give the domain of the logarithmic function function below. Hint: Use transformations to sketch a graph.
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We have the function given
[tex]f(x)=1-ln(x+5)[/tex]The graph of the function is given below
From the domain of the function is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: x>-5\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-5,\: \infty\: \mright)\end{bmatrix}[/tex]
Related Questions
how do I find the area of this shape ?
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So this is a shape that can be subdivide into triangles and squares.
So let us first consider the triangle with dimensions 2 and 6. As it is clear that it forms a right angled triangle, the area is,
[tex]\frac{1}{2}6\times2=6[/tex]Then there is a square of each side 2. So the area is, 4; since(2*2).
Then there is another triangle of dimneions 2 each . Thus the area is,
[tex]\frac{1}{2}2\times2=2[/tex]And again there forms a traingle with base 4 and height 10; (2+2+6 from the dotted lines.). Its area is,
[tex]\frac{1}{2}\times4\times10=20[/tex]So the total area is, 6+4+2+20=32.
How many terms of the series (-4)+(-1)+2+5….yield a sum of 1022?
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Given:
The series is,
[tex]-4-1+2+5+\text{.}\ldots.\ldots\ldots[/tex]The common difference is 3.
The sum of first n terms of the given arithmetic series is given as,
[tex]\begin{gathered} S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ a=\text{ first term}=-4 \\ d=\text{ common difference}=3 \\ S_n=1022 \\ 1022=\frac{n}{2}\lbrack2(-4)+(n-1)3\rbrack \\ 2\cdot1022=n(-8+3n-3) \\ 2044=3n^2-11n \\ 3n^2-11n-2044=0 \\ \text{Use the quadratic formula,} \\ n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},a=3,b=-11,c=-2044 \\ n=\frac{-\left(-11\right)\pm\sqrt{\left(-11\right)^2-4\cdot\:3\left(-2044\right)}}{2\cdot\:3} \\ n=\frac{11\pm\: 157}{6} \\ n=\frac{11+157}{6},n=\frac{11-157}{6} \\ n=\frac{168}{6},n=-\frac{146}{6} \\ n=28,n=-\frac{73}{3} \\ \text{But n=-}\frac{73}{3}\text{ is not possible value} \end{gathered}[/tex]It gives n=28.
Answer: the 28 terms of the given series yield a sum of 1022.
484 in standard form
Answers
In order to express the number 484 in standard form, consider that such a form is given by m x 10ⁿ, where m is a number between 1 and 10 and n is an integer number.
Consider that 484 can be written as 4.84 x 100 = 484, moreover, take into account 100 can be written as 10².
Then, you can write:
484 = 4.84 x 100 = 4.84 x 100²
Then, you have m = 4.84 and n = 2.
Hence, the given number in standard form is 4.84 x 10²
Tyrell was late for class 3 times in the month of June . Each time he was late he missed 5 and 1/2 minutes of class time . What is the total amount of class time Tyrell missed in the month of June ? A. 8 and 1/2 B . 15 minutes C . 16 and 1/2
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Tyrell was late 3 times, each time he was late for 5 1/2 minutes, to determine how much time he missed in June, you have to multiply 5 1/2 by 3
[tex]5\frac{1}{2}\cdot3[/tex]First, express the mixed number as a fraction:
-Divide the whole number by 1 and add 1/2
[tex]5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}[/tex]-Multiply the first fraction by 2, to express it as its equivalent with denominator 2, and add both fractions:
[tex]\frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{10+1}{2}=\frac{11}{2}[/tex]Multiply the result by 3
[tex]\frac{11}{2}\cdot3=\frac{11}{2}\cdot\frac{3}{1}=\frac{11\cdot3}{2}=\frac{33}{2}[/tex]Express the result as a mixed fraction:
Divide 33 by 2:
[tex]33\div2=16.2[/tex]The whole number of the result is 16 and there are 0.5 remainings.
0.5 expressed as a fraction is 1/2.
