Answers
Answer: Second Option
[tex]P (-1.17 <z <1.17) = 0.7580[/tex]
Step-by-step explanation:
The shaded area corresponds to the interval
[tex]-1.17 <z <1.17.[/tex]
By definition, for a standard normal distribution the area under the curve in the interval (b <z <h) is equal to:
[tex]P (b <z <h)[/tex]
So in this case we look for:
[tex]P (-1.17 <z <1.17)[/tex]
This is:
[tex]P (-1.17 <z <1.17) = P (z <1.17) - P (z <-1.17)[/tex]
Looking at the standard normal table we have to:
[tex]P (z <1.17) = 0.8790\\P (z <-1.17) = 0.1210[/tex]
So:
[tex]P (-1.17 <z <1.17) = 0.8790- 0.1210\\\\P (-1.17 <z <1.17) = 0.7580[/tex]
Related Questions
Which expression is equal to a + (b + c)?
(a + b) + c
(a + b) ⋅ c
a + bc
b + ac
Answers
Answer:
The correct option is (a+b)+c
Step-by-step explanation:
The correct option is (a+b)+c
According to the Associative property for Addition:
a+(b+c)=(a+b)+c
The associative property states that you can add or multiply regardless of how the numbers are grouped.
.If you are adding or multiplying it does not matter where you put parenthesis.
Thus the correct option is A....
[tex]\huge{\boxed{(a+b)+c}}[/tex]
For example, [tex]2+(3+4)=2+7=9[/tex].
If we group the terms differently, it doesn't matter. [tex](2+3)+4=5+4=9[/tex]
This is called the associative property of addition. As long as you still have all of the terms, and there are no other operations (subtraction, multiplication, etc.), the final answer will remain the same no matter how the terms are grouped.
The perimeter of ΔABC is 13 cm. It was dilated to create ΔA'B'C'. What is the perimeter of ΔA'B'C'? 13 cm 26 cm 39 cm 52 cm
Answers
Answer:
The answer is 52
Step-by-step explanation:
We need figure out the dilated by doing OB’/OB. 5+15= OB’. OB’ = 20. We already know that OB is 5. We used the substitution property. 20/5 = 4. Now, we got 4 as dilation. 13 cm x 4 = 52 cm. Therefore, our answer is 52
Perimeter of ΔA'B'C' is 52 cm.
The perimeter of ΔABC is =13 cm
Length of OB = 5 cm
Length of OB' = 15 + 5 = 20 cm
The Dilation factor can be found out b
ΔOCB and ΔOC'B' are similar as BC|| B'C'
From triangles ΔOCB & ΔOC'B' the dilation factor can be found out
by the formula below
[tex]\frac{BC}{B'C'} = \frac{5}{20}[/tex]
B'C'= 4[tex]\times[/tex]BC
so the dilation factor = 4
hence the new perimeter of the triangle = 13 [tex]\times[/tex] 4 = 52 cm
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Divide 27x3 - 72x2 + 36x by 9x.
Answers
Answer:
3x^2 - 8x + 4.
Step-by-step explanation:
Dividing each term by 9x we get:
3x^2 - 8x + 4.
As per cubic equation, the result is [tex](3x^{2}-8x+4)[/tex].
What is a cubic equation?A cubic equation is an equation where the highest power of the variable is 3.
The given linear equation is:
[tex]\frac{27x^{3}- 72x^{2}+ 36x}{9x} \\= \frac{27x^{3}}{9x} -\frac{72x^{2}}{9x}+\frac{36x}{9x}\\ = 3x^{2}-8x+4[/tex]
The result is [tex](3x^{2}-8x+4)[/tex].
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Solve the inequality 2x2 + 10x < –8
Answers
Answer:
-4<x<-1
Step-by-step explanation:
To solve the problem, we divide the whole expression by 2:
2x^2 + 10x < –8 → x^2 + 5x < –4
→ x^2 + 5x + 4 < 0
Factorizing
→ (x+4)(x+1) < 0
The expression is ONLY negative when:
x>-4 and x<-1
Therefore, the solution is:
-4<x<-1
The inequality 2x2 + 10x < -8 should be rearranged to 2x2 + 10x + 8 < 0. It can't be factored so we must use the quadratic formula to solve it. The solution involves finding the values of x that make the function positive or negative.
