Answer:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Step-by-step explanation:
Given
[tex]log_3(\frac{21}{5})[/tex]
Required
Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]
[tex]log_3(\frac{21}{5})[/tex]
Express 21 as 7 * 3
[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]
Apply law of logarithm
[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]
[tex]log_3(3) = 1[/tex]. So, we have:
[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]
Rewrite:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
graph the following system of inequalities. y ≤ 1 3 x − 2 x < 4
By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
How to graph a system of inequalities?An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Given the following system of inequalities:
y ≤ 1/3x ⇒ y - 1/3x ≤ 0
y - 2x < 4
By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
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Complete Question:
Graph the following system of inequalities.
y ≤ 1/3x and y - 2x < 4
Evaluate
I don’t know how to type this out so I have the photo
Answer:
3.959797975
Step-by-step explanation:
1. Find the square root of 98 which is 9.899494937
2. Divide 9.899494937 by 2.5 which is 3.959797975
(sorry if it's wrong, but I think it's correct)
i need help with this question, thxs
The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.
RockA rock refers to a solid substance formed from the fusion of organic minerals.
Types of rockSedimentary rock: They are firmed from sediments, that is, dead plant and animals, silt etc.Metamorphic rock: They are firmed from previously existing rocks.Igneous rock: They are formed from the pressure of molten magma.Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.
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What is the equation of the parabola?
coordinate plane with a parabola facing down with vertex at 0 comma 5, the point 0 comma 3 and a horizontal line going through 0 comma 7
y = −one eighthx² + 5
y = one eighthx² + 5
y = one eighthx² − 5
y = −one eighthx² − 5
Option 2. The equation of the parabola is given as y = one eighthx² + 5
How to read the graphWe have the coordinate plane to be passing through the graph at point C on the y axis. This is used to represent the slope.
Hence the slope is 5
The equation of the line is given as y=x²+C
Hence we can see that there is a rising slope. So the answer is Option 2.
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You decide to buy a laptop for $750. You make a down payment of $150 and the company will allow you to pay off the remainder in 12 payments over the next year at 13.5% interest with a finance charge of $25. Make a table of all payments over the next year including the initial down payment and finance charge. Show the difference between paying in cash for the laptop and this financial arrangement. Show all equations and calculations you used. Explain the benefits and downsides of financing your laptop and describe when you would advise someone to finance this kind of purchase. Upload your payment table and answers below.
Total amount paid over the next year including the initial down payment and finance charge = $856
The difference between paying in cash for the laptop and this financial arrangement = $106
Cost of laptop=$750
Down payment=$150
Finance charges = $25
Remaining amount =$600
Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12
=$56.75
Total amount paid over the next year including the initial down payment and finance charge = 56.75*12+150+25 = $ 856
The difference between paying in cash for the laptop and this financial arrangement = $106
Benefits of financing laptop:
A costly laptop can be yours without having to pay in full.
Bank loans and conventional credit card services are not required.
Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.
Downsides of financing laptop:
It's dangerous to borrow money because late payments might result in fees and excessive interest rates.
A credit score may suffer if there is no interest charged.
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The product of two powers is 11^8 and their quotient is 11². What are the two powers? Explain.
Answer:
The powers are 3 and 5.
Step-by-step explanation:
When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:
11^a * 11^b = 11^(a+b)
11^a/ 11^b = 11^(a-b)
So, from the information given:
a + b = 8
a - b = 2 Adding:-
2a = 10
a = 5.
and substituting in the second equation
5 - b = 2
b = 3.
The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4
Provide the next step to derive the quadratic formula.
x squared plus b over a times x minus quantity b over 2 times a all squared equals negative c over a minus quantity b over 2 times a all squared
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
x squared plus b over a times x minus quantity 2 times a over b all squared equals negative c over a minus quantity 2 times a over b all squared
x squared plus b over a times x plus quantity 2 times a over b all squared equals negative c over a plus quantity 2 times a over b all squared
Answer:
[tex]\huge\boxed{\sf Option \ B}[/tex]
Step-by-step explanation:
Step 3:[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)
The next step will be:to find the b² for the expression on the left.How to find b²:Take the expression
[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]
We can also write it as:
[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]
According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,
b² will be:
[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]
So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)
For STEP 4, the equation will become:
[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
The next step is to divide b/a by 2 then square it and add to both sides.
This creates a perfect square quadratic on left side.
So the answer is :
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
The average weight of full-grown beef cows is 1,470 pounds with a standard deviation of 230 pounds. if the weights are normally distributed, what is the percentile rank of a cow that weighs 1,750 pounds? (1) 89th (2) 76th (3) 49th (4) 35th
Answer: The percentile is 89
Step-by-step explanation:
This question can be solved using concept for t tables
In a normal distribution the curve. [tex]\mu= 1470 , \sigma = 230, x=1750[/tex]
The relationship between z score, mean and standard deviation is given by
[tex]x = \mu+z\sigma[/tex]
So the z value according to this is given by the formula
[tex]1750=1470+z(230)\\ z=\frac{280}{230} \\\\z = 1.217[/tex]
From the z table we can infer that p value for z=+1.217 is 88.82
So 1750 is 89th percentile
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2. What is the domain and range of the
graph shown?
