[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]
What is the next number??49,66,83,100 __
hello I need help understanding a slope and y-intercept math problem I need a tutor that will please allow me to ask for the question so I can better understand what I'm working on thank you
ANSWER
EXPLANATION
Slope is defined as the numerical value that determines the steepness of a line
Mathematically, slope is expressed below as
[tex]\text{ Slope = }\frac{\text{ rise }}{\text{ run}}[/tex]I need help solving this it’s a radical equation I would appreciate the help:0
The given expression is
[tex]\sqrt[]{6x\text{ }}+\text{ 3 = }\sqrt[]{9x\text{ + 19}}[/tex]We would square both sides of the expression. It becomes
[tex]\begin{gathered} (\sqrt[]{6x}+3)^2\text{ = (}\sqrt[]{9x+19)^2} \\ (\sqrt[]{6x}\text{ + 3)(}\sqrt[]{6x}\text{ + 3) = 9x + 19} \\ On\text{ the left, we would multiply each term in both parentheses. } \\ \sqrt[]{6x}\times\sqrt[]{6x}\text{ + 3}\sqrt[]{6x}\text{ + 3}\sqrt[]{6x}\text{ + 3}\times3\text{ = 9x + 19} \\ 6x\text{ + 6}\sqrt[]{6x}\text{ + 9 = 9x + 19} \\ \text{Collecting like terms, we have} \\ 6\sqrt[]{6x}\text{ = 9x - 6x + 19 - 9} \\ 6\sqrt[]{6x}\text{ = 3x + 10} \\ \text{There is still a radical on the left hand side. We would square both sides} \\ of\text{ the equation.} \\ (6\sqrt[]{6x)^2}=(3x+10)^2 \\ 6^2\times6x\text{ = (3x + 10)(3x + 10)} \\ 216x=9x^2\text{ + 30x + 30x + 100} \\ 216x=9x^2+60x\text{ + 100} \\ 9x^2\text{ + 60x - 216x + 100 = 0} \\ 9x^2-\text{ 156x + 100 = 0} \end{gathered}[/tex]We have a quadratic equation. The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing our equation with the quadratic equation, we have
a = 9, b = - 156, c = - 100
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ =}\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ } \\ \text{substituting the given values, } \\ x\text{ = }\frac{-\text{ - 156 }\pm\sqrt[]{(-156)^2^{}-\text{ 4}\times9\text{ x }100}}{2\times9} \\ x\text{ = }\frac{156\text{ }\pm\sqrt[]{24336-\text{ 3600}}}{18} \\ x\text{ = }\frac{156\text{ }\pm\sqrt[]{20736}}{18} \\ x\text{ = }\frac{156\text{ + 144}}{18}\text{ or x = }\frac{156\text{ - 144}}{18} \\ x\text{ = }\frac{300}{18}\text{ or x = }\frac{12}{18} \end{gathered}[/tex]Dividing the numerators and denominators by 6, we have
x = 50/3 or x = 2/3
Courtney ran at a rate of 6.5 miles per hour. At this rate, about how many kilometers can she run in 2 hours? 0 10.5 km O 13 km O 21 km 0 24.8 km
6.5 miles per hour
How many km in 2 hours ?
6.5 miles per hour in two hours would be 2(6.5) = 13 miles
13 miles in kilometers are 13(1.60934) = 20.92142 which is almost 21 Km
Answer:
21 Km
4. It was 12°C when Amelia got home from school
The weather report shows a storm front moving
in that will drop the temperature by 17°C. What
is the expected temperature after the drop?
The expected temperature after the drop is -5°C.
Here, we performed the Subtraction operation on two degrees 17°C and 12°C to get the difference of -5°C.
What is Subtraction?The process of subtracting one number from another is known as Subtraction. It is a basic arithmetic operation that is represented by the subtraction symbol (-) and is used to calculate the difference between two numbers.
We know that,
To find out the expected temperature we have to subtract 17°C from 12°C.
So,
12°C - 17°C = -5°C
Therefore, the expected temperature after the is -5°C.
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For each diagram, write and solve an inequality for x.
7.
2x - 5
X
In given inequality the value of x is 5 < x
What is inequalities ?Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The Pythagorean theorem ?A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
2x - 5 > x
-5 > -x
5 < x
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An amusement park sells hats, T-shirts and stuffed toys. The table on the top gives the number of each type of souvenir sold during a two-week period. The table on the bottom gives the price of each souvenir. Find the total amount spent on souvenirs each week.
Hats
T-shirts
Toys
Week 1
128
240
58
Week 2
130
215
89
Item
Price
Hats
$14
T-Shirts
$18
Toys
$24
a.
Week 1: $426, Week 2: $434
b.
Week 1: $6048, Week 2: $6128
c.
Week 1: $7504, Week 2: $7826
d.
Week 1: $482, Week 2: $480
The total amount spent on souvenirs each week for an amusement park sells hats, T-shirts and stuffed toys is c. Week 1: $7504, Week 2: $7826
How to find the total amount spent each weekAmount of Hats per week
week 1
= 128 * $14
= $1792
Week 2
= 130 * 14
= $1820
amount of T-Shirts per week
week 1
= 240 * $18
= $4320
Week 2
= 215 * 18
= $3870
amount of Toys per week
week 1
= 58 * $24
= $1392
Week 2
= 89 * $24
= $2136
Total amount for week 1
= 1792 + 4320 + 1392
= $7504
Total amount for week 2
= 1820+ 3870+ 2136
= $7826
therefore option c is the correct option
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Your friend has a fish tank that can hold 15 ft of water. Hewants to get a few more fish and now needs a bigger tank. Ifhe wants a tank that is 1.5 times bigger, how much water canwill it hold?
As given by the question
There are given that the fish tank can hold 15 ft water.
Now,
According to the question, he wants a tank that is 1.5 times bigger.
Then,
Suppose the size of the first tank is x,
That means, in the x size of the tank, there are a total of 15 ft of water
Then,
After some time, he increased the size of the tank 1.5 times bigger
That means, the size of the new tank was 1.5x
Then,
[tex]\begin{gathered} x\rightarrow15ft \\ 1.5\rightarrow15\times1.5 \\ =22.5ft \end{gathered}[/tex]Hence, a total of 22.5 ft of water can will it hold in the new tank.
i need help with this
Answer:
18084, 180968Step-by-step explanation:
You want to find the value of x, given that supplementary angles are 83° and (12x+1)°.
Step 1The two angles shown are supplementary, so their sum is 180°:
[tex]83^\circ+(12x+1)^\circ=\boxed{180}^\circ[/tex]
Step 2Simplifying the expression by combining like terms and dividing by °, we have ...
[tex]12x +\boxed{84}=\boxed{180}[/tex]
Step 3Subtracting 84 from both sides gives ...
[tex]12x=\boxed{96}[/tex]
Step 4Dividing both sides by 12, we get ...
[tex]x=\boxed{8}[/tex]
During a sleepover, Jayden played karaoke with her friends. Her song was 5 minutes long. She had already sung for 2 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 5
x + 3 = 5
x − 2 = 5
x + 2 = 7
Answer:
A or #1: x+2=5
Step-by-step explanation:
There is an unknown amount of minutes left to sing, and we already know that she has sung for 2 minutes. so x+2. And we know that she is singing a 5 min. song, so the unknown value plus the 2 minutes we know she has already sung should add up to 5 mins.. So x+2=5 would be the correct answer.
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(-15. **)
Given: The polar coordinate below
[tex](-1.5,\frac{3\pi}{4})[/tex]To Determine: The position of the point given in the circular grid shown
Solution
Note that the each of the circular grid line is 0.5 units apart
The point of the coordinate given is as shown below
It can be observed from the graph above that point is located between the 5th and 6th circular grid as counted from the center (that is between the red and the blue circular grid) above.
Calculus question need help asap
The first derivative of the given function is :
g'(x) = 24x²-24x-288
The second derivative of the function is:
g''(x) = 48x-24
The value of g''(-3) is:
-168
At x=-3 the graph of g(x) is concave down.
At x=-3 there is local maximum.
Given the function is g(x) = 8x³-12x²-288x
The first derivative of the function is:
g'(x) = 8(3)x³⁻¹ - 12(2)x²⁻¹ - 288(1)x¹⁻¹
g'(x) = 24x₂-24x-288
g'(X) = 24(x²-x-12)
Now, the second derivative of the function is :
g'(x) = 24(x²-x-12)
or x²-x-12 = 0
x²-4x+3x-12=0
x(x-4)+3(x-4) = 0
(x-4)(x+3)
x=4 and x=-3
now, g''(x) =24(2)x²⁻¹ - 24(1)x¹⁻° - 12(0)
g''(x) = 48x-24
Now find the local maximum and local minimum.
for x=4
g''(x) = 48x-24
g''(x) = 48(4)-24
g''(x) =168
Since, g''(x)>0 sox=4 is local minimum.
for x=-3
g''(x) = 48x-24
g''(x) = 48(-3)-24
g''(x) = -168
Since, g''(x)<0,so x=-3 is the local maximum.
Hence at x=-3 the graph of g(x) is concave down.
Hence we get the desired results.
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Rewrite (108 +224) using factoring.
A. 2(106 + 112)
B. 4(27 +56)
C. 6(17+6)
D. 12(8+27)
Answer:
B
Step-by-step explanation:
108/4 = 27
224/4 = 56
The other ones don't work if you distribute the outside numbers.
The solution of the expression after factoring is,
⇒ 4 (27 + 56)
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is,
⇒ 108 + 224
Now, We can factor as;
⇒ 108 + 224
⇒ 4 × 27 + 4 × 56
⇒ 4 (27 + 56)
Thus, The solution of the expression after factoring is,
⇒ 4 (27 + 56)
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If g(x) = x2 + 3, find g(4).
11
19
16
8
I need help with math
The general equation is:
[tex]\frac{b^{2k}\cdot b^{3k}}{b^{4k}}=b^k[/tex]In the firs case, b = 5 and k = 1.
[tex]\begin{gathered} \frac{5^{2\cdot1}+5^{3\cdot1}}{5^{4\cdot1}}=5^1 \\ \frac{5^2+5^3}{5^4}=5^{} \end{gathered}[/tex]In the second case, b = 9 and k = 2.
[tex]\begin{gathered} \frac{9^{2\cdot2}+9^{3\cdot2}}{9^{4\cdot2}}=9^2 \\ \frac{9^4+9^6}{9^8}=9^2 \end{gathered}[/tex]In the third case, b = 2 and k = 3.
[tex]\begin{gathered} \frac{2^{2\cdot3}+2^{3\cdot3}}{2^{4\cdot3}}=2^3 \\ \frac{2^6+2^9}{2^{12}}=2^3 \end{gathered}[/tex]In the fourth case, b = 3 and k = 4.
[tex]\begin{gathered} \frac{3^{2\cdot4}+3^{3\cdot4}}{3^{4\cdot4}}=3^4 \\ \frac{3^8+3^{12}}{3^{16}}=3^4 \end{gathered}[/tex]Write each set in the indicated form.If you need to use "..." to indicate a pattern, make sure to list at least four elements of the set.D00....Хc.?(a) Set-builder form: {x | x is an integer and 2 -7}{yly is an integer and –6 Sy=-3}{yly is an integer and -6
Solution
a)
Set builder form:
[tex]\begin{gathered} \lbrace\text{x \mid x is an integer and 2 }\leq\text{ x }\leq\text{ 5 \textbraceright} \\ Roster\text{ form: \textbraceleft2, 3, 4, 5\textbraceright} \end{gathered}[/tex]b)
Roster form: {-6, -5, -4, -3, ...}
[tex]\begin{gathered} \text{Set builder form: \textbraceleft y \mid y is an integer and y >-7\textbraceright} \\ \end{gathered}[/tex]13. DIG DEEPER I am an odd number. When you multiply me by 6, then
divide the product by 3, the quotient is 10. What number am I?
Answer:
Your answer should be 5. 5x6=30, divided by 3 =10
Step-by-step explanation:
-5g - 6 for g = -2
04
O 16
O 10
O-13
Answer: A (4)
Step-by-step explanation: -5 (-2) - 6 = 4
The country of Freedonia has decided to reduce its carbon-dioxide emission by 35\%35%35, percent each year. This year the country emitted 404040 million tons of carbon-dioxide.
The tons of carbon emission for the following year is 26 million tons.
How to calculate the carbon emission?From the information, the country of Freedonia has decided to reduce its carbon-dioxide emission by 35 percent each year and in the year given, the country emitted 40 million tons of carbon-dioxide.
The carbon for the next year will be:
= Total carbon emmision - Reduction in emissions
= 40 million - (35% × 40 million)
= 40 million - 14 million
= 26 million
The complete information is given below.
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Complete question
The country of Freedonia has decided to reduce its carbon-dioxide emission by 35 percent each year. This year the country emitted 40 million tons of carbon-dioxide. What is the carbon emission for the next year.
What is the PEMDAS for this question: 1 x 4 + 40 / (6 + 2) + 8 - 8
Find (f • g) (0) when f(x) = 4x + 7 and g(x) = 1/x.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Given\text{ that:} \\ (f\text{ o g \rparen \lparen x \rparen = f\lparen g\lparen x\rparen\rparen} \\ But\text{ g\lparen x\rparen = }\frac{1}{x} \\ Then,\text{ we have that:} \\ f(\frac{1}{x}) \\ But\text{ f\lparen x\rparen = 4 x + 7} \\ Then\text{ f\lparen}\frac{1}{x})\text{ = 4\lparen}\frac{1}{x})\text{ + 7}_ \\ This\text{ means that: } \end{gathered}[/tex][tex]\begin{gathered} (f\text{ o g\rparen \lparen x\rparen = f\lparen g\lparen x\rparen \rparen = f\lparen}\frac{1}{x})\text{ =4\lparen}\frac{1}{x}\text{ \rparen + 7} \\ Then,\text{ we have that:} \\ (f\text{ o g \rparen \lparen 0 \rparen = 4 \lparen}\frac{1}{0})\text{ + 7 = undefined \lparen OPTION A \rparen} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]undefined\text{ \lparen OPTION A \rparen}[/tex]The Busy Bee store bottles fresh jars of honey at a constant rate. In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey.
Determine the constant of proportionality.
36
12
4
0.08
The constant of proportionality that Busy Bee store bottles of fresh jars of honey is 12 hours.
What is the constant of proportionality?The rate at which the fresh jars of honey is stored increases with time. This means that there is a direct proportional relationship between the jars of honey stored and time.
When there is a direct proportion, the two variables move in the same direction. As time increases, the jars of honey stored increases.
The equation that is used to represent direct proportion is:
y = bx
Where:
y = dependent variable = jars of honey stored b = constant of proportionality x = independent variable = number of hours36 = b3
b = 36 / 3
b = 12 hours
84 = 7b
b = 84 / 7
b = 12 hours
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Answer:
12 hours!
Step-by-step explanation:
Below i will place my work.
36 = b3
b = 36 / 3
b = 12 hours
84 = 7b
b = 84 / 7
b = 12 hours
Therefore your answer is 12 hours!!!!
I know its a late answer, but brainiest is always appreciated if you want!
Thx! (goodluck on your exam)
The square shown is divided into five cells. Starting at any cell, how many paths can be drawn that move only to adjacent cells and that include all five cells?
If we start in the cells in the corner and we can only move to adjacent cells and we have to include all cells, this means that we are going to move 4 times. but we can choose any adjacent cell.
homework question . Some tutor said they couldn’t solve it ?
The points that will apply will be where x>1 and y>7
Relevant points: A, B and E
Consider the following graph of two functions(2) + (-1)Step 2 of 2 Hind/(?) + (-1)Enable Zoom/Pan8(x) = x? - 2 - 1(0) --10Submit Ar
Okay, here we have this:
Considering the provided graph, we are going to perform the requested operation, so we obtain the following:
So to find the values at which the functions are evaluated we will look at the graph to see what value y takes when it is at the given value of x, then we have:
f(2)+g(-1)
=-1+2
=1
Finally we obtain that the requested operation is equal to 1.
What is the slope of this line?
−3/4
3/4
−4/3
I don't know.
The slope of the line is -3/4.
Here there are two points (0,7) and (4,4)
We have to find the slope of the line.
The formula for the slope is:
slope(m) = [tex](y_{2} - y_{1} ) /( x_{2} - x_{1})[/tex]
[tex](x_{1} , y_{1} )[/tex] = (0,7)
([tex]x_{2} , y_{2}[/tex]) = (4,4)
Putting the value we have,
m = (4-7)/ ( 4-0)
= -3/ 4
Therefore the slope of a line is -3/4.
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3. Elena is ordering dried chili peppers and corn husks for her cooking class. Chilipeppers cost $16.95 per pound and com husks cost $6.49 per pound. Elenaspends less than $50 ond pounds of dried chili peppers and h pounds of cornhusks. Here is a graph that represents this situation.Scorn husks (pounds)4682dried chilis (pounds)
SOLUTION
3.a. From the question, we can know that chilli pepper cost $16.95 per pound and corn cost $6.49 per pound, and she has to spend less than $50 on d chilli pepper and h corn,
This means that d represents pepper and h represents the corn, So we have
[tex]\begin{gathered} (16.95\times d)+(6.49\times h)<50 \\ 16.95d+6.49h<50 \end{gathered}[/tex]Hence the inequality that represents this is
[tex]16.95d+6.49h<50[/tex]3.b. Now from the equation, we have that
[tex]\begin{gathered} 16.95d+6.49h<50 \\ so\text{ we will substitute d for 2 and h for 4} \end{gathered}[/tex]If we get less than 50, then the answer is yes. We have
[tex]\begin{gathered} 16.95d+6.49h \\ 16.95(2)+6.49(4) \\ 33.9+25.96 \\ 59.86\text{ } \end{gathered}[/tex]Hence the answer is No because based on our calculation, she will spend $59.86 which is greater than $50.
3.c. We will again substitute 1.5 for d and 3 for h into the equation and see if we get less than 50, we have
[tex]\begin{gathered} 16.95d+6.49h \\ 16.95(1.5)+6.49(3) \\ 25.425+19.47 \\ =44.895 \\ =44.90 \end{gathered}[/tex]Hence the answer is YES because based on our calculation, she will spend $44.90 which is less than $50.
Ciara budgeted $30 per month for entertainment. Movies cost $7 and sports games cost $5.
Let x represent the number of movies she attended in a given month and let y represent the number of sports games she attended in the same month.
What inequality models this problem?
_____x + y ≥ ________
The inequality that models the given problem is:
7x + 5y ≥ 30
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The budgeted amount for the month = $30
Cost of the movie = $7
Cost of sports games = $5
x = represent the number of movies she attended.
y = represents the number of sports games she attended.
The inequality that models the situation above is:
7x + 5y ≥ 30
Thus,
The inequality that models the situation above is:
7x + 5y ≥ 30
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Which function has the greatest y-intercept?Group of answer choicesf(x)g(x)h(x)All three functions have the same y-intercept.
Three functions are given. It is required to find the greatest y-intercept of the three functions.
To do this, find the y-intercept of each function and check which of them has the greatest value.
The given equation for f(x) is:
[tex]f(x)=-3x-5[/tex]Notice that this is a linear function in the slope-intercept form, y=mx+c.
Where m is the slope and c is the y-intercept.
Compare to the given equation; it follows that the y-intercept of f(x) is c=-5.
The y-intercept of f(x) is -5.
The graph of g(x) is given.
Recall that the y-intercept is the point where the graph of a function intersects the y axis.
Hence, the y-intercept of g(x) is -3.
The equation for h(x) is:
[tex]h(x)=2\cos\left(2x-\pi\right)+4[/tex]To find the y-intercept, substitute x=0 into the equation:
[tex]\begin{gathered} h(0)=2\cos\left(2(0)-\pi\right)+4 \\ \Rightarrow h(0)=2\cos\left(0-\pi\right)+4=2\cos(-\pi\rparen+4 \\ \Rightarrow h(0)=2(-1)+4=-2+4=2 \end{gathered}[/tex]Hence, the y-intercept of h(x) is 2.
It follows that h(x) has the greatest y-intercept.
(-26, -11) and (39, 34).
Answer:
Sorry I don't get the question but have a good day!
Step-by-step explanation:
