The correct option is A.
domain: x > -2; range: all real numbers
Which is the domain and range of the given function?
Here we have a logarithmic function.
Remember that the argument of a logarithm must be larger than zero, in this case the argument is:
x + 2
So we must have:
x + 2 > 0
x > -2
Then the domain is: x > -2.
And the range of any logarithmic function is the set of all real numbers.
Then the correct option is A.
domain: x > -2; range: all real numbers
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Find the missing side length of the triangle
Answer:
b = 24 meter
Step-by-step explanation:
Using Pythagoras theorem:
a² + b² = c²
Here given: a = 10 m, b = ?, c = 26 m
Insert values
10² + b² = 26²
b² = 26² - 10²
b² = 676 - 100
b² = 576
b = √576
b = 24
Answer:24
Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.
so according to formula,h squared=b squared+p squared
so,26 squared=10 squared+p squared.
in order to find p
p squared=26 squared -10 squared
which gives us 576
and p squared =576
the square on the p will go on the other side and become an underroot.
take the underoot of 576
which gives us p=24.
so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula
John ate a whole pizza which has 2,368 Cal. If he burns 125 Cal by walking for 30 minutes, how long would it take to burn off the entire pizza by walking
The time taken to burn off the entire pizza by walking is 568.32 minutes.
Time taken to burn caloriesTotal calories in pizza = 2,368Total calories burnt per 30 minutes walk = 125Number of 30 minutes walk to burn all calories = w2,368 = 125 × w
2,368 = 125w
w = 2,368 / 125
w = 18.944
Total time needed to burn all calories = 30 minutes × 18.944
= 568.32 minutes
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a senator wishes to estimate the proportion of united states voters who favor new road construction. what size sample should be obtained in order to be 95% confident
The size of the sample should be obtained at 2401 in order to be 95% confident
Given that:
Margi of error, [tex]ME=0.02[/tex]
Population proportion, [tex]p=0.50[/tex]
To Find: The size of the sample that should be obtained in order to be 95% confident
Let the size of the sample be n
Using formula,
[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]
Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident
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In the following exercises, multiply the binomials. Use any method.
248. (m + 11)(m − 4)
Answer:
Hence the expression [tex]$$(m+11)(m-4)=m^2+7m-44$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (m+11)(m-4).We have to multiply the given expression.Multiply the (m+11) by -4, multiply the (m+11) by m then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$[/tex]
Find the value of a.
The value of a is (c) 86
How to solve for a?The given parameter is:
Angle C = 86
By vertical angle theorem, we have:
Angle A = Angle C = 86
This implies that:
Angle A = 86
The arc A subtends angle A
This means that:
Arc A = 86
Hence, the value of a is (c) 86
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Use your graphing calculator to find the equation of the trend line for the scatterplot below.
The equation of the trend line is y = 3x + 15
How to determine the equation of the trend line?Start by entering the table of values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 21Sum of Y = 153Mean X = 3.5Mean Y = 25.5Sum of squares (SSX) = 17.5Sum of products (SP) = 52.5The equation of the trend line is represented as:
y = bx + a
Where
b = SP/SSX = 52.5/17.5 = 3
a = MY - bMX = 25.5 - (3*3.5) = 15
This gives
y = 3x + 15
Hence, the equation of the trend line is y = 3x + 15
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Can someone help me please
Answer:
y = 3x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6
y = 3x - 6 ← equation of line L
Use the point and the slope to graph each line. Write the equation of the line :
The line passes through the point (1,-1) and is parallel to a line that has slope 1.
What is the equation of the line
Answer:
Step-by-step explanation:
Since the new line is parallel to the one that has a slope of 1, we can write:
y = 1x + b for the new line
Remember that y=mx+b, where m is the slope and b the y-intercept, the value of y when x=0.
We need to find a value of b that forces the line through point (1,-1). Use (1,-1) in the equation and solve for b:
y = 1x + b
-1 = 1*(1)+b
b = -2
The equation of the line parallel to one with slope of 1 and going through point (1,-1) is:
y = 1x - 2
I am totally horrible at geometry! can someone help me please
Answer: 6
Step-by-step explanation:
We will set up a proportion to solve. Let x be equal to ?.