Explanation:To solve the inequality 2x2 + 10x < -8, we first need to arrange the terms. To do so, we can subtract 8 from each side of the inequality obtaining 2x2 + 10x + 8 < 0.
However, this is a quadratic inequality that is best solved by factoring, if possible. Let's try to factor our quadratic expression, but keep in mind that not all quadratic expressions can be factored. In this case, it is not factorable. Therefore, it must be solved by using the quadratic formula, which is x = [-b ± sqrt(b2-4ac)]/2a.
Take note the a, b, and c values from our inequality (a=2, b=10, c=8), and substitute these values into the quadratic formula. However, this approach will solve for 'x' in an equation, not an inequality.
To solve for 'x' in the inequality, we have to find the values of 'x' that make the function positive or negative, depending on the type of the inequality. We determine those values by solving the equation f(x) = 0, where f(x) is the left side of our inequality.
It is a complex process that requires understanding of both quadratic functions and inequalities. Following these steps and calculating correctly should lead you to the solution.
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5 / 3 + 43 / 9 what is the answer
Answers
Answer:
58/9
Step-by-step explanation:
5/3 +43/9
Lets take the L.C.M first
The L.C.M would be 9
Solve the term by taking 9 as L.C.M
=15+43/9
Add the numerator.
=58/9
The answer is 58/9 ....
if h(x)=4X^2-16 were shifted 5units to the right and 2 down, what would the new equation be
Answers
Answer:
4(x - 5)^2 - 18.
Step-by-step explanation:
For a move 5 to the right f(x) ----> f(x - 5).
For a move of 2 down f(x - 5) ----> f(x - 5) - 2.
For this case we have that by definition of function transformation is fulfilled:
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph[tex]y = f (x + h),[/tex] the graph moves h units to the left.
Let k> 0:
To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
So, we have the following function:
[tex]h (x) = 4x ^ 2-16[/tex]
5 units on the right:
[tex]h (x) = 4 (x-5) ^ 2-16[/tex]
2 units down
[tex]h (x) = 4 (x-5) ^ 2-16-2\\h (x) = 4 (x-5) ^ 2-18[/tex]
Answer:
[tex]h (x) = 4 (x-5) ^ 2-18[/tex]
Find the range of the following set of data.
13. 11, 4,5,6, 9, 10, 12, 15, 16
Answers
Answer:
12
Step-by-step explanation:
First put the set in order from least to greatest:
4, 5, 6, 9, 10, 11, 12, 15, 16
To find the range you subtract the largest number by the smallest number.
4, 5, 6, 9, 10, 11, 12, 15, 16
So 16 - 4 = 12
So the range is 12.
Answer:
12
Step-by-step explanation:
The greatest value in the data is 16.
The lowest value in the data is 4.
The range is the difference between the highest and the lowest values.
range = 16 - 4 = 12
Find x if a= 13 and c= 47
Answers
13^2 + b^2 = 47
169 + b^2 = 2,209
Move constant to the right
b^2 = 2,209 - 169
Subtract the numbers
b^2 = 2,040
Take the root of both sides
The final steps an answers are above on the image;)
Without a specific equation or context, we can't find a specific value for x. If the equation were a+c=x, with a=13 and c=47, then x would equal 60.
Explanation:This question appears to be missing some information to find a specific value for x. If this were an algebraic equation such as a+c=x where a and c are declared as 13 and 47 respectively, you would simply add these two numbers together. So if a=13 and c=47, then x (your answer in this case) would be 60. However, without a given equation or context, it's impossible to determine the exact value for x.
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A diet is to include at least 140 milligrams of Vitamin A and at least 145 milligrams of Vitamin B. These requirements can be obtained from two types of food. Type X contains 10 milligrams of Vitamin A and 20 milligrams of Vitamin B per pound. Type Y contains 30 milligrams of Vitamin A and 15 milligrams of Vitamin B per pound. If type X food costs $12 per pound and type Y food costs $8 per pound how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost? Round to the nearest hundredths.
Answers
To minimize the cost of the diet while meeting the vitamin requirements, we can use a system of linear equations to solve a linear programming problem. The optimal solution will provide the pounds of each type of food to be purchased.
