Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.
Define log(Logarithm).The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
What is a function?A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).
Given the equation 17v = 62, we can take the logarithm base 17 of both sides:
log(17^v) = log(62)
v*log(17) = log(62)
Dividing both sides by log(17) gives us:
v = log(62) / log(17)
This is the solution for v, the unknown variable in the equation.
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Calculate the sector area: 16 in 90°
Therefore , the solution of the given problem of area comes out to be
r = 8.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Here,
A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as
Sector Size/Sector Area = Circle Area/360
16 ft2/90 = n/360
(360) (16 ft2)/90 = n
(4)(16 ft2) = n
The total size of the circle is n = 64 ft2.
Since Area of a Circle equals r2,
∏r2 = 64
r2 = 64/∏
r = √(64/∏)
We multiply by / to get by rationalizing the denominator.
r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of
r = √(64∏)/∏
r = 8
Therefore , the solution of the given problem of area comes out to be
r = 8.
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APQR is dilated from the origin at a scale factor of to create APQ'R'.
2
Select the option that completes the statement:
The triangles are
because their corresponding sides are
O congruent, similar, proportional
O congruent, proportional; similar
O similar, congruent; proportional
Osimilar, proportional; congruent
and their corresponding angles are
Below are graphs of several functions. Which functions have the specified
domain and range? There may be more than one correct answer.
Domain: (x | x ≥ 3/2)
Range: (-00, 2)
Note: Be sure to select ALL correct answers.
B
For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.
What do you mean by function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
What are domain and range of the function?A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.
domain : (x | x [tex]\geq[/tex] 3/2)
range : (-∞ , 2)
For these values, Option B , C and E holds that they exists when x [tex]\geq[/tex] 3/2 and it's output that is y exists between (-∞ , 2).
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Identify two angles that are marked congruent to each other on the diagram
below. (Diagram is not to scale.)
Answers:
TSO for the first boxQRP for the second boxExplanation:
The angles TSO and QRP are marked with the same double angle arc markers. This signifies they are congruent or the same measure. For example, they both could be 30 degrees each.
The naming "angle TSO" is the same as saying "angle OST". The order of the letters does not matter as long as point S is in the middle. Similarly, saying "angle QRP" is the same as "angle PRQ".
160.7 is what percent of 128?
Answer:
125.54%
Step-by-step explanation:
160.7/128 = 1.2554
1.2554 *100 = 125.54%
A deck of cards ..something I don't get ..Please help
=======================================================
Explanation:
I'm assuming your teacher meant to say "same number or letter" instead of "same number of letter" at the very end of the problem.
The best case scenario is that the person selecting the cards is very lucky to select say a king of hearts and king of clubs. This shows that 2 cards is the lowest amount of cards to select here.
----------
Of course, such a scenario is not that likely. That person is likely to get some other card compared to the 1st selection.
Let's assume the person selecting the cards has the worst luck possible. This means they select each card 1,2,3,...,10,J,Q,K exactly once in any order. If this happens, then the person does not have any pairs just yet. The person has selected 13 cards so far with this worst case scenario.
The 14th card is guaranteed to pair up with some other card previously chosen. There simply aren't any other options left once you've exhausted all possibilities. See the pigeonhole principle for more information.
So this is why you would need to select 14 cards to guarantee having at least two pair up together (i.e. you would have 2 or more pairs).
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
3a+14b
I'm not good at math, it's my weakest subject
On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.
What are similar angles?Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.
Given:
m ∠1 = m ∠2
m ∠2 = m ∠4
We have to prove that m ∠ABC = m ∠EDC
∠EDC = ∠3 + ∠4
m ∠ABC = m ∠1 + m ∠2
m ∠EDC = m ∠3 + m ∠4
m ∠1 + m ∠2 = m ∠3 + m ∠4
m ∠ABC = m ∠EDC
Hence, by using the given information we can prove that
m ∠ABC = m ∠EDC.
