We have to use the change-of-base formula of logarithms to simply write this log.
The logarithm to convert is:
[tex]\log _410[/tex]The change of base formula (using natural logarithms) is:
[tex]\log _ab=\frac{\ln b}{\ln a}[/tex]Matching this with the logarithm, we can write it as:
[tex]\log _410=\frac{\ln 10}{\ln 4}[/tex]What is the slope of a line that goes through (2,6) and (4,12)?
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
CAN SOMEONE HELP WITH THIS QUESTION?✨
The value of sin Ф will be [tex]2\sqrt{6} /5[/tex] .
What are trigonometric function?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The term "Circular" is another name for trigonometric functions. A triangle's angle functions can be used to define functions. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides. There are several trigonometric identities and formulas that show the relationship between the functions and aid in determining the triangle's angles. Here is an in-depth explanation of all these trigonometric functions and their formulas.
sin²Ф + cos²Ф = 1
sinФ = [tex]\sqrt{1 - 1/25}[/tex]
= [tex]2\sqrt{6} /5[/tex]
To know more about trigonometric function, visit:
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write 77.56 as a scientific notation
The scientific notation/standard form of 77.56 can be represented below
[tex]7.756\times10^1[/tex]The logic behind it is we shift the dot backward until it get to the last number. The number of step we took represent the exponential of 10.
The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second
Given distance,
[tex]d(t)=2t^3[/tex]Let v is the speed of the beetle.
It is given by
[tex]v=\frac{d(t)}{t}[/tex]Now,
[tex]\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}[/tex]At t = 0 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}[/tex]At t = 2 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}[/tex]So, the average speed of the beetle is 8 m/sec.
Hello, I need help simplifying question 16 i please, thanks
Given -
i. 5cot²θ + 5
To Find -
Simplification =?
Step-by-Step Explanation -
We know that
[tex]cot\theta\text{ = }\frac{\cos\theta}{\sin\theta}[/tex]So, simply putting it in the given equation:
[tex]\begin{gathered} =\text{ }5\frac{\cos^2\theta}{\sin^2\theta}\text{ + 5 } \\ \\ =\text{ 5}\frac{\lparen\cos^2\theta+\sin^2\theta\rparen}{\sin^2\theta} \\ \\ We\text{ know taht }\sin^2\theta\text{ + }\cos^2\text{ = 1} \\ \\ So,\text{ } \\ \\ =\text{ }\frac{5}{\sin^2\theta} \end{gathered}[/tex]Final Answer -
= 5/sin²θ
find the values for A and B. explain of show your reasoning
Answer:
The value of a is 5, and b is 6.
Explanation:
The points on the line are (6,10), (a,8), (4,b) and (2,2).
• The slope of a straight line is always constant.
First, determine the slope using the points (6,10) and (2,2).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Next, using points (6,10) and (a,8):
[tex]\begin{gathered} m=\frac{10-8}{6-a} \\ 2=\frac{2}{6-a} \\ \text{Cross multiply} \\ 2(6-a)=2 \\ 12-2a=2 \\ -2a=2-12 \\ -2a=-10 \\ a=-\frac{10}{-2} \\ a=5 \end{gathered}[/tex]Next. using points (6,10) and (4,b):
[tex]\begin{gathered} m=\frac{10-b}{6-4} \\ 2=\frac{10-b}{2} \\ \text{Cross multiply} \\ 10-b=2\times2 \\ 10-b=4 \\ b=10-4 \\ b=6 \end{gathered}[/tex]The value of a is 5 and b is 6.
Pizza Orders Pizza Corner sells medium andlarge specialty pizzas. A medium Meat Lovers pizza costs$10.95, and a large Meat Lovers pizza costs $14.95. OneSaturday a total of 50 Meat Lovers pizzas were sold, andthe receipts from the Meat Lovers pizzas were $663.50.How many medium and how many large Meat Loverspizzas were sold?
Let x = number of medium Meat Lovers pizza sold
Let y = number of large Meat Lovers pizza sold
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lovers pizza sold is $663.50
This
Answer:
Let x = number of medium Meat Lovers pizzas sold
Let y = number of large Meat Lovers pizzas sold.
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lover's pizza sold is $663.50
This
Step-by-step explanation:
need help with the the association property etc
Line 1:
[tex](2+x)x[/tex]Line 2:
[tex]x(2+x)[/tex]Line 1 to Line 2 is:
Commutative property of Multiplication.