[tex]\displaystyle \frac{3}{5} =\frac{x}{x+4}[/tex]
Now, we will cross-multiply.
3 * (x + 4) = 5 * x
3x + 12 = 5x
12 = 2x
6 = x
How many different student body governments are possible if there are 7 seniors, 3 juniors, and 4 sophomores running for the student body offices of senior class president, junior class president, and sophomore class president
There are 84 possible student body governments
The number of student body governmentsThe given parameters are:
Senior = 7
Junior = 3
Sophomore = 4
The number of student body governments is calculated as:
n = Senior * Junior * Sophomore
This gives
n = 7 * 3 * 4
Evaluate
n = 84
Hence, there are 84 possible student body governments
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Line l contains points (2,4) and (5,1). Point P has coordinates (1,1). Find the distance from P to l.
The least distance from point P to line l is approximately equal to 3.536 units.
How to find the least distance between a line and a point outside the line
There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:
Vector parallel to the line l
[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]
[tex]\overrightarrow{AB} = (3, - 3)[/tex]
A vector from one point on the line l to the point P
[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]
[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]
Now we proceed to find the vector distance by using the following vectorial formula:
[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]
[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]
[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]
[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]
[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]
The magnitude of the vector distance is determined by Pythagorean theorem:
[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]
d ≈ 3.536
The least distance from point P to line l is approximately equal to 3.536 units.
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The intersection of lines y=-14x+3 and y=-32x+3 is .
The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)
How to determine the intersection of the lines?The lines are given as:
y = -14x + 3 and y = -32x+3
Substitute y = -32x+3 in
-32x+3 = -14x + 3
Evaluate the like terms
-18x = 0
Divide by -18
x = 0
Substitute x = 0 in y = -14x + 3
y = -14(0) + 3
Evaluate
y = 3
Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)
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6. The city needs to buy grass to cover
the driving range. The measurement of the
driving range is 100 by 372 yards. If one bag
of grass seed covers 75 square yards, how.
many bags will the city need to buy to seed.
the driving range?
(A) 160
(B) 357
(C) 496
(D) 653
Answer:
(C) 496
Step-by-step explanation:
area = 100 yd × 372 yd = 37,200 yd²
37,200 yd² / 75 yd² = 496
Answer: (C) 496
How many solutions does this system of equations have? x² + y² = 25
x² - 6=0
The system of equation have one solution.
How to solve system of equation?x² + y² = 25
x² - 6 = 0
x² = 6
x = √6
Therefore, let's substitute the value of x in equation (i)
x² + y² = 25
(√6)² + y² = 25
y² = 25 - 6
y² = 19
hence,
y = √19
Therefore, the system of equation have one solution.
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(b) An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Also find:
(i) how many use only Radio?
(ii) how many use only Television?
(iii) how many use Television and Magazine but not radio?
Answer:
Here you go with your correct answer
peating decimal 0.353535...? 35+ 0.35 +0.0035 + ... 0.0035 + 0.000035 + 0.00000035 + ... 0.35 +0.0035 + 0.000035 + ... OMPLETE he first term of the geometric series is 0.35.- v COMPLETE vity Intro Final COMPLETE The simplified fractional representation of 0.353535... is 35 99 COMPLETE X0.01. 10 of 11 O TU peating decimal 0.353535 ... ? 35+ 0.35 +0.0035 + ... 0.0035 + 0.000035 + 0.00000035 + ... 0.35 +0.0035 + 0.000035 + ... OMPLETE he first term of the geometric series is 0.35.- v COMPLETE vity Intro Final COMPLETE The simplified fractional representation of 0.353535 ... is 35 99 COMPLETE X0.01 . 10 of 11 O TU
The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035
How to Identify a Repeating Decimal?
We want to find the option that is equal to the repeating decimal 0.353535.
Option A; 35 + 0.35 + 0.0035
When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.
Option B; 0.0035+ 0.000035 + 0.00000035
When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.
Option C; 0.35 + 0.0035 + 0.000035
When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.
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Answer:
1.) C - 0.35+0.0035+0.000035+...
2.) The first term of the geometric series is 0.35.
3.) The common ratio of the geometric series is 0.01
4.) The simplified fractional representation of 0.353535... is 35 / 99
Step-by-step explanation:
Edge
A thunderstorm cloud holds about 6,200,000,000 raindrops .which of the following shows this number in scientific notation?
Answer: [tex]6.2 *10^9[/tex]
Step-by-step explanation:
Scientific notation is large numbers expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10
So the first number cannot be 6200 or 62 or 0.6, it has to be 6.2 because 6.2 > 1 and 6.2 < 10
count your numbers right of the decimal and you should get:
[tex]6.2 *10^9[/tex]
In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of the cocktail is orange juice?
Give your answer as a fraction in its simplest form.
30+20+50 = 100 ml total. 20 ml is orange juice.
So, 30/100 reduce by dividing top and bottom by 30 gives
3/10 is the proportion of orange juice in the fruit cocktail.
Hope this helps! :)
Answer:
3/10
Step-by-step explanation:
First, find the total amount of liquid for a drink with 30 mls of orange juice
Assume volumes can be added
30+20+50 = 100 ml
the percentage/proportion of orange juice in the drink is the number of mls of orange juice divided by the total volume
so
30/100
which can be reduced to 3/10
Math
The equation 5 + 10x = 20 can be used
to find x, the cost of a ride ticket at
an amusement park. Which statement
explains the best possible first step to find
the cost of a ride ticket?
1
A Add 5 to both sides.
BSubtract 20 from both sides.
CMultiply both sides by 10.
D Subtract 5 from both sides.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\large\textsf{(We will solve for your given question as well because it}\\\large\textsf{pops up in solving for your question.)}[/tex]
[tex]\huge\textbf{Solving for your original answer:}[/tex]
[tex]\mathbf{5 + 10x = 20}[/tex]
[tex]\mathbf{10x + 5 = 20}[/tex]
[tex]\huge\textbf{SUBTRACT 5 to BOTH SIDES:}[/tex]
[tex]\mathbf{10x + 5 - 5 = 20 - 5}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{10x = 20 - 5}[/tex]
[tex]\mathbf{10x = 15}[/tex]
[tex]\huge\textbf{DIVIDE 10 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{10x}{10}=\dfrac{15}{10}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{15}{10}}[/tex]
[tex]\mathbf{x = \dfrac{15\div5}{10\div5}}[/tex]
[tex]\mathbf{x = \dfrac{3}{2}}[/tex]
[tex]\mathbf{x = 1 \dfrac{1}{2}}[/tex]
[tex]\mathbf{x = 1.5}[/tex]
[tex]\huge\textbf{Therefore, the overall answer should be:}[/tex]
[tex]\huge\boxed{\star\boxed{\mathsf{\ x= \dfrac{3}{2} \ }}\star}[/tex]
[tex]\huge\textbf{And to answer your question, the very}\\\\\huge\textbf{first step in solving for this equation}\\\\\huge\textbf{[5 + 10x = 20] is:}[/tex]
[tex]\huge\boxed{\textsf{Option D. Subtract 5 to both sides}}\huge\checkmark\\\\\\\\\\\large\text{Look at the explanation above to see how we chose that.}\\\\\large\text{Remember: addition opposite is subtration \& subtraction opposite}\\\large\text{is addition, whereas multiplication is division \& divsion is}\\\large\text{is multiplication.}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
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53:34
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Option 3 and 4. The two options that shows the correct representation of the inequality are:
- 6x + 15 < 10 - 5xAn open circle is at 5 and a bold line starts at 5 and is pointing to the right How to solve the inequality–3(2x – 5) < 5(2 – x)
We have to open up the brackets by multiplying the sides
= -6x + 15 < 10 - 5x
Hence the third option is certified to be correct.
