Answers
The correct answer for number 2 is B: b - 8
Correct answer for number 3 is C: The quotation of three and some number times five
For number 4 the correct answer is C: 10x + 5
Related Questions
use exponential form to evaluate log8(2)
Answers
Answer: [tex]\frac{1}{3}[/tex]
Explanation:
let y = [tex]log_{8} (2)[/tex]
whenever we transfer base from log from one side to other it will remain be base after shifting to the other side.
Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]
here we have n = y, m=2, x=8 by substituting the values
we will get
[tex]8^{y} = 2[/tex] (1)
we can write 8 in power of 2 that is [tex]2^{3}[/tex]
we will rewrite the above equation (1) as
[tex]2^{3y} = 2[/tex]
we can equate the power when base is same then we will get
3y = 1
then
[tex]y=\frac{1}{3}[/tex]
The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
Let the given logarithmic function be x to have:
[tex]log _82=x[/tex]
This can be transformed into indices to have:
[tex]8^x = 2[/tex]
Solve the resulting indices for "x" a shown:
[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]
Cancel the base and equate the power to have:
[tex]3x = 1\\x = \frac{1}{3}[/tex]
Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
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The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 80% pure fruit juice?
Answers
**
let x=pints of 25% pure fruit juice
100-x=pints of 75% pure fruit juice
25%x+75%(100-x)=35%(100)
Write an equation of the line passing through the point A(−6, 5)that is parallel to the line
y = 1/2 x−7.
Answers
Please help! The very last question has 2 answers.
Answers
P2. A
3.D i think
4. C and D maybe
What number needs to be added to both sides of the equation in order to complete the square? x2+14x=−32
Answers
49 is the number to be added to both the sides of the equation to complete the square.
The equation given in the question is
[tex]x^{2} +14x=-32[/tex]Which can be written as [tex]x^{2} +2\times (7x)=-32[/tex]
We have to convert it into square form.
Since the standard form of the equation in square form is
(a + b)² = a² + 2ab + b²
By comparing this standard equation with the given equation,
a = x
&
b = 7
By substituting the values of 'a' and 'x' in the standard square form,
x² + 14x + 7² = -(32) + 7²
x² + 14x + 49 = -32 + 49
(x + 7)² = 17
Therefore, 49 should be added in both the sides of the equation in order to complete the square.
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Prove that a parallelogram is a square iff its diagonals are both congruent and perpendicular
Answers
The lengths of the sides are a and b.
The lengths of the diagonals are 2x and 2y.
Because the diagonals are both congruent and perpendicular, therefore there are two right triangles as shown.
Note that x = y.
Because x = y, each right triangle is isosceles and has the angles 90°, 45° and 45°.
From the Pythagorean theorem,
For one right triangle,
a² = x² + y² = x² + x² = 2x².
For the other right triangle,
b² = y² + x² = x² + x² = 2x²
Therefore
a² = b²
a = b
It follows that all sides of the parallelogram are equal and each angle is
45+45 = 90°
Therefore the parallelogram is a square.
How many feet are in 2000 meters?
Answers
Next, multiply
2000 m • 3.28084 = 6561.68 ft
Jessica increases the temperature of a block of ice by 20º. Which integer represents the amount by which Jessica must change the temperature for the block of ice to return to its starting temperature? A. –40 B. –20 C. 20 D. 40
Answers
Answer:
B. -20
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Eric has a gift card to his favorite restaurant. Every Tuesday he has the same meal at the restaurant. This table shows the balance of money in dollars left on Eric’s gift card at different times. Time (weeks) 2, 4 ,6 ,8 Balance ($) 125, 100, 75, 50 What is the equation that represents Eric’s gift card balance, where x represents the time and y represents the balance?
