The logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.
The logarithm of a number is the exponent to which a base number must be raised to produce that number. For example, the logarithm of 10 with base 2 is 3, since 2 to the power of 3 is equal to 10. In this case, the logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.
This is because logarithms have the property that logb b = 1. This means that the logarithm of a number with the same base as the number itself is always equal to 1. This is why, in the case of log7 7, the answer is 1.
Logarithms can be used to simplify mathematical equations, as logarithms of multiplication and division are equal to the sums and differences of the logarithms of the individual numbers. They are also used in many scientific and engineering applications, such as calculating the pH of a solution.
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On the home screen of Olivia's tablet she had 6 rows of apps with 8 apps on each row. If she deleted 19 apps, how many would she have left on her home screen?
Answer:
29
Step-by-step explanation:
The total number of apps can be determined by multiplying the number of rows of apps by the number of apps in each row:
6*8 = 48
If she deleted 19 apps, then:
48-19 = 29 apps
Therefore if she deleted 19 apps she'd have 29 remaining.
4. When asked the question, "What is your favorite pizza
topping?" Aiko responded with the claim, "What is your
favorite pizza topping?"
What is the correct word to replace the word claim ?
Two parallel lines are cut by a transversal as shown below.
Suppose m /_4 = 81. Find m /_ 5 and m /_ 7.
When the parallel lines are cut by a transversal, the values for the measurement of ∠5 and ∠7 is 99° each.
What are parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.
Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
In the given diagram the parallel lines are cut by a transversal.
The measure of angle 4 is, m∠4 = 81°.
It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.
So, m∠4 + m∠5 = 180°
81° + m∠5 = 180°
m∠5 = 180° - 81°
m∠5 = 99°
Now, as it can be seen in the image ∠5 and ∠7 are vertically opposite angles.
So, they will be congruent or equal to each other.
So, it is obtained that -
m∠5 = m∠7
m∠7 = 99°
Therefore, the measures of angles are m∠5 = 99° and m∠7 = 99°.
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Pls tell me how to solve this question ASAP
A road map of Hamilton has a scale of 1 cm: 0.5 km. If Birch Avenue is 3.2 cm long on the map, what is the actual length of the street.
Answer:
The scale of the map is 1 cm: 0.5 km, which means that 1 cm on the map represents 0.5 km in real life.
If Birch Avenue is 3.2 cm long on the map, we can use this scale to find the actual length of the street. To do this, we can multiply the length of the street on the map (3.2 cm) by the scale factor (0.5 km/cm).
3.2 cm * 0.5 km/cm = 1.6 km
So, the actual length of the Birch Avenue is 1.6 km.
10(x-2) Distributive Property to rewrite
Answer:
[tex]10x+20[/tex]
Step-by-step explanation:
[tex]10(x-2)[/tex] Using Distributive property
[tex]10x+20[/tex]
2. Ahmed puts aside money from his summer job to spend on his PlayStation Plus Extra
subscription. The amount of money Ahmed has left as a function of the number of months
he subscribes can be modeled by the equation y = 120 - 15x.
c. Graph the equation
What is the domain and range
The domain and range of the linear function y = 120 - 15x is (-∞, ∞)
Graph of linear functionA graph of a linear function is a straight line that represents the relationship between two variables. A linear function is a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line represents the rate of change of one variable with respect to the other variable, and the y-intercept represents the value of the dependent variable when the independent variable is zero.
When a linear function is graphed, it creates a line that can be represented by two key features: the slope and the y-intercept. The slope of a linear function is the rate of change of the function, and the y-intercept is the point where the line crosses the y-axis.
In the given problem, the linear function is y = 120 - 15x
Kindly find the graph attached below;
The domain of the function is (-∞, ∞)
The range of this function is (-∞, ∞)
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A path 5 m wide runs along inside a rectangle field of length 80m and breadth 60m. Find the cost of cementing the path at the rate of ₹5/m²
The cost of cementing the path at the rate of ₹ 5 per m² is ₹ 6500.