Next this inequality has to be shown on a number line.
To do this we have to solve the inequality completely
From -6x + 15 < 10 - 5x
we have to take like terms
-6x+5x < 10 - 15
-x < -5
x<5
The sign of inequality has to be reversed given that the coefficient of x was negative.
Hence x>5. The number line would start from the right and it would move towards the right
From the solution here, we can see that the two correct options are
–6x + 15 < 10 – 5x An open circle is at 5 and a bold line starts at 5 and is pointing to the right.Read more on number lines here:
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A toilet is leaking at the rate of 1 fluid ounces per minute. How many gallons is
the toilet leaking per hour?
O 0.47 gal/hr
O 0.94 gal/hr
O 28.13 gal/hr
O 2.13 gal/hr
1 gallon (gal) = 128 fluid ounce (fl oz)
1 hour (hr) = 60 minutes (min)
Convert 1 fl oz/min to gal/hr.
[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]
Translate the statement into a mathematical equation.
9 times a number subtracted from 7 times the number is 26.
Answer:
7x - 9x = 26
Step-by-step explanation:
9 times a number = 9x
7 times the number = 7x
=26 because it says so
and 9x subtracted from 7x is 7x - 9x
Jason bought 10 of the 30 raffle tickets for a drawing. assuming that he chooses the winning ticket each time, what is the probability that jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away?
Answer: 2.96% rounded
Step-by-step explanation: 10/30) x (9/29) x (8/28) = 720 / 24,360 = 6/203 = 2.96%
Find the area of the following shape
Answer:
56.8 m²
Step-by-step explanation:
This shape is clearly a trapezium / trapezoid. So :
Area of a trapezium is given by the formula :
[tex]\frac{a+b}{2} h[/tex]
Substitute values given in diagram :
a = 4.2
b = 10
h = 8
[tex](\frac{4.2+10}{2} )8[/tex]
7.1 × 8 = 56.8
Units will be m² as this is area
Giving us our final answer of 56.8 m²
THAT IS THE QUATION OF Y=7X+300
Answer:
Slope=14.000/2.000=7.000
x-intercept = 300/-7 = -42.85714
y-intercept = 300/1 = 300.00000
Step-by-step explanation:
how do u write 99.09 - 98.29 in a long subtraction line by line and where do u put the answer?
The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
How to calculate the value?It should be noted that the subtraction line is simply used to subtract numbers.
In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
When subtracting the numbers on the number line, we will move towards the left hand side of the number line.
An illustration of the number line is given.
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Point R is between points Q and S. Label the
picture, then find x and the measure of QS.
3x+7
1---
8x
28
The measure of angle QS based on the information given when Point R is between points Q and S is 11x + 35.
How to depict the information?From the information given,
PR = 3x + 7
QR = 8x + 28
The value of QS will be:
PR + QR
= (3x + 7) + (8x + 28)
= 11x + 35
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pls help The surface area of a cone is given by the formula
S= al +712. Solve the formula for 2.
Answer:
l = (S/pi)-r^2
Step-by-step explanation:
Just rearrange the equation.
S = pi*l + pi * r^2
S-pi*r^2 = pi*l
l = (S-pi*r^2)/pi
l = (S/pi)-r^2
If the acute angle made by lines /and mis 24° and AABC is reflected across line /
followed by a reflection across line m, find the angle through which AABC is rotated.
B
m
The angle through which ΔABC is rotated is; Option A: 48°
How to Interpret Transformation Reflection?Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.
In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°
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The unit digit of a two digit number is one less than the ten digit number. If the number is increase by 8 and then divided by the unit of the digits, the results is 8. Find the number.
The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
Lets simplify the problem,
Let assume the "tens" digit be x
Then the "units" difference = (x-1), according to the condition.
Hence, the number itself is N = 10x + (x-1).
Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.
From the last statement of the problem, we have this equation
[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]
Simplify and find "x"
[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].
Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
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