Answers
Answer:
y − 100 = -12.5 (x − 4)
Step-by-step explanation:
Pick two points on the line to calculate the slope:
m = (y₂ − y₁) / (x₂ − x₁)
m = (100 − 125) / (4 − 2)
m = -12.5
Next, use point-slope form to write the line equation.
y − y₁ = m (x − x₁)
y − 100 = -12.5 (x − 4)
Can someone please help me?
Answers
Answer: -1.9
Step-by-step explanation:just add up the values for the weight change
(-1.8)+(0.9)+(-1.4)+(0.4)
-1.9
The figure shows △ABC . BD is the angle bisector of ∠ABC .
What is AD ?
Enter your answer in the box as a fraction.
____ units
Answers
[tex]\dfrac{|AD|}{|DC|}=\dfrac{|BA|}{|BC|}\\\\\\\dfrac{|AD|}{|DC|}=\dfrac{8}{10}=\dfrac{4}{5}[/tex]
Moreover:
[tex]|AD|+|DC|=6[/tex]
so:
[tex]|DC|=6-|AD|[/tex]
and
[tex]\dfrac{|AD|}{|DC|}=\dfrac{4}{5}\\\\\\\dfrac{|AD|}{6-|AD|}=\dfrac{4}{5}\qquad\qquad\text{cross multiplying}\\\\\\ 5\cdot|AD|=4\cdot\big(6-|AD|\big)\\\\5\cdot|AD|=24-4\cdot|AD|\\\\5\cdot|AD|+4\cdot|AD|=24\\\\9\cdot|AD|=24\qquad|:9\\\\\\|AD|=\dfrac{24}{9}=\boxed{\dfrac{8}{3}}[/tex]
The length of AD is [tex]\dfrac{8}{3}[/tex].
Given:
BD is the angle bisector of the triangle ABC.
The figure of the triangle ABC.
To find:
The length of AD.
Explanation:
According to the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the same proportion of the other two sides.
Let [tex]x[/tex] be the length of AD. Then, the length of DC is [tex]6-x[/tex].
Using the Angle Bisector Theorem, we get
[tex]\dfrac{8}{10}=\dfrac{x}{6-x}[/tex]
[tex]\dfrac{4}{5}=\dfrac{x}{6-x}[/tex]
[tex]4(6-x)=5(x)[/tex]
[tex]24-4x=5x[/tex]
[tex]24=5x+4x[/tex]
[tex]24=9x[/tex]
[tex]\dfrac{24}{9}=x[/tex]
[tex]\dfrac{8}{3}=x[/tex]
Therefore, the length of AD is [tex]\dfrac{8}{3}[/tex].
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At a high school with 1100 students, Jake is in the 70th percentile for height. How
many students at the school are either the same height or shorter than Jake?
Answers
30% of 1100 would be 0.3*1100 = 330.
So there are 330 students that are either at the same height or shorter than Jake.
david kalb started a pet-walking business , he charges $20 to walk one dog, twice a day. He walks six dogs five days a week for four customers. He walks three dogs seven days a week for three other customers. How much money does David get from his customers each week? If his weekly expenses are $350, what is the profit?
Answers
Answer:
David earns $1,020 a week, and his weekly profit is $670.
Step-by-step explanation:
Since David walks six dogs per day, and each dog is $20, he earns a total of $120 per day from those six dogs. Also, knowing that he walks the six dogs five days a week, he earns $600 from walking the six dogs for five days per week alone. Using this same logic for the three dogs he walks seven days a week, we can conclude that he gets $60 from walking those three dogs. Knowing he walks those three dogs seven days a week, he gets $420 from walking those three dogs. Combining the totals gives us $1,020, the amount of money he earns per week. Since his weekly expenses are $350, we subtract that from $1,020 to get his weekly profit: $670.
The sum of two numbers is 67 . the smaller number is 9 less than the larger number. what are the numbers? larger number: smaller number:
Answers
Smaller Number is L -9
Larger # + Smaller # = 67
L + L - 9 = 67
2L - 9 = 67
2L = 67 + 9
2L = 76
L = 76/2
L = 38
Smaller Number = Larger Number - 9
38 - 9
Smaller # = 29
Check. .. 38+29=67 CORRECT!