Line 3:
[tex]x(x+2)[/tex]Line 2 to Line 3 is:
Commutative property of Addition
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 75% pure fruit juice. How many pints of each ofthe two existing types of drink must be used to make 170 pints of a mixture that is 75% pure fruit juice?First fruit drink:pintsХ5?Second fruit drink: pints
Let
x ----> number of pints of the First fruit drink
y ----> number of pints of the Second fruit drink
we have that
x+y=170 -------> x=170-y ----> equation A
65%=0.65
90%=0.90
75%=0.75
so
0.65x+0.90y=0.75(170) -----> equation B
Solve the system of equations
substitute equation A in equation B
0.65(170-y)+0.90y=0.75(170)
solve for y
110.5-0.65y+0.90y=
What’s 51,053 minus 12,947?
Answer:
The answer you're looking for would be 38,106.
Step-by-step explanation:
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a chemist has 30% and 60% Solutions of acid available how many liters of each solution should be mixed to obtain 120 liters of 34% acid solution
Answer:
104 litres of 30% solution and 16 litres of 60% solution.
Explanation:
Let us call x the litres of 30% solution and y the litres of 60% solution.
Now, we know that the end result is 120 litres of a solution; therefore, we have
[tex]x+y=120[/tex]Morover, we are also
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.
[4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution
Given system of equations:
[tex]\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}[/tex]Let us attempt to solve the equations
From equation 1:
[tex]y\text{ = 7x -4}[/tex]Substituting the expression for y into equation 2:
[tex]\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}[/tex]This imples that there is no solution to the system of equations.
We can plot the graph of the equations to better visualize and see that the lines don't intersect
The lines are parallel and do not intersect. Hence, there is no solution to the system of equations
how does you solve Vertices: (0,7), (0,-7) Co vertices: (2,0), (-2,0)
As according to given conditions let us draw these 4 points on the graph:
So the center is (0,0)
So the equation is:
[tex]\frac{(x-0)^2}{4}+\frac{(y-0)^2}{49}=1[/tex]Aline has a slope of -3/4 and a y-intercept of 5. Write an equation insiope-intercept for that could represent this situation."
Here, we want to write an equation in the slope-intercept form
Mathematically, we have this as;
[tex]y\text{ = mx + b}[/tex]b is the slope and m is the y-intercept
Thus, substituting the values we have in the question;
m = -3/4 and b = 5
Thus, we have the equation as;
[tex]y\text{ = -}\frac{3}{4}x\text{ + 5}[/tex]-3x^2 – 24x – 13 = -13
oh,
17. Write the equation of the line in slope-intercept form with the given information. 17. Passes through (-2, 6) with a slope of (-1/4)
Given:
Slope of line is m = -1/4 and passes through point (-2,6).
Explanation:
The general equation of line with slope m and passing through point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,6) and have slope of -1/4.
[tex]\begin{gathered} y-6=-\frac{1}{4}(x-(-2)) \\ y-6=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot2 \\ y=-\frac{x}{4}-\frac{1}{2}+6 \\ y=-\frac{x}{4}+\frac{11}{2} \end{gathered}[/tex]So equation of line is,
y = -x/4 + 11/2
19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm
Given:
Length of the edge of wooden box = 20 cm
Required:
The volume of wooden box.
Explanation:
The volume of cubical box is given as,
[tex]\begin{gathered} Volume\text{ = Edge}^3 \\ Volume\text{ = 20 cm }\times\text{ 20 cm }\times\text{ 20 cm} \\ Volume\text{ = 8000 cm}^3 \end{gathered}[/tex]Answer:
Thus the volume of the wooden box is 8000 cu. cm. The correct answer is option B.
Please help me resolve this, I’m not able Part (a)
To determine the volume of a cylinder you can use the following formula:
[tex]V=\pi r^2h,[/tex]where h is the height, and r is the radius of the cylinder.
Substituting:
[tex]\begin{gathered} r=6ft, \\ h=9ft \end{gathered}[/tex]in the formula, you get:
[tex]V=\pi(6ft)^2(9ft).[/tex]Finally, you get:
[tex]V=324\pi ft^3.[/tex]Answer: [tex]324\pi ft^3.[/tex]Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
Graph the solution set of each system of inequalities.19. 4x-y52x + 2y <6
The graph is given by:
what is the solution for y=2x+2 and y = 3x. I need a system of equation.