-8-64
10-
8-
B
4+
2-
4+
6+
do do t
-10
2 4 6 8 10 12
Answer:
domain: x ≥ 0range: y ≥ 0Step-by-step explanation:
The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.
DomainThe domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).
RangeThe range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).
Robinsons tapestry all measure 1.5m x 1 m. express the tapestries night to width using round numbers and ratio notation
The ratio of the tapestries' height to breadth is 3:2 when using full integers.
CalculationThe ratio of two numbers is used to indicate proportions.
A/b, for example, is the ratio of a to b.
Given the subsequent sides, it is a tapestry.
Height = 1.5 m
Width = 1 m
So, height : width= 1.5:1
or, the fraction = 1.5/1=15/10= 3/2
or, it can be said 3:2
Since entire numbers are used, the ratio of the tapestries' height to breadth is 3:2.
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What is the volume of this rectangular prism?
3/2cm
1/2
4 cm
Answer:
7.62
Step-by-step explanation:
length* width* height = 3/2*1/2*4=7.62 cm
K
Use the commutative law of multiplication to write an
14+ ab
equivalent expression.
....
Applying the commutative law to our question, we have; 14 + ab = ab + 14
How to use the commutative law?The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;
ab + cd = cd + ab
similarly, fg * jk = jk * fg
Applying the above commutative law to our question, we have;
14 + ab = ab + 14
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The following is a 3-step proof. Complete the proof.
Given: 1 = 2
AP = BP
1) [tex]\angle 1=\angle 2[/tex], [tex]AP=BP[/tex] (given)
2) [tex]\angle APD=\angle BPC[/tex] (vertical angles are equal)
3) [tex]\triangle ABD \cong \triangle BAC[/tex] (ASA)
i will mark brainlyist
The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:
Minimum: 6Lower quartile: 8Median: 21.Upper quartile: 27Maximum: 35Interquartile range: 19What are the median and the quartiles of a data-set? How to find the interquartile range using it?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:
Me = (19 + 23)/2 = 21.
The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.
The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.
The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.
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If n is a whole number, and 0.01 is between 1/n and 1/n+2, what is the value of n?
The value of n is 99
Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.
Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.
Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.
W = {0, 1, 2, 3, 4, …}
All natural numbers are integers.
All integers are real numbers.
It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.
1/n+2 < 0.01 < 1/n
1/n+2 < 1/100 < 1/n
n< 100 < n +2
Put n = 99, then we get
99 < 100 < 101
Hence the value of n is 99.
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Aster first walks 70m in the direction of 37degree north of east then walks 82m 20 degree south of east ,and finally walks 28m inthe direction of 30 degree west of north ,find displacement and angle from initial point ?
Answer:
Step-by-step explanation:
The displacement is 90.7 meter from initial point.
According to the statement
Aster first walks 70m in the direction of 37 degree north of east
Aster walks 82m 20 degree south of east
Aster finally walks 28m in the direction of 30 degree west of north
We use
β= 37 degree +(30 degree −20 degree) = 47 degree
We can use cosine law to solve for R.
R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2
R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2
R = (4900 + 784 + 3920*0.682)^1/2
R = (4900 + 784 + 2673.5)^1/2
R = (8357.5)^1/2
R = 90.7 m
So, The displacement is 90.7 meter from initial point.
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I can not factor the denominators on any online calculator so I'm unsure of how to do this. Please help!
Answer: 17/y-5
Step-by-step explanation:
Identify a ray in the following figure. WILL MAKE BRAINLIEST
Answer:
The answer is A
Step-by-step explanation:
Answer:
, a ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction.
Then the answer will the first
On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.
The perimeter of his garden is
meters.
The perimeter of the garden is 46 units.
How to calculate the perimeter?To calculate for the perimeter of the garden, we have to solve for the measures of each of the sides of the four-sided polygon. That is calculated by getting the distances between consecutive points.
The equation for the distance is:
d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)
Distance from G and A,
d = sqrt ((4 - -8)² + (8 - 3)²)
d = 13
Distance from A to R,
d = sqrt ((10 - 4)² + (0 - 8)²)
d = 10
Distance from R to D,
d = sqrt ((-2 - 10)² + (-5 - 0)²
d = 13
Distance from D to G,
d = sqrt ((-8 --2)² + (-5 -3)²)
d = 10
Summing up all the four calculated distances will give us an answer of 46.
Thus, the perimeter of the garden is 46 units.
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Answer: 46 meters.
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
What is the domain of the function shown on the graph?
Answer:
domain {x:x≥-2}or in interval notation [-2,∞)
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]
[tex]c^2 = 169[/tex]
[tex]c = \sqrt{169}[/tex]
c = 13.
Hence AB = 13.
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What is the solution to the equation? 4√x-4 =3
A. -8 B. 16 C. 85 D. no solution
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt[4]{x - 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x - 4 = (3) {}^{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x - 4 = 81[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 81 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 85[/tex]
So, the correct choice is 85
Answer:
Step-by-step explanation:
4√(x-4) = 3
√(x-4) = 3/4
Square both sides:
x - 4 = 9/16
x = 4 + 9/16
x = 4 9/16.
Which expression represents the product of ³ + 2x - 1 and 4 -³ +3?
I7-214-3
1¹+2x+2
1¹2-1⁹ +²+2x³ +6x-3
27-26 +225-3x² + 4x³ + 6x - 3
Don
The expression that gives the product of the polynomials x³ + 2x + 1 and 4x³ + 3 is:
[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]
How do we multiply polynomials?We multiply them applying the distributive property, multiplying all the terms and then combining the like terms.
In this problem, the factors are given as follows:
x³ + 2x + 1,4x³ + 3.Hence the multiplication will be given by:
[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]
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Can you please solve this I need help
Answer:
7k - 7
Step-by-step explanation:
- k - (- 8k + 7) ← distribute parenthesis by - 1
= - k + 8k - 7 ← collect like terms
= 7k - 7
please help with these 3 questions
Answer:
1. D) Both b) and c)
2. B) Cosine Law
3. B) Find the measures of angles and sides that we can't physically measure.
Step-by-step explanation:
1. To solve non-right triangles we use Sine Law and Cosine Law.
2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.
3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.
Some band members have raised much more money than other. which measure can be used to show this?explain.
A ratio measure can be used to show this.
What is a ratio measure?A ratio in mathematics describes how many times one number contains another.The highest (most sophisticated) level of measurement that a variable can have is referred to as a ratio measure.A 3 to 5 ratio (3:5) A 3:5 ratio can be written as 3:5, 3/5, or 3/5. Furthermore, 3 and 5 can represent any number or measurement, including pupils, fruit, weights, heights, speed, and so on. A 3 to 5 ratio simply means that for every three of something, there are five of something else, for a total of eight.Therefore, a ratio measure can be used to show the given situation.
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14. Kathy lives directly east of the park. The football field is directly south of the park. The library (1 point) sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.
Park
Home
9 miles
Library
12 miles
Football field
a. How far is the library from the park?
b. How far is the park from the football field?
6.√3 miles; 6.7 miles
6.7 miles: 6.3 miles
√33 miles. √21 miles
√21 miles, √33 miles
Answer:
(a) 6√3, 6√7
Step-by-step explanation:
The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.
Geometric mean relationsUsing P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...
PF/FH = FL/PF ⇒ PF = √(FH·FL)
PL/FL = HL/PL ⇒ PL = √(FL·HL)
PH/HL = HF/PH ⇒ PH = √(HL·HF)
Application(a) The distance from the park to the library is ...
PL = √(FL·HL) = √(12·9) = 6√3 . . . miles
(b) The distance from the football field to the park is ...
PF = √(FH·FL) = √(21·12) = 6√7 . . . miles
Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.
In the diagram of circle C, what is the measure of ∠1?
17°
35°
70°
71°
The measure of the ∠1 is 35 degrees.
How to determine the angleit is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.
Also, the angle subtended by the arc at the center of the circle is the angle of the arc
From the diagram, we have
m ∠ of external angle = half of the difference of arc angles
The arc angles are
106°36°m ∠ of external angle = ∠ 1
Let's substitute the angles
∠1 = [tex]\frac{106 - 36}{2}[/tex]
∠ 1 = [tex]\frac{70}{2}[/tex]
∠ 1 = 35°
We can see that the external angle 1 measures 35 degrees.
Note that the complete image is added.
Thus, the measure of the ∠1 is 35 degrees.
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What is the expansion of the series
sum from n equals 1 to 4 of 4 to the n plus 1 power
4 + 8 + 12 + 16
4 + 16 + 64 + 256
16 + 64 + 256 + 1,024
16 + 20 + 24 + 28
The expansion of the series is 16 + 64 + 256 + 1024
How to expand the series?The series is given as:
[tex]\sum\limits^4_{n=1} 4^{n+1}[/tex]
When n = 1, we have:
[tex]4^{n+1} = 4^{1+1} = 16[/tex]
[tex]4^{n+1} = 4^{2+1} = 64[/tex]
[tex]4^{n+1} = 4^{3+1} = 256[/tex]
[tex]4^{n+1} = 4^{4+1} = 1024[/tex]
Hence, the expansion of the series is 16 + 64 + 256 + 1024
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Answer:
C). 16 + 64 + 256 + 1,024
Step-by-step explanation:
I took the test and got it right :)
What catergory does -36/12 belong in
Answer:
Improper fraction
Step-by-step explanation:
-36/12 is indeed an improper fraction. An improper fraction is usually a fraction where the numerator is larger than the denominator. Which in order for the fraction to be a "proper" fraction, the fraction has to have a numerator that is smaller than the denominator. Not only is this fraction an improper one, but it can also be heavily reduced (or simplified) by dividing the numerator/denominator by a common factor, which you would still have an improper fraction speaking how the numerator will still be greater than the denominator.
Hope this helps.
Answer:
Proper Fraction
Step-by-step explanation: