Answer:
[tex] {3}^{x} = 243 = {3}^{x} = {3}^{5} = 5[/tex]
Write a compound inequality for the graph shown below.
Use x for your variable.
Check the picture below.
Look at this graph.
y
x
-100
-80
-60
-40
-20
20
40
60
80
100
-100
-80
-60
-40
-20
20
40
60
80
100
0
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of the line in the graph in slope-intercept form is: y = -5x - 30.
How to Write an Equation of a Line in Slope-intercept Form?To be able to write the equation of a line in slope-intercept form, y = mx + b, find the value of the slope (m) = rise/run, and the value of the y-intercept (b), which is the value of y where the line intercepts the y-axis.
From the given graph, we have:
Slope (m) = rise/run = -50/10
Slope (m) = rise/run = -5
The y-intercept (b) = -30
Substitute m = -5 and b = -30 into y = mx + b:
y = -5x + (-30)
y = -5x - 30
Thus, the equation of the line in the graph in slope-intercept form is: y = -5x - 30.
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Life expectancy for all the different countries in the world ranges from a low of only 52.2 years (in sierra leone) to a high of 84.7 years (in hong kong). life expectancies are clustered at the high end, with about half of all the countries having a life expectancy between about 74 and the maximum of 84.7. a few countries, such as sierra leone, have a very low life expectancy.
a. what is the shape of the distribution of life expectancies for all countries?
a) symmetric.b) skewed to the right.c) skewed to the left.d) none of these.b. from the information given, estimate the median of the life expectancies.c. will the mean be larger or smaller than the median?
From the given distribution, we have that:
a) The distribution is skewed to the left.
b) The median is of 74.
c) The mean will be smaller than the median.
Figuring the skewness with the mean and the median:Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedSince life expectancies are clustered at the high end, the outliers are small life expectancies, meaning that the mean will be smaller than the median and the distribution is skewed to the left.
The median of a data-set is the 50th percentile, the value that separates the bottom 50% of the data-set from the upper 50%.
In this problem, we have that about half of all the countries having a life expectancy between about 74 and the maximum of 84.7, meaning that 74 is the median.
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|5x|=3
this is absolute value of five x equals three
The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.
What is a modulus function ?In mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.
According to the given question |5x| = 3.
We know |x| = a implies x = a or x = -a.
∴ |5x| = 3 is
5x = 3
x = 3/5
Or
5x = -3.
x = -3/5.
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What is the logarithmic form of each equation?
b. 8/27 = (2/3)³
The expression becomes 3log₁₀2-3log₁₀3
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
logₐb where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logₐbc where a is the base is given as logₐb + logₐc
logₐbc where a is the base is given as logₐb-logₐc
Now it is given to us to find the logarithmic form of 8/27=(2/3)^3
Let us consider the base of the logarithm to be 10
thus log₁₀8/27=log₁₀(2/3)^3
log₁₀8/27=log₁₀(2/3)^3
We know that logₐb can be written as log₂b/log₂a
Hence
log₁₀8/27= 3(log2/3)
log₁₀8/27=3(log2-log3)
log₁₀8/27= 3log2-3log3
Hence the expression becomes 3log2-3log3
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PLEASE HELP ASAP!!!
Will give 15 points!!
B is between A and C, AB=13.7 and BC=8.3. Find AC.
AC = 20
AC = 22
AC = 17
AC = 19
Answer:
22
Step-by-step explanation:
add ab and bc to get ac
11. Reflected over the x-axis, 2 units left and down 5 units. what is the equation?
Answer: its (2,5) or (2,-5)
Step-by-step explanation:
basically it depends on the location like for example: if a dot is in the Q4 area which is (-x,-y) or Q3 is (-x,y) and Q2 is (x,-y) and Q1 is (x,y) so yeah hope it helps
What is this " the temperature is 1f at dusk. it is 8 degrees colder at dawn what is the temperature at dawn?'
The temperature at dawn is -7 F.
What is the temperature at dawn?If it is 8 degrees colder at dawn than it is at dawn, it means that the temperature is lower in the dawn than it is in the dusk. Thus, to determine the temperature at dawn, subtract 8 from the temperature at dusk.
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.
Temperature at dawn = termpature at dusk - difference in termpature
1 - 8 = -7
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Last year at a certain high school, there were 150 boys on the honor roll and 84 girls
on the honor roll. This year, the number of boys on the honor roll decreased by 12%
and the number of girls on the honor roll decreased by 25%. By what percentage did
the total number of students on the honor roll decrease? Round your answer to the
nearest tenth (if necessary).
The total percentage decrease in the number of students on the honor roll is 16.67%.
What is the percentage decrease?
Percentage is a measure of frequency that is used to express a number as a fraction of an amount out of 100. The sign used to denote percentage is %. In order to convert a number to percentage, multiply the number by 100.
The first step is to determine the number of boys on the honor roll this year.
Number of boys on the honor roll this year : (1 - percentage decrease) x number of boys last year
(1 - 0.12) x 150
0.88 x 150 = 132
The second step is to determine the number of girls on the honor roll this year.
