solving absolute value inequalities[tex]8 - 9 |6x - 10| \ \textgreater \ - 82[/tex]please help with steps, I keep getting stuck on this one
For (1):
[tex]\begin{gathered} 6x-10<82 \\ \text{Add 10 to both sides:} \\ 6x<82+10 \\ 6x<92 \\ \text{Divide both sides by 6:} \\ x<\frac{92}{6} \\ x<\frac{46}{3} \\ \end{gathered}[/tex]For (2):
[tex]\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-\frac{72}{6} \\ x>-12 \end{gathered}[/tex]Therefore, the solution is:
[tex]-12Need help with a precalc question
Given that
The equation is
[tex][/tex]Find the radius of a circle on which a central angle measuring 5π/6 radians intercepts an arc on the circle with a length of 35π centimeters.A. 42 cmB. 37 cmC. 61 cmD. 44 cm
Solution:
the arc lenght s, of a circle of radius r, with central angle θ, is given by the following equation:
[tex]s\text{ = }r\theta[/tex]solving for r, we get the following equation:
[tex]r\text{ = }\frac{s}{\theta}[/tex]now, replacing in the previous equation the data given in the problem we get:
[tex]r\text{ = }\frac{s}{\theta}\text{ = }\frac{35\pi}{5\pi\text{ / 6}}\text{ = }\frac{(35\text{ }\pi)\text{ 6 }}{5\pi}\text{ = 42 }[/tex]so that, we can conclude that the correct answer is:
[tex]42\text{ cm}[/tex]5 1 point A high rise apartment is on fire. 1 There are two people in a window that is 14.5 feet above the What angie must the ladder make with the ground in order to 2 Type your answer... 3 4
Detrmine the angle of ladder by uisng the trigonometric ratio.
[tex]\begin{gathered} \sin \alpha=\frac{14.5}{22} \\ \alpha=\sin ^{-1}(0.66) \\ =41.29 \\ \approx41^{\circ} \end{gathered}[/tex]So answer is 41 degree.
Which line represents the best fit for the scatter plot data?
A line of best fit can be roughly determined by drawing a straight line on a scatter plot so that the number of points above and below the line is about equal and the line passes through as many points as possible.
When we look at the fits in B and C, we notice that the line is not following the behavior of the data accurately, so we can rule out these options.
When we look at option D, we can see that the line is above all the points, we can also notice that this line doesn't go through any point of the data, that's why option A, is the best fit for this set of data, since it passes through some points and there are points above and below the line.
The correct graph is A
Summer earns 15% commission onsales for a software company. If inone week she makes three sales.one at $375, one at $1.200, and oneat $900. how much did Summerearn that week?
She made
[tex]375+1200+900=2475[/tex]in sales. Then, she earned
[tex]0.15(2475)=371.25[/tex]$371.25 that week.
what is the distance between points A(3,12) and B(6,15)? round to the nearest whole number
The distance between two points is given by:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then, in our case, we have:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(6-3)^2+(15-12)^2} \\ =\sqrt[]{(3)^2+(3)^2} \\ =\sqrt[]{9+9} \\ =\sqrt[]{18} \\ =4.2426 \end{gathered}[/tex]Therefore the distance between the points (rounded to the nearest whole number) is 4.
brainstorm some real-world applications where integration could be helpful, then describe your examples and explain how integration fits in
Given
Integration
Find
some real-world applications where integration could be helpful
Explanation
In real life , integrations are used in vaarious fields such as engineering , where engineers use integrals to find the slope of the building
In physics , it is used in the centre of gravity .
In field of graphical representation , where three- dimensional models are demonstrated.
Final Answer
Hence , above are the some real world applications.
How many solutions does the following system of equation have y = 2 x + 22y = 4x + 4
How many solutions does the following system of equation have
y = 2 x + 2
2y = 4x + 4
The answer is : Infinitely many solutions ( because they lie on each other ).
Which equations of the three lines are parallel, perpendicular, or neither?
The given lines are
[tex]6x-4y=8;y=\frac{3}{2}x+6;2y=3x+5[/tex]Convert each equation in the form
[tex]y=mx+c_{}[/tex]Therefore it follows:
[tex]\begin{gathered} 6x-4y=8\Rightarrow y=\frac{3}{2}x+2 \\ y=\frac{3}{2}x+6\Rightarrow y=\frac{3}{2}x+6 \\ 2y=3x+5\Rightarrow y=\frac{3}{2}x+\frac{5}{2} \end{gathered}[/tex]Therefore the slopes of all three lines are:
[tex]\begin{gathered} m_1=\frac{3}{2} \\ m_2=\frac{3}{2} \\ m_3=\frac{3}{2} \end{gathered}[/tex]The slopes of all three lines are equal therefore all three lines are parallel with each other.