Explanation:To solve this problem, we can use a system of linear equations. Let's assume that we buy x pounds of type X food and y pounds of type Y food. The requirements for Vitamin A and Vitamin B can be expressed as the following inequalities: 10x + 30y ≥ 140 (for Vitamin A) and 20x + 15y ≥ 145 (for Vitamin B). We also need to minimize the cost, which can be expressed as the objective function: Cost = 12x + 8y. So, we have a linear programming problem.
To find the minimum cost, we can graph the feasible region defined by the inequalities and find the corner point with the lowest cost. Alternatively, we can use a method like the Simplex algorithm to solve the system of equations and find the optimal solution. The solution will give us the values of x and y that satisfy the requirements and minimize the cost.
Once we find the optimal solution, we can round the values of x and y to the nearest hundredths and provide the student with the pounds of each type of food to be purchased.
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Elise picks 6 pounds of apples.She uses 1/2 pounds to make 1 container of apple sauce. How many containers of applesauce can Elise make with all apples?
Answers
Answer:
12 Containers
Step-by-step explanation:
given it takes 1/2 a pound to make one container, we can deduce:
1 pound makes 2 containers
2 pounds makes 4 containers
thus the amount of containers is equal to 2x (x being pounds of apples picked)
so
2(6)=12
Elise can make 12 containers of applesauce. Here's how to calculate it:
Step 1: Determine the total amount of apples Elise has:
Elise has picked 6 pounds of apples.
Step 2: Identify how many pounds of apples are needed for one container of applesauce:
According to the information provided, 1/2 pound of apples is needed to make 1 container of applesauce.
Step 3: Calculate how many containers Elise can make:
To find out how many containers of applesauce Elise can make, divide the total pounds of apples by the pounds of apples per container.
The calculation is as follows:
6 pounds of apples ÷ (1/2) pound per container = 12 containers
Therefore, with 6 pounds of apples, Elise can make 12 containers of applesauce.
The weight of 1000 identical samples of a substance are 1 pound. What is the weight of 10 samples?
Answers
Answer:
.01 lbs
Step-by-step explanation:
If the weight of 1000 things are 1 pound that means 1 thing has a weight of 1/1000 lbs. So ten things have a weight of 10/1000 lbs or 1/100 lbs or .01 lbs.
What are the values of a and b?
a = 14, b = 6
a = 14, b = 8
a = 17, b = 6
a = 17, b = 8
Answers
According to the question the values of a and b are 17 and 6 respectively
What is a kite?A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
According to the Definition:
Sides FJ = HJ ( from the diagram)
Hence (3b + 6) = 24cm
3b = 24 - 6
3b = 18
b = 6
Sides FG = GH (from the diagram)
(2a - 4) = 30
2a = 30 + 4
a = 34/2
a = 17
Hence the value of a and b are 17 and 6 respectively.
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Answer: C
Step-by-step explanation:
Vince bought 6 boxes of worms to use as bait while fishing with his friends. If each person uses exactly 3/8 of a box of worms, how many people can share the worms.
Answers
We are given the following information:
each person uses 3/8 a box
there are 6 boxes
Because each box is [tex]\frac{8}{8}[/tex], and there are 6 boxes, we know that 1 person is [tex]\frac{3}{8*6}[/tex], or [tex]\frac{3}{48}[/tex].
In order to find how many people can use the 6 boxes, we can divide it by 3 (for each use):
48 / 3 = 16
Therefore, 16 people can share the worms.
Hope this helps! :)
what is 7/8 to a decimal rounded to the nearest eighth
Answers
[tex]\dfrac{7}{8}=\dfrac{875}{1000}=0.875[/tex]
Answer:
[tex]\large\boxed{\dfrac{7}{8}=0.875}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\dfrac{7}{8}=\dfrac{7\cdot125}{8\cdot125}=\dfrac{875}{1,000}=0.875\\\\\bold{METHOD\ 2:}\\\\\dfrac{7}{8}=7:8\qquad\text{divide 7 by 8 (look at the picture)}\\\\7:8=0.875[/tex]
Divide 1,600 by 84, and then divide the answer by 3
Answers
Answer:
6.3
Step-by-step explanation:
1,600 / 84 = 19.04
19.04 / 3 = 6.3
To answer the student's question, we first divide 1,600 by 84 which gives around 19.0476, and then divide this result by 3, which gives the final answer of 6.3492.
