9^(2-x) = 3 -> 2-x = 1/2
into details about why it is 1/2 (ill call 2-x as y for easier demonstration)
9^y = 3
(3^2)^y = 3
And we have : (x^m)^n = x^mn
-> (3^2)^y = 3^2y = 3
-> 2y = 1
y = 1/2, therefore 2-x = 1/2.
So, x = 2 - 1/2 = 3/2.
Find the equation of the line that is perpendicular to the line y = 5x+6 and passes through the point (-3 , 3). Write the equation in point slope form.
Please help
(College Algebra)
Equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.
As given in the question,
Equation of the given line :
y = 5x + 6
Slope of the given line m₁ = 5
Required line is perpendicular to the given line
Slope of the required line is m₂ = -5
Required line is passing through the point (x₁ , y₁) = (-3, 3)
Equation of the required line in slope form
y -y₁ = m₂( x -x₁ )
⇒ y - 3 = -5(x - (-3))
⇒ y -3 = -5x -15
⇒ y = -5x -12
Therefore, equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.
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The table represents an absolute value function f(x).
x f(x)
−5 1
−4 0
−3 1
−2 2
−1 3
0 4
1 5
2 6
3 7
What are the vertex and range of the function?
The vertex of the function is (4, 0) and the range of the function is [0, 7]
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the vertex of the function?The table of values represents the given parameter
As a general rule, the vertex of a function is the smallest or the largest value of the function
On the table of values, we have the smallest function value is 0
The corresponding x value is -4
When these values are paired, we have
(x, y) = (4, 0)
This means that the vertex of the function is (4, 0)
How to determine the range of the function?The table of values represents the given parameter
Using the definition of range stated above, we have
Smallest function value = 0
Largest function value = 7
This means that the range of the function is [0, 7]
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a) Give an example of discrete data that might consist of some decimal numbers.
b) Give an example of continuous data that might not have any numbers with fractional parts
Step-by-step explanation:
discretion data is something that will never change
continous data is data that will continue to become either larger or smaller
discret = ticket sales, number of employees
continuous = age,height
HELP
Determine which equation is false based on the solution set. S:{3}
−28 = 2(4p − 4)
5(b + 3) = 30
7 = 3y − 2
1/3 x + 18 = 19
If the solution set S ={3}, then the equation 1 is false
The solution set S = {3}
Equation 1
-28 = 2(4p-4)
4p-4 = -28/2
4p-4 = -14
4p = -14+4
4p = -10
p = -10/4
p = -5/2
This equation is false
Equation 2
5(b+3) = 30
b+3 = 30/5
b+3 = 6
b = 6-3
b = 3
This equation is true
Equation 3
7 = 3y-2
3y = 7+2
3y = 9
y = 9/3
y = 3
This equation is true
Equation 4
(1/3)x+18 = 19
(1/3)x = 19-18
(1/3)x = 1
x = 1 ÷1/3
x = 1×3
x = 3
This equation is true
Hence, If the solution set S ={3}, then the equation 1 is false
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Graph the equation.
y=5|x|-5
Determine Angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
Answer:
C) 180°
Step-by-step explanation:
You want the angle of rotation between triangle ABC and triangle A'B'C' given that the center of rotation is point P.
AngleThe angle of rotation will be the measure of the angle APA'. We see that this angle is a straight angle with a measure of 180°.
The angle of rotation is 180°.
__
Additional comment
Another clue regarding the answer is that 90° CW is equivalent to (and indistinguishable from) 270° CCW, and vice versa. This means each of the other answer choices is repeated, so one is as good as the other. The only possible single answer choice is 180°.
The angle of rotation can always be found this way. Form an angle between a preimage point, the center of rotation, and the corresponding image point. The measure of that angle is the angle of rotation.
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( 4, 2 ) is a solution to the system of equations below: 2x + 4y = 16 ( 1 / 2 ) x − 2y = 4
The system of equations has two solutions, that is (4, 2).
Given,
There is a system of equations:
Equation 1: 2x + 4y = 16
Equation 2: (1/2)x - 2y = 4
The solution to the system of equations = (4, 2)
Lets check for the solution:
The equations are in the form of,
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Here,
a₁ = 2 , a₂ = 1/2
b₁ = 4 , b₂ = 2
c₁ = 16 , c₂ = 4
Now we know that,
a₁/a₂ = b₁/b₂ = c₁/c₂
So,
a₁/a₂ = 2 / (1/2) = 4/1 = 4
b₁/b₂ = 4/2 = 2
c₁/c₂ = 16/4 = 4
Therefore, the system of equations has two solutions, that is (4, 2).
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solve the following equation 18x-3=4x+11
Answer:
Hope this helps
fist add three to both sides
then subtract 4x from both sides
then divide both side with the same factor
20% tip on a bill of $60.53
Answer:
12.106$
Step-by-step explanation:
20/100×60.53
1210.6/100
=12.106
pls pls help whoever gets it right gets marked brainliest
Answer:
option b) 5 units
Answer:
5 units
Step-by-step explanation:
You use Pythagoras' theorem
3squared + 4 squared = 25
square root of 25 is 5
A gate is made out of 7 panels of wood, each in which is 15.7 cm wide. between the panels there is a gap of 14.9 cm how wide is the gate in total and in cm?
Answer:
Total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm
Step-by-step explanation:
GIVEN-
A gate is made out of 7 panels of wood, each of which is 15.7 cm wide. between the panels, there is a gap of 14.9 cm
THIS IS AN EASY SUMMATION PROBLEM-
FOR ONE PANEL WIDTH =15.7
FOR 7 PANEL'S WIDTH =15.7*7=109.9;
NOW, between the 7 panels, 6 gaps create
one gap =14.9 cm
six gap =14.9 * 6 =89.4 cm
so, the total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm
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55=(5x+5) value of x
Answer:
x = 10
Step-by-step explanation:
55 = 5x + 5 Subtract 5 from both sides of the equation
50 = 5x Divide both sides by 5
10 = x
Answer:10
Step-by-step explanation:- 5 on both sides then you get 50=5x 50/5=10
Morgan chewed 3 1/2 sticks of gum every day for 5 consecutive days. How many sticks of gum did he chew in that time?
Ryan has $16 in a savings account. The interest rate is 15% per year and is not compounded. How much will she have in 1 year? Use formula i=p*r*t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years
Answer:
$18.4
Explanation:
At the end of the year, Ryan will have the initial saving plus the interest earned.
So, to calculate the interest earned we will use the given equation:
i = p*r*t
So, replacing p by 16, r by 0.15, and t by 1, we get:
i = 16 x 0.15 x 1
i = 2.4
Then, after 1 year, she will have:
$16 + $2.4 = $18.4
Therefore, the answer is $18.4
Find the slope of the line that passes
through these two points.
Point 1
(-4,6)
X1 Yı
m =
Point 2
(-1,3)
X2 Y2
92-91
X2-X1
m = [?]
The slope of the line is -1.
A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by the symbols y and x, respectively to calculate the slope.The common form for two-variable linear equations is Ax + By = C , where the slope is -A/C.For instance, the linear equation 7x + 3y = 1 uses standard form. Finding an equation's two intercepts (x and y) is fairly straightforward with this procedure, the slope is -7/3 .The cartesian equation for a straight line is Y = mx + c, where m stands for the gradient or slope of the line and c for the point at which it intersects the y-axis.Now the given points are : (-4,6) and (-1,3)
We know that the slope of a line is given by :
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]
Now we can put the values of the points to get the slope as
[tex]m=\frac{3-6}{-1-(-4)}\\\\[/tex]
or , m = -1
Hence the slope of the line is -1
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Write the equation of the line that is parallel to line 3x - 2y = 8 and passes through the point (6, -3). Show ALL steps!