Therefore it follows that:
[tex]l_1\parallel l_2\parallel l_3[/tex]Find the midpoint of AC.B (0, a)C (a, a)D (a,0)a(4)2A (0,0)Enter the value thatbelongs in the green box.Midpoint Formula: M = (*¹*²₁¹²)RE
The formula to calculate the midpoint between two points is given by
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]we have the coordinates
A(0,0) and C(a,a)
substitute the given coordinates
[tex]\begin{gathered} M=(\frac{0+a}{2},\frac{0+a}{2}) \\ \\ M=(\frac{a}{2},\frac{a}{2}) \end{gathered}[/tex]Solve the equation.56 = 13 + d
ANSWER
d = 43
EXPLANATION
We want to solve the equation for d.
The given equation is:
56 = 13 + d
To solve it, we collect like terms and simplify. That is:
56 - 13 = d
=> d = 43
That is the solution.
what is 4 2/3 + 7/9 as a fraction
The calculation is
[tex]4\cdot\frac{2}{3}+\frac{7}{9}[/tex]First step is to solve the multiplication.
4 means that there are four wholes, if you express in in thirds
[tex]\begin{gathered} 1\text{whole}=\frac{3}{3} \\ 4\text{wholes}=\frac{3\cdot4}{3}=\frac{12}{3} \end{gathered}[/tex]Then the multiplication you have to do is
[tex]\frac{12}{3}\cdot\frac{2}{3}=\frac{8}{3}[/tex]Now that the multiplication is done add 7/9
[tex]\frac{8}{3}+\frac{7}{9}=\frac{31}{9}[/tex]Consider the function.f(x) = x2 − 1, x ≥ 1
t Given
[tex]f(x)=\sqrt{x^2-1}[/tex]Find
inverse of f(x)
domain and range of function and its inverse
Explanation
Let y = f(x)
[tex]y=\sqrt{x^2-1}[/tex]replace all x with y and y with x
[tex]x=\sqrt{y^2-1}[/tex]now solve for y
[tex]\begin{gathered} \sqrt{y^2-1}=x \\ y^2-1=x^2 \\ y^2=x^2+1 \\ y=\pm\sqrt{x^2+1} \end{gathered}[/tex]so, the inverse is
[tex]\pm\sqrt{x^2+1}[/tex]domain of f(x) is
[tex]x\epsilon R:x\leq-1\text{ or x}\ge1[/tex]range of f(x) is
[tex]y\epsilon R:y\ge0[/tex]domain of inverse is
[tex]R[/tex]range of inverse function is
[tex]y\epsilon R:y\ge1[/tex]What lengths are possible for pieces cut from the 27-cm piece of string? Select all that apply. A. 2 cm B. 7 cm C. 5 cm D. 3 cm E. 9 cm F. 27 cm G. 18 cm H. 1 cm
Answer:
D, E, F, and H
Step-by-step explanation:
D. 27/3=9
E. 27/9=3
F. 27/27=1
H. 27/1=27
Answer: D,E,F, and H
Step-by-step explanation:
1, 3, 9, and 27 are the multiples of 27 itself
It can’t be 2 because it’s not an even number
It can’t be 7 because the closest number that is a multiple of 7 is 28 and it’s one over
It can’t be 5 because it doesn’t end in 5 or 0
it can’t be 18 because 18 + 18 equals 36 and that is 9 over the original number
I will make seafood salad using strawberries and blueberries he uses 5 cups of strawberries for every 3 cups of blueberries which measure represents the amount of strawberries Alan uses for every bowl of fruit salad
His salad calls for 8 cups of salad to maintain the given ratio. (5 cups of strawberries for every 3 cups of blueberries) So the ratio is 5/8 for the strawberries.
Let x be what he needs for 1 cup of fruit
5/8 = x
That's because there are 5 cups of strawberries for every 8 ( 5 strawberries + 3 blueberries ) items he needs.
I will be attaching a picture of the question as you can see the question has already been answered my teacher wants me to type out how she got the answer I need it fast bc this is due in an hour.
we calculate the radius, i.e. the distance between two points
[tex]\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ r=\sqrt[]{(-1-2)^2+(-8-(-3))^2} \\ r=\sqrt[]{(-3)^2+(-8+3)^2} \\ r=\sqrt[]{(-3)^2+(-5)^2} \\ r=\sqrt[]{9+25} \\ r=\sqrt[]{34} \end{gathered}[/tex]then, we have that the equation of the circle is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where} \\ h=2 \\ k=-3 \\ r^2=(\sqrt[]{34})^2=34 \end{gathered}[/tex]therefore the equation is
[tex]\begin{gathered} (x-2)^2+(y-(-3))^2=34 \\ (x-2)^2+(y+3)^2=34 \end{gathered}[/tex]What is the linear equation ( slope intercept equation ) for the line that passes through points (0,4) and (2,8) ?
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
Consideing the given points,
x1 = 0, y1 = 4
x2 = 2, y2 = 8
m = (8 - 4)/(2 - 0) = 4/2
m = 2
We would find the y intercept, c by substituting m = 2, x = 0 and y = 4 into the slope intercept equation. It becomes
4 = 2 * 0 + c
c = 4
Substituting m = 2 and c = 4 into the slope intercept equation, it becomes
y = 2x + 4
The last option is correct
Which measurement is the best estimate for the volume of the figure? Roundeach measurement to the nearest whole number to get your estimate.A. 9 cubic metersB. 12 cubic metersC. 6 cubic metersD. 8 cubic meters
we have that
The volume of the rectangular prism is given by
[tex]V=L*W*H[/tex]where
L=3.5 m --------> 4 m
W=0.7 m -------> 1 m
H=2.2 m -------> 2 m
substitute
[tex]\begin{gathered} V=(4)(1)(2) \\ V=8\text{ m}^3 \end{gathered}[/tex]The answer is option DWhat is the value of x in the solution to this system of equations? 3x-5 y=22 y=-5x+ 32
The value of x in the system of equations is 6.5
The system of equation:
3x - 5y = 22
y = -5x + 22
Now arrange the above equation in proper order :
As,
3x - 5y = 22
5x + y = 22
Now solve the above equation as:
(3x - 5y = 22) x 1
(5x + y = 22) x 5
We have:
3x - 5y = 22
25x + 5y = 110
On solving above equation by elimination :
28x = 132
x = 6.5
Hence, the value of x in the system of equations is 6.5
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Find a recursive rule for the nth term of the sequence.7, 28, 112, 448, ...
Solution
Given the sequence 7, 28, 112, 448, ...
The sequence is a Geometric sequence because it has a common ratio
[tex]Common\text{ ratio, r = }\frac{28}{7}=4[/tex]First term, a = 4
[tex]\begin{gathered} The\text{ nth term of a gp = ar}^{n-1} \\ Where\text{ n=number of terms} \\ a=\text{ first term } \\ r=common\text{ ratio} \end{gathered}[/tex][tex]T_n=7\text{ \lparen4\rparen}^{n-1}[/tex][tex]\begin{gathered} For\text{ recursive, } \\ T_n=r.T_{n-1} \\ T_n=4(T_{n-1}) \end{gathered}[/tex][tex]The\text{ recursive rule is 4\lparen T}_{n-1})[/tex]Determine the scale factor of the dilation. Write your answer as a fraction if necessary.
The scale factor of the dilation is 1.5
Here, we want to determine the scale factor of the dialtion
From what we can see, we have the smaller, being moved to the bigger and thus, we expect a scale factor higher than 1
We can work with any of the side lengths to determine the scale factor
Let us look at the base
For the smaller shape, we have a length from (1,-2) to (-2,-2)
For the bigger shape, we have a length from (1.5,-3) to (-3,-3)
Calculating these distances, we have a unit of 3 units in the smaller and a unit of 4.5 units in the bigger
So, we have the scale factor as;
[tex]\frac{4.5}{3}\text{ = 1.5}[/tex]Find the slope from the tableA. 3B. 2C. -3D. -1
Use 2 of the given ordered pairs to find the slope of the function. Use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where y2 and y1 are the y coordinates of the ordered pairs and x2 and x1 are the x coordinates. Replace for the given values:
[tex]m=\frac{2-5}{-2-(-3)}=-\frac{3}{1}=-3[/tex]The slope of the function is -3.
find the coordinates of the ordered pair where the maximum value occurs for equation P equals 5 x + 5y + 42 given these constrains
Given the equation:
[tex]P=5x+5y+42[/tex]Given the constraints:
[tex]\begin{gathered} -2x+4y\ge-4 \\ x\ge-8 \\ y\le9 \end{gathered}[/tex]Let's find the ordered pair where the maximum value occurs for P.
From the inequality of let's solve for x and y.
