If g(x) = x2 + 3, find g(4).
11
19
16
8
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
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]
What is the next number??49,66,83,100 __
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.
Which are the better statistics to use to compare the team scores?27Team A's scoresHO27 29 31 33 35 37 39 41Team B's scoresHhi2931 3335 37 39 4143 4543 45
A. Median and I
1) When we have to face questions like these in which there are two boxplots, we can compare the medians to locate the middle number of each distribution.
Team A's scores' median: 33
Team B's scores' median: 31
2) The next item to check is the dispersion of the data, so we'll resort to the Interquartile Range.
3) Thus, the answer is A
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.
A side of the triangle below has been extended to form an exterior angle of 135°. Find the value of xx.
For the given measures of exterior angle and angles in a triangle , the unknown measure of angle x is equal to 23°.
As given in the question,
In a given triangle,
Measure of exterior angle is equal to 135°
Exterior angle +Adjacent interior angle = 180°
⇒ 135° + Adjacent interior angle = 180°
⇒ Adjacent interior angle = 180° -135°
⇒ Adjacent interior angle = 45°
In a triangle,
Sum of opposite interior angles = Measure of exterior angle
⇒ x° + 112° = 135°
⇒ x° = 135° -112°
⇒ x° = 23°
Therefore, for the given measures of exterior angle and angles in a triangle , the unknown measure of angle x is equal to 23°.
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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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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]Points A,B,C are collinear points where B is between A and C. if AC = 22, AB =10. find BC
ANSWER
[tex]BC=12[/tex]EXPLANATION
First, let us make a sketch of the three points:
As we can see, AC is made up of AB and BC.
This means that the length of AC is the sum of the lengths of AB and BC.
That is:
[tex]\begin{gathered} AC=AB+BC \\ \Rightarrow BC=AC-AB \\ BC=22-10 \\ BC=12 \end{gathered}[/tex]The value of BC is 12.
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
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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y={4x+2, if x < -4 } {2x-6, if x>= -4 }Graph the piecewise function.
For values of x less than -4 , the function is
y= 4x+ 2 ( not including -4)
y=mx+b
Where:
m= slope (rise / run)
b= y-intercep ( where the line crosses the y axis)
For values of x greater or equal to -4, the function is y=2x-6
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.
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.
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.
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.
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
I need to see which ones are translations,dilations,reflections and I forgot the other one
option A and option C are dilation.
Option B and option D are translation.
No reflection.
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)
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:
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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What is the PEMDAS for this question: 1 x 4 + 40 / (6 + 2) + 8 - 8
Solve the inequality. Using a verbal statement, in simplest terms, describe the solution of the inequality. Be sure to include the terms, "greater than", "greater than or equal to", "less than", or "less than or equal to".
Solution:
Given the expression:
[tex]-3<0[/tex]In verbal statement, we can conclude that:
negative three is less than zero.
The third option is the correct answer.
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]2 to the negative fifth power
Answer: 0.03125
Step-by-step explanation:
Answer:
.03125
Step-by-step explanation:
2^-5 = 1 / 2^5 = 1/32 = .03125
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.
James counts down in 9's starting from 345 until he passes zero. Which will be the last
positive number which he counts?
Answer:
3
i worked it out the hard way
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
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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