[tex] - 2y = 8 - 3x \\ \frac{ - 2y}{ - 2} = \frac{8}{ - 2} - \frac{3x}{ - 2} \\ y = \frac{3}{2} x - 4[/tex]
PARALLEL LINES HAVE EQUAL GRADIENTS.AS WE SEE IN THE EQUATION ABOVE THE GRADIENT IS
[tex] \frac{3}{2} [/tex]
IT MEANS THE GRADIENT OF THE NEW EQUATION IS ALSO
[tex] \frac{3}{2} [/tex]
NOW GIVEN THE POINTS WE CAN USE THE KNOWNS TO GET THE VALUE OF C IN THE NEW EQUATION.
[tex] - 3 = \frac{3}{2} (6) + c \\ - 3 = 9 + c \\ - 3 - 9 = c \\ c = - 12[/tex]
[tex]y = \frac{3}{2} x - 12[/tex]
Translate this sentence into an equation: "The difference between three-fifths of a number a 7 is –36."
The expression represented by the mathematical sentence is 3/5a - 7 = –36
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?The expression is given as
"The difference between three-fifths of a number and 7 is –36."
Three-fifths of a number a means multiply 3/5 and the number i.e. 3/5 * a
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ The difference between 3/5a and 7 is –36
difference means subtraction
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 is –36
"is" means =
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 = –36
Hence, the expression represented by the difference between three-fifths of a number and 7 is –36 is 3/5a - 7 = –36
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40 POINTS MATCH THEM PLS
What is the expression in factored form? x 2 + 13 x + 42
The expression in factored form for x² 13 x + 42 will be (x + 6)(x + 7).
What is an expression?It should be noted that an expression is simony used in Mathematics to show the relationship between the variables that are expressed.
In this case, the expression in factored form for x² 13 x + 42 will be:
x² + 13x + 42
x² + 6x + 7x + 42
x(x + 6) + 7(x + 6)
(x + 6)(x + 7)
The expression is (x + 6)(x + 7).
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D is the midpoint of EF. ED = 4x + 27, DF = 5x + 21. Find x, ED, DF, and EF
The price of a phone is AED 600. It is discounted by 18%. You also have a 7% discount voucher on the
sale price.
How much will you pay for this phone?
Answer:
You will pay $457.56.
Step-by-step explanation:
600 x .18 = 108 This is the amount taken off
600 - 108 = 492 Now we will take 7% off of 492
492 x .07 = 34.44
492 - 34.44 = 457.56
What is the special angle pair relationship between 1 and 3?
Answer:
These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Angle 1 and angle 3 are on the same side of the two parallel lines with a transversal line on them.
The special angle pair relationship between 1 and 3 is called the corresponding angles.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
We have,
Angle 1 and Angle 3.
The angles are on the same side of the two parallel lines with a transversal line on them.
The angles can be called the corresponding angles.
Thus,
The special angle pair relationship between 1 and 3 is called the corresponding angles.
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In the morning, the temperature in Westfield City was
–
2°F. By afternoon, a north wind caused the temperature to drop another 8°F. What was the afternoon temperature in Westfield City?
To solve the problem, Martin subtracted
–
2–(
–
8) and came up with an answer of 6°F. Is Martin correct? Why or why not?
Martin's answer is wrong. The afternoon temperature in Westfield city is -10°F.
Given,
The temperature in Westfield city in morning = -2°F
The drop down temperature by afternoon = 8°F
We have to find the temperature in afternoon:
Temperature in afternoon = Temperature in morning - Drop down temperature
= -2 - 8 = -10
The afternoon temperature in Westfield city is -10°F
Martin subtracted like:
-2 - (-8) = -2 + 8 = 6
This is wrong.
That is,
We can conclude like:
Martin's answer is wrong. The temperature in Westfield city in afternoon is -10°F
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Using the formula r=d/t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 227.5 miles in 3.5 hours?
Answer: 35 mile/hour
Step-by-step explanation:
[tex]r=\frac{d}{t}[/tex]
∴ [tex]r=\frac{227.5}{3.5}=65[/tex]
= 65 mile/hour
HELP ASAP NEEDS TO BE DONE BY TONIGHT (HELP WITH THE OTHER QUESTIONS TO CLICK MY PROFILE)
Hello!
Let's convert the equation, 3x + 4y = 7, into slope-intercept form:
⇒ slope-intercept form is where the y-variable is isolated to one side
[tex]3x + 4y = 7\\\\4y=-3x + 7\\\\y=-\dfrac{3}{4}x +7[/tex]
The other line that is parallel to the equation: has the same slope
==> thus this other's line slope is -3/4
Let's set up the point-slope form for this other line:
[tex](y-y_0)=m(x-x_0)[/tex]
(x₀,y₀): (-3, -9) <-- any point on the linem: -3/4 <-- slope of line[tex](y+9)=-\dfrac{3}{4} (x+3)\\\\y + 9=-\dfrac{3}{4}x-\dfrac{9}{4} \\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -9\\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -\dfrac{36}{4} \\\\[/tex]
[tex]y = -\dfrac{3}{4}x -\dfrac{45}{4}[/tex] <== Answer
Hope that helps!
Determine which equation is false based on the solution set.
S:{3}
−28 = 2(4p − 4)
5(b + 3) = 30
7 = 3y − 2
one third times x plus 18 equals 19
Based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
As given in the question,
Given solution set S:{3}
Equation which is false based on the solution set
1. −28 = 2(4p − 4)
Divide by 2 from both the sides
⇒ -14 = 4p -4
⇒ p = -10/4 ≠ 3
2. 5(b + 3) = 30
Divide by 5 from both the sides
⇒b + 3 =6
⇒ b = 3
3. 7 = 3y − 2
⇒ 3y = 9
⇒ y = 3
4. One third times x plus 18 equals 19
(1/3)x + 18 = 19
⇒(1/3)x =1
⇒x =3
Therefore, based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
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Select the expression that is equivalent to (3d¹)²
6d6
A
9d8
B
9d6
C
3d8
D
The equivalent expression of (3d^4)² is 9d^8. Option B
What are algebraic expressions?Algebraic expressions are defined as expressions made up of terms, constants, factors, coefficients and variables.
They also consist of some mathematical operations, such as;
AdditionSubtractionMultiplicationParenthesesBracketDivision, etcWhat are equivalent expressions?Equivalent expressions are defined as expressions that have the same solution but usually differ in the arrangement of the values.
Given the expression;
(3d^4)²
Now, let's expand the bracket, we have
(3)²(d)^4×2
Find the squares
9d^8
Thus, the expression is 9d^8
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The complete question:
Select the expression that is equivalent to (3d^4)²
I need help with this question
Let's solve figure by figure
Figure A
This figure has a total of 5 sides, therefore it is a pentagon.
Figure B
This figure has a total of 8 sides, therefore it is an octagon.
Figure C
This figure has a total of 3 sides, therefore it is a triangle.
According to the answer table, it would be
Pentagon: Figure A
Octagon: Figure B
Hexagon: None
Exterior angle, theorem, and triangle sum theorem
Answer:
x = 4
The two interior angles are
14x + 6 = 14 x 4 + 6 = 62°
16x + 4 = 16 x 4 + 4 = 68°
Step-by-step explanation:
The exterior angle of a triangle is the sum of the interior angles:
Here the exterior angle is 130° and the interior angles are
16x + 4 and 14x + 6
So 16x + 4 + 14x + 6 = 130
Gathering like terms and simplifying:
16x + 14x + 4 + 6 = 130
30x + 10 = 130
30x = 120 (subtract 10 from both sides)
x = 4
The two interior angles are
14x + 6 = 14 x 4 + 6 = 62°
16x + 4 = 16 x 4 + 4 = 68°
Which function has a domain of (-1, ∞) and a range of (-∞, ∞)?
O A. f(x) = log₂x - 1
OB. f(x) = log₂ (x-1)
C. f(x) = log₂(x + 1
D f(x) = log₂ x+ 1
The two essential characteristics of functions are domain and range. Function has a domain of (-1, ∞) and a range of (-∞, ∞), f(x) = log₂x - 1.
What is domain and range?Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.
A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger. As a result, range refers to potential outputs, or in this case, soda tastes in machine. Let's discover how to graph and determine domain and range of a given function.
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