At x = -8:
[tex]\begin{gathered} -2x+4y=-4 \\ -2(-8)+4y=-4 \\ \\ 16+4y=-4 \\ \\ \text{Subtract 16 from both sides:} \\ 16-16+4y=-4-16 \\ 4y=-20 \\ \\ \text{Divide both sides by 4:} \\ \frac{4y}{4}=\frac{-20}{4} \\ \\ y=-5 \\ \\ \text{Thus, we have the points:} \\ (x,y)\Longrightarrow(8,-5) \end{gathered}[/tex]At y = 9:
[tex]\begin{gathered} -2x+4y=-4 \\ -2x+4(9)=-4 \\ -2x+36=-4 \\ \\ \text{Subtract 36 from both sides:} \\ -2x+36-36=-4-36 \\ -2x=-40 \\ \\ \text{Divide both sides by -2:} \\ \frac{-2x}{-2}=\frac{-40}{-2} \\ \\ x=20 \\ \\ \text{thus, we have the point:} \\ (x,y)\Longrightarrow(20,9) \end{gathered}[/tex]Input the values of x and y into the equation and solve for evaluate for P.
• (x, y) ==> (-8, -5):
P = 5x + 5y + 42
P = 5(-8) + 5(-5) + 42
P = -40 - 25 + 42
P = -23
• (x, y) ==> (20, 9):
P = 5x + 5y + 42
P = 5(20) + 5(9) + 42
P = 100 + 45 + 42
P = 187
We can see the maximum value of P is 187 at (20, 9)
The maximum value occurs at (20, 9)
• ANSWER:
(20, 9)
Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)O A. y - (x - 1)(x+5)OB. y - (x + 1)(x+5)O C. y - (x + 1)(x - 5)O D. y = (x - 1)(x-5)
The graph of the function intersect the x-axis at x = 1 and x = 5. So zeos of the function is,
[tex]x=1\text{ and x = 5}[/tex]So factorization quation of polynomial equation is,
[tex]y=(x-1)(x-5)[/tex]Answer: y = (x - 1)(x - 5)
3. If the function below (left) has a reflection about the "Y-AXIS", its new functionwould be below (right). *y=√xy = – VĩO TrueO FalseOther:
The graph for the original function y=√x is:
And the graph for the new function y=-√x
As we can see, the reflection is about the x-axis, not the y-axis.
So, the Answer is FALSE.
The perfect squares between 54 and 102.
The perfect squares are between 54 and 102.
54 and 102 are taken,
7 × 7 = 49
8 × 8 = 64
9 × 9 = 81
10 × 10 = 100
11 × 11 = 121
Here, the perfect squares between 54 and 102 are 8, 9, 10.
So, answer is 8 × 8, 9 × 9, 10 × 10
Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs. Find the kinetic energy for a mass of 4 grams and a velocity of 6 centimeters per second.
72 ergs
Explanation
Step 1
Kinetic energy varies jointly as the mass and the square of the velocity,then
[tex]E_k=\lambda\cdot m\cdot v^2[/tex]where
m is the mass, v is the velocity and
[tex]\lambda\text{ is a constant}[/tex]A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs
[tex]\begin{gathered} E_k=\lambda m\cdot v^2 \\ 36\text{ erg=}\lambda\cdot8\cdot3^2 \\ 36=\lambda\cdot8\cdot9 \\ 36=\lambda\cdot72 \\ \text{divide both sides by 72} \\ \frac{36}{72}=\lambda \\ \lambda=\frac{1}{2} \end{gathered}[/tex]so, the equation is
[tex]\begin{gathered} E_k=\lambda\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot m\cdot v^2 \end{gathered}[/tex]Step 2
now , we know the equation to find the kinetic energy of a object if we know its mass and its velocity
Let
mass= 4 grams
velocity = 6 cms per sec
then
[tex]\begin{gathered} E_k=\frac{1}{2}\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot(6\frac{\operatorname{cm}}{\sec})^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot36\frac{\operatorname{cm}}{\sec ^2} \\ E_k=72\text{ erg} \end{gathered}[/tex]I hope this helps you
Which equation shows that the Pythagorean identity is true for 0 = 0?
Charnaie owns her own tutoring service. She charges new clients $20 for a placement test and then $10 per hour for every hour of tutoring.
Drag and drop the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
What is the independent variable in this real-world situation? Explain your reasoning.
The independent variable is the Response area because Response area.
What is the dependent variable in the real-world situation? Explain your reasoning.
The dependent variable is the Response area because Response area.
The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She charges new clients $20 for a placement test and $10 per hour for every hour of tutoring.
Now,
Let total cost of charge = T
And, Number of hours = h
So, We can formulate by the given condition as;
⇒ T = $20 + $10h
Thus, The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
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