The results of the expression are given by;
\[tex]\mathbf{log_3(27) = 3}\\\\\mathbf{log_{11}(121) = 2}\\\\mathbf{log_{5}(125) = 3}\\\mathbf{log_{2}(128) = 7}\\\mathbf{(a) log_3(27)}\\[/tex]
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Expressions can be expressed using logarithms;
Express 27 as 3³
[tex]\mathbf{log_3(27) = log_3(3^3)}[/tex]
Apply law of logarithm;
[tex]\mathbf{log_3(27) = 3log_3(3)}[/tex]
So,
[tex]\mathbf{log_3(27) = 3\times 1}\\\mathbf{log_3(27) = 3}\\\mathbf{(b)\ log_{11}(121)}[/tex]
Express 121 as 11³
[tex]\mathbf{log_{11}(121) = log_{11}(11^2)}[/tex]
So, we have:
[tex]\mathbf{log_{11}(121) = 2\times 1}\\\mathbf{log_{11}(121) = 2}\\\mathbf{(c)\ log_{5}(125)}[/tex]
Express 125 as 5³
[tex]\mathbf{log_{5}(125) = log_5(5^3)}[/tex]
Apply law of logarithm;
[tex]\mathbf{log_{5}(125) = 3log_5(5)}[/tex]
So, we have;
[tex]\mathbf{log_{5}(125) = 3\times 1}\\\mathbf{log_{5}(125) = 3}\\\mathbf{dc)\ log_{2}(128)}[/tex]
Express 128 as 2^7;
[tex]\mathbf{log_{2}(128) = log_2{2^7}}[/tex]
Apply law of logarithm;
[tex]\mathbf{log_{2}(128) = 7log_2{2}}[/tex]
So, we have;
[tex]\mathbf{log_{2}(128) = 7\times 1}\\\mathbf{log_{2}(128) = 7}[/tex]
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Solve and graph the solutions of the equation –|x – 2| + 9 > 6
[tex]\boxed{-1<x<5}[/tex]
Graph:
Option c.
Explanation:
In this exercise we have the following inequality:
[tex]-\mid x - 2 \mid + 9 > 6[/tex]
Step 1. Subtract 9 from both sides:
[tex]-\mid x - 2 \mid + 9-9 > 6-9 \\ \\ -\mid x - 2 \mid > -3[/tex]
Step 2. Multiply by -1 to both sides
[tex]\mid x - 2 \mid < 3 \ \text{The direction of the inequality changes when multiplying by -1}[/tex]
Step 3. Apply property
[tex]\mid x \mid <a \rightarrow -a<x<a[/tex]
So:
[tex]\mid x - 2 \mid < 3 \rightarrow -3<x-2<3 \\ \\ Adding \ 2: \\ \\ -3+2<x-2+2<3+2 \\ \\ \boxed{-1<x<5}[/tex]
So the correct option is C.
The point U (-2,0) is translated 1 unit up. What are the coordinates of the resulting point, U’?
Answer:
Point U' (-2, 1)
Step-by-step explanation:
When moving up and down on a graph, this affects the y coordinate only.
Since it is moving up 1 unit, we have to add 1 to the y coordinate. So U' will end up being (-2, 1).
Answer:
U x 1U = -3 , 1
Step-by-step explanation:
U=1 x=1
y= -2 x 0 =-2
0=-2x-2 +1
y=-2x2+1
y=-4-1
y=-3
Skylar is filling a barrel with water. The graph shows the relationship between time in minutes and the gallons of water in the barrel. Write an inequality showing the times there will be more than 10 gallons in the barrel. Explain your answer.
Answer:
t>15
Step-by-step explanation:
A table has a square top. The area of the table top measure 18 square feet. Find the length of one side of the table top (61)
Answer:
Side of the top of the table =4.243 feet
Step-by-step explanation:
A Square has all its sides equal with all the four angles at right angles.
Area of the top of the square table=18 Square feet
Area of a square=[tex]Side^2[/tex]
Side ≈ [tex]18=Side^2\\\\Side=\sqrt{18} \\\\4.243[/tex]
The side of the top of the table is 4.243 feet
Jacks tent is shaped like an isosceles triangle. The height of the tent measures 7 feet and the diagonal side measures 9 feet. Find the length of the base
Answer:
The length of the tent's base is [tex]8\sqrt{2}[/tex].
Step-by-step explanation:
Given : Jacks tent is shaped like an isosceles triangle. The height of the tent measures 7 feet and the diagonal side measures 9 feet.
To find : The length of the base ?
Solution :
Let x denote the length of the tent's base.
Refer the attached figure below.
Using Pythagorean Theorem,
[tex]9^{2} =7^{2} +(\frac{x}{2} )^2[/tex]
[tex]81=49+\frac{x^{2} }{4}[/tex]
[tex]324=196+x^{2}[/tex]
[tex]x^{2} =128[/tex]
Taking square root on both sides,
[tex]x=\sqrt{128}[/tex]
[tex]x=8\sqrt{2}[/tex]
Therefore, the length of the tent's base is [tex]8\sqrt{2}[/tex].
Answer:
5/2
Explanation:<3
Slide the green dot from 0 to plot the number at the correct
location.
Plot V5
Plot the numbers on the number line.
V5, V8, V13
Which inequalities are true? Check all that apply
0 V5 <3
V8 > 3
V8 < 513
013 = 3.6
2.2< V5 <2.3
3.6 > 3> 3.7
The true inequalities are √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7. The false inequalities are √8 > 3 and √13 = 3.6. The truth value of √8, √13 is inconclusive due to the incomplete expression. These comparisons highlight the relative magnitudes of square roots in the given range of numbers.
The given numbers √5, √8, and √13 can be compared using various inequalities to determine their relative magnitudes. First, √5 is less than 3, as √5 is approximately 2.24. However, √8 is not greater than 3, as it is approximately 2.83, rendering the second inequality false.
The inequality √8, √13 is incomplete, making it impossible to determine its truth value without a specific comparison operator. Moving on, √13 is not equal to 3.6; in fact, it is approximately 3.61, making the statement false.
On the other hand, the range-based inequality 2.2 < √5 < 2.3 holds true, as √5 is approximately 2.24, falling within the given range. Similarly, the range-based inequality 3.6 > √13 > 3.7 is true since √13 is approximately 3.61, falling within the specified range.
In summary, √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7 are true inequalities, while √8 > 3, √13 = 3.6, and √8, √13 are inconclusive or false based on the provided information. These comparisons highlight the relative sizes of square roots within the given numerical context.
1. Zoie's recipe calls for 2/3 of a 16-ounce bag of chocolate chips.
How many ounces does she need?
Answer:
10.6666666666666666
Step-by-step explanation:
Determine whether the given length can be side lengths of a right triangle. 12m, 60m, 61m
Answer:
No
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the longest side squared is equal to the sum of the squares of the other 2 sides then the triangle is right.
The longest side = 61, thus
61² = 3721
12² + 60² = 144 + 3600 = 3744 ≠ 3721
Thus these sides do not form a right triangle.
I need help. Pls fill in all the black
Answer:
12 * 6 = (10 + 2) * 6
= (10 * 6) + (2 * 6)
= 60 + 12
= 72
Answer: 2 is the answer in the first line
2 is the answer in the second line
12 is the answer in the third line
72 is the answer in the fourth line
Step-by-step explanation:
12 x 6= (10 + ?? ) x 6 :: subtract 10 from 12 on the left hand side, that is, 12 - 10 = 2
(10 x 6) + (?? x 6) : since 2 is the answer in the first line, this is factored. And it is still 2
60 + ?? : multiply 2 x 6 = 12
??: Add 60 + 12 = 72
I hope this helps, mark as brainliest please
Evaluate 14 - 2xy when x=-6 and y= 2.
10
28
384
52
Answer:
I got 38
Step-by-step explanation:
14 - 2 (-6) (2) = 38
Answer:
thats a great answer i got the same
Step-by-step explanation:
Write the equation that represents the data in the table shown. Explain your answer.
The equation that represents the data in the table is y = 4x – 2.
Solution:
Take any two point from the table.
Let the points taken are (0, –2) and (3, 10).
[tex]x_1=0, y_1=-2, x_2=3, y_2=10[/tex]
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{10-(-2)}{3-0}[/tex]
[tex]$m=\frac{12}{3}[/tex]
m = 4
Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=4(x-0)[/tex]
[tex]y+2=4x[/tex]
Subtract 2 from both sides, we get
y = 4x – 2
The equation that represents the data in the table is y = 4x – 2.
A processing machine crushes 3 1/4 kilograms of dry fruits in 3/4 minute. What is the rate, in kilograms per minute, at which the machine crushes dry fruit?