Explanation:To solve this problem, we first need to divide 1,600 by 84. That will give us the first result. Next, we must take this first result and divide it by 3.
Let's take it step by step:
1,600 ÷ 84 ≈ 19.0476 (You can take it to the nearest 4 decimal points for simplicity). Now, take this result (19.0476) and divide it by 3. The answer is around 6.3492.
So after you divide 1,600 by 84, and then divide the answer by 3, the final result should be around 6.3492.
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What is the solution to 3|–3x + 9| = –18?
Answers
Answer:
X=5
Step-by-step explanation:
i hope this helps
Answer:
equation has no solutions
Step-by-step explanation:
3|–3x + 9| = –18 (divide both sides by 3)
|–3x + 9| = –6
because by definition, for any value a, |a| must be non-negative
hence |–3x + 9| must give a value that is greater or equal zero
because the right side of the equation is a negative integer, hence the equation has no solutions.
A culture started with 1000 bacteria. After 6 hours it few to 1300 bacteria. Predict how many bacteria will be present after 10 hours.
Answers
Answer:
1350
Step-by-step explanation:
If a culture started with 1000 bacteria and after 6 hours it few to 1300 bacteria, there would be 1350 present after 10 hours.
1000 to 1100 is an increase of 100 bacteria per 6 hours.
1100+250= 1350
Answer:
1500
Step-by-step explanation:if it grows 300 in 6 hours you can assume that each hour would increase the pop by 50 so 10 hours times 50 it will become 1500.
What is the coordinates of point S?
Answers
Answer:
(-0.75, 0.5)
or in fractions:
(-3/4, 1/2)
Step-by-step explanation:
Consider the combined function. f(X) + g(X) = 9x + 4 . If f(x) = 4x - 3, find g(x)
Answers
Answer:
g(x)=5x+7
Step-by-step explanation:
f(x)+g(x)=9x+4
We are given f(x)=4x-3.
So we insert 4x-3 for f:
4x-3+g(x)=9x+4
Subtract 4x on both sides:
-3+g(x)=5x+4
Add 3 on both sides:
g(x)=5x+7
Check:
f(x)+g(x)
=(4x-3)+(5x+7)
=(4x+5x)+(-3+7)
=(9x) +(4)
=9x+4
Bingo. We did it! :)
The function g(x) can be found by rearranging the equation f(X) + g(X) = 9x + 4 and substituting f(x) = 4x - 3 into it. This leads to g(x) = 5x + 7.
Explanation:The given combined function is f(X) + g(X) = 9x + 4 and we know that f(x) = 4x - 3. To find g(x), we need to rearrange the combined function to make g(x) the subject. So step 1: subtract f(x) from both sides of the equation, giving: g(x) = 9x + 4 - f(x).
Then, we substitute f(x) into the equation, resulting in: g(x) = 9x + 4 - (4x - 3). Simplifying this gives us g(x) = 9x + 4 - 4x + 3, which further simplifies to g(x) = 5x + 7. This is the function g(x).
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f(x)=5x-10 and g(x)=x-16
Which of the following represents h(x)=F(x)+g(x)
Answers
Answer:
6x - 26
Step-by-step explanation:
f(x) + g(x) = 5x - 10 + x - 16 ← collect like terms
= 6x - 26
Answer:
B
Step-by-step explanation:
The graph of y= -4x + 7 is:
Answers
Answer:
Your y-intercept is at (0,7). To plot other points, use your slope: -4. (go down 4, go right 1 OR go up 4 and left 1)
Step-by-step explanation:
Answer:
Graph is attached below
Step-by-step explanation:
[tex]y= -4x + 7[/tex]
To graph this linear function , we make a table
Assume some random number for x and find out y. Assume some positive and negative numbers for x
x y=-4x+7
-1 -4(-1)+7=11
0 -4(0)+7=7
1 -4(1)+7=3
The points we got are (-1,11) (0,7) (1, 3)
Plot all the points and join all the points by a line
The graph is attached below
if f(x)=x/2-3 and g(x)=3x2+x-6, find (f+g)(x)
Answers
Answer:
[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x)=\frac{x}{2}-3 \,\, and\,\, g(x) = 3x^2+x-6[/tex]
We need to find [tex](f+g)(x)[/tex]
(f+g)(x) can be found by adding f(x) and g(x)
(f+g)(x) = f(x) + g(x)
[tex](f+g)(x) = \frac{x}{2}-3+(3x^2+x-6) \\(f+g)(x) = \frac{x}{2}-3+3x^2+x-6\\(f+g)(x) = 3x^2+\frac{x}{2}+x-3-6\\(f+g)(x) = 3x^2+\frac{3x}{2}-9\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
so, (f+g)(x) is:
[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
Answer:
Step-by-step explanation:
A sphere and a cylinder have the same radius and height. The volume of the cylinder have the same height and radius. The volume of the cylinder is 27pi ft. What equation gives the volume of the sphere ?