The given system of equations are,
[tex]\begin{gathered} y=2x+2 \\ y=3x \end{gathered}[/tex]Equating both equation implies,
[tex]\begin{gathered} 2x+2=3x \\ x=2 \end{gathered}[/tex]Put 2 for x in the equation y=2x+2 implies,
[tex]\begin{gathered} y=(2\times2)+2 \\ y=6 \end{gathered}[/tex]The solutions are x=2 , y=6.
A square coffee table has an area of 1936 square inches. What is the length of one side of the table?
The area of square is 1936 sq.inches.
Explanation :To find the side of the coffee table.
Use the area of square .
[tex]A=side^2[/tex]Substitute the value of area to find the side.
[tex]\begin{gathered} 1936=side^2 \\ \text{side}=\sqrt[]{1936} \\ \text{side}=44in \end{gathered}[/tex]Answer :Hence the length of one side of the table is 44 in.
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal There are ? calories in 246.5 grams of this cereal ( round to the nearest whole number as needed )
We can solve this question by means of the rule of three, which can be stated as
[tex]\begin{gathered} 110\text{ calories ----------- 177.4 grams} \\ \text{ x ---------------- 246.5 grams} \end{gathered}[/tex]then by using cross-multiplication to calculate x, we have
[tex]x\cdot177.4\text{ grams=(110 calories)}\cdot(246.5\text{ grams)}[/tex]so, by dividing both sides by 117.4 grams, x is given as
[tex]\begin{gathered} x=\frac{\text{(110 calories)}\cdot(246.5\text{ grams)}}{177.4\text{ grams}} \\ x=152.54667\text{ calories} \end{gathered}[/tex]Therefore, by rounding this result to the nearest whole nuymber, there are 153 calories in 246.5 grams of cereal
Find the distance between each pair of points using the distance formula - round to the nearest 10th
Explanation: Below we have the distance formula
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step 1: Now let's identify the values of the variable as follows
Step 2: Now we can substitute the values on the distance formula as follows
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-4_{}-(-2))^2+(4_{}-0_{})^2} \\ d=\sqrt[]{(-4_{}+2)^2+(4_{}_{})^2} \\ d=\sqrt[]{(-2)^2+16^{}} \\ d=\sqrt[]{4^{}+16} \\ d=\sqrt[]{20} \\ d=4.472135955 \\ d\cong4.5 \end{gathered}[/tex]Final answer: So the distance between the pair of points rounded to the nearest tenth is 4.5
what is the x intercept?
Answer:
x intercept is -2
Step-by-step explanation:
I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]10,720MasteryLook at the image below.4Course suRatios, rateArithmetic10Course cheTest yourthe skillsWhat is the area of the triangle?
The given triangle is not the regular drawing of a triangle. We need to identify the height and base.
From the diagram, the height = 10
base = 4
Substitute the values:
[tex]\begin{gathered} \text{Area of the triangle = }\frac{1}{2}\times\text{ 10}\times4 \\ \text{Area of the triangle = 20 units}^2 \end{gathered}[/tex]7. On Friday, Stock 1 dropped 3/4 point and Stock 2 dropped 5/8 point. Based on this information, which statement is true? Stock 2 dropped more Stock 1 dropped more The stocks dropped the same amount O Both stocks sold at the same price Clear selection
Let's divide each fraction
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \end{gathered}[/tex]As you can observe, 3/4 is greater than 5/8.
Hence, Stock 1 dropped more.To find the equation of a regression line, ŷ = ax + b, you need these formulas:Sya=rstb=ỹ alA data set has an r-value of 0.553. If the standard deviation of the x-coordinates is 3.996, and the standard deviation of the y-coordinates is 6.203,what is the slope of the line to three decimal places?A. 0.858B. 1.165C. 2.807D. 0.356
Solution
- The solution steps are given below:
[tex]\begin{gathered} r=0.553 \\ S_x=3.996 \\ S_y=6.203 \\ \\ \text{ We have been given that:} \\ a=r\frac{S_y}{S_x} \\ \\ \text{ Since }a\text{ is the slope, we have that:} \\ a=0.553\times\frac{6.203}{3.996} \\ \\ a=0.8584231...\approx0.858 \end{gathered}[/tex]Final Answer
The slope is 0.858
Answer:
.0858
Step-by-step explanation: