The slope-intercept form of the equation of the given line which passes through the point (2, 7) and has a slope of 8 is:
y = 8x - 9
What is meant by slope-intercept form of the line equation?
The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.
Given the line passes through a point (2,7) and the slope is 8.
When a point on the line and slope are given, the equation of the line is:
y - y₁ = m ( x - x₁)
m = slope = 8
Substituting,
y - 7 = 8 ( x - 2)
y - 7 = 8x -16
y = 8x - 9
Therefore the slope-intercept form of the equation of the given line is:
y = 8x - 9
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I will give brainliest, if you get this correct
Depend on the following data
30 25 23 41 39
27 41 24 32
Find
A. The arithmetic mean, median, mode and range.
B. The upper and lower quartile, 7 and 50 .
C. Variance and coefficient of variation.
D. Pearson coefficient of skewness and kurtosis
Answer:
A.
Arithmetic mean: The sum of the data divided by the number of data points. (For the first set of data: (30+25+23+41+39)/5 = 31.4)
Median: The middle value when the data is arranged in order. (For the first set of data: 30, 23, 25, 39, 41 => 25)
Mode: The value that appears most frequently in the data. (For the first set of data: No value appears more than once, so there is no mode.)
Range: The difference between the highest and lowest values in the data. (For the first set of data: 41-23 = 18)
B.
To find the upper and lower quartile, you need to first arrange the data in order and then divide it into four equal parts.
Lower quartile (Q1) is the median of the lower half of the data.
Upper quartile (Q3) is the median of the upper half of the data.
For the first set of data: Q1 = (23+25)/2 = 24, Q3 = (39+41)/2 = 40
7th and 50th Percentile:
To find 7th percentile, pick 7th item from ordered data set and if not possible then take the average of 6th and 8th items.
To find 50th percentile, pick the median of the data set.
For the first set of data: 7th percentile = 25, 50th percentile = 25
C.
Variance: A measure of the spread of the data. It is calculated by taking the average of the squared differences from the mean.
Coefficient of variation (CV) : A normalized measure of the spread of the data. It is the ratio of the standard deviation to the mean.
D.
Pearson coefficient of skewness: A measure of the asymmetry of the data about the mean. A positive skewness indicates that the tail on the right side of the probability density function is longer or fatter than the left side. Conversely, a negative skewness indicates that the tail on the left side is longer or fatter than the right side.
Kurtosis: A measure of the "peakedness" of the data. A high kurtosis means that the data has heavy tails (outliers) or a distinct peak near the mean, whereas a low kurtosis means that the data has light tails (no outliers) or a flat peak near the mean.
Find the value of x. Write your answer as a decimal.
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6 cm
3 cm
7 cm
(4x+17) cm
& Check
Q: Solution
Answer:
Step-by-step explanation:
1.75?
a straight line passes through point (2,6) and 9,20) what is the equation of the line in slope-intercept form
Answer:
y = 2x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 6 ) and (x₂, y₂ ) = (9, 20 )
m = [tex]\frac{20-6}{9-2}[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then
y = 2x + c ← is the partial equation of the line
to find c substitute either of the 2 points into the partial equation
using (2, 6 ), then
6 = 2(2) + c = 4 + c ( subtract 4 from both sides )
2 = c
y = 2x + 2 ← equation of line
Find the multiplicative inverse of 6 + 2i.
1/(6-2i)
3/20+1/20 i
3/20-1/20 i
06-2 i
The multiplicative inverse of 6 + 2i is 3/20 - 1/20i.
When a number is multiplied by its original number, the multiplicative inverse of that number, or x-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2-1 since it fulfills the formula: 2 x 2-1 = 2 x 12 = 1. It is also known as a number's reciprocal.
Use the following method to determine a complex number's multiplicative inverse:
The original complex number is reciprocated to find the inverse. The complex number (6+2i) has a reciprocal of 1/6+2i. Simplify by multiplying the reciprocal's numerator and denominator by the conjugate of the denominator:
1/6+2i × 6 - 2i/6 - 2i
3/20 - 1/20i.
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fully factor (x^2 + 4)(x -3)
Answer: x³ - 3x² + 4x - 12
Step-by-step explanation:
Using FOIL:
x³ - 3x² + 4x - 12
Answer:
x=1
Step-by-step explanation:
(x^2+4)(x-3)
"x^2=x*x=x"
(x+4)(x-3)
x+1
x/x/
x=1
There is a 60% chance for snow over the next three days. Find the probability that it snows all three days
Answer:
21.6%
Step-by-step explanation:
Each day is independent, so the probability of snow all three days is:
(0.60)³ = 0.216
There is a 21.6% chance that it snows all three days.
- Grace is trying to read as many books
over the summer as she can. Grace
has already read 15 books. She plans
to read 2 additional books per week.