Answers
The equation of the volume of the sphere is 4/3 × 27π
The volume of a cylinder is expressed as
V = πr²h
Since the cylinder has thesame height and radius, therefore, the volume of the cylinder will now be
V = πr² × r
V = πr³
The volume of a sphere is expressed as
V = 4/3(πr³)
Therefore we can say
the volume of sphere = 4/3 × volume of the cylinder
Volume of cylinder = 27π
volume of sphere = 4/3 × 27π
= 4 × 9
= 36πft³
If (s-3)^2=0, what is the value of (s+3) (s+5)?
Answers
Here,
(s-3)²=0
→s-3=0
→s=3
Substituting s=3 in,
(s+3)(s+5)
=(3+3)(3+5)
=(6)(8)
=48
The solution to the equation (s-3)²=0 is s=3. Subsequently, the value of (s+3)(s+5) can be calculated by substituting s with 3, giving us the answer 48.
To solve the given equation, (s-3)²=0, we need to find the value of s. This equation means that the value inside the parenthesis, s - 3, when squared equals zero. The only way for a real number squared to equal zero is for that number itself to be zero. Therefore, s - 3 must equal zero. Solving for s, we find that:
s - 3 = 0
s = 3
Now that we know s is 3, we can find the value of (s + 3)(s + 5) by substituting the value of s:
(3 + 3)(3 + 5) = 6 x 8 = 48
Therefore, the value of (s + 3)(s + 5) when (s - 3)² = 0 is 48.
How can 65% be broken down with friendly percents to find 65% of a number?
25% + 25% + 10%
25% + 10% + 10% + 10% + 10%
50% + 10%
50% + 25%
Answers
Answer:
The correct ans would be B, 25%+10%+10%+10%+10%
Step-by-step explanation:
When percentages are found, the best way to calculate them is to break them down to the simplest percentage form, and 10% is the simplest percentage that a person can calculate of whatever digit. So if someone wishes to find out the friendly percents, then the easiest would be to calculate the 10% of the figure, add them four times, then add them 2 times plus the half of 10%, which will become 25%, and then add them all to get the 65% of that figure.
Answer:
B.
Step-by-step explanation:
i took the test
Use function notation to write a recursive formula to represent the sequence: 3, 6, 9, …
A. f(n) = f(n − 1) + 3
B. f(n) = f(n − 1) + 2
C. f(n) = f(n − 1) ⋅ 3
D. f(n) = f(n − 1) ⋅ 2
Answers
Final answer:
The recursive formula for the sequence 3, 6, 9, ... is represented by option A: f(n) = f(n - 1) + 3, which states that each term is 3 more than the previous term, starting with f(1) = 3. Option a
Explanation:
To write a recursive formula for the sequence 3, 6, 9, ..., we need to observe the pattern of the sequence. Since each term increases by 3 from the previous term, we can express this as:
f(n) = f(n − 1) + 3 for n > 1,
with a starting value f(1) = 3. This represents the first term in the sequence. Therefore, the correct answer is A: f(n) = f(n − 1) + 3.
The other options suggest either multiplying the preceding term by 2 or 3, or adding 2 to the preceding term, but those operations do not describe the given sequence. Option a
nala wants to determine if x-5 is a factor of p(x)=x^3-5x^2-x+5. Help Nala organize her steps.
Step 1-?
Step 2-?
Step 3-?
options:
1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x)
2) apply the factor theorem, the remainder is not 0 so x-5 is not a factor of p(x)
3) evaluate p(x) for x=5
4) apply the polynomial theorem, the remainder is 0, so x-5 is a factor of p(x)
5) divide
6) simplify and find the remainder
7) evaluate p(x) for x=-5
Answers
Answer:
I only used two steps: 3) then 6) then 1).
Step-by-step explanation:
Ok, if x-5 is a factor of p(x), then p(5)=0 by factor theorem.
This also goes the other way around:
If p(5)=0 then x-5 is a factor of p(x) by factor theorem.
Let's check. I'm going to evaluate p(x) for x=5.
[tex]p(5)=5^3-5(5)^2-5+5[/tex]
[tex]p(5)=125-5(25)-5+5[/tex]
[tex]p(5)=125-125-5+5[/tex]
[tex]p(5)=0+0[/tex]
[tex]p(5)=0[/tex]
This implies x-5 is a factor since we have p(5)=0.
The first step I did was 3) evaluate p(x) for x=5.
The second step I did 6) simplify and find the remainder. I did this when I was evaluating p(5); that was a lot of simplification and then I found the remainder to be 0 after that simplification. The last step was 1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x).
To determine if x-5 is a factor of the polynomial, evaluate p(x) when x=5. If the result is 0, then the Factor Theorem implies that x-5 is a factor. If not, x-5 is not a factor.
Explanation:To determine if x-5 is a factor of p(x)=x^3-5x^2-x+5, you can follow these steps:
When you evaluate p(x) for x=5, if you get 0, it demonstrates, according to the factor theorem, that x-5 is a factor of p(x) because it results in the polynomial function equaling zero. If you don't get zero, then it's not a factor.
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Find the value of X in the picture.
Answers
Answer:
The measure of the arc x is 130°
Step-by-step explanation:
we know that
The semi-inscribed angle is half that of the arc it comprises
so
65°=(1/2)[arc x]
solve for x
arc x=(2)(65°)=130°
what is the value of the natural logarithm when x=3?
Answers
Answer:
Step-by-step explanation:
[tex]f(x)=ln(x)\\f(3)=ln(3) = 1.099[/tex]
f(3)=In(3)= 1.099
Find the zeros of f(x) = x^2 + 7x + 9
Answers
Answer:
-7/2 ±1/2sqrt(13) = x
Step-by-step explanation:
f(x) =x^2 + 7x + 9
To find the zeros, set this equal to zero
0 = x^2 + 7x + 9
I will complete the square
Subtract 9 from each side
0-9 = x^2 + 7x + 9-9
-9 =x^2 + 7x
Take the coefficient of the x term, 7
divide by 2, 7/2
Then square it, (7/2)^2 = 49/4
Add this to both sides
-9 +49/4=x^2 + 7x + 49/4
-36/4 +49/4 = (x+7/2)^2
13/4 = (x+7/2)^2
Take the square root of each side
±sqrt(13/4) = sqrt( (x+7/2)^2)
± sqrt(13) /sqrt(4)= (x+7/2)
± 1/2 sqrt(13) = (x+7/2)
Subtract 7/2 from each side
-7/2 ±1/2sqrt(13) = x+7/2-7/2
-7/2 ±1/2sqrt(13) = x
The function f(x) = x^2 + 7x + 9 has no real-number zeros as the discriminant is negative, indicating that the quadratic formula solution involves an imaginary number.
Explanation:The student is asking to find the zeros of the quadratic function f(x) = x^2 + 7x + 9. To solve for the zeros, we need to find the values of x that make the function equal to zero. We can use the quadratic formula, which is [tex]x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}[/tex], where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, our equation is already in the correct form with a = 1, b = 7, and c = 9. Plugging these into the quadratic formula, we get:
[tex]x = \frac{{-7 \pm \sqrt{{7^2 - 4(1)(9)}}}}{{2 \cdot 1}}[/tex]
Upon further calculation, we find that the equation has no real-number solutions as the discriminant (b^2 - 4ac) is negative (49 - 36 = 13), leading to an imaginary number in the square root. Therefore, we conclude that the function does not cross the x-axis and has no zeros on the real number line.