A. 3/13
B. 16/39
C. 2 7/16
D. 4 1/3
(PLEASE INCLUDE STEP BY STEP)
Answer:
D
Step-by-step explanation:
Kg : min
3¼ : ¾
13/4 : 3/4
13 : 3
13/3 : 1
13/3 = 4 ⅓
There are 250 cells in Petri dish.the cells are increasing at a rate of 4% per hour.Model this situation with an equation .
Answer:
250÷4%= x per hour
Step-by-step explanation:
Final answer:
The situation where 250 cells in a Petri dish are increasing at a rate of 4% per hour can be modeled using the equation is 260 cells.
Explanation:
To model the situation where 250 cells in a Petri dish are increasing at a rate of 4% per hour, we use the formula for exponential growth:
N = N0ert
Where N is the future population size after time t, N0 is the initial population size, e is the base of the natural logarithm (approximately equal to 2.71828), r is the growth rate per unit of time, and t is the number of time units.
Here, N0=250 cells, r=0.04 (4% growth per hour, converted to decimal), and t will be the number of hours passed. Let's make t equal to 1 to see the number of cells after one hour:
N = 250e0.04(1)
After one hour, the Petri dish would have:
N = 250e0.04 ≈ 250(1.04081) ≈ 260 cells
Thus, this equation models the exponential growth of the cell population in the Petri dish over time.
When Madiha was born, her aunt opened a certificate of deposit in her honor to help send her to college someday. now at the age of 18, there is $31,066 in Madiha's account. how much did her aunt originally invest if the interest rate was 6.5%? (round to the nearest dollar)
A.$375
B.$12,500
C.$10,000
D.$8,000
Answer:
C.$10,000
Step-by-step explanation:
Let X be the amount of initial investment, 6.5% be the compound interest, n=18years and $31,066 as the final amount:
#Using compound interest:
[tex]A=P(1+i)^n\\\\\Where \ A=31066,i=6.5\%, n=18,P=X\\\\31066=P(1+6.5\%)^{18}\\\\31066=P(1.065)^{18}\\\\P=\frac{31066}{3.106654}\\\\P\approx10000[/tex]
Hence, the amount initially ionvested is $10,000
what is two thirds times negative one
Answer:
-1/3
Step-by-step explanation:
2/3 times -1 is -1/3
It is -2/3 or negative two thirds
Antonio drove 26 miles north, and then drives west. At the end of his drive, it is determined that he is 50 miles from where he started. How far did he drive west
Answer:
42.7
Step-by-step explanation:
Final answer:
To find out how far Antonio drove west, we can use the Pythagorean theorem. The distance driven north (26 miles) and the distance west form the two legs of a right triangle, with the total displacement from starting point (50 miles) as the hypotenuse. Solving the equation, we find Antonio drove approximately 42.70 miles west.
Explanation:
The question asks to determine how far Antonio drove west given that he first drove 26 miles north and then drove west, ending up 50 miles from where he started. This can be solved using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this scenario, the distance Antonio drove north and the distance he drove west form the two legs of a right triangle, with the overall displacement from his starting point being the hypotenuse.
To solve the problem, let x be the distance Antonio drove west. We already know the northward distance is 26 miles, and the hypotenuse is 50 miles. Setting up the equation based on the Pythagorean theorem gives us:
26² + x² = 50²
Solving for x:
x² = 50² - 26²
x² = 2500 - 676
x² = 1824
x = √(1824)
x = 42.70 miles
So, Antonio drove approximately 42.70 miles west.
please help me again
Answer:
y = 5
Step-by-step explanation:
The sum of all three angle measures of a triangle is ALWAYS equivalent to 180 degrees. Using this information, (4y + 10) + 75 + (3x) = 180
This is also an equilateral triangle, meaning those bottom two angles will be equivalent. 75 = 3x
So you can plug in the value for 3x into the first equation: (4y + 10) + 75 + 75 = 180
First, simplify the equation by adding the 75 and 75 together: (4y + 10) + 150 = 180
Now, subtract 150 from both sides of the equation: 4y + 10 = 30
Then subtract 10 from both sides: 4y = 20
And divide both sides by 4: y = 5
I hope this helps!
Answer:
y = 5
Step-by-step explanation:
75 / 3 = 3x / 3
25 = x
75 + 3(25) + 4y + 10 = 180
75 + 75 + 4y + 10 = 180
4y + 160 - 160 = 180 - 160
4y / 4 = 20 / 4
y = 5
Answer: y = 5
please help me on this math problem
Answer:
-21/8 or -2 5/8
Step-by-step explanation:
When dividing fractions by other fractions you use keep change flip, you keep the first fraction, change the division into multiplication and you flip the second fraction. We do this because we don't have to convert the fractions into decimals this was and its easier with fractions.