Define a variable for the number of
weeks she reads additional books. Use
the variable to write an expression
for the total number of books Grace
reads over the summer.
Step-by-step explanation:
let the number of weeks be w
the total number of books Grace reads will always be 15 + something because we start with 15 and cannot unread a book
for each week, she reads 2 books. this can be represented as 2 * w
books Grace already read + books Grace reads each week = total books
15 + 2 * w = total books
Danny takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If
the piece of fabric is 9 centimeters long and 12 centimeters wide, how long is the diagonal
cut that Danny made?
Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.
The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)
So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm
Therefore, the diagonal cut that Danny made is 15 centimeters long.
Step-by-step explanation:
if the line passing through the points (a,2) and (4,9) is parallel to the line passing through the points (3,11) and (a+1,3) what is the value of a?
Answer:
a = 18
Step-by-step explanation:
The slopes of parallel lines are equal as
[tex]m_{2}=m_{1}[/tex]
We know that the slope formula is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2, x2, y1, and y2 are any two points.
Thus, since the slopes are equal, we can use the slope formula to find the slopes of both lines and set them equal to each other to find a:
[tex]\frac{9-2}{4-a}=\frac{3-11}{(a+1)-3} \\\\\frac{7}{4-a}=\frac{-8}{a-2} \\\\7(a-2)=-8(4-a)\\7a-14=-32+8a\\7a=-18+8a\\-a=-18\\a=18[/tex]
If we plug in a for any of the two lines, we see that the slope is -1/2
Line 1 w/ (a, 2) & (4, 9):
[tex]\frac{9-2}{4-18}\\ \frac{7}{-14}\\ \frac{-1}{2}[/tex]
Line 2 w/ (3, 11) & (a+1, 3):
[tex]\frac{3-11}{18+1-3}\\ \frac{-8}{19-3}\\ \frac{-8}{16}\\ \frac{-1}{2}[/tex]
Solve each equation. 2 1/3(2x-3)=2 1/3
Answer: x = 2
Step-by-step explanation:
Multiply each term between the parentheses by 2 1/3.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the expression of the multiplication.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the multiplication and division of rational numbers.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]
We convert the mixed fraction to improper.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]
We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]
We move the constant to the right side and change the direction of the sign.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]
for each pair expalin why they are equivelent 5:6 15:18
The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.
Why are the two ratios equivalent?Here we want to explain why the two ratios:
5:6 and 15:18
Are equivalent, where equivalent means that these two ratios mean the same thing.
Now, if we take any ratio
a:b
and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.
k*a: k*b
Now, let's look to our ratios:
5:6
If we multiply these 2 numbers by 3, we will get.
3*5: 3:6
15: 18
So yes, these are equivalent.
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Expresa estas fracciones como un número mixto realizando para ello la división correspondiente
The representation of the fraction 10/8 as a mixed number is given as follows:
[tex]\frac{10}{8} = 1\frac{1}{5}[/tex]
How to convert a fraction to mixed number?The fraction in this problem is given as follows:
10/8.
A mixed number is composed by two parts, as follows:
Integer part.Fractional part.The integer part and the fractional part are defined as follows:
Integer: quotient of the numerator by the denominator.Fractional part: remainder of the fraction divided by the divisor.For the division of 10 by 8, we have that:
The quotient is of 1.The remainder is of 2.Then the mixed number is given as follows:
[tex]1\frac{2}{10}[/tex]
The fraction 2/10 can be simplified as 1/5, hence the simplified representation is given as follows:
[tex]1\frac{1}{5}[/tex]
Missing Information and TranslationThe problem asks to represent the fraction 10/8 as a mixed number
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Select the correct answer. What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)? A. y = 3 B. x = 3 C. x = 5 D. y = -5
Answer:
Choice B: x = 3
Step-by-step explanation:
The standard equation of a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]
where
(h, k) is the vertex and |p| is the focal length
The given equation is
[tex](y - 3)^2 = 8(x - 5)[/tex]
Convert this to standard form and compare with general equation
Switch the sides of the equationAnswer: Choice B: x = 3
Calculate the combinations of 5 things 3 at a time
Answer:
5 combination 3
5 fictorial divided by (5-3)! 3!
by using the above method 10 will be your answer
Joey is making accessories for the soccer team. He uses 876.52 inches of fabric on headbands for 31 players and 3 coaches. He also uses 288.61 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
The number of fabric used for headband and wristband for each player is 25.8in and 9.3 in
What is world problem?Word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations.