What is a rectangle field?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Here, we have
Given:
Length of the whole field = 80m
The breadth of the whole field = 60m
∴ Area of the whole field = ( Length × breadth )
= 80m × 60m
= ( 80 × 60 ) m²
= 4800m²
Length of the field excluding the path
= [ 80 - ( 5 + 5 ) ] m
= [ 80 - 10 ] m
= 70m
The breadth of the field excluding the path
= [ 60 - ( 5 + 5 ) ] m
= [ 60 - 10 ] m
= 50m
∴ Area of the field excluding the path
= 70m × 50m
= ( 70 × 50 ) m²
= 3500m²
Now, the area of the path,
= 4800m² - 3500m²
= ( 4800 - 3500 ) m²
= 1300m²
According to the question,
The cost of cementing the path at the rate of ₹ 5 per m² is,
= ₹ ( 1300 × 5 )
= ₹ 6500
Hence, the cost of cementing the path at the rate of ₹ 5 per m² is ₹ 6500.
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Is quadratic form also factored form?
No, the quadratic form is not the same as the factored form of a quadratic equation.
A quadratic function can usually be represented by many equivalent expressions. For example, a quadratic function might be defined by f(x) = x² + 3x + 2. The quadratic expression f(x) = x² + 3x + 2 is called the standard form, the sum of a multiple x² of and a linear expression (3x + 2 in this case).
In general, the standard form is ax² bx + c
We refer to 'a' as the coefficient of the squared term 'x²', 'b' as the coefficient of the linear term 'x', and 'c' as the constant term.
The function 'f' can also be defined by the equivalent expression (x +2)(x + 1). When the quadratic expression is a multiplication of two factors where each one is a linear expression, this is called the factored form.
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Which has more people, County A with an area of 108 mi2 and a population density of 36 people km2 or County B with an area of 36 km2 and a population density of 108 people mi2
Answer:
County B
Step-by-step explanation:
You want to know the greater population, given a county's area and population density:
County A: 108 mi², 36 people/km²County B: 36 km², 108 people/mi²PopulationThe population is the product of area and density:
[tex]P_A=(108\text{ mi}^2)\dfrac{36\text{ people}}{\text{km}^2}=(108\cdot36\text{ people})\left(\dfrac{\text{mi}}{\text{km}}\right)^2\\\\P_B=(36\text{ km}^2)\dfrac{108\text{ people}}{\text{mi}^2}=(108\cdot36\text{ people})\left(\dfrac{\text{km}}{\text{mi}}\right)^2[/tex]
ComparisonTo determine which product is greater, we simply need to know the relationship between kilometers and miles:
1 mi ≈ 1.609 km
The factor (km/mi) is greater, so the population of County B is greater.
__
Additional comment
There are 1.609 km/mi, and about 0.6214 mi/km. The population of County B is about 6.7 times the population of County A.
County A has about 1501 people; County B has 10,070 people.
Identify the taxable income interval for a
head of household who pays tax of
$12,352.
A qualifying child or dependent is typically required to be eligible for head of household filing status.
What is a head of household?Individual American taxpayers can file under the heading "Head of Household." For those who are single and supporting dependents who qualify, it offers lower tax rates and a greater standard deduction. An individual must meet the following requirements in order to file as the Head of Household: You need to: Cover more than half of the household's expenses in order to file as the head of the household. be regarded as single as of the final day of the tax year, and. A eligible dependent or child must be yours. When filing as a head of household, you will pay taxes at a lower rate and with a larger standard deduction than a single filer.To learn more about head of household refer to:
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What is the best estimation of the equation of 7/8 - 6/11?
Answer:
when doing my math the answer I got was 1/2 hope it helps
The population of China was 1,355,692,544 people in 2014 . Round the population to the nearest million people.
Answer:
In 2014, the population of China was 1,356 million people
in quadrilateral $abcd$, sides $\overline{ab}$ and $\overline{bc}$ both have length 10, sides $\overline{cd}$ and $\overline{da}$ both have length 17, and the measure of angle $adc$ is $60^\circ$. what is the length of diagonal $\overline{ac}$?
The length of the diagonal is 17.
Given that, In quadrilateral ABCD, sides AB and BC both have a length of 10, and sides CD and DA both have a length of 17.
The measure of ∠ADC = 60°
AD = CD ( according to the question)
So, Δ ABC is an isosceles triangle with ∠DAC = ∠DCA.
According to the image,
Angles in a triangle add up to 180°, and since ∠ADC = 60°, the other two angles are also 60°.
And Δ ADC is an equilateral triangle.
Therefore, AC = DA = 17
S0, the diagonal of quadrilateral ABCD is 17.
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How do you tell if an equation has one two or no solutions?
To determine how many solutions an equation has, you must first solve the equation. If the equation has an exact solution, then it has exactly one solution.
To determine how many solutions an equation has, you must solve the equation. If you can solve the equation exactly, then it has one solution. However, if the equation has two different solutions, then it has two solutions. This means that the equation has two different values that can make the equation true. On the other hand, if the equation does not have any solutions, then it has no solutions. This means that the equation does not have any values that can make it true. Therefore, to determine how many solutions an equation has, you must solve the equation and check if it has one, two, or no solutions.
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Angela has 3x many than brian. Brian has 4 fewer than carlos. Carlos has 12 cans. Everyone has more than Danielle
Angela has 15 cans
Brian has 8 cans
Carlos has 12 cans
Danielle has 0 cans
what is comparison theory?Comparison theory is a mathematical tool used to compare the complexity of algorithms.It is based on the idea of comparing two different algorithms and then determining which one is faster. It is based on the principle that a faster algorithm is better than a slower one.Comparison theory can be used to determine the complexity of a problem, which can be used to determine the best algorithm for the problem.
This question uses the comparison theory.
Step 1: Carlos has 12 cans.
Step 2: Brian has 4 fewer than Carlos, so Brian has 8 cans.
Step 3: Angela has 3x many than Brian, so Angela has 24 cans.
Step 4: Everyone has more than Danielle, so Danielle has 0 cans.
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The point p on the graph means that the car can travel ___ miles(s) per ____ gallon(s) of gasoline.
1 3 10. 30
Answer:
The car can travel 30 miles per 1 gallon.
the net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. what is the modal net income?
The modal net incomes (in $millions) of a sample of steel fabricators will be b. $86
The goal of measures of central tendency, also known as measures of location, is to identify the data set's most "representative value." The mode, mean, and median are the three values listed here.
A data set's mode is its most frequent value. The mode of a distribution of probabilities has the highest probability. As a result, the mode can be quickly determined for a small number of observations. Any number of modes, or none at all, may exist for a given set of values. So, the value that will be sampled with the highest probability is the mode.
Note that the full question is:
The net incomes (in $ millions) of a sample of steel fabricators are: $86, $67, $86, $67, $86 and $85. What is the modal net income?
a. $85
b. $86
c. $85.5
d. $67
e. None of the above.
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Solve for f
a= 9/f-7
The solution to the formula using f as the subject is given by f = 9/(a + 7)
How to make f the subject of formula?a = 9/f - 7
Add 7 to both sides
a + 7 = 9/f
cross product
f(a + 7) = 9
divide both sides by a + 7
f = 9/(a + 7)
Hence, the formula a = 9/f - 7 can be written as f = 9/(a + 7) using f as the subject.
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What is the length of the hypotenuse of the triangle 8cm 15cm?
The length of the hypotenuse is 17 cm.
Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a²+b²=c²
However, it can also be written in the form of c²=a²+b²
In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.
As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.
3²=9 and 4²=16.
As you're looking for C, you've got to add these together
9+16=25
As a²+b²=c², this means that the answer for C is the square root of 25.
√25= 5
We are given that a = 8 cm and b = 15 cm.
Using Pythagoras' theorem,
c² = a² + b²
Substitute the values,
⇒ c² = 8² + 15²
⇒ c² = 64 + 225
⇒ c² =289
∴ c = 17
Thus, the length of the hypotenuse is 17 cm.
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Multiple Choice: Which interval on the graph below is increasing?