So Tyrell missed 16 and 1/2 minutes in the month of June
Given the following histogram for a set of data, how many values in the data set are between 5.5 and 8.5?765Frequency210|3.54.55.58.56.5 7.5Values9.510.5
Answers
To solve the exercise, we add the frequency between the intervals 5.5 - 6.5, 6.5 - 7.5, and 7.5 - 8.5:
• Frequency between 5.5 and 6.5: 7
,• Frequency between 6.5 and 7.5: 5
,• Frequency between 7.5 and 8.5: 5
[tex]7+5+5=17[/tex]Therefore, there are 17 values in the data set between 5.5 and 8.5.
Solve this equation: 3/5 (× - 10) = 18 - 4× - 1
Answers
you have to multiply by
X+4 divided by 2=9 what's the value of the variable
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(x + 4) / 2 = 9
x = ?
Step 02:
[tex]\begin{gathered} \frac{x+4}{2}=9 \\ x+4=9\cdot2 \\ x\text{ + 4=18} \\ x\text{ = 18-4} \\ x\text{ = 14} \end{gathered}[/tex]The answer is:
The value of x is 14
3 Write the missing power of 10 in each equation. Write your answers in the blanks. 0.06 X ____= 6____X 0.3 =
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We are given the following relationship:
[tex]0.06\times10^x=6[/tex]To find the exponent we need to have into account that to transform 0.06 into 6 we need to move the decimal point 2 units to the right, therefore, the exponents must be 2, that is:
[tex]0.06\times10^2=6[/tex]Now we are given the following:
[tex]0.06\times10^3[/tex]In this case, we have to move the decimal point 3 spaces to the right, like this:
[tex]0.06\times10^3=60[/tex]The quotient of thrice a number and the number Translate into a variable
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Ok, so
Here we have the expression:
The quotient of thrice a number and the number.
First, let "x" be the number.
If "x" is the number, the sentence "thrice the number" can be written as 3x.
Now, the quotient of thrice a number (3x) and the number (x), will be:
[tex]\frac{3x}{x}[/tex]If we simplify, this is 3.
Richard Gorman is 65 years old and about to retire. He had 740000 saved to supplement his pension and social security and would like to withdraw it in equal annual dollar amounts so that nothing is left after 18 years. How much does he have to withdraw each year if he earns 6 percent interest in his money
Answers
Answer:
Given that,
Richard Gorman is 65 years old and about to retire.
He had 740000 saved to supplement his pension and social security and would like to withdraw it in equal annual dollar amounts so that nothing is left after 18 years.
Let x be the amount withdraw each year.
Rate of interest is 6%.
Total amount received after 18 years is equal to the amount withdraw each year.
we get,
[tex]18\times x=740000\times(1+\frac{6}{100})^{18}[/tex][tex]x=\frac{740000}{18}\times(\frac{106}{100})^{18}[/tex][tex]x=\frac{740000}{18}\times(2.854)[/tex][tex]x=117345.054[/tex]Amount withdraw each year is $117345.054
The circuifference of a circular garden is 138.16 feet. What is the radius of the garden? Use 3.14 for it and do not round your
Answers
The circumference of a circle is given as:
[tex]C=\pi D[/tex]where D is the diameter. Plugging the value given and solving for D we have:
[tex]\begin{gathered} 138.16=(3.14)D \\ D=\frac{138.16}{3.14} \\ D=44 \end{gathered}[/tex]Now, the radius is twice the diameter, that means that:
[tex]r=\frac{D}{2}=\frac{44}{2}=22[/tex]Therefore the radius is 22 ft.
Question 15 of 25On a number line, where would 2.87 be located?OA. To the right of 2.88O B. Between 2.7 and 2.8OC. To the left of 2.86OD. Between 2.8 and 2.92.87
Answers
We can solve this problem graphing a number line.
The graph shows how the number of gallons of water in abathtub changes as the tub is being filled.a. What is the slope of the line?b. How can you show that the slope of the line is constant?
Answers
a. What is the slope of the line?
The slope of the line in this case (using the points (1,4) and (2,8)) is:
[tex]S=\frac{8-4}{2-1}=\frac{4}{1}=4[/tex]That function moves 4 units up for each unit to the right.
b. How can you show that the slope of the line is constant?
We can see it because regardless of the points we take, it will always be the same. When graph the slope we can see that similar triangles are always obtained.