The problem changes to
3/8 times -7/1
Now we multiple the numerators together and the denominators together and then put it back into a fraction
3 * -7 = -21
8 * 1 = 8
-21/8
If you need it as a mixed number it is
-2 5/8
The cruising speed of the bullet train will be no less than 130 miles per hour.
Use s to represent the train's cruising speed (in miles per hour).
The representation of the speed will be s ≥ 130.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
The problem raises the following statement: "The cruising speed of the bullet train will be at least 130 miles per hour"
Which means that the train has a speed of 130 miles for now or higher, knowing this we can pose the inequality.
Knowing that "s" is the train's cruising speed (in miles per hour), we have to:
s ≥ 130
This would be the inequality that the statement represents.
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Final answer:
The variable 's' represents the train's cruising speed in mph, and the given condition is translated into the inequality 's ≥ 130', indicating the speed is at least 130 mph.
Explanation:
To represent the cruising speed of the bullet train using a variable, we can assign s to indicate the train's cruising speed in miles per hour. Given the statement 'The cruising speed of the bullet train will be no less than 130 miles per hour,' we can translate this into an inequality: s ≥ 130. This inequality means that the value of s, the train's cruising speed, must be greater than or equal to 130 mph.
How does a compass allow you to draw perfect circles?
Answer:
it makes like a guide to go around to end up as a circle
-angie:) pls mark me brainliest!
Step-by-step explanation:
Charles earns an annual salary of $61,870. If he is paid weekly, much would his pay be each week?
rewrite each expression by factoring out the greatest common factor 9b+12
Answer:
3(3b +4)
Step-by-step explanation:
The greatest common factor (GCF) of 9 and 12 is 3, so you're being asked to factor that out.
9b +12 = 3(3b +4)
_____
The GCF can be found a couple of ways. One of them is to list the prime factors and identify those that are common.
9b = 3 × 3 × b
12 = 2 × 2 × 3
For these two terms, the only common factor is 3.
If the expression 5+2x was evaluated for x=4 it’s value would be
Answer: 13
Step-by-step explanation:
5+2x
When x=4
5+2(4)
5+8
= 13
what is the value of N? N+ 2 1/3=4 2/3
Answer:
N = 2 1/3
Step-by-step explanation:
N + 2 1/3 = 4 2/3 (Given)
N = 2 1/3 (Subtract 2 1/3 on both sides.)
Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.
Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going in different directions.
Which statement is true about lines a and b?
They are parallel lines.
They are perpendicular lines.
They are skew lines.
They will intersect.
Answer: I have included an image of the correct answer.
They are skew lines
Answer:
C: They are skew
if you cant read upside down.
Step-by-step explanation:
Edge 2021
Kayla purchased a used truck that had 27,544 kilometers on it. Later on, she sold the truck when it had 80,452 kilometers on it. How many kilometers did Kayla put on the truck
Answer:
Kayla put 52,908 km on the truck.
Step-by-step explanation:
Subtract 27,544 km from 80,452 km to answer this question:
80,452 km
- 27,544 km
-------------------
52,908 km
Kayla put 52,908 km on the truck.
How do you write 825 in scientific notation
Answer:
8.25 * 10^2
Step-by-step explanation:
825 = 8.25 * 100 = 8.25 * 10^2
8.25×10 to the power of 2
Is x greater than less than or equal to 110
Based on the image you sent, the correct answer is: C. x = 110°
Here's why:
The image shows a diagram with two angles marked. One angle is labeled 110°, and the question asks about the measure of angle x.
Since there are no markings or indications otherwise, we can assume that angle x is congruent to the labeled angle.
Therefore, the measure of angle x is also 110°.
The other answer choices are not supported by the information in the image:
A. x > 110°: There's no evidence to suggest that angle x is greater than 110°.
B. x < 110°: There's no evidence to suggest that angle x is less than 110°.
So, angle z will be equal to 110° by vertically opposite angles.
Hence, the correct option will be C. z = 110°.
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold. $1,530 = $17t
What is a equivalent expression for 5times v+6
Answer:
5v +30
Step-by-step explanation:
[tex]5(v + 6) \\ = 5v + 5 \times 6 \\ = 5v + 30[/tex]