Larger #: 38
Smaller #: 29
To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.
The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.
Let's define the larger number as x and the smaller number as y. According to the problem:
x + y = 67 (Equation 1)y = x - 9 (Equation 2)Substitute Equation 2 into Equation 1:
x + (x - 9) = 67
2x - 9 = 67
2x = 67 + 9
2x = 76
x = 38
Now, we can find y using Equation 2:
y = x - 9
y = 38 - 9
y = 29
Therefore, the larger number is 38 and the smaller number is 29.
How to simplify rational expressions
Answers
[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b) \\\\\\ \textit{also recall that }i^2=-1\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{-3-7i}{7+10i}\cdot \cfrac{7-10i}{7-10i}\implies \cfrac{(-3-7i)(7-10i)}{(7+10i)(7-10i)}\implies \cfrac{(-3-7i)(7-10i)}{7^2-(10i)^2} \\\\\\ \cfrac{-21+30i-49i+70i^2}{7^2-(10^2i^2)}\implies \cfrac{-21+30i-49i+70\left( \boxed{-1} \right)}{7^2-\left[10^2\left( \boxed{-1} \right)\right]} \\\\\\ \cfrac{-21+30i-49i-70}{49-(-100)}\implies \cfrac{-91-19i}{149}\implies -\cfrac{91}{149}-\cfrac{19i}{149}[/tex]
62394 rounded to the nearest tenth
Answers
all it is 5 and up are the next tenth or hundred etc.
and anything below 5 is hundredth it already is
Really hope this helps and if it does I would continue with is strategy
If f(x) = 2/x and g(x) = x^2 what is f of g
Answers
is that right?
Answer: The required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
Step-by-step explanation: We are given two functions as follows :
[tex]f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.[/tex]
We are to find f of g, i.e., f(g(x)).
To find the required value, first we have to find the f value of the function g(x).
We have
[tex]f(g(x))=f(x^2)=\dfrac{2}{x^2}.[/tex]
Thus, the required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
Which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?
The range contains only natural numbers.
The domain contains only natural numbers.
Exponential bases must be whole numbers.
Initial values must be whole numbers.
Answers
The correct answer is:
The domain contains only natural numbers.
Step-by-step explanation:The graphs of geometric sequences are a series of unconnected points rather than a smooth curve because:
The domain contains only natural numbers.
As the geometric sequence us given as:
[tex]a_1=a,a_2=ar,a_3=ar^2,....[/tex]
where a is the first term of the sequence and r is the common ratio of the geometric sequence.
Also [tex]a_n[/tex] denotes the nth term of the sequence where n belongs to natural numbers that is the domain of the function is natural numbers.
The reason why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve is because: B. The domain contains only natural numbers.
What is a geometric sequence?A geometric sequence is typically a series of real and natural numbers that are calculated by multiplying the next number by the same number each time.
Mathematically, a geometric sequence is given by the expression:
[tex]a, \;ar, \; ar^{2} ....a_n[/tex]
Where:
r is the common ratio.a is the first term of a geometric sequence.In a geometric sequence, the graphs of geometric sequences comprises a series of unconnected points rather than a smooth curve is because the domain is made up of only natural numbers.
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The sum of two numbers is
40
. One number is
4
times as large as the other.
Answers
∠A
and
∠B
are vertical angles with
m∠A=x
and
m∠B=4x−30
.
What is
m∠A
?