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3 ratios that are equivalent to 15/40
Answer:
3.8 ,6.16 , 9.24
Step-by-step explanation:
The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?
The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f'(x) = x² - 2 - 3xcosx.
We know a function f(x) is decreasing if f'(x) is < 0.
Therefore,
x² - 2 - 3xcosx < 0.
x² - 3xcosx < 2.
x(x - 3cosx) < 2.
Now, 3cosx can be [- 3, 3].
x(x - 3) < 2 and x(x + 3) < 2.
x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.
x < 2 Or x < 5 and x < 2 or x < - 1.
But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).
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Calculate The Double Integral. ∫∫ 4x 1 + Xy DA, R = [0, 4] × [0, 1]
Answer:
[tex]20\ln(5)-16\approx16.18876[/tex]
Step-by-step explanation:
[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]
Pls help! Step by step
Answer:
x = 55
Step-by-step explanation:
Since the sides of the shape are parallel, AngleC and AngleD will add up to 180° (see "parallel lines cut by a transversal" or maybe you have learned a big pile of parallelogram theorems)
Use this relationship to set up an equation.
2x + 20 + 50 = 180
combine like terms
2x + 70 = 180
subtract 70
2x = 110
divide by 2
x = 110/2
x = 55
x is 55
Answer:
The value of x is 55°
Step-by-step explanation:
GivienTwo adjacent angles of a parallelogram are (2x + 20)° and 50° respectivelySince we know that opposite angles of a parallelogram are equal
m∠C = m∠B = (2x + 20)°m∠D = m∠A = 50°The sum of any two adjacent angles is supplementary. This means, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180.
So,
∠C + ∠D = 180°
(2x + 20)° + 50° = 180°
2x + 70° = 180°
2x + 70° - 70° = 180° - 70°
2x = 110°
2x/2 = 110°
x = 55°
Thus, The value of x is 55°
A new pair of shoes you would like to purchase is 65% off. If you paid $135 for the shoes, how much was the original cost?
Solving the equation the original cost of the shoes before the discount will be obtained as $385.
To find the original cost of the shoes before the discount, you can use the following equation:
original cost = final cost÷ (1 - discount percentage)
In this case:
original cost = $135 ÷ (1 - 0.65)
To find the final cost you need to multiply 135 by 1 - 0.65.
0.65 is the equivalent to 65% when it's represented as a decimal.
0.65 represents the proportion of the original price that was removed (65% or 0.65)
So:
original cost = $135 ÷ (1 - 0.65)
original cost = $135 ÷ (1 - 0.65) = $135 ÷ 0.35 = $385
The original cost of the shoes before the discount was $385.
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Summary
Suppose a quadratic expression in standard form has a value of c = 0. Can this quadratic expression be
factored? How do you know?
Answer:
yesx is a factorStep-by-step explanation:
You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.
C = 0When the constant is zero, the equation becomes ...
ax² +bx = 0
Factoring out x, we have a factored form as ...
x(ax +b) = 0
showing that the equation can always be factored.
4 to the power of 3 space end exponent minus space 60 space divided by space 15 space plus space 6 space cross times space 2 space
Answer: 4/27 or 0.148148
First you solve for any grouping symbols ( absolute value, parentheses, brackets, etc.) Since there aren’t any you move on to exponents, 4^3 is the same as 4*4*4 which equals 64. Next you do multiplication 6*2 is 12 so our problem is currently
64-60 over 15+12. Next you simplify, which make the problem 4/27. You can divide which makes your problem 0.148148 but most of the times you keep it as a fraction.
The physician orders 3 mg/kg of medication twice a day. The patient’s weight is 315 lb. How much medication does the patient receive each day?
Answer: To find out how much medication the patient receives each day, you need to determine the patient's weight in kilograms and then calculate the total dosage per day.
You can convert the patient's weight from pounds (lb) to kilograms (kg) by dividing the weight by 2.2.
So,
315/2.2 = 142.72 kg
Next, we can use this weight to determine the dosage per day:
3 mg/kg * 142.72 kg = 428.16 mg
Now, since the physician ordered twice a day, we will multiply the dosage per day with 2:
428.16 mg * 2 = 856.32 mg
So the patient receives 856.32 mg of medication each day.
Step-by-step explanation:
NTP2PS
Write 3 equivalent ratios.
For the given ratio.
12/14
Answer:
4 7
Step-by-step explanation:
A recreational area is formed by a rectangular shaped pool and a cement patio surrounding the pool. the pool has a length of 3x-3 meters and a width of 2x+7 meters. The patio extends x meters around to pool, on all sides of the pool. Write a polynomial expression that gives the total area of the recreational area.
The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.
The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.
The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:
20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35
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A _____ is a flat surface that has no thickness.
The product of all of the solutions of (4x + 2k)(2 -5x ) = 0 is (−15). Find k.
Answer:
k = 75------------------------------
Given equation:
(4x + 2k)(2 - 5x) = 0Its solutions are:
4x + 2k = 0 and 2 - 5x = 04x = - 2k and 2 = 5xx = - 0.5k and x = 0.4The product of the solutions is -15:
- 0.5k * 0.4 = - 15- 0.2k = - 15k = - 15/- 0.2k = 75An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram. What is the area, in square units, of parallelogram ABCD? Enter your answer in the box.
In the new logo, what fraction of the parallelogram is shaded.
a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.
b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).
How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:
Area = base x height.
The base and the height for this problem are obtained counting the number of dots, hence:
Base: 4 units.Height: 6 units.Hence the area is given as follows:
Area = 4 x 6
Area = 24 units squared.
The shaded region is composed by a triangle with base 4 and height 3, hence:
Area shaded = 0.5 x 4 x 3 = 6 units squared.
(formula for the area of the triangle).
Meaning that the fraction is given as follows:
6/24 = 1/4.
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The quotient of s and 60
Answer:
60/s or s/60
Quotient means divide so you divide the following, s and 6 by each other.
Step-by-step explanation:
Hope it helps! =D
The population of a town grows uniformly at the rate of 4% every year. In how many years will the population of the town grow from 15,62,500 to 17,57,600?
Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.
What is percentage?A figure or ratio that is stated as a percentage of 100 is referred to as a percentage in mathematics. However, the percent symbol ("%) is usually used to denote it." The percent amount is flat. When the numerator is 100, percentages are really just fractions. Put the standard form (%) next to a number to show that it is a percentage. For instance, if you correctly respond to 75 out of questions in total on a test, you receive a 75% (75/100).
Here,
Given: 1757600 more people overall
Population as of now: 1562500
According to the issue,
=> 1562500[tex](1 + 4/100 )^{n}[/tex] = 1757600
=> [tex](26/25)^{n}[/tex] = 1757600/ 1562500
=> [tex](26/25)^{n}[/tex]= [tex](26/25)^{3}[/tex]
On comparing,
n=3
Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.
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Ethan has 3pounds of mixed nuts how many ounces of mixed nuts does Ethan have ?
Answer:
48 ounces of Mixed Nuts
Step-by-step explanation:
You need to convert pounds to ounces to find the answer to this problem.
1 pound is 16 ounces, so multiply 3 by 16 for your answer,
MODELING REAL LIFE When the average price of an item increases from $p_1$ to $p_2$ over a period of $n$ years, the annual rate of inflation $r$ (in decimal form) is given by $r=\left(\frac{p_2}{p_1}\right)^{1/n}-1$
. Find the rate of inflation for each item in the table.
Per pound Per pound
2009 2019
Potatoes $0.620 $0.749
Oranges $0.910 $1.280
Ground beef $2.251 $3.775
Potatoes:
, or %
Oranges:
, or %
Ground beef:
, or %
The rate of inflation of potatoes is 0.019.
The rate of inflation of Oranges is 0.019.
The rate of inflation of Ground beef is 0.019.
What is Rate of Inflation?Inflation is an increase in the level of prices of the goods and services that households buy. It is measured as the rate of change of those prices.
Given:
Here, the annual rate of inflation r (in decimal form) is given by
r = [tex](p_2/ p_1)^{1/n[/tex] - 1
Now, The average price of a potatoes increased from $0.620 in 2009 to $0.749 in 2019.
Thus, The required rate of inflation,
r = [tex](0.749/ 0.620)^{1/10[/tex] - 1
r = 1.019 - 1
r = 0.019
Now, The average price of a Oranges increased from $0.910 in 2009 to $1.280 in 2019.
Thus, The required rate of inflation,
r = [tex](1.280/ 0.910)^{1/10[/tex] - 1
r = 1.034 - 1
r = 0.034
Now, The average price of a Ground beef increased from $2.251 in 2009 to $3.375 in 2019.
Thus, The required rate of inflation,
r = [tex](3.775/ 2.251)^{1/10[/tex] - 1
r = 1.0321 - 1
r = 0.0321
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x³ - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
the formula is written as x3 -10x = 100.
We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.
We've made multiple tries and have:
x = 5.4 (roughly) (approximately)
In x3 -10x = 100, replace x with 5.4.
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
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DUE PLS HELP!! Kayla has $45 and wants to buy three shirts that are originally priced at $18 each. They are on sale for 20% off. After applying 5% tax, does Kayla have enough money to purchase the three shirts?
Complete each statement.
The cost of the shirts after the discount is $43.20.
A 5% tax adds an additional $2.16 so the total bill comes to 45.36.
Kayla does not have enough money to buy the three shirts.
Does Kayla have enough money to purchase the three shirts?The first step is to determine the total cost of the three shirts.
Total cost of the three shirts = cost of one shirt x total number of shirts
$18 x 3 = $54
Cost of the shirt after the sale = (1 - discount/100) x total cost of the shirt
(1 - 20/100) x $54
(1 - 0.2) x $54
= 0.8 x $54
= $43.20
Price after the tax : (1 + tax/100) x cost of the shirt after the discount
(1 + 5/100) x $43.20
(1 + 0.05) x $43.20
1.05 x $43.20 = 45.36
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5
Jasmine is a receptionist at a doctors office. She books 36 appointments each day.
Four out of every 24 appointments are cancelled. How many appointments are cancelled
each day?
6
Kendrick's Kennel has 2/spots for cats for every spots for dogs. If he has a total of
(144 spots for both cats and dogs, then how many more spots does he have for dogs
Answer:
5. 6 appointments are cancelled
6. 80 more spots
Step-by-step explanation:
5. Jasmine has 36/24 = 1.5 times as many appointments as cancellations each day.
Since 1.5 times 4 is 6, Jasmine has 6 cancellations each day.
6. Kendrick's kennel has 2 spots for cats for every 7 spots for dogs. If he has a total of 144 spots for both cats and dogs;
Spots for cats = 2x ;
So, spots for dogs will be = 7x ;
Total spots for cats and dogs will be = 2x + 7x = 144 ;
x = 144/9 = 16 ;
So, spots for cats = 2 * 16 = 32 ;
Spots for dogs = 7 * 16 = 112 ;
spots for dogs more than cats are = 112 - 32 = 80 .
Kendrick kennel has 80 more spots for dogs than cats.
I need to know the first and last one
The lines FE and GH are parallel to each orther.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given that
ΔPEI = ΔGHI
here ∠pie = ∠gih
PI =HI
GI=EI
So both triangles are congruent
So the FE║GH.
Hence the lines FE and GH are parallel to each orther.
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Ricky went to sleep at 9:45 pm and woke up at 6:30 the next morning. For how long did he sleep?
Answer:
8 hours and 45 minutes.
Step-by-step explanation: