Answer:
(-9, 6) This ordered pair is used to find the function value f(-9)=6
or the given function value, write a corresponding ordered pair.
Step-by-step explanation:
For the given function value, write a corresponding ordered pair.
f(-9) = 6
The ordered pair of each function can be written as (x,y).
For any function, for example, g(x)= 10x, the input is x, and the output y is 10x. So ordered pair is (x,10x)
The given function value is: f(-9) = 6
Here input x=-9 and y value is 6
So, he corresponding ordered pair is (-9, 6)
What is the circumference of the circle with a radius of 2.5 meters? Approximate using π = 3.14. 61.62 meters 19.63 meters 15.70 meters 7.85 meters
the circumference of the circle with a radius of [tex]2.5[/tex] meters, approximated using [tex]\pi = 3.14[/tex], is [tex]15.7[/tex] meters. Thus, option C is correct.
What is circumference?The circumference of a closed curved object, such a circle or an ellipse, is the length around its perimeter.
The circumference of a circle is the distance around its perimeter. [tex]C = 2r[/tex] , where r is the radius (the distance from the centre of the circle to any point on its border), and pi is a mathematical constant roughly equal to [tex]3.14159[/tex], is the formula for a circle's circumference.
The formula for the circumference of a circle is [tex]C = 2\pi r[/tex] , where r is the radius of the circle.
Substituting the given value of the radius, we get:
[tex]C = 2 \times 3.14 \times 2.5 = 15.7[/tex] meters (approx.)
Therefore, the circumference of the circle with a radius of [tex]2.5[/tex] meters, approximated using π = 3.14, is 15.7 meters.
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answer pls my state test is cominggggg
Answer:
- 9/16
Step-by-step explanation:
When multiplying fractions, you can multiply them straight across.
We can focus simply on the fractions first and then add the negative back in later since you always get a negative number when you multiply a negative and positive number:
- (3 /4) * (3 / 4)
- (3 * 3) / (4 * 4)
- (9/16)
-9/16
find the inverse of f(x)=2^x+2
us the function odd, even, or neither?
A 360-ounce bag of rice has a serving size of 7 ounces on its label. How many full servings does the bag contain?
Jackie, a marine biologist, is tracking migratory patterns of a group of whales. The endpoints
of the whales' current migration route are 9 inches apart on Jackie's chart. If the scale of the
map is 1 inch: 0.6 miles, then what is the actual distance between the whales' starting and
ending points?
Answer:
1 inch = 0.6 miles
= 9 inches = 0.6 miles*9
= 9 inches = 5.4 miles
Hence, the answer is 5.4 miles.
Please mark me as brainliest...
Which of these expressions is equivalent to log (128^)?
OA. log (8) - log (12)
OB. 8 log (12)
C. log (8) log (12)
D. log (8) + log (12)
.
7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
a. To build the airport at the same distance from the center of each town, they should locate the intersection of the perpendicular bisectors of the segments connecting each pair of towns.
b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town
Where would the precise location be?The precise location of the airport will be the point where these perpendicular bisectors intersect. This point will be equidistant from the center of each town.
b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town. This point is the precise airport location. Equidistant from all connecting roads.
They could find the intersection of the medians of the triangle formed by the three towns. The airport is located at the centroid of a triangle, equidistant from 3 towns at the intersection of medians.
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Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
Please solve
1.) 4(v + 1) = 16
Answer:
it's an easy one
Step-by-step explanation:
1. combine those -->4v+4=16
2. subtract the like terms--> 4v=16-4--> 4v=12
3. divide--> v=12/4-->3
4. Answer--> v=3
Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
Therefore, the correct answer is option C that is LM is reflected over the y-axis to L'M.
What is transformation?In mathematics, a transformation refers to a change in the position, shape, or size of a geometric figure. Transformations can be classified into four types: translation, rotation, reflection, and dilation.
Here,
The transformation of LM to L'M' involves both translation and reflection. To see the translation, we can compare the x- and y-coordinates of L and L', as well as M and M':
The x-coordinate of L' is 5 units more than the x-coordinate of L: -2 = -7 + 5.
The y-coordinate of L' is 2 units less than the y-coordinate of L: -4 = -2 - 2.
The x-coordinate of M' is 5 units more than the x-coordinate of M: 5 = 0 + 5.
The y-coordinate of M' is 2 units less than the y-coordinate of M: 3 = 5 - 2.
Therefore, we can conclude that LM is translated 5 units right and 2 units down to L'M'. This eliminates options OB and OD. To see the reflection, we can compare the x-coordinates of L and M, and their respective x-coordinates in L' and M':
The x-coordinate of L is negative and the x-coordinate of M is positive.
The x-coordinate of L' is negative and the x-coordinate of M' is positive.
Therefore, we can conclude that LM is reflected over the y-axis to L'M'. This eliminates option OA. Therefore, the correct answer is option OC.
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In the xy-plane, what is the y-intercept of the graph of the equation y=6(x-1/2)(x+3)?
Answer:
The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).
Step-by-step explanation:
To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:
y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9
Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).
Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.
Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6
Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21
Create and interpret a 98% confidence interval for the difference in the placebo and the new drug. (10 points)
A: The data provides convincing evidence, at α=0.02 level, that the glucose drug is effective in reducing mean glucose level.
B: The 98% confidence interval for the difference in mean reduction of glucose level between placebo and drug groups is 3.5 to 13.7 mg/dL, supporting the effectiveness of the glucose drug
A: To test whether the glucose drug is effective in producing a reduction in mean glucose level, we will use a two-sample t-test with equal variances assuming normality of the differences.
Let μA be the true mean reduction in glucose level for the placebo group and μB be the true mean reduction in glucose level for the glucose drug group. The null hypothesis is H0: μA - μB = 0, and the alternative hypothesis is Ha: μA - μB < 0
Using the given data, the sample mean reduction for the placebo group is 9.7 mg/dL and for the glucose drug group is 18.3 mg/dL. The pooled sample standard deviation is 8.064 mg/dL, and the t-statistic is calculated to be:
t = (xB - xA) / (sP × √(1/nA + 1/nB))
= (18.3 - 9.7) / (8.064 × √(1/10 + 1/10))
= 2.551
where xA and xB are the sample means, sP is the pooled sample standard deviation, and nA and nB are the sample sizes.
B: To create a 98% confidence interval for the difference in the placebo and the new drug, we will use the formula:
CI = (xB - xA) ± tα/2,sP × √(1/nA + 1/nB)
where xA and xB are the sample means, sP is the pooled sample standard deviation, nA and nB are the sample sizes, and tα/2,sP is the t-value corresponding to a 98% confidence level with 18 degrees of freedom.
Using the values from Part A, we have:
CI = (18.3 - 9.7) ± 2.101 × 8.064 × √(1/10 + 1/10)
= 8.6 ± 5.103
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The correct question is:
Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.
Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6
Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21
Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level?
Part B: Create and interpret a 98% confidence interval for the difference in the placebo and the new drug.
The high school basketball team is selling donuts to raise money for the new uniforms. This team Mexico to sell at least $1000 in donuts. They are selling a half dozen box of donuts for eight dollars and a full dozen box of donuts for $12. They write the inequality 8X +12 Y is greater than or equal to 1000 to determine how many boxes they need to sell where X is the number of half dozen boxes and why is the number of four dozen boxes they sell which of the following solutions available in terms of the given context select all that apply.
The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
Understanding Word Problem in Solving MathsWe can derive an inequality from the problem statement which is:
8X + 12Y >= 1000
This inequality represents the amount of money the basketball team needs to raise by selling donuts.
X is the number of half dozen boxes sold
Y is the number of full dozen boxes sold.
To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:
If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:
8(50) + 12(50) = $400 + $600 = $1000
So this is a valid solution that meets the fundraising goal.
If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:
8(100) + 12(0) = $800
This is not enough to meet the fundraising goal, so it is not a valid solution.
If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:
8(0) + 12(100) = $1200
This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.
Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
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Which expression is equivalent to (x-3)(2x^(2)-3x-1)
The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.
In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).
We have to find the equivalent-expression for (3x-1)-2(x+2);
⇒ (3x-1)-2(x+2),
⇒ (3x - 1) - 2x - 4,
Combing the like-terms together in the above expression,
We get,
⇒ 3x - 2x -1 - 4,
⇒ x - 5,
Therefore, the correct equivalent expression is Option (c).
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The given question is incomplete, the complete question is
Which of the following expression is equivalent to (3x-1)-2(x+2)?
(a) x+3
(b) x+1
(c) x-5
(d) x-3
What is the slope-intercept form of the equation 3x-5y=2
Answer: y = 3/5x - 2/5
Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.
Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.
Use the following formula to find the correct answers: FV = PV. (1+i)"
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years. How much money will you have by then?
O$677.23
O $746.93
$467.39
O $725.30
The savings amount balance in the account is $ 467.39
Given data ,
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.
Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.
PV = $300 (the initial deposit)
i = 0.03 (the interest rate per period)
n = 15 years (the number of periods)
FV = $300 (1 + 0.03)^15
FV = $300 ( 1.5579 )
FV = $467.39
Hence , after 15 years, the savings account will have a balance of $ 467.39
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can someone solve -4 + 2 + -2 + -3x (with tiles!!!!!)
The simplified expression of given term is: -4 + 2 + -2 + -3x = -4 - 3x
What do you mean by Simplification ?Simplification refers to the process of reducing an expression to its simplest form by combining like terms, removing parentheses, and performing any necessary operations such as addition, subtraction, multiplication, and division. The goal of simplification is to make an expression easier to read and work with, and to reveal any patterns or relationships that may not have been obvious in the original expression. Simplification is an important part of solving equations, evaluating expressions, and performing mathematical operations in general.
We can simplify the expression by combining like terms.
Starting with -4, we add 2 to get:
-4 + 2 = -2
Next, we subtract 2 from -2:
-2 - 2 = -4
Finally, we subtract 3x from -4:
-4 - 3x
So the simplified expression is:
-4 + 2 + -2 + -3x = -4 - 3x
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Help me with this question please
Answer:
[tex]c. 1/5[/tex]
Step-by-step explanation:
You have the points (-5, 0) and (0, 1).
To find the slope, b, of the original line, you can use the formula [tex](y_{1}-y_2) /(x_1-x_2)[/tex].
[tex]b = (0-1)/(-5-0) = -1/-5 = 1/5.[/tex]
The slope of a line parallel to the original line would have the same slope as the original line, therefore [tex]1/5.[/tex]
5. Kamal said that he can measure
area using squares that are 2 units
long and 1 unit wide. What mistake
did Kamal make?
Answer:
A square's length & width are equal
Step-by-step explanation:
Kamal's shape is not a square, because a square is equilateral (equal length in all sides), but his square is 2:1,
what's equivalent to x^2-4x-l2
Answer:
Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:
(x - 6)(x + 2)
Step-by-step explanation:
This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:
(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12
Drag-and-Drop Technology-Enhanced
An expression is shown.
14a +7+ 5b+ 2a + 10b
Move words into the columns to describe the parts of the expression. Not all words will be used, and each column should
have at least one word to describe it.
14a
sum
term
factor
7
5
product
quotient
coefficient
2a + 10b
The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7
Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given the expression as;
14a +7+ 5b+ 2a + 10b
Combine like terms;
14a + 2a + 10b +7+ 5b
16a + 15b + 7
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help pls im failing 100 POINTS IF U HELP
Answer: 44%, 26%, less likely
Step-by-step explanation:
just do the math!!
Screenshot below i have no idea how to solve this
Answer:
x^1/4 + 8x^1/4 + 12
Step-by-step explanation:
Using the FOIL method, we get x^1/4 + 8x^1/4 + 12
Select the correct answer from each drop-down menu.
Consider the expression below.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.
What is like term?In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).
The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.
Simplifying the expression we het 10 x + 5.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.
2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.
3. If the expression is set equal to -10x + 5, there would be only one solution.
10x + 5 = -10x + 5
20x = 0
x = 0
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A list 7 members at the gym 10, 64, 52, 46,54,67,54. find the median
The calculated value of the median of the A-list 7 members at the gym is 54
Finding the median of the A-list 7 members at the gymFrom the question, we have the following parameters that can be used in our computation:
10, 64, 52, 46,54,67,54.
When the numbers are sorted in ascending order, we have
Sorted list = 10, 46, 52, 54, 54, 64, 67
The median is the middle number of the sorted list
So, we have
Middle number = 54
Thsis means that
Memdian = 54
Hence. the median of the A-list 7 members at the gym is 54
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Models that represent z+9=14 ASAP
To represent z+9=14, we can start by subtracting 9 from both sides of the equation:
z + 9 - 9 = 14 - 9
Simplifying the left side of the equation gives:
z = 5
Therefore, the solution to the equation z+9=14 is z=5.
Solve for x. Round to the nearest tenth, if necessary.
x=15.4 units
Step-by-step explanation:First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Working the problem
For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse. We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.
For this triangle, the "opposite" leg is known. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for this triangle is the Sine function.
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]
Multiply both sides by x, and divide both sides by sin(17°)...
[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]
Make sure your calculator is set to degree mode, and calculate:
[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]
[tex]x=15.391366289249...[/tex] units
Rounded to the nearest tenth...
[tex]x=15.4[/tex] units
Find the trig ratio, reduce and enter your answer in the lowest terms. Please help!
The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.
What does the trigonometric ratio mean? a trigonometric ratioTrigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).
The given triangle is a right angle,
To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.
[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]
Therefore [tex]cosA= \frac{3}{5}[/tex]
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Need the answer ASAP
A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].
What is a translation?In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.
Based on the information provided, the transformed function should be written as follows:
y = √x
g(x) = (√x + 9)
[tex]y=\sqrt{x+9}[/tex]
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Can anyone please help me answer this question?
Find the limit of p(x)= (x^4 - x^3 - 1)/ x^2 (x + 1) as x approaches -3
Answer:
Step-by-step explanation:To find the limit of p(x) as x approaches -3, we can first simplify the expression by factoring the numerator:
p(x) = (x^4 - x^3 - 1) / x^2(x + 1)
= [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]
Now, when x approaches -3, the denominator of the fraction becomes zero, which means we have an indeterminate form of the type 0/0. To evaluate the limit, we can use L'Hopital's rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.
Taking the derivative of the numerator and denominator, we get:
p'(x) = [(3x^2 - 2x - 1)(x^2 + 2x) - 2(x - 1)(2x + 1)] / [x^3(x + 1)^2]
Now, plugging in x = -3 into the derivative, we get:
p'(-3) = [(3(-3)^2 - 2(-3) - 1)((-3)^2 + 2(-3)) - 2((-3) - 1)(2(-3) + 1)] / [(-3)^3((-3) + 1)^2]
= [28 - 44] / [(-3)^3(-2)^2]
= -16 / 108
= -4 / 27
Since the derivative is defined and nonzero at x = -3, we can conclude that the original limit exists and is equal to the limit of the derivative, which is:
lim x->-3 p(x) = lim x->-3 [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]
= p'(-3)
= -4 / 27
Therefore, the limit of p(x) as x approaches -3 is equal to -4/27.
Answer:
[tex]\lim_{x \to -3}p(x) =-\dfrac{107}{18}[/tex]
Step-by-step explanation:
Given the function [tex]p(x)=\dfrac{x^4-x^3-1}{x^2(x+1)}[/tex]
Let's give the expressions in the numerator and denominator their own function names so they are easy to refer to:
n, for numerator: [tex]n(x)=x^4-x^3-1[/tex]
d, for denominator: [tex]d(x)=x^2(x+1)[/tex]
So [tex]p(x)=\dfrac{n(x)}{d(x)}[/tex]
Now, we want the limit of p(x) as x goes to -3.
[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}[/tex]
For limits of quotients, it is important to analyze the numerator and the denominator.
Take a moment to observe that inputting -3 into the denominator is defined and does not equal zero: [tex]d(-3)=(-3)^2((-3)+1)=-18\ne0[/tex]
Also, observe that inputting -3 into the numerator is defined: [tex]n(-3)=(-3)^4-(-3)^3-1=81+27-1=107[/tex]
Importantly, both functions n & d are polynomials, which are functions that are continuous over [tex]\mathbb{R}[/tex].
Since both functions n & d are continuous, both n & d are defined at [tex]x=-3[/tex], and [tex]d(-3)\ne0[/tex], then the limit of the quotient is the quotient of the limits:
[tex]\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}[/tex]
From here, again, since n & d are continuous over [tex]\mathbb{R}[/tex] and defined at the limit, [tex]\lim_{x \to -3}n(x)}=n(-3)[/tex] and [tex]\lim_{x \to -3}d(x)}=d(-3)[/tex].
Therefore,
[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}=\dfrac{n(-3)}{d(-3)}=\dfrac{107}{-18}=-\dfrac{107}{18}[/tex]