Answer:
[tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
Step-by-step explanation:
i) [tex]$\log_{nb} x[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
ii) therefore simplifying i) we get
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
iii) Hence the equation is proved.
The price of a movie ticket increased from $25 to $30 What does this mean about the new price?
Choose the correct answer below
O A. The new price is 80% of the old price because 25-30 s 8. or 80%
OB. The new price is 80% of the old price because the price decreases by 20%, which is subtracted from 100%
OC. The new price is 125% of the old price because the price increases by $5, which is multiplied by the original price 5x 25 = 125%
O D. The new price is 20% of the old price because the price increases by 55 and 55 is 20% of $25
OE. The new price is 120% of the old price because the price increases by 20%, which is added to 100%
O F. The new price is 750% of the old price because 25 x 30 = 750
The correct option will the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
What is percent of change?Percent of change is determined by the difference between the two values divided by the orginal one, then multiplied by 100.
i.e. percent of change=(change in value/original value)*100
So according to the asked question,
old value of the shoes=$25
new value of the shoes=$30
change in value=30-25=$5
percent of change=((30-25)/25)*100=20%
hence price increases by 20%.
If the old price is 100 and price increases by 20% then new price will be 120.
So the new price is 120% of the old one.
in another way we can calculate that
old value*x%=new value
⇒old value*x/100=new value
⇒x=new value*100/old value=30*100/25=120%
Therefore the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
Learn more about Percent of change
here: https://brainly.com/question/809966
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A large wedding is organised.
one third if the guests choose beef.
five twelfths choose chicken.
69 of the guests choose vegetarian.
How many guests were at the wedding?
Please help! An angle measuring 3.5 radians is equal to which of the angle measures given below? (Use 3.4 for pi). Check ALL that apply.
A) 630 degrees
B) 200.64 degrees
C) 200 degrees 38'24"
D) 210 degrees
The measure of the angle is;
200.64 degrees ⇒ B
200 degrees 38' 24" ⇒ C
Step-by-step explanation:
To convert the measure of an angle from degrees to radians or from radians to degrees use these rules
If the measure of the angle is x°, then multiply it by [tex]\frac{\pi }{180}[/tex] to find its measure in radiansIf the measure of the angle is x radians, then multiply it by [tex]\frac{180}{\pi }[/tex] to find its measure in degrees∵ The measure of an angle is 3.5 radians
- We need to change its measure to degree, use the 2nd rule
∵ π = 3.14
∴ Its measure in degree = [tex](3.5).(\frac{180}{3.14})[/tex]
∴ Its measure in degree = 200.64°
To find its measure in degree, minutes and seconds, multiply the number before decimal point by 60 to find the number of minutes
∵ 1° = 60'
∵ 0.64 × 60 = 38.4
- That means the number of minutes is 38
∵ 1' = 60"
∵ 0.4 × 60 = 24
- That means the number of seconds is 24
∴ The measure of the angle is 200° 38' 24"
The measure of the angle is;
200.64 degrees
200 degrees 38' 24"
Learn more:
You can learn more about the radians measure in brainly.com/question/12939121
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Can I get a check to see if these are right please?
The domain is all possible values for x.
Here we can see a parabola the goes sideways.
The vertex of the parabola is at (3,-1).
That means the domain is [tex]x\geq 3[/tex]
Think about it this way, is there any point on the parabola that can have a x coordinate of 4?
The range of a function is all possible y values. Is seems that the parabola stretches infinitely up and down, meaning that all values of y are possible.
What is y =x-2
Y=4x+1
Answer:
According to my calculations, the answer is (x, y)= ( -1, -3 ). In other words, x= -1 and y= -3
Step-by-step explanation:
How do the values of the 4s in 64.723 and 9.048 compare? Select from the drop-down menu to correctly complete the statement. The value of the 4 in 64.723 is times the value of the 4 in 9.048. choose 10 100 1,000
Answer:
Dividing 4 × 1 by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100
Step-by-step explanation:
i) the value of 4 in 64.723 is given by 4 × 1 = 4, because 4 is the one's place
ii) the value of 4 in 9.048 is is given by 4 × 0.01 = [tex]\dfrac{4}{100}[/tex] = 0.04, because 4 is in the hundredth's place
iii) the value of 4 in 64.723 is 100 times the value of 4 in 9.048 which we get by dividing 4 × 1 by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100
Answer:
100
Step-by-step explanation:
Odette plants basil from seed and each day measures the height of the plants compared to the soil line. She records her measurements in a scatter plot. Odette calculates the equation of the least squares regression line: Predicted Height = 0.32 • Days in Soil – 1.72 Use the drop-down menus to complete the statements below about what this linear model tells you about the height of a basil plant.