Algebra: Refer to the figure to complete each proportion [tex] \frac{?}{b} = \frac{b}{s} [/tex]
Answers
The proportion would be:
[tex]\frac{c}{b}=\frac{b}{s}[/tex]this comes from the fact that we have to divide the hypotenuse of the triangle by the leg.
please help ASAP!!!!
Answers
We are given the below equation
[tex]\frac{x^2\text{ + 20}}{x(x-2)}\text{ = 14 -x / x -2}[/tex]Open the parenthesis
x^2 + 20/ x^2 - 2x = 14 - x / x - 2
Introduce cross multiply
(x^2 + 20)(x - 2) = x2 - 2x(14 - x)
Open the parentheses
x^3 - 2x^2 + 20x - 40= 14x^2 - x^3 - 28x + 2x^2
Collect the like terms
x^3 - 2x^2 + 20x - 40 = 14x^2 + 2x^2 - x^3 - 28x
x^3 + x^3 - 2x^2 - 16x^2 + 28x - 40 = 0
2x^3 - 18x^2 + 28x - 40 = 0
2 is common so factorize 2 out
2(x^3 - 9x^2 + 14x - 20) = 0
2 = 0 or x^3 - 9x^2 + 14x - 20 = 0
x^3 - 9x^2 + 14x - 20 = 0
You make two separate investments for a total of $4,000. The percent return on Charles Schwab & Co. at the end of the year was 5% and the percent return on Merrill Lynch with 7%. The combined return on both funds was $256. How much should you invest in each fund?
Answers
Let x represent the amount invested in Charles Schwab & Co.
Let y represent the amount invested in Merrill Lynch.
Given that the total amount invested is $4000, it means that
x + y = 4000
x = 4000 - y equation 1
The percent return is also known as the interest.
The interest from the amount invested with Charles Schwab & Co is 5%. The amount of interest is
5/100 * x = 0.05x
The interest from the amount invested with Merrill Lynch is 7%. The amount of interest is
7/100 * y = 0.07y
Given that the combined return on both funds was $256, it means that
0.05x + 0.07y = 256 equation 2
Substituting equation 1 into equation 2, it becomes
0.05(4000 - y) + 0.07y = 256
200 - 0.05y + 0.07y = 256
- 0.05y + 0.07y = 256 - 200
0.02y = 56
y = 56/0.02
y = 2800
x = 4000 - y = 4000 - 2800
x = 1200
$1200 should be invested with Charles Schwab & Co and $2800 should be invested with Merrill Lynch
is 4x1 = 1? Im iw furst grade
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4 x 1 ?
When you have four apples and you share it among your four friends
This implies that each of your friends will have one apple each
To calculate the total apples you have all together
1 + 1 + 1 + 1
= 4
This implies that 4 x 1 = 4
20 Which of the equations below has a slope of 1/4I. y = 1/4 x - 5II. ( y - 3.5) = 0.25 ( x - 2.75)III. 5x - 20y = 32IV. 5x + 20y = 32
Answers
We need to find which of the equations has a slope of 1/4
At first we should know that, the general form of the slope intercept form is
y = mx + b
Where m is the slope
So, we will check the options:
I. y = 1/4 x - 5
Compare to the general form
so, the slope = 1/4
II. ( y - 3.5) = 0.25 ( x - 2.75)
so,
y - 3.5 = 0.25x - 0.25 * 2.75
y = 0.25x -2.25 * 2.75 + 3.5
so, the slope = 0.25
III. 5x - 20y = 32
-20y = -5x + 32
Divide all terms by -20
y = (-5/-20) x - 32/20
y = 0.25 x - (32/20)
so, the slope = 0.25
IV. 5x + 20y = 32
20y = -5x + 32
Divide all terms by 20
y = (-5/20) + 32/20
y = -0.25 x + (32/20)
so, the slope = -0.25
As a result
The answer is option h). I , II and III only
thefind the slope of the line that goes through.givonpoints (8,9) (8,1)
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The formula used to calculate the slope of a line given the coordinates on the line is given to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points:
[tex]\begin{gathered} (x_1,y_1)=(8,9) \\ (x_2,y_2)=(8,1) \end{gathered}[/tex]Therefore, we can calculate the slope to be:
[tex]\begin{gathered} m=\frac{1-9}{8-8}=\frac{-8}{0} \\ m=undefined \end{gathered}[/tex]Therefore, the slope is undefined.
How do you find the area of a regular polygon given the perimeter?
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Given the perimeter, the area of a polygon is given by:
[tex]A=\frac{pa}{2}[/tex]Where "a" is the apothem, that is the perpendicular distance from the center of the polygon to one of its sides.
Find the multiplicative inverse of 0.3. Provide your answer below:
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1) Multiplicative inverses are the numbers whose product by the original number yields 1.
2) So examining the number 0.3 we can rewrite it as:
[tex]\frac{3}{10}[/tex]3) And therefore the multiplicative inverse of that is the number:
[tex]\frac{3}{10}\times\frac{10}{3}=\frac{30}{30}=1[/tex]SO the multiplicative inverse of 0.3 is:
[tex]\frac{10}{3}[/tex]GuitarPianoGirls 8113Did a larger percentage of the girlsor the boys pick piano?GirlsBoys
Answers
Answer: Larger percentage of boys pick piano
Explanation:
From the diagram, number of girls that pick piano = 12
Total number of girls = 8 + 12 = 20
∴ percentage of girls that pick piano = (number of girls that pick piano)/((total number of girls x 100
i.e )percentage of girls that pick pian = 12/20 x 100 = 60%
Similarly for boys, onumber ofboyls that pick piano =82
Total number of boys = 4 + 8 = 12
∴ percentage of boys that pick piano = (number of boys that pick piano)/(total number of boys) x 100
i.e percentage of boys that pick piano = 8/12 x 100 = 66.67%
Since 66.67% for boys is greater than 60% for girsl, then lLarger percentage of boys pick piano
Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(9x^2+3x-20\right)}{\left(3x^2-7x+4\right)}\div \frac{\left(6x^2+4x-10\right)}{\left(x^2-2x+1\right)}The numerator is AnswerThe denominator is Answer
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Using the definition of fractions division:
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}[/tex]Therefore:
[tex]\begin{gathered} \frac{9x^2+3x-20}{3x^2-7x+4}\div\frac{6x^2+4x-20}{x^2-2x+1}=\frac{(9x^2+3x-20)(x^2-2x+1)}{(3x^2-7x+4)(6x^2+4x-10)} \\ \end{gathered}[/tex]Using distributive property:
[tex]\frac{9x^4-15x^3-17x^2+43x-20}{18x^4-30x^3-34x^2+86x-40}[/tex]Factor:
[tex]\frac{(3x-4)(3x+5)(x-1)^2}{2(x-1)^2(3x-4)(3x+5)}[/tex]Simplify:
[tex]\frac{1}{2}[/tex]Answer:
The numerator is 1
The denominator is 2
someone someone please help it keeps cutting it off but it says determine which equation is parallel to line JK and which is perpendicular to line JK not all equations will be used so I have to put them in a perpendicular box and then the parallel box if somebody could help me
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Given the information, we have that the line passes through the points (-5,5) and (-2,0), therefore, we can find the equation like this:
[tex]\begin{gathered} \text{First we find the slope:} \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-5}{-2-(-5)}=-\frac{5}{3} \\ m=\frac{5}{3} \\ \text{Now we use the point-slope formula (using the point (-2,0)):} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-0=-\frac{5}{3}(x-(-2)) \\ \Rightarrow y=-\frac{5}{3}x-\frac{10}{3} \\ \text{Multiplying both sides by 3 we get:} \\ 3y=-5x-10 \\ \Rightarrow3y+5x=-10 \end{gathered}[/tex]Now that we have the equation of the line, we can easily find the parallel and perpendicular. For the parallel, we need that the line use the same slope (m=-5/3), therefore, from the options, the equation 5x+3y=13 is the only parallel to the original line. Now, for the perpendicular we have:
[tex]\begin{gathered} m_p=-\frac{1}{m}=-\frac{1}{-\frac{5}{3}}=\frac{3}{5} \\ \text{ Using the same point as before (-2,0) we get:} \\ y-0=\frac{3}{5}(x+2) \\ \Rightarrow y=\frac{3}{5}x+\frac{6}{5} \\ \text{Multiplying both sides by 5 we get:} \\ 5y=3x+6 \\ \Rightarrow-3x+5y=6 \end{gathered}[/tex]Therefore, the equation of the perpendicular line is -3x+5y=6
The equation y = ax² +bx+c goes through the coordinates (-3, -34), (5,-2), and (7,-14). What are the values of a, b, and c?
Answers
The values of a, b and c in the quadratic equation y = ax² + bx + c are a = -1, b = 6, y = -7
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the quadratic equation:
y = ax² + bx + c
At the point (-3. -34):
-34 = a(-3)² + b(-3) + c (1)
At the point (5. -2):
-2 = a(5)² + b(5) + c (2)
At the point (7, -14):
-14 = a(7)² + b(7) + c (3)
From the three equations:
a = -1, b = 6, y = -7
The values of a, b and c are a = -1, b = 6, y = -7
Find out more on equation at: https://brainly.com/question/2972832
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Can you prove only based on what is marked, that the triangles are congruent? If so, which triangle congruence theorem would you use? Explain how.
Answers
Answer
They are congruent by the HL congruence theorem
Step-by-step explanation
Given:
• Triangles MPQ and NPQ are right triangles
,• The hypotenuses of both triangles are congruent (MP is congruent to NP)
,• The leg PQ in MPQ is congruent to the leg PQ in NPQ
Then, applying the hypotenuse-leg (HL) congruence theorem, triangles MPQ and NPQ are congruent
5.) explain how you can use cubes to determine the cube root of a perfect cube. Use drawings or liking cubes to help you
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Note that the volume formula of a cube is :
[tex]V=s^3[/tex]where s = side of a cube
In a cube, all sides are equal.
And we know that the volume is s^3 which is definitely a cubic number.
Cubic number :
A number when multiplied by itself three times is a cubic number.
Getting the cube root of a perfect cube is like getting the measurement of one side of a cube given its volume.
When solving the side of a cube, we take the cube root of the volume.
[tex]\begin{gathered} V=s^3 \\ \sqrt[3]{V}=s \end{gathered}[/tex]Richard went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $6 per game. Joey went Thursday, paying $3 per game, plus rental fees of $16. By coincidence, they played the same number of games for the same total cost. How much did each one spend? How many games did each one play?
Answers
Richard went to play miniature golf on Monday when it cost $7 to rent the club and ball, plus $6 per game. Joey went Thursday, paying $3 per game, plus rental fees of $16. By coincidence, they played the same number of games for the same total cost. How much did each one spend? How many games did each one play?
________________________________________
Richard
Monday $7 to rent the club and ball, plus $6 per game.
7 + 6* G = Total cost (I)
Joey
Thursday, paying $3 per game, plus rental fees of $16.
16 + 3* G = Total cost (II)
__________________________
Solving the system of equations
(I) = (II)
7 + 6* G = 16 + 3* G
6G - 3G = 16 -7
3 G = 9
G = 3
___________________
Can you see the updates?
______________________
Total cost (3 games)
Richard
7 + 6* 3 = 25
Joey
16 + 3* 3 = 25
___________
Answer
Each one played 3 games and spent $25.
What is this expression in simplified form?V12 · 4V36244 157.
Answers
Answer
Option B is correct.
Answer = 24
Explanation
We are asked to simplify,
√12 . 4√3
= √12 × 4√3
= √(4 × 3) × 4√3
= √4 × √3 × 4√3
= 2 × √3 × 4 × √3
= 2 × 4 × √3 × √3
= 8 × √3 × √3
= 8 × 3
= 24
Hope this Helps!!!
The area of a triangle is 36 square inches (in^2). It's altitude (h) is 9 inches. How long is it's base?
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The length of the base can be determined as,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ 36in^2=\frac{1}{2}b(9in) \\ b=\frac{36in^2\times2}{9in} \\ b=8in \end{gathered}[/tex]Thus, the length of the base is 8 in.