/tex]Thus, the approximate value of f'(2) is 4.9.
A box is filled with 3 yellow cards, 2 blue cards, and 7 brown cards. A card is chosen at random from the box. What is the probability that it is a yellow or abrown card?Write your answer as a fraction in simplest form.
We need to find the probability of the card chosen at random is yellow or brown.
So, since there are 3 yellow cards and 7 brown cards, the total numbers of cards that are yellow or brown is:
[tex]3+7=10[/tex]Now, the probability that the chosen card is yellow or brown can be found by dividing the above value by the total number of cards in the box.
The total number of cards in the box is:
[tex]3+7+2=12[/tex]Thus, that probability is given by:
[tex]\frac{10}{12}=\frac{10\div2}{12\div2}=\frac{5}{6}[/tex]Therefore, the answer is:
[tex]\frac{5}{6}[/tex]What is the volume of the figure in cubic inches?
Solution
First, we need to convert the dimensions in feet to inches
[tex]\begin{gathered} \text{ since } \\ 1\text{ ft}=12\text{ inches} \\ \\ \Rightarrow1.5\text{ ft}=1.5\times12\text{ inches}=18\text{ inches} \\ \Rightarrow0.5\text{ ft}=0.5\times12\text{ inches}=6\text{ inches} \end{gathered}[/tex]Hence, the volume is;
[tex]V=l\times b\times h[/tex][tex]V=4\times18\times6=432\text{ inches cubic}[/tex]If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less then the sun if the first and twice the second of the integers
If Tanisha wants the top of the ladder to reach exactly 8 feet up the building, what is X, the distance between the building and the base of the ladder in feet?
Solution:
Given:
The right triangle can be sketched as shown below;
To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ \\ \text{where;} \\ \text{hypotenuse}=10 \\ \text{adjacent}=x \\ \text{opposite}=8 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ 10^2=x^2+8^2 \\ 100=x^2+64 \\ 100-64=x^2 \\ 36=x^2 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Therefore, the distance between the building and the base of the ladder in feet is 6 feet.
composition of functions, interval notation
Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]a standard Normal distribution, what percentage of observationnd the z-table here.4.95%5.48%6.06%95.05%
SOLUTION:
Case: Z-scores and probabilities
Given: z-score of standard normal distribution, z= 1.65
Required: To get the percentage of observation
Method: We will be reading it off the z-score table
Step 1: First we see what the table looks like
Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title
Step 3: We observe the value is 0.4505
This translates to 45.05%.
However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score
To get the z-score above this, we do:
1 - 0.9505
P(> z) = 0.0495 or 4.95%
Final answer:
A) The answer is 4.95%
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. The total value of the coins was $7.90. The number of Dimes was 7 less than triple the number of Quarters. Write a system of equations that represents this situation. Use N, D, and Q.
A Nickel is 5 cents = 5/100 = $0.05
A dime is 10 cents = 10/100 = $0.1
A quarter is 25 cents = 25/100 = $0.25
Let N represent the number of nickels
Let D represent the number of dimes
Let Q represent the number of quarters
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that
N + D + Q = 81
The total value of the coins was $7.90. It means that
0.05N + 0.1D + 0.25Q = 7.9
The number of Dimes was 7 less than triple the number of Quarters. It means that
D = 3Q - 7
The system of equations is
N + D + Q = 81
0.05N + 0.1D + 0.25Q = 7.9
D = 3Q - 7
Divide 8 A) 3 B) 0) 7 16 D) 7. 32
Answer
3(1/2) or (7/2) or 3.5
Step-by-step Explanation
The question wants us to divide (7/8) by (1/4).
[tex]\frac{7}{8}\div\frac{1}{4}[/tex]The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.
That is, in changing ÷ into ×, (1/4) changes to (4/1)
So,
[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]Hope this Help!!!
In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.
Explanation
Step 1
the sum of the internal angles in a triangle equals 18o, so
[tex]\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ \frac{10x}{10}=\frac{170}{10} \\ x=17 \end{gathered}[/tex]Step 2
now, replace the value of x in angle Q to find it
[tex]\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}[/tex]I hope this helps you
having trouble solving quadratic equations using factoring, examples are fine
Let's solve the quadratic equation using factorization:
x²-9x -22= 0
In order to solve using this method, we should beforehand factorize the polynomial:
The middle number is -9 and the last number is -22.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...
These numbers will be -11 and 2:
-11 +2= 9
-11*2= -22
So the factorization is:
(x+2)*(x-11) = 0
That means:
x + 2 =0
and
x - 11 = 0
Solving the equations:
x= -2
x= 11
S= {-2, 11}
Find the coordinates of each point under the given rotation about the origin (-5, 8); 180
As given by the question
There are given that the point, (-5, 8).
Now,
The given coordinate of point (-5, 8) which is lies on the second quadrant.
Then,
According to the question,
Rotate it through 180 degree about the origin
Then,
The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative
Then,
The new coordinat will be, (5, -8).
Hence, the coordinate is (5, -8).
I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}[/tex]Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
Please help nobody knows the answer to my question. Round to 2 decimal places.
To answer this question we will use the z-score.
Recall that the z-score is given as follows:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]The z-score of 54 is:
[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]The z-score of 56 is:
[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:
[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(0.8Answer: 0.10.There are 73 students in a classroom, and the desired ratio of students to computers is 6 to 1. How many computers are needed to achieve the desired ration?
Answer: 12
Explanation:
Given:
Total number of students in a classroom = 73
Ratio of students to computers = 6:1
To find the number of computers needed to achieve the desired ration, we use the ratio:
[tex]\begin{gathered} \frac{\text{Total number of students}}{\text{Total number of computers}}=\frac{6}{1} \\ We\text{ plug in what we know} \\ \frac{\text{7}3}{\text{Total number of computers}}=\frac{6}{1} \\ \text{Simplify and rearrange} \\ \text{Total number of computers = 73(}\frac{1}{6}) \\ \text{Calculate} \\ T\text{otal number of computers = }12.16\text{ =12} \\ \end{gathered}[/tex]Therefore, the number of computers needed is 12.
A simple random sample from a population with a normal distribution of 98 body temperatures has x=98.20°F and s=0.61°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Click the icon to view the table of Chi-Square critical values. °F
from the question;
we are to construct 99% confidence interval. this can be done using
[tex]\bar{}x\text{ }\pm\text{ z}(\frac{s}{\sqrt[]{n}})[/tex]where,
[tex]\bar{x}\text{ = }98.20,\text{ s = 0.61, n = 98 z= 2.576}[/tex]inserting values
[tex]\begin{gathered} 98.20\text{ }\pm2.576\text{ }\frac{0.61}{\sqrt[]{98}} \\ 98.20\text{ }\pm\text{ 2.576}\times0.0616 \\ =\text{ 98.20 }\pm\text{ }0.159 \\ =98.20\text{ + }0.159\text{ or 98.20 - 0.159} \\ =\text{ 98.359 0r 98.041} \end{gathered}[/tex]therefore the 99% confident inter vale is between 98.041 to 98.359
What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21
Answer:
84=2^2 x 3 x 7
Explanation:
A prime number is any number that has only two factors: 1 and itself.
To find the prime factorization of 84, we are required to express it as a product of its prime factors.
[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]
Therefore, the prime factorization of 84 is:
84=2^2 x 3 x 7
720÷5 WORK OUT NEEDED
144
Explanation:[tex]720\text{ }\div\text{ 5}[/tex]working the division:
The process:
7 ÷ 5 = 1 R 2
add the 2 to the next number: this gives 22
22 ÷ 5 = 4 R 2
add 2 to the next number: this gives 20
20 ÷ 5 = 4 R 0
The result of 720 ÷ 5 = 144
A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answer: 15cm
Step-by-step explanation:
Your welcome
Solve the inequality: y-5-20Which of the following is the graph of the solution?
Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
Write the percent as fraction or mixed number in simplest form 750%
Answer
[tex]7\frac{1}{2}[/tex]Explanation
The 750 percent as a fraction or mixed number in simplest form is calculated as follows:
[tex]750\%=\frac{750}{100}=\frac{75}{10}=\frac{15}{2}=7\frac{1}{2}[/tex]I need help with a word problem in algebra 2 please
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]simplify -5m²n³ × 15m⁴ n⁶
To simplify the given expression we will use the following property of exponents:
[tex]a^n\times a^m=a^{n+m}.[/tex]Using the above property we get:
[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]Answer:
[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]Let a represent the row number in this pattern. Write a rule that tells you the number of dots, d, in row n (Hint: Your rule should begin with "d=") Row 1 Row 2 Row 3 Row 4
The rule to show the number of dots in the pattern is
d = 2aWhat is a pattern?A pattern is a repetition of items, when the repetition is in ordered then the pattern can be forecasted.
The given pattern is ordered by the rule at which it was formed. The rule helps to forecast the number of dots in the next row
How to get the rules of the patternThe information given in the question include:
Let a represent the row number in this patternA picture image shoeing the rows and dotsYour rule should begin with "d="row 1 = 2 dots
row 2 = 4 dots
row 3 = 6 dots
it can be seen that
2 * number of rows = number of dots
Hence:
d = 2 * a
d = 2a
checking the rule for the 4th row
d = 2 * 4
d = 8
counting the dots confirms the rule is okay
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Question 23 of 25
What is the effect on the graph of f(x) = when it is transformed to
g(x) = +17?
A. The graph of f(x) is shifted 17 units down.
B. The graph of f(x) is shifted 17 units to the right.
OC. The graph of f(x) is shifted 17 units up.
OD. The graph of f(x) is shifted 17 units to the left.
Answer:
C. The graph of f(x) is shifted 17 units up.
Step-by-step explanation:
When + is outside the equation, it means up.
write in point slpoe form an equation of the line that passes through th griven point and has the given slope (1, -3); m = 4
A linear equation in slope-point form looks like this:
y -y0= m(x-x0)
Where m is the slope of the line and (x0,y0) is a point of the line.
In this case, we know that the slope of the line equals 4 and that the line goes through the point (1, -3), then, we can substitute these values into the general form to get:
y-(-3) = 4(x-(1))
Does anyone know the answer to this?
The most appropriate choice for equation of line in slope intercept form will be given by
x + 2y = -16 is the required equation of line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
[tex]m=tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
The line passes through (0, -8) and (-2, -7)
Slope =
[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]
The line passes through (0, -8)
Equation of line
[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]
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what does -1 3/4+4.7=
-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95
3/4 = 0.75, so -1 3/4 is -1.75
-1.75 + 4.7 = 2.95
Answer: 2.95
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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