Answer:
The slope of the least squares regression line is:
0.32
The units of the slope of the line are:
centimeters per day.
The slope of the line tells you that for each new day you can predict that a plant's height will increase by about 0.32 centimeters.
The y-intercept of the least square regression line is:
-1.72
The units of the y-intercept of the line are:
centimeters.
The y intercept:
Typical height compared to the soil line.
Step-by-step explanation:
Are 4(3y-2) and 12y-8 equivalent
Answer:
Yes! 4(3y-2)=12y-8
Answer:
yes 4(3y - 2) = (12y - 8)
Step-by-step explanation:
because if you should expand 4(3y - 2) by multiplying each value within the bracket by 4, you will have 12y - 8
Rachel ordered early learning software for her daughter from an online retailer. Each item costs
$7.50, and there is a shipping fee of $7.50 for the entire order.
9. What is the cost of Rachel's order if she buys 7 items?
Answer:
60$
Step-by-step explanation:
Shipping is 7.50 and the 7 items are 52.5 total
The country of Sylvania has decided to reduce the number of its illiterate citizens by 3/5 each year. This year there are 9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today. asking for khan
The function to calculate the number of illiterate people in Sylvania t years from today is P(t) = 9000 * (3/5)^t.
Explanation:To write a function that gives the number of illiterate people in Sylvania, P(t), t years from today, we can use the following formula:
P(t) = 9000 * (3/5)^t
This formula represents the reduction in the number of illiterate people by 3/5 each year. To calculate the number of illiterate people t years from today, we multiply the initial number of illiterate people (9000) by the reduction factor (3/5) raised to the power of t.
Answer: 9000( 1 - 3/5 ) ^t
4 5 6 7 8 9 10
TIME REMAINING
59:55
A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 9), (2, negative 6), (negative 5, 4), (1, 2), (6, 0).
What is the domain of the function shown in the mapping
Answer:
Step-by-step explanation:
(-3,-9) , (2,-6), (-5,4), (1,2), (6,0)
the domain is gonna be ur x values
so the domain of this function is [ -5,-3,1,2,6] <==
** the domain is ur x values and the range is ur y values
Answer: -1
Step-by-step explanation:
i just answered if off of edg.
What is an equation that passes through the points (3,8) and (1,0)
Answer:
y=4x-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(0-8)/(1-3)
m=-8/-2
m=4
y-y1=m(x-x1)
y-8=4(x-3)
y=4x-12+8
y=4x-4
Answer:y - 4x + 4 = 0
Step-by-step explanation: Formula for equation of a line passing through two coordinates is
y - y₁ y₂ - y₁
______ = ______
x - x₁ x₂ - x₁
Therefore, y₂ -y₁
y - y₁ = ____ × ( x - x₁ )
x₂ - x₁
where x₁ =3, y₁ =8, x₂ = 1 and y₂ 0
Now substitute for the value
y - 8 = 0 - 8
______ x ( x - 3 )
1 - 3
Therefore y - 8 = -8/-2 × (x - 3 )
y - 8 = -8/-2 × (x - 3)
y -8 = 4 × (x - 3 )
y - 8 = 4( x - 3 )
y - 8 = 4x - 12, when the brackets are open,
So y = 4x - 12 + 8
y = 4x - 4
Therefore the equation of the line is
y - 4x + 4 = 0
Match each three-dimensional figure to its volume based on the given dimensions. (Assume T = 3.14.)
a right cylinder with radius 4 cm
and height 3 cm
314 cu cm
a cone with radius 5 cm and
height 12 cm
160 cu cm
a pyramid with base area
16 sq cm and height 30 cm
48 cu cm
a pyramid with a square base of
length 3 cm and height 16 cm
150.72 cu cm
A right circular cylinder with radius 4 cm and height 3 cm-150.72 cu cm
A cone with radius 5cm and height 12 cm-314 cu cm
A pyramid with base area 16 sq cm and height 30 cm-160 cu cm
A pyramid with a square base of length 3 cm and height 16 cm-48 cu cm
Explanation
volume of cylinder=[tex]\pi r^2h[/tex][tex]3.14*4^2*3=150.72[/tex] cu cm
volume of cone=[tex]1/3 \pi r^2 h[/tex]=314 cu cm
volume of pyramid=[tex](base area*height)/3=(16*30)/3[/tex]=160 cu cm
volume of pyramid=
=[tex](base area*height)/3\\square base length=3 cm\\base area=a^2 =3^2 =9\\volume=(9*16)/3=48cm^3[/tex]
Solve by elimination. 4x=14-3y 3x-3y=11
Solving by elimination...