Answers
Factoriza completamente las siguientes expresiones;
1. 3a²-a
2. 7ab³-14b
3. x³-x²+x
4. 12x³-xy²
5. 5x-6x²+7x³
6. 7a+8ab+9a²
7.3x²-3xy+6xy²
Answers
2. 7ab³-14b = 7b(ab^2 - 2)
3. x³-x²+x = x(x^2 - x + 1)
4. 12x³-xy² = x(12x^2 - y^2)
5. 5x-6x²+7x³ = x(5 - 6x + 7x^2)
6. 7a+8ab+9a² = a(7 + 8b + 9a)
7.3x²-3xy+6xy² = 3x(x - y + 2y^2)
A tour group with 22 people in it is getting rooms in a motel to stay in for the night. no more than 3 people can stay in each room. how many rooms will they need
Answers
Hope I helped :)
8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is a tour group of 22 people. The group is looking for rooms in a motel to stay in for the night and no more than 3 people can stay in each room.
The number of people who can live in 1 room = 3
This means, we have 3 people for 1 room.
For 1 people, we will have - (1/3) room
For 22 people, we will need -
(22/3)
7.3 rooms
Approximately, 8 rooms will be needed and the last room will have only one member of the group.
Therefore, 8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
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Solve be graphing , elimination , or substitution
Answers
We will multiply the first equation by 4, so we can eliminate the y variable.
#1 [tex]4(2x-y) = 4(-1)[/tex]
#2 [tex]8x-4y=-4[/tex]
After simplifying, we can use Linear Combination method to solve for the variables, which is adding both equations.
Linear Combination:
#1 ([tex]8x-4y=-4[/tex]) + ([tex]5x+4y=17[/tex])
#2 [tex]13x = -13 [/tex]
#3 [tex]x = -1 [/tex]
After this, you can plug in x into the first equation, to find y:
#1 [tex]2(-1)-y=-1[/tex] (Simplify)
#2 [tex]1-y=-1[/tex]
#3 [tex]-y=-2[/tex]
#1 [tex]y=2[/tex]
Now we have our solution ordered pair, which is (-1, 2). Hooray!!
How to solve for quadratic equations with inequalities?
Answers
q, and p
Tina is the top seller of the store. She earns a salary plus 2%. Tina's salary is $30,000 a year. This month her sales were $48,500. How much was Tina paid this month?
Answers
If the above is true, her monthly pay is calculated as follows:
Commission: 48500 * 0.02 = $970
Monthly salary: 30000 ÷ 12 = $2500
So monthly pay is $2500 + $970 = $3470
Harry enlarged a picture to a height of 30 inches. The original picture was 7" wide by 5" tall. Write a proportion to find the width of the enlargement and then solve for the width of the enlargement.
Answers
original height was 5" and it was enlarged to 30"
find the ratio by dividing 30 by 5
30 / 5 = 6
so ratio would be 1/6 meaning for every 1 inch of the original the new one is 6 inches
now you need to multiply the original width by 6 to find the new width
7" x 6 = 42"
new width = 42"
Write an algebraic expression to answer the question below. if 10 calculators cost d dollars, how much, in dollars, does each calculator cost?
Answers
For exercises 14-19, find an equation for the line that satisfies the conditions
Answers
Use the numbers 8, 6, and 2 and one operation to write and expression that includes an exponent and has a value of 8. Use each number only once
Answers
The suitable way to use the numbers 8, 6, and 2 to create an expression with an exponent that results in the value of 8 is by utilizing the equation 2^3. This equation means 'two raised to the power of three', meaning 2 multiplied by itself thrice, giving us the desired result, 8.
Explanation:To solve this question, we need to consider the mathematical operation of exponentiation, which involves a base number and an exponent. The exponent represents the number of times the base number is to be multiplied by itself.
Given the numbers 8, 6, and 2, we aim to use each number only once to create an expression that includes an exponent and yields a value of 8. The suitable way to do this is by following the equation 2^3 (where 2 is the base number and 3 is the exponent).
To explain further, an exponent is the number of times a number, known as the base, is multiplied by itself. For instance, 2^3 should be read as 'two raised to the power of three', essentially depicting 2 * 2 * 2, resulting in 8. This follows the standard rules of Exponential Arithmetic.
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What is f(6) ? Thanks
Answers
f(6) =4(6)-6 = 18