Represent the number of fabric used on headband by x and the number of fabric used on wristband by y
Therefore;
31x +3x = 876.52
34x = 876.52
divide both sides by 34
x = 876.52/34
x = 25.8 inches
31y = 288.61
dive both sides by 31
y = 288.61/31
y = 9.3 inches
therefore 25.8 inches of fabrics and 9.3 inches of fabrics are used on headband and wristband of each player
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Find general solution. Show steps of derivation. Check your answer by substitution.
y´=sec^2(y)
So on solving the provided question we cans ay that trigonometry y =sec^2(y); y = 1/[tex]\sqrt{2}[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
y´=sec^2(y)
here, y = 90
y = sec^2(90)
y = 1/[tex]\sqrt{2}[/tex]
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What is the slope of the line that passes through the points (3,8) and (-2,13)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]
Answer:
[tex]\boxed{\bf Slope(m):-1}[/tex]
Step-by-step explanation:
We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).
The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.
[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]
[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]
[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]
[tex]\bf m=-\cfrac{5}{5}[/tex]
[tex]\bf m=-1[/tex]
Therefore, the slope is -1.
__________________
Hope this helps!
Have a great day!
riley needs to make punch for a party. One batch of punch has the ingredients shown.
cranberry juice 4 cups, lemon lime soda 1 cup, orange juice 2 cups, pineapple juice 2 cups. Write and interpret a ration that compares the cups of orange juice to the total cups in one batch of punch. Then find the cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups
If riley needs to make punch for a party. One batch of punch has the ingredients shown. The cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups is 6 cups.
How to find the cups of orange juice?Total cup of juice for one batch:
Total cup of juice for one batch = 4+ 1 +2 +2
Total cup of juice for one batch = 9
Since 2 cup of the 9 cups are orange juice so 2/9 of each batch will be orange and since the bowl can hold 27 cups now let find the cups of orange juice.
Cups of orange juice = 2/9 ×27
Cups of orange juice =6 cups
Therefore we can conclude that the cups of orange juice is 6 cups.
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If P(E)= 0.9 and P(F) = 0.8, show that P(EF) >0.7. In general, show that
P(EF) > P(E) + P(F) - 1
Answer:
P(EF) > 0.72 and in general, P(EF) > P(E) + P(F) - 1
Step-by-step explanation:
We know that P(EF) = P(E and F) = P(E|F) * P(F) = P(F|E) * P(E) (by the definition of conditional probability).
For the specific case given, P(E)= 0.9 and P(F) = 0.8,
P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > P(E) * P(F) = 0.72
In general,
P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > min(P(E|F) * P(F), P(F|E) * P(E) ) = P(E) * P(F)
P(EF) > P(E) * P(F) = P(E) + P(F) - 1
This is because P(E|F) and P(F|E) are always less or equal to 1.
What is an equation of the line that passes through points (-1,3) and (-2,-1)?
Answer:
[tex]\boxed{y = 4x + 7}[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
where m is the slope and b the y-intercept
To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values
Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]
Difference in y values [tex]= -1 -3 = -4[/tex]
Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]
Slope
[tex]m = \dfrac{-4}{-1} = 4[/tex]
So the equation of the line is of the form
[tex]y = 4x + b[/tex]
To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b
Let's take point (-1, 3)
Plug in values:
[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]
Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]
Let u and v be two vectors in space with u =2i-j-2k and |v|| = 12. If u and v are parallel, then find the vector v.
Therefore , the solution of the given problem of vectors comes out to
be -25.
Why do they have the name "vectors"?An object with both magnitude and direction is referred to as a vector. A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
Here,
Given:
lul=3,|v|=4 and |w|=5
Also, u+v+w=0
On squaring both sides, we get
=> u2+v2+w2+2(u.v+v.w+w.u) = 0
=> 32+42+52 +2(u.v+v.w+w.u) = 0
=> 9+16+25+2(u.v+v.w+w.u) = 0
=> u.vv.w+w.u
=> -50 = -25
Therefore , the solution of the given problem of vector comes out to
be -25.
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Which of the following show an equation and it’s solution?
The ones which are equation are
[tex]\frac{3}{4}l = -9\\ 4m + 2m = 72[/tex]
What is an equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
here
-3 = d/-8
or, d = 24 (different from answer)
14 = 25 - k
or, k = 11 (different from answer)
j + 1 = j/3
or, 3j + 3 = j
or, j = -3/2 (different from answer)
3/4 l = -9
or, l = -12 ( same as answer)
-15 = n + 8
or, n = -23 (different from answer)
4m + 2m = 72
or, m = 12 (same as answer)
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Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
The value of 3x₁ + x₂ is 7/2
How to find the value of 3x₁ + x₂?
A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
5/x - 2/x² = 2
The LCM of x and x² is x². So we have:
(5x - 2)/x² = 2
Cross multiply:
5x - 2 = 2x²
2x² - 5x + 2 = 0
Factorize:
(2x - 1)(x - 2) = 0
2x - 1 = 0 or x - 2 = 0
2x = 1 or x = 2
x = 1/2 or x = 2
Thus, x₁ = 1/2 and x₂ = 2
Therefore, the value of 3x₁ + x₂ will be:
3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2
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Samuel will arrive at the airport on the first plane after 10 am Airplanes arrive every 50 mins beginning at 6 am when will samuels plane arrive?
Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.
What is algebraic expression?An algebraic expression is a mathematical expression that uses coefficients, unknown variables, algebraic operations, and constants. However, it is not acceptable to use an equality symbol in an expression.
Mathematical expressions and sentences come in a wide variety. the relationships between equations, numerical expressions, and algebraic expressions.
The difference between 10 am and 6 am
is 4 hours, So the the time he arrives will be a multiple of 50 grater than 4 hours
50x > 4 × 60
50x > 240
x > 240/50
x > 4.8
x = 5 (as 5 is nearest single digit no. to 4.8)
50x = 50 × 5
= 250 minutes
250 mins = 4 hours and 10 mins
6 am + 4 hours and 10 mins
= 10 hour and 10 min or 10:10 am
Thus, Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.
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What is the terminal point of the vector a=⟨4,3⟩ based at P=(5,2)?
Answer:
Step-by-step explanation:
The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:
Terminal point = (x,y) = (Px + ax, Py + ay)
= (5 + 4, 2 + 3)
= (9,5)
Answer:
Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3) whose base is at the point P=(5,2).
✔️ Add to point P and that
✔️Point that the vector is pointing at to find the terminal point....
➖So we can say That
✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-
(5,2)+(4,3)=(9,6)
your welcome !
4. Solve the triangle using either Law of Cosines or Law of Sines. In △DEF, f=25, e=8 and m∠F=131°.
AngleD= AngleE= Angle d=
Round your final answer to the nearest tenth. **
Using cosine law and sine law, the value of angle E and D are 14° and 35° and the length of side d is 19 units
What is Law of CosineThe law of cosines is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).
In this given problem, triangle DEF can be;
f² = e² + d² - 2(e)(d) cos(F)
But we don't know the length of side d
Using sine law
f / sin F = e / sin E
25 / sin 131 = 8 / sin E
sin E = 8 * sin 131 / 25
E = 13.97°
E = 14°
Using sum of angles in a triangle
D + E + F = 180°
D = 180 - (14 + 131)
D = 180 - 145
D = 35°
Using cosine law;
d² = e² + f² - 2(e)(f)cos(D)
Substituting the values into the formula;
d² = 8² + 25² - 2(8)(25)cos(35)
d = 19
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write an equation of a line that passes through (1,0) and is parallel to 2x+y=-4
The equation of the line that passes through (1, 0) and is parallel to the line 2x + y = -4 is: y = -2x + 2.
How to Write the Equation of Parallel Lines?The equation of a line, in slope-intercept form is y = mx + b, if two lines are parallel to each other, then the value of the slope, m, would be the same for both of them.
Given the equation, 2x + y = -4, rewrite the equation in slope-intercept form to determine the slope (m):
2x + y = -4
y = -2x - 4
The slope (m) is -2.
This means the line that passes through (1, 0) will also have a slope of -2. Substitute m = -2 and (x, y) = (1, 0) into y = mx + b, to find the y-intercept (b) of the line:
0 = -2(1) + b
0 = -2 + b
2 = b
b = 2
To write the equation of the parallel line, substitute m = -2 and b = 2 into y = mx + b:
y = -2x + 2.
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Pls help. I think it's only one answer, but I need help just to make sure two more of the answers are not part of it, since the question says to choose all possible answers. Pls help quickly, I'll mark you Brainliest if it is correct.
Answer:
-5 and -3
Step-by-step explanation:
-2x + 1 > 6
[tex]-2(-\frac{5}{2}) + 1 > 6\\6 > 6[/tex]
Not an answer
-2(-5) + 1 > 6
11 > 6
An answer
-2(-2) + 1 > 6
5 > 6
Not an answer
[tex]-2(-\frac{3}{2}) + 1 > 6\\4 > 6[/tex]
Not an answer
-2(0) + 1 > 6
1 > 6
Not an answer
-2(-3) + 1 > 6
7 > 6
An answer
4. The thickness of a textbook is b mm. Write the expression for each of the following:
The thickness of 5 stacked textbooks?
The thickness of each page, if the pages are numbered to 225?
When the thickness of a textbook is b mm the expressions for:
thickness of 5 stacked textbooks = 5b mm
thickness of each page, if the pages are numbered to 225 = b / 225
How to write the expressions for each conditionThe thickness for each of the condition is written as follows
For the thickness of 5 stacked textbooks
= b + b + b + b + b
= 5b
For thickness of each page, if the pages are numbered to 225
In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book
= b / 225
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A small city has a population of 34000 in 1994. The population growth after 1994 is modeled by the following function where is the number of years after 1994.
P(t)=34000e 0.04t
During what year will the population reach 68000?
[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]
that's about 74 years and 325 days more or less.
based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.