4x=14-3y ---> 12x=42-9y
×3
3x-3y=11 ----> 12x-12y=44
×4
12x=42-9y
-(12x-12y=44)
--------------------
12y=-2-9y
21y=-2
y=-2/21
3x-3(-2/21)=11
3x+2/7=11
3x=10 5/7
x=25/7
Answer:
4x=14-3y 3x-3y=11
Step-by-step explanation:
Ronnie's dog eats 1/2 of a pound of food each day. Ronnie has a bag containing 4 1/2 pounds of dog food. How many days will the bag feed Ronnie's dog?
Point A(7, 3) is translated to A prime (16, negative 9). Which rule describes the translation? (x, y) right-arrow (x minus 9, y minus 12) (x, y) right-arrow (x minus 9, y + 12) (x, y) right-arrow (x + 9, y + 12) (x, y) right-arrow (x + 9, y minus 12)
Answer:
[tex](x,y) -----> (x+9,y-12)[/tex]
Step-by-step explanation:
we know that
[tex]A(7, 3) ----> A'(16,-9)[/tex]
The rule of the translation is equal to
[tex](x,y) -----> (x+a,y+b)[/tex]
Find the values of a and b
[tex](7,3) -----> (7+a,3+b)[/tex]
we have that
[tex]7+a=16[/tex] ----> [tex]a=16-7=9[/tex]
[tex]3+b=-9[/tex] ---->[tex]b=-9-3=-12[/tex]
substitute the values of a and b
[tex](x,y) -----> (x+9,y-12)[/tex]
That means----> The translation is 9 units right and 12 units down
Answer:
Option D:
(x, y) -> (x + 9, y minus 12)
Step-by-step explanation: Honestly all people want are the answers so I don't really care to write an explanation.
Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.
What is the greatest possible whole-number length of the unknown side?
The greatest whole possible whole number length of the unknown side is 9 inches
Solution:
Two sides of an acute triangle measure 5 inches and 8 inches
The length of the longest side is unknown
We have to find the length of unknown side
The longest side of any triangle is a hypotenuse
For a acute triangle we know:
If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition that relates these three sides are given as:
[tex]c^2<a^2+b^2[/tex]
Here in this sum,
a = 5 inches
b = 8 inches
c = ?
Substituting we get,
[tex]c^2< 5^2+8^2\\\\c^2 < 25 + 64\\\\c^2 < 89\\\\c < 9.4[/tex]
On rounding to nearest whole number,
c < 9
Hence, to the greatest whole possible whole number length of the unknown side is 9 inches
Answer:
The greatest whole possible whole number length of the unknown side is 9 inches
Step-by-step explanation:
Changing all of the values in a data set in the same way is called transmitting
the data.
O A. True
O B. False
Answer:
It’s FALSE
Step-by-step explanation:
Next in sequence 3, 9, 27, _?
Answer: +81
Explanation: To find the next term in the pattern, begin by studying the pattern. Here, notice that 3 x 3 is equal to 9 and 9 x 3 is equal to 27.
Continuing the same pattern, 27 x 3 is equal to 81.
So the next term in the pattern is +81.
A student is asked to find the sum of 197+413 which expression can the student use to find the answer?
addition (+) expression the students used to find the answer.
Solution:
Given data: A student is asked to find the sum of 197 and 413.
Sum means adding two numbers or variables.
For addition, we use + symbol to add two numbers.
First add last digit of the numbers (7+3) = 10.
Put 0 in last and carry 1 to the next left digit top.
Add middle digits with carry over 1 (1 + 9 + 1) = 11
Put 1 and carry another 1 to the next left digit top.
Add first digit of the numbers with carry over 1 (1 + 1 + 4) = 6
Sum of 197 + 413 = 197 + 413
= 610
The addition image attached below.
Hence, addition (+) expression the students used to find the answer.
52 is 0.4% of what number?
HELP!!! 12 points
1. In the figure, KJ and KL are opposite rays. <1 = <2 and KM bisects
2. Measure the angle and classify it as right, acute, or obtuse.
Answer:
1. m∠MKN = 41°
Step-by-step explanation:
1.
KM bisects so NKM and MKL are equal
2 (3x + 5) + 8x + 2 = 180 (straight angle)
6x + 10 + 8x + 2 = 180
6x + 8x = 180 - 10 - 2
14x = 168
x = 168/14
x = 12
3*12+5 = 41
m MKN = 41
Consider the following piece-wise function. Which of the below correctly describes the graph shown?
Answer:
C
Step-by-step explanation:
The function is formed of 2 straight lines
The equation of a straight line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate the slope using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line
m = [tex]\frac{-2+5}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 for x < 2 ( arrow on line points left )
Repeat
with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line
m = [tex]\frac{1+2}{3-2}[/tex] = [tex]\frac{3}{1}[/tex] = 3, thus
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 1), then
1 = 9 + c ⇒ c = 1 - 9 = - 8
y = 3x - 8 for x ≥ 2 ( arrow on line points right )
Solve y=4x+8x for x
Answer:
x = y/12
Step-by-step explanation:
The vertical change between 2 points.
Answer:
what does it look like we need that
Step-by-step explanation:
Answer:
Rise
Step-by-step explanation:
The vertical change between two points is called the rise, and the horizontal change is called the run. Just think of the rise as your going up from the bottom to the top. And run as if you were just going from one side to the other.
A middle class family with two working parent receives $100,000 annually. About 40% is withheld (taken out of their paycheck for income tax and retirement plan). What is this family monthly income after the 40% is taken off?
Answer:
$60,000
Step-by-step explanation:
100,000 / 10 = 10,000, 10- 4=6, 10,000 * 6 = 60,000
To determine the monthly income of a family after 40% is withheld from a $100,000 annual income, subtract the amount withheld ($40,000) from the annual income and divide by 12, yielding a monthly income of $5,000.
To calculate the monthly income after taxes for the family, we first need to determine the amount withheld from the annual income for taxes and retirement plans. With an annual income of $100,000 and 40% being withheld, we do the following calculation:
Amount withheld: $100,000 times 0.40 = $40,000After-tax annual income: $100,000 - $40,000 = $60,000Monthly income after tax: $60,000 / 12 months = $5,000Therefore, the family's monthly income after the 40% is taken off would be $5,000.
A cone with a radius of 6 cm and a height of 8 cm has the same volume as a cylinder with a height of 6 cm. What is the radius
of the cylinder?
A)4 cm
B)4 cm
C)6 cm
D) 8 cm
Answer:
The radius of the cylinder is 4 cm.
Step-by-step explanation:
Given:
radius of cone = 6 cm
height of the cone = 8 cm
height of cylinder = 6 cm
We need to find the radius of cylinder.
Solution:
First we will find the volume of cone.
Volume of cone is one third time square of radius times height times π.
framing in equation form we get;
Volume of cone = [tex]\frac{1}{3}\pi r^2h = \frac{1}{3}\pi\times 6^2\times 8 \approx 301.44 \ cm^3[/tex]
Now Volume of cylinder is given by square of radius times height times π.
framing in equation form we get;
Volume of cylinder = [tex]\pi r^2h=18.84r^2[/tex]
Now it has been given that;
Volume of cone is equal to Volume of cylinder.
so we can say that
[tex]18.84r^2=301.44[/tex]
Dividing both side by 18.84 we get;
[tex]\frac{18.84r^2}{18.84}=\frac{301.84}{18.84}\\\\r^2\approx16[/tex]
Taking square root on both side we get;
[tex]\sqrt{r^2}=\sqrt{16} \\\\r=4\ cm[/tex]
Hence the radius of the cylinder is 4 cm.
In AABC, mZA=x, mZB = 2x +2, and
m_C= 3x +4. What is the value of x?
1) 29
2) 31
3) 59
4 61
Answer:
x = 29
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
x + 2x + 2 + 3x + 4 = 180, that is
6x + 6 = 180 ( subtract 6 from both sides )
6x = 174 ( divide both sides by 6 )
x = 29
I need help please and thank you
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”
Answer:
1. Translation 5 units to the left and 1 unit down
2. Reflection across the x-axis
Step-by-step explanation:
Triangle XYZ has its vertices at points X(-6,2), Y(-4,7) and Z(-2,2).
1. Translate triangle XYZ 5 units to the left and 1 unit down. This translation has the rule:
[tex](x,y)\rightarrow (x-5,y-1)[/tex]
Then
[tex]X(-6,2)\rightarrow X'(-11,1);[/tex]
[tex]Y(-4,7)\rightarrow Y'(-9,6);[/tex]
[tex]Z(-2,2)\rightarrow Z'(-7,1).[/tex]
2. Reflect triangle X'Y'Z' across the x-axis. This reflection has the rule:
[tex](x,y)\rightarrow (x,-y)[/tex]
Then
[tex]X'(-11,1)\rightarrow X''(-11,-1);[/tex]
[tex]Y'(-9,6)\rightarrow Y''(-9,-6);[/tex]
[tex]Z'(-7,1)\rightarrow Z''(-7,-1)[/tex]
These points are exactly the vertices of the triangle X''Y''Z''.
The sequence of transformations is translation, rotation, reflection, and dilation.
Explanation:The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is:
Translation: Move the triangle in a linear direction without rotating it.
Rotation: Rotate the triangle about a fixed point or axis.
Reflection: Mirror the triangle across a line known as the axis of reflection.
Dilation: Increase or decrease the size of the triangle while preserving its shape.
By applying these transformations in the specified sequence, triangle XYZ can be mapped onto triangle X"Y"Z".