Yes it is possible to make the prediction about Ramiro's School but not completely.
It is possible to use the information from Ramiro's sample to make predictions about the school-wide results, but it is important to note that the sample may not be fully representative of the entire population of students at the school. There may be sampling biases or other factors that affect the results.
With that said, based on the information provided, we can calculate the proportion of students in Ramiro's sample who use the library in a certain way, and then use that proportion to estimate the number of students at the school who use the library in that way.
For example, if Ramiro's sample shows that 40 out of the 60 people he surveyed use the library to study, we can estimate that approximately 40/60 = 67% of the school's students use the library to study. We can then use this proportion to estimate that approximately 540 x 67% = 361 students at the school use the library to study.
It's important to note that these predictions are based on sample data and they may not be accurate. To make more accurate predictions, a larger, more representative sample would be needed.
For more information about prediction visit: brainly.com/question/27154912
#SPJ4
need help with #7 a and b. i’m in Algebra 1 and this is lesson 5 Exponential Algebra and Functions.
There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.
A ratio is what?A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.
Here,
The ratio of, say, the highest-degree words serves as the upper bound as x grows.
There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.
To know more about ratio visit:
brainly.com/question/13419413
#SPJ1
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
-1, 0, 4
Step-by-step explanation:
2f - 8 ≤ 6f + 4
-4f ≤ 12
f ≥ 12/-4 **flip the inequality when you divide by a negative number
f≥ -3
Check all the answers that are ≥ -3
Find the volume of given solid figure.
Answer:
48cm3
Step-by-step explanation:
Volume of a rectangular box = a.b.c
The volume of the solid figure: (2.2.5) + (7.2.2) = 20 + 28 = 48 cm3
Hi, please help (see image)
I need help on question b) and c)
This homework is due very soon !!! ( SOS)
Answer:
b: Two thousand four hundred and forty (2440)
c: 1.33 x 10^27
Step-by-step explanation:
I'm uncertain by what an ordinary number is, but to calculate the answer for part b, you need to divide the diameter of Mercury by 2, which would give the aforementioned answer.
As for part c, you will need to subtract the masses of Jupiter and Saturn:
mass of Jupiter - mass of Saturn = 1.33 ×[tex]10^{27}[/tex]
20. Below are massesof students taken in a medical centre. 37 60 35 38 59 34 56 42 55 48 39 33 36 35 43 52 39 64 41 35 20 31 29 45 32 54 66 44 47 45 27 24 48 28 55 (a) Starting with the class 20-29 and class size of 10, make a frequency distribution table for the data. (2 marks)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Class} & \text{Frequency}\\\cline{1-2}20-29 & 5\\\cline{1-2}30-39 & 12\\\cline{1-2}40-49 & 9\\\cline{1-2}50-59 & 6\\\cline{1-2}60-69 & 3\\\cline{1-2}\end{array}[/tex]
=====================================================
Explanation:
The given data set is
{37, 60, 35, 38, 59, 34, 56, 42, 55, 48, 39, 33, 36, 35, 43, 52, 39, 64, 41, 35, 20, 31, 29, 45, 32, 54, 66, 44, 47, 45, 27, 24, 48, 28, 55}
It sorts to
{20, 24, 27, 28, 29, 31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39, 41, 42, 43, 44, 45, 45, 47, 48, 48, 52, 54, 55, 55, 56, 59, 60, 64, 66}
The five values 20,24,27,28,29 are between 20 and 29. This means the first class or bin will have a frequency of 5.
The next interval spans from 30 to 39. There are 12 items in this interval, and those 12 items are this subset {31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39}. This means we have a frequency of 12 for the interval from 30 to 39.
Keep this process going until you get to the end of the data set.
What range of values is not a possible scale factor (k)?
A) k 1
D) all are possible
A range of values which is not a possible for scale factor (k): k = 0
We know that the scale factor is the number (also called the conversion factor) which is used to change the size of a figure without changing its shape.
It is used to expand or compress the size of an object.
The scale factor formula is:
Scale factor = Dimensions of the transformed shape ÷ Dimensions of the original shape
If the scale factor k > 1, the object is enlarged.
If the scale factor is 0< k <1, the object is compressed.
If the scale factor is k = 1, the shape of object remains the same.
And the scale factor cannot be zero.
Learn more about the scale factor here:
https://brainly.com/question/11349851
#SPJ4
What is perimeter also called?
Perimeter is the total length of all sides of a shape, also known as the circumference.
Perimeter is a measure of the distance around a two-dimensional shape. It is the sum of the lengths of all the sides of a shape. Perimeter is also known as the circumference. When calculating perimeter, you measure the length of each side of the shape and add them together. For example, the perimeter of a square with sides of 4 inches each would be 16 inches. Perimeter is an important concept in geometry, and it can be used to calculate area, the space within a shape or figure. It can also be used to calculate the distance between two points. Knowing the perimeter of a shape can help you solve many problems in math, design, and science.
Learn more about perimeter here
https://brainly.com/question/6465134
#SPJ4
A sine function has an amplitude of 3, a period of π, and a phase shift of [tex]\frac{\pi }{4}\\[/tex]. What is the y-intercept of the function?
3
0
-3
[tex]\frac{\pi }{4}[/tex]
The y-intercept of the sine function is -3
We know that the standard form of the sine function is, y = a sin(bx + c) + d
where, amplitude = |a|
period = 2π/b
phase shift = -c/b
and vertical shift = d
Here, a sine function has an amplitude of 3, a period of π, and a phase shift of π/4
a = 3,
So, 2π/b = π
⇒ b = 2
And phase shift -c/b = π/4
⇒ -c/2 = π/4
⇒ -c = π/2
⇒ c = -π/2
So, a sine function would be,
y = 3 sin(2x + -π/2) + 0
y = 3 sin(2x + -π/2)
When x = 0,
y = 3 sin(0+ -π/2)
y = 3 sin(-π/2)
y = 3 × (-1)
y = -3
Learn more about the sine function here:
https://brainly.com/question/12015707
#SPJ4
nter (A,B,C,D)in order below if $A$, $B$, $C$, and $D$ are the coefficients of the partial fractions expansion of $$12\cdot\frac{x^3 4}{(x^2-1)(x^2 3x 2)}
The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.
A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.
The denominator is
(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)
(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)
So by partial fraction expansion
(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))
(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²
A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4
(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4
Thus from coefficients of x³, x², x and 1,
A + B + C = 1
2A + 4B + C + D = 0
-A + 5B - C + D = 0
-2A + 2B - C - 2D = 4
Solving
A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2
--The question is not clear, the question is given below--
"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of
[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex] "
To know more on partial fractions expansion
https://brainly.com/question/30079928
#SPJ4
The point A (1,1) and the point B(5,-1) lie on the line L. Find the equation of the line L
23. Factor each polynomial completely.
a. 5a²c-3a²d + 5b²c3b²d
b. x2 + 6x" +9
Step-by-step explanation:
a. 5a²c-3a²d + 5b²c3b²d l can't this question but l can calculate a. 5a²c-3a²d + 5b²c-3b²d.
I this your question is a little worng.
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
2nd choice: -3x - 5 = 10
Step-by-step explanation:
10 - x = -5
-x = -5 - 10 = -15
-3x - 5 = 10
-3x = 10 + 5
x = 15/-3 = -5
. Which of the following equations
represents an identity? Justify your
choice.
1) 2x+1=3x+4
2) 4x-3=2(2x+7)
3) 6x+3=2x+10
4) 4(5x+2) = 20x+8
The correct equation which represent an identity will be;
⇒ 4(5x+2) = 20x+8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
All the equations are,
1) 2x + 1 = 3x + 4
2) 4x - 3 = 2(2x + 7)
3) 6x + 3 = 2x + 10
4) 4(5x + 2) = 20x + 8
Now,
Solve each equation and find an identity as;
1) 2x + 1 = 3x + 4
⇒ 1 - 4 = 3x - 2x
⇒ - 3 = x
⇒ x = -3
Thus, It is not represent an identity.
2) 4x - 3 = 2(2x + 7)
⇒ 4x - 3 = 4x + 14
⇒ - 3 ≠ 14
Thus, It shows no solution.
3) 6x + 3 = 2x + 10
⇒ 6x - 2x = 10 - 3
⇒ 4x = 7
⇒ x = 7/4
Thus, It is not represent an identity.
4) 4(5x + 2) = 20x + 8
⇒ 20x + 8 = 20x + 8
⇒ 20x - 20x = 8 - 8
⇒ 0 = 0
Clearly, '0' is an additive identity.
Thus, This equation shows an identity.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Can the sine ratio of an acute angle be greater than 1?
No, the sine ratio of an acute angle cannot be greater than 1. The sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio will always be less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's important to note that if you were to give an angle value greater than 90 degrees, the sine of the angle will be a negative value, but the ratio will still be less than one.
The sine ratio is a value between -1 and 1, and it is impossible for the sine of an acute angle to be greater than 1.
Learn more about sin angle
brainly.com/question/68324
#SPJ4
How the addition of 2 and 2 become 5?
In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia
#4 Real World Scenario
A bird starts flying away from a
tree and goes exactly 6 miles
south. It then turns and flics
exactly 3 miles east. What is
the shortest distance it needs to
fly to return to the original
tree? If necessary, round your
answer to the nearest tenth.
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
what is pythagoras theorem ?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool.
given
by pythagoras theorem :-
shortest distance = [tex]c^{2} = a^{2} + b^{2} \\[/tex]
[tex]c^{2} = 6^{2} + 3^{2} \\c^{2} = 36 + 9\\c^{2} = 45\\c = 3\sqrt{5}[/tex]
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
To know more about pythagorus theorem visit :-
https://brainly.com/question/14461977
#SPJ1
MODELING REAL LIFE The volume of a sphere is given by the equation $V=\frac{1}{6\sqrt{\pi}}S^{3/2}$ , where $S$ is the surface area of the sphere. Find the volume of a water walking ball, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for $\pi$ .
The volume of the water walking ball is 43.71 m³
What are the surface area and volume of a sphere?Surface Area of a Sphere. A = 4 π r2. The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle
Given :
[tex]$V=\frac{1}{6\sqrt{\pi}}S^{3/2}$[/tex] and surface area of water walking ball is 60 m²
putting the values in the equation we get
V= 464.758/10.632
V=43.71
Hence, the volume of the water walking ball is 43.71 m³
Learn more about the volume of a sphere here:
https://brainly.com/question/2855746
#SPJ1
What is the plotting method?
Plotting method is the graphical representation of mathematical expression.
What is mean by plotting?A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.
What are the steps of plotting method?At first, we need to choose the coordinate system by which we plot the point.
suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.
besides, we need to determine the required value that will be plotted on the plan.
if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.
we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.
To know more about Plotting visit:
https://brainly.com/question/10276775
#SPJ4
Which of the following is equivalent to (X - 2) (x + 9) =0
The equivalent quadratic equation to (x - 2)(x + 9) = 0 is x² + 7x - 18 = 0.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
We know if α and β are the roots of a quadratic equation ax² + bx + c = 0,
Then we can construct the equation by the factors (x - α)(x - β).
Given, We have to construct a quadratic equation with (x - 2)(x + 9) = 0.
Now, Multiply the terms we have,
x² + 9x - 2x - 18 = 0.
x² + 7x - 18 = 0.
So, Our required quadratic equation is x² + 7x - 18 = 0.
learn more about forming of quadratic equations here :
https://brainly.com/question/29011747
#SPJ1
What is the slope of this line? (5 points)
Show all work.
Answer:
-2,2
Step-by-step explanation:
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Rob collects model planes one of his planes uses a sacks in which 1 inch represents 1. 5 feet if the length of the model airplane is 12 inches find the length of the actual airplane on feet
If 1 inch represents 1.5 feet, we can use this conversion factor to find the length of the actual airplane in feet. Thus 12 inches of model airplane represents an actual length of the actual airplane of 18 feet.
Therefore the answer is 18 feet.
To convert the length of the model airplane (12 inches) to feet, we can multiply it by the conversion factor (1 inch = 1.5 feet)
= 12 inches × 1.5 feet/inch
= 18 feet
So the length of the actual airplane is 18 feet.
It is important to pay attention to the units of measurement when performing conversions and make sure to use the correct conversion factor. And also it's a good practice to always check your answer to make sure it makes sense in the context of the problem.
To know more on unit conversion
https://brainly.com/question/10983660
#SPJ4
the monthly cost for 43 min is $17.96 and the monthly cost for 94 min is $24.72 what is the monthly cost for 88 min
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
y = mx + b
(50,13.98)(78,17.06)
slope = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11
slope(m) = 0.11
use either of ur points...(50,13.98)...x = 50 and y = 13.98
now sub into the formula and find b, the y int
13.98 = 0.11(50) + b
13.98 = 5.5 + b
13.98 - 5.5 = b
8.48 = b
so our equation is : y = 0.11x + 8.48.......for 94 minutes...sub in 77 for x
y = 0.11(94) + 8.48
y = 8.47 + 8.48
y = 16.95 <=== this is the cost for 94 minutes
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
use substitution to solve each system of equations
2. y= 4x+5
2x+y=17
6. 3x +4y= -3
x+2y= -1
8. -1=2x - y
8x-4y=-4
10. y= -4x + 11
3x + y=9
15. -5x+4y=20
10x-8y= -40
I think it's answer this .
Suppose you throw a ball straight up from the ground with a velocity of 176 feet per second. As the ball moves up, gravity slows it. Eventually, the ball begins to fall back to the ground. The height h of the ball after t seconds in the air is given by the equation h=−16t2+176t. Use the given information to answer parts a through c.
a. Find the height of the ball after four seconds
Therefore, the height of the ball after four seconds is 448 feet.
Define height.Height refers to the vertical distance between something's top and bottom or its base and anything above it. Height is used to describe everything that may be measured vertically, high or low.
What is distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
We need to plug t = 4 into the equation h = -16t^2 + 176t.
h = -16(4^2) + 176(4)
h = -16(16) + 704
h = -256 + 704
h = 448 feet.
So, 448 feet is the height after four seconds.
To know more about velocity visit: https://brainly.com/question/18084516
#SPJ4
Please answer #6a and 6b
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
To learn more about the triangle inequality theorem visit:
https://brainly.com/question/1163433.
#SPJ1
F(x)=2(x-3)squared it’s graphing and I forgot how to solve it
The solution of the function f(x) = 2(x - 3)² is at x = 3 as shown in the graph.
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial can be classified based on degree as linear, quadratic, cubic.
Given the function:
f(x) = 2(x - 3)²
The graph of f(x) is plotted. The solution of the graph can be gotten from its x intercept. Hence the solution is at x = 3
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Explain the process how would you estimate the solution of system of equation to the nearest tenth place
The actual solution must be approximated to the tenth place.
How do you solve an equation to the nearest tenth?
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth place.
To estimate the tenth place, you have to determine the actual solution and the approximate.
Assume the solution to the system of equations is:
(x, y), (1.25, 1)
1.25 is to the hundredth place.
So, the next thing is to approximate 1.25 to 1.3 (the tenth place).
So, we have:
(x, y), (1.3, 1)
Hence, the actual solution must be approximated to the tenth place.
To learn more about the nearest tenth visit,
https://brainly.com/question/2226590
#SPJ4
CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
Answer:
see explanation
Step-by-step explanation:
if the denominator of a rational expression is zero then the expression will be undefined.
the numerator is the part of the rational expression that makes it zero.
solve the numerators in each to find values of x
1
[tex]\frac{x+6}{x-4}[/tex]
x + 6 = 0 ( subtract 6 from both sides )
x = - 6 ← value that makes expression equal to zero
2
[tex]\frac{(x+4)(x-2)}{x+6}[/tex]
(x + 4)(x - 2) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
x = - 4 and x = 2 make the expression equal to zero
3
[tex]\frac{2x+10}{3x-12}[/tex]
2x + 10 = 0 ( subtract 10 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5 ← value that makes expression equal to zero
Answer:
1) x = -6
2) x = -4 and x = 2
3) x = -5
Step-by-step explanation:
A rational expression is undefined when the denominator equals zero.
A rational expression equals zero when the numerator equals zero.
Question 1Given rational expression:
[tex]\dfrac{x+6}{x-4}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies x+6=0[/tex]
[tex]\implies x=-6[/tex]
Question 2Given rational expression:
[tex]\dfrac{(x+4)(x-2)}{x+6}[/tex]
Set the numerator to zero:
[tex]\implies (x+4)(x-2)=0[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Question 3Given rational expression:
[tex]\dfrac{2x+10}{3x-12}[/tex]
Factor the numerator and denominator:
[tex]\dfrac{2(x+5)}{3(x-4)}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies 2(x+5)=0[/tex]
[tex]\implies x+5=0[/tex]
[tex]\implies x=-5[/tex]
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
''By taking log'' on both side Mike solve this equation.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 37ˣ = 12
Now,
Since, The expression is,
⇒ 37ˣ = 12
Solve this expression as;
⇒ 37ˣ = 12
Taking log both side, we get;
⇒ log 37ˣ = log 12
⇒ x log 37 = log 12
⇒ x = log 12 / log 37
⇒ x = 1.08 / 1.57
⇒ x = 0.69
Thus, The value of x = 0.69
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1