Number of girls on the honor roll this year : (1 - percentage decrease) x number of girls last year
(1 -0.25) x 84
0.75 x 84 = 63
Total number of students on the honor roll last year = 150 + 84 = 234
Total number of students on the honor roll this year = 63 + 132 = 195
Percentage decrease :[ (195 /234) - 1] x 100 = 16.67%
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-3xy = ? when x = 8 and y = -9
Answer:
[tex] {6}^{12} \times 36 =[/tex]
Answer:
216
Step-by-step explanation:
If x = 8 & y = -9
Put in place -3 (8)(-9)
-24 * -9 = 216
How to solve system of equations?
8q-15r=-40
4q+2r=56
Answer:
q=10, r=8
Step-by-step explanation:
You have to first cancel one of the variables.
8q-15r=-40
4q+2r=56
To do this, multiply the second equation by -2.
8q-15r=-40
-2(4q+2r)=(56)(-2)
Multiply it out.
8q-15r=-40
-8q-4r=-112
Combine like terms.
-19r = -152
Divide by -19 to get the value of r.
r=8
Substitute r back into one of the equations, it does not matter which one. I'll do both.
8q-15(8)=-40
8q-120=-40
8q=80
q=10
4q+2(8)=56
4q+16=56
4q=40
q=10
You should get the same value for q for both.
In the instance where the variables are x and y, which they usually are, you would write your answer as an ordered pair, (x, y).
(10, 8)
Answer:
q=10 and r=8
Step-by-step explanation:
8q-15r=-40 ...........equation(i)
4q+2r=56................eqn(ii)
Now,
Multiplying eqn (ii) by 2 then we get,
8q+4r=112..........eqn(iii)
Here, Subtracting eqn (i) and (iii)
8q-15r=-40
8q+4r=112
(-) (-) (-)
---------------------
-19r=-152
r= -152/-19
r= 8
Again, Putting the value of r in eqn (ii)
4q+2r=56
4q+2×8=56
4q=56-16
q=40/4
q=10
I need help please……
Answer:
Its 3D 6U
or -2/-2
Step-by-step explanation:
12z=108 what’s the value of z
Answer:
z = 9Step-by-step explanation:
12z=108 what’s the value of z
12z = 108
z = 108 : 12
z = 9
check
12 * 9 = 108
108 = 108
the answer is good
Solve each inequality using a table.
(Hint: For more accurate results, set ΔTbl=0.001 .)
5(3)x ≤ 2
After solving the given inequality the answer is x∈(-∞, 2/15].
What precisely do we mean by inequality?In mathematics, an inequality is a relationship that arises from a non-equal comparison of two numbers or other mathematical expressions.It is most commonly used on a number line to compare the sizes of two numbers.So,
Given: 5(3)x ≤ 2Then,
5(3)x≤215x≤2x∈(-∞, 2/15]Therefore, after solving the given inequality the answer is x∈(-∞, 2/15].
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What can be concluded from the graph shown here?
Correct answer is D. Nothing can be determined from the given graph.
What may a graph be used to analyze?A graph is a type of graphic used to display data and show relationships. Graph analysis is helpful for identifying the overall trend, connecting experiment findings to the hypothesis, and creating hypotheses for next studies.
You may compare various figures, comprehend how various components affect the overall, or examine patterns using a chart or graph. Charts and graphs can also be helpful for seeing data that deviates from what you're used to or for assisting in the understanding of group relationships.
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Find the acceleration of a car that takes 4 seconds to stop at a red light from a velocity of 80 km/h
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
What is the acceleration of the car?
Newton's first equation of motions states that;
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration and t is time.
Given the data in the question;
Since the car is stopping, final velocity v = 0Initial velocity u = 80 km/hTime elapsed t = 4sAcceleration = ?First, convert the unit of the initial velocity from kilometer per hour to meter per seconds
Initial velocity = 80 km/h = ( 80 × 5/18 )m/s = 2.2222 m/s
Now, plug these values into the equation above and solve for a.
v = u + at
0 = 22.2222m/s + ( a × 4s )
a × 4s = -22.2222m/s
a = 22.2222m/s ÷ 4
a = -5.56m/s²
Negative sign shows that the car is slowing down.
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
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Solve each equation.
log x-log 2=3
value of x in given logarithmic equation is = 2000
What is logarithmic function ?In, mathematics a logarithmic function is inverse of exponential function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]a^x = N[/tex] is and exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log x - log 2 =3
using formula, log a - log b = log a/b
=> log x/2 = 3
=> x / 2 = 10³
=> x = 2 . 10³ = 2000
Thus solution for this equation is x =2000.
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In the proof below, determine which reason should go in each line.
Given: 5x+4)= 6x-5
Prove: x = 25
The function
models the height of a gymnast on a trampoline over time, where
is feet above the ground level and is the number of seconds since the start of their jump.
Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?
The approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to approximate the height of the gymnast above the ground level after 1.2 seconds?The complete question is added at the end of the solution
The equation of the height function is given as
h(t) = -5t² + 10t+4
After 1,2 seconds, we have:
t = 1.2
Substitute t = 1.2 in the equation h(t) = -5t² + 10t+4
So, we have
h(t) = -5 x 1.2² + 10 x 1.2 + 4
Evaluate the exponent
So, we have
h(t) = -5 x 1.44 + 10 x 1.2 + 4
Evaluate the products
So, we have
h(t) = -7.2 + 12 + 4
Evaluate the sum
So, we have
h(t) = -7.2 + 16
Evaluate the difference
So, we have
h(t) = 8.2
Hence, the approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
This means that the required approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
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Complete question
The function h(t) = -5t² + 10t+4 models the height of a gymnast on a trampoline over time, where is feet above the ground level and is the number of seconds since the start of their jump.
Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?
Please help me with this.
Consider the function f(x)= -3x^3-4x^2+x+2
A partial graph is shown below, find all the zeros of the function using division and factoring. Please show all work.
Using division and the graph, the zeroes of the function are given as follows:
x = -1 with multiplicity 2.x = 2/3 with multiplicity 1.How do we find all the zeros of the function?The function in this problem is defined as follows:
f(x) = -3x³ -4x² + x + 2.
From the graph, we have that x = -1 is a zero of the function, meaning that it can be written as follows:
-3x³ -4x² + x + 2 = (x + 1)(ax² + bx + c).
The other zeros will be the zeros of ax² + bx + c. To find the coefficients, we use a system of equations, hence:
(x + 1)(ax² + bx + c) = -3x³ -4x² + x + 2
ax³ + (a + b)x² + (c + b)x + c = 2.
Hence the coefficients are given by:
a = -3.c = 2.a + b = -4 -> b = -1.Thus the quadratic equation that we have to solve is:
-3x² - x + 2 = 0
3x² + x - 2 = 0.
Hence:
[tex]\Delta = 1^2-4(3)(-2) = 25[/tex][tex]x_1 = \frac{-1 + \sqrt{25}}{6} = \frac{2}{3}[/tex][tex]x_2 = \frac{-1 - \sqrt{25}}{6} = -1[/tex]The zeroes of the function are given as follows:
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Is the equation: x² + y² = 9
a function. Explain.
Answer: x² + y² = 9 is not a function
Step-by-step explanation: In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation. and therefore the equation is not a function.
x^2+y^2=9
if for example x=0
There are two values for y(namely+3 and -3) which satisfy the equation and therefore the equation is not a function
Amy bought 8 packs of cherry fruilt snacks. Each pack has 7 fruilt snacks Mary bought tropical fruit snacks. Each tropical fruit snack packs has 9 trult
snacks
Amy bought 11 more fruit snacks than Mary. How many packs of tropical fruit snacks pid Mary buy?
A 12
B 5
C 8
D 10
Answer:
B - 5
Step-by-step explanation:
Amy = 8 packs × 7 snacks
Amy = 56 snacks altogether
Mary = Amy - 11
Mary = 56 - 11
Mary = 45 snacks altogether
Mary = 45 snacks / 9 tropical fruit snacks
Mary = 5 packs of tropical fruit snacks
Hope this Helps! :)
- Riona
eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. of the aircraft that are discovered, 65% have an emergency locator, whereas 82% of the aircraft not discovered do not have such a locator. suppose a light aircraft has disappeared. (round your answers to three decimal places.)
the y-intercept is (0,12)
the axis of summer is x=4
the vertex is ( , )
f(x)=x^2-8x+12
Answer:
The vertex is (4,-4)
Step-by-step explanation:
Plug in x=4 in the equation
What is the value of the expression below when y=5?
3y^2 +7y+2
Answer:
112
Step-by-step explanation:
3y^2 + 7y + 2
if y = 5, then 3(5^2) + 7(5) + 2
= 3(25) + 35 + 2
= 75 + 37
= 112
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The graph shown represents a linear function.
Which of the following equations represents the graph?
A. Y= - 5/3x -5
B. Y= - 5/3 x -3
C. Y= - 3/5x -5
D. Y= - 3/5x -3
Jack cleans windows for extra income. He charges $3.00 for a main floor window and $5.00 for a second-story window. How much will he earn if he cleans a house with 7 main floor windows and 6 second-story windows?
Answer:
51
Step-by-step explanation:
$3 time 7 = $21
$5 time 6 =30
21+30 = $51
5+5/3-3/2 giải hộ mình với cảm ơn bạn nhiều
Answer:
5.16666666,...
Step-by-step explanation:
5 + (5/3) - (3/2)
5 + 1.66666666667 - 1.5
5 + 0.16666666666
5.16666666666,...
Nhân chia trc cộng trừ sau
Answer:
31/6 ( or 5 1/6)
Step-by-step explanation:
5 + 5/3 - 3/2 =
5 + 1/6 =
31/6
Given f(x) = x² + 5x +6 and g(x) = x +2, find (g ◦ f)(x)
Answer:
x² + 5x + 8
Step-by-step explanation:
This issue is about "function composition",
(g ° f) means
g(f(x)) = g(x² + 5x +6)
= x² + 5x +6 + 2
= x² + 5x +8