An interval on the graph above that is increasing include the following: B. -2 < x < 2.
What is an increasing function?For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.
On the other hand (conversely), if the output value (range) is decreasing when the input value (domain) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph above, we can reasonably infer and logically deduce that it is increasing over the interval -2 < x < 2.
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A number ,a, rounded to 1.d.p is 49.3
Another number ,b, rounded to 1.d.p is 7.6
what are the lower and upper bounds of a - b
The lower bound for the given numbers is 41.66. the maximum: 42.19
What methods are used to find upper and lower boundaries?The top and lower boundaries of a rounded number are as follows: Determine the claimed level of accuracy's place value. Multiply this place value by two. Add this amount to the given value to determine the upper bound, and subtract this amount to determine the lower bound. The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits.
The lower: a=49.35. b=7.69
so the lower bounds is:
a-b=49,35-7.69 =41.66 = a=49.49.34.
b=755 the upper = a= So the upper bounds is = a-b= 42.79.
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The pharmacist has a 2.8 L bottle of cough syrup. If she fills a bottle that is 1,200 ml, how many ml of cough syrup does the pharmacist have left?
The amount of cough syrup the pharmacist have left is 1600 millilitres.
How to find the amount of cough syrup left ?The pharmacist has a 2.8 L bottle of cough syrup. She fills a bottle that is 1200 ml . The amount of cough syrup the Pharmacist has left can be calculated as follows:
Let's convert litres to millilitres
Therefore,
1 litres = 1000 millilitres
2.8 litres = ?
cross multiply
Therefore,
amount of syrup in millilitres = 2.8 × 1000
amount of syrup in millilitres = 2800 millilitres.
Therefore,
amount of cough syrup the pharmacist has left = 2800 - 1200 = 1600 millilitres.
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What is the least common multiple of 12 and 16?
48
28
16
12
Answer:
Step-by-step explanation:
It is 48.
The ratio of teachers to students in a school is 2 to 45. How many
teachers are in the school if there is a total of 1410 students and
teachers altogether in the school?
If there are 1410 students and teachers together, then there are 60 teachers present.
what is proportionality ?Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle provide an example.
given
total=1410
students=45x
teachers=2x
2x + 45x = 1410
47x = 1410
x = 3
students=45x
=45×30
=1350
teachers=2x
=2×30
=60
If there are 1410 students and teachers together, then there are 60 teachers present.
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Work out the volume of this prism. 11cm 19cm 15cm 14cm 11cm The diagram is not drawn to scale.
The volume of this prism is 3150 cm³.
How to find the volume of the prism?step1:
given 11cm, 19cm, 14cm, 11cm
To find: volume of given prism
the given prism is combination two prism
Triangular prism
cuboidal prism
volume of cuboidal prism =l*b*h
=(15*14*11) cm^3
=2310cm^3
step2:
volume of triangular prism=1/2*l*b*h
=1/2*15*8*14
=840cm^3
step3:
volume of given prism=volume of cuboid + volume of triangular prism
=(2310+840)cm^3
=3150cm^3
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9. Write a rational
expression that is
equal to the following
rational expression
whenx doesn’t =3 or — 5.
-
(x+9)(x+5)/
(x+5)(x-3)
A mathematical expression is a statement made up of variables, constants, and arithmetic operators. For the equation -3 x^2-9/x+3 , the rational expression is x+3 , Option A
What exactly is a mathematical expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression’s structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
The complete question is
“Which of the following is equal to the rational expression when x does not equal 1 or 3 ( )
The options are
a. X+3
b. X-3
c. (x -3)/(x+3)”
The expression given in the question is
( )
And have been asked among the option which represents the rational expression when x does not equal 3 or 1
Therefore for the following equation -3 x^2-9/x+3 , the rational expression is x+3 .
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Which value of f makes 3f+5=323f+5=323, f, plus, 5, equals, 32 a true statement?.
The value of f which satisfies the given equation 3f + 5 = 32 is 9. The correct option is C.
What is meant by Algebra?The area of mathematics known as algebra deals with manipulating and using arithmetic to operate on abstract symbols rather than integers. For instance, algebraic equations include x + y = z and b - 2 = 5, but not 2 + 3 = 5 and 73 * 46 = 3,358.Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are only a few of the sub-branches that make up algebra.A common thread that runs through nearly all of mathematics is algebra, which is the study of variables and the rules for using them in formulas. All applications of mathematics require knowledge of elementary algebra since it deals with manipulating variables as though they were numbers.Given question is incorrect
Correct question :
Which value of f makes 3f+5=32 a true statement?
a. f=6
b. f=8
c. f=9
d. f=12
Given data :
It is required to find the value of f for which the equation 3f + 5 = 32 is satisfied.
Use simple rules of algebra to get the value of f which satisfies the given equation,
3f + 5 = 32
3f = 32 - 5
3f = 28
f = 28 / 3 = 9
Therefore, the value of f which satisfies the given equation 3f + 5 = 32 is 9 is correct option.
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A young crocodile is 0.4 feet long. An adult crocodile is 13.5 times as long. How many feet long is the adult crocodile than the young crocodile?
The length of the adult crocodile more than the young crocodile is 5.0 feet.
How to find the length of the young crocodile?A young crocodile is 0.4 feet long. An adult crocodile is 13.5 times as long. The length the adult crocodile is more than the young crocodile can be calculated as follows:
Hence,
length of the adult crocodile = 13.5(0.4)
length of the adult crocodile = 13.5 × 0.4
length of the adult crocodile = 5.4 feet
Therefore,
the length of the adult crocodile more than the young crocodile = 5.4 - 0.4 = 5.0 feet
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What is the equation of a line that passed through the points 3/6 and 8 4?
The equation of line that passed through the points (3, 6) and (8, 4) is 5y = -2x + 40.
In the given question, we have to find the equation of a line that passed through the points (3, 6) and (8, 4).
The point-slope approach is typically used when two points that sit on a specific line are specified.
A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.
Firstly we find the value of m using the formula
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
From the given points x(1) = 3, y(1) = 6, x(2) = 8, y(2) = 4.
Now putting the value
m = [tex]\frac{4-6}{8-3}[/tex]
Now solving
m = [tex]-\frac{2}{5}[/tex]
Now we finding the equation of line. We can use any one point in the given points.
Now taking the points (3, 6), x(1) = 3 and y(1) = 6
Now putting the value in equation y - y(1) = m(x - x(1)).
y - 6 = [tex]-\frac{2}{5}[/tex](x - 3)
Multiply by 5 on both side, we get
5(y - 6) = -2(x - 5)
Using the distribution property
5y - 30 = -2x + 10
Add 30 on both side, we get
5y = -2x + 40
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The complete question is:
What is the equation of a line that passed through the points (3, 6) and (8, 4)?
Cassie is making hair bows for her friends. She needs 1/12 yard of fabric to make each bow. She has 17/20 yard of fabric. Does Cassie have enough fabric to make 10 bows?
Yes, Cassie has enough fabric to make 10 bows. 17/20 yard of fabric is equal to 1.7 yards, and 1/12 yard is equal to 0.083 yards. When 1.7 yards is multiplied by 0.083 yards, the result is 0.14 yards, which is more than enough to make 10 bows.
1. Convert 17/20 yard of fabric to yards:
17/20 yard = 17/20 x 1 yard = 1.7 yards
2. Convert 1/12 yard to yards:
1/12 yard = 1/12 x 1 yard = 0.083 yards
3. Calculate how much fabric is needed to make 10 bows:
1.7 yards x 0.083 yards = 0.14 yards
4. Determine if Cassie has enough fabric:
Yes, Cassie has 0.14 yards which is enough to make 10 bows.
Yes, Cassie has enough fabric to make 10 bows. 17/20 yard of fabric is equal to 1.7 yards, and 1/12 yard is equal to 0.083 yards. When 1.7 yards is multiplied by 0.083 yards, the result is 0.14 yards, which is more than enough to make 10 bows.
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