The required pair of number are -3 and -6
The factored form of the trinomial is (x-3) and (x-6)
The standard form of a quadratic equation is expressed as:
[tex]ax^2+bx+c=0[/tex]
Given the expression [tex]x^2 - 9x + 18.[/tex]
[tex]a=1\\b=-9\\c=18[/tex]
We are to get two values that we must add to get b, and that we will multiply that will give c.
The given values are -6 and -3
Check:
[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]
Factorize the trinomial
[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]
Hence the factored form of the trinomial is (x-3) and (x-6).
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Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ
Answer:
The graph of polar equation is symmetric about the x-axis.
Step-by-step explanation:
The given polar equation is
[tex]r=-5-5\cos \theta[/tex]
If [tex](r,\theta)[/tex] and [tex](r,-\theta)[/tex] lie on the graph then the graph of polar equation is symmetric about the x-axis.
Substitute [tex]\theta=-\theta[/tex] in the given equation.
[tex]r=-5-5\cos (-\theta)[/tex]
Cosine is an even function.
[tex]r=-5-5\cos \theta[/tex] [tex][\cos (-\theta)=\cos (\theta)][/tex]
Point [tex](r,-\theta)[/tex] lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.
Can someone factor this problem for me?
(a)at davidson's bike rentals, it costs $14 to rent a bike for 3 hours. how many dollars does it cost per hour of bike use?
which other angle must also measure 130°
opposite angles are identical so if angle 1 = 130
than angle 3 is also 130 degrees
Answer:
Angle 3
Step-by-step explanation:
we know that
[tex]m<1=m<3[/tex] -----> by vertical angles
we have
[tex]m<1=130\°[/tex]
therefore
[tex]m<3=130\°[/tex]
An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides
a $9 fee plus $4 oper ride
let T = total cost
X= number of rides
T=9.00+4.00X
What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5?
Answer: 12.496
Step-by-step explanation:
The formula to find the sum of geometric progression is given by :-
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Given : The first term : [tex]a_1=10[/tex]
Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]
Then , the sum of first five terms of a geometric series is given by :-
[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]
Hence, the sum of the first five terms of given geometric series =12.496
What is the projection of (4 4) onto (-7 3) open study?
What is the slope of the line that is perpendicular to the line whose equation is 2x + y = 4.
Answer:
The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
Given : Equation is 2x + y = 4.
To find : What is the slope of the line that is perpendicular to the line.
Formula used : equation of line y = m[tex]m_{1}[/tex] x + c.
Solution : We have 2x + y = 4.
Rearranging the equation : y = - 2x + 4.
On comparing m[tex]m_{1}[/tex] = - 2.
Condition for slope of the line that is perpendicular to the line :
m[tex]m_{1}[/tex] × m[tex]m_{2}[/tex] = -1 .
So, -2 × m[tex]m_{2}[/tex] = -1 .
On dividing by 2 both we get ,
m[tex]m_{2}[/tex] = [tex]\frac{1}{2}[/tex].
Therefore, The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is [tex]\frac{1}{2}[/tex].
A sandwich shop offers ham, turkey, tuna, chicken salad, and roast beef. It has Swiss, American, and provolone cheese. You can order a sandwich on white, wheat, or rye bread. If a person orders a sandwich and chooses a meat, cheese, and bread at random, how many sandwich choices are there?
5 different meats
3 different cheeses
3 different breads
5x3x3 = 15*3 = 45
there are 45 choices
The sandwich shop offers a total of 45 different sandwich combinations based on the given options of meats, cheeses, and breads. Each sandwich consists of one type of each category.
Explanation:The question asked is related to the concept of combinations in mathematics. It gives a variety of choices for making a sandwich - 5 types of meats, 3 types of cheeses, and 3 types of breads. Assuming that each sandwich will have one meat, one cheese, and one type of bread, we can calculate the total combinations by multiplying the number of options in each category together. Combinations are used when the order of selection does not matter.
So, the total number of sandwich combinations would be 5 (meats) * 3 (cheeses) * 3 (breads) = 45 different sandwich choices.
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What is the quotient (3x3 + 10x2 + 10x + 4) ÷ (x + 2)?
a. 3x2 + 16x + 42
b. 3x2 + 4x + 2
c. 3x2 − 16x + 42
d. 3x2 − 4x + 2
Answer:
Option B is correct.
[tex]3x^2+4x+2[/tex].
Step-by-step explanation:
We are asked to find the quotient obtained by dividing the expression [tex](3x^3+10x^2+10x+4)[/tex] by the expression [tex](x+2)[/tex]
We can also write this expression as i.e. we are asked to find the value of the expression:
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}[/tex]
We can write the expression on the numerator as:
[tex]3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)[/tex]
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=\dfrac{(3x^2+4x+2)(x+2)}{x+2}[/tex].
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=3x^2+4x+2[/tex].
Hence, option B is correct.
Hence, the quotient is:
[tex]3x^2+4x+2[/tex].
in order to use a normal distribution to calculate confidence intervals for p, what conditions on np and nq need to be satisfied? Select one: a. n and q must be integers b. n must be positive c. np>10 and nq<0 d. np and nq must be > 5
Final answer:
To use normal distribution for calculating confidence intervals for proportion p, both np and nq must be greater than or equal to 5.
Explanation:
In order to use a normal distribution to calculate confidence intervals for a population proportion p, the conditions on np and nq need to be such that both np ≥ 5 and nq ≥ 5. These conditions are necessary because they ensure that the shape of the binomial distribution is similar to that of a normal distribution, which allows for the approximation of the binomial distribution by the normal distribution. When performing a hypothesis test of a single population proportion, it is imperative that the sample data meet these conditions to ensure a valid test. Therefore, the correct answer to the question is d. np and nq must be > 5.
If 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?
The possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:
(-9,-3) i.e. [tex]-9<\dfrac{8}{3}-5mx<-3[/tex]
Step-by-step explanation:We are given a set of inequalities of the form:
[tex]9<15mx-8<27[/tex]
Now when we divide all of the inequality by 3 we get that:
[tex]\dfrac{9}{3}<\dfrac{15mx}{3}-\dfrac{8}{3}<\dfrac{27}{3}\\\\i.e.\\\\3<5mx-\dfrac{8}{3}<9[/tex]
Now when we multiply the inequality by -1 then the sign of the inequality gets interchanged.
i.e.
[tex]-3>-(5mx-\dfrac{8}{3})>-9\\\\i.e.\\\\-3>\dfrac{8}{3}-5mx>-9[/tex]
i.e.
[tex]-9<\dfrac{8}{3}-5mx<-3[/tex]
Hence, the possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:
(-9,-3) i.e. between -9 and -3 with -9 and -3 excluded from the range.
place a square on a coordinate graph and label each vertex with variables. prove that the diagonals of a square are congruent and perpendicular to each other.
Final answer:
To prove that the diagonals of a square are congruent and perpendicular, label the vertices of a square on a coordinate grid and calculate the slopes and lengths using the slope formula and distance formula respectively. The diagonals have slopes of +1 and -1, proving they are perpendicular, and they have equal lengths, proving they are congruent.
Explanation:
To prove that the diagonals of a square are congruent and perpendicular, we place a square with its vertices on a coordinate grid and label each vertex with variables.
Let's consider a unit square where c = 1 for simplicity, which means the length of each side is 1 unit. Place the square so that one vertex is at the origin (0,0), and label the vertices A(0,0), B(1,0), C(1,1), and D(0,1).
The diagonal AC will have endpoints at A(0,0) and C(1,1), and diagonal BD will have endpoints at B(1,0) and D(0,1). The slope of diagonal AC is (1 - 0)/(1 - 0) = 1, and the slope of diagonal BD is (1 - 0)/(0 - 1) = -1. Since the product of their slopes is -1 (1 * -1 = -1), this proves that they are perpendicular to each other.
To show they are congruent, we calculate their lengths using the distance formula: the distance between two points (x1,y1) and (x2,y2) is √[(x2 - x1)² + (y2 - y1)²]. Applying this to AC and BD reveals both lengths to be √[(1-0)² + (1-0)²] = √[1 + 1] = √2, proving the diagonals are congruent.
Multiply 3 [ 1 5 -5 6 0 0 ]
Simply multiply the number outside the brackets with each one inside it..
3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you.
Temperature dropped from 11 below zero to 4 below zero how much did the temperature drop
A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?
The angle of depression represents the angle from a horizontal layout to a lower surface. The distance between the two stadiums is 3115.1 meters
The given parameters have been illustrated using the attached image of triangles.
The stadiums are represented with A and B.
First, calculate distance BO using:
[tex]\tan T =\frac{BO}{TO}[/tex]
Where:
[tex]\angle T = 90 -75.2 = 14.8[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(14.8^o) = \frac{BO}{1100}[/tex]
Make BO the subject
[tex]BO = 1100 * \tan(14.8^o)[/tex]
[tex]BO = 1100 * 0.2642[/tex]
[tex]BO = 290.62[/tex]
Next, calculate distance AO using:
[tex]\tan T =\frac{AO}{TO}[/tex]
But in this case:
[tex]\angle T = 90 -17.9 = 72.1[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(72.1^o) = \frac{AO}{1100}[/tex]
Make AO the subject
[tex]AO = 1100 * \tan(72.1^o)[/tex]
[tex]AO = 1100 * 3.0961[/tex]
[tex]AO = 3405.71[/tex]
The distance AB between the 2 stadiums is:
[tex]AB = AO - BO[/tex]
[tex]AB = 3405.71-290.61[/tex]
[tex]AB = 3115.1[/tex]
Hence, the distance between the 2 stadiums is 3115.1 meters.
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Daria applied a transformation to triangle ABC to obtain triangle A′B′C′. The two triangles are not congruent. Which of the following could be the transformation Daria applied?
If f(x) is an odd function, which statement about the graph of f(x) must be true?
It has rotational symmetry about the origin.
It has line symmetry about the line y = –x.
It has line symmetry about the y-axis.
It has line symmetry about the x-axis.
An odd function, by definition, is a function that is symmetric about the origin.
An even function, by definition, is a function that is symmetric with respect to the y-axis.
Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.
ANSWER: symmetric about the origin.
Answer:It has rotational symmetry about the origin.
Step-by-step explanation:
An odd function : is a function that is symmetric about the origin.
An even function : is a function that is symmetric with respect to the y-axis.
Since , f(x) is an odd function, it has rotational symmetry about the origin.
its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Therefore, It has rotational symmetry about the origin.
what is the area of a triangle that has a base of 8 yd and height of 3 yd
area = 1/2 x b x h
1/2 x 8 x 3 = 12
area is 12 square yards
evaluate 2^-3
No, there are no answer choices, but it has to be in fraction form.
I'm not sure what this is exactly?
If the value of 2x3 is 2, then what is the value of x?
In a certain? country, the true probability of a baby being a girlgirl is 0.4640.464. among the next fivefive randomly selected births in the? country, what is the probability that at least one of them is a boyboy??
Final answer:
Calculate the probability of at least one boy being born among the next five randomly selected births in a country where the true probability of a baby being a girl is known.
Explanation:
The probability of at least one boy being born among the next five randomly selected births can be calculated by finding the probability of all girls being born and subtracting it from 1. This is known as the complement rule in probability.
Step-by-step calculation:
Find the probability of all births being girls: 0.4645 = 0.00532Subtract this from 1 to get the probability of at least one boy: 1 - 0.00532 = 0.99468
Therefore, the probability of at least one of the next five births being a boy in this country is approximately 0.99468 or 99.468%.
3 -1 ___ 1/4 which one is the correct answer.
=
<
>
3-1 = 2
2 is greater than 1/4
so > is the answer
The equation of a line is 2(y+1)=10x+3
The y-intercept of the line is ___, and the slope of the line is ___.
Answer: The answer is 0.5 and 5.
Step-by-step explanation: The given equation of the line is
[tex]2(y+1)=10x+3.[/tex]
We are to find the y-intercept and the slope of the given line.
We know that the slope-intercept form of a line is given by
y = mx + c, where, 'm' is the slope and 'c' is the y-intercept of the line.
We have
[tex]2(y+1)=10x+3\\\\\Rightarrow 2y+2=10x+3\\\\\Rightarrow 2y=10x+3-2\\\\\Rightarrow 2y=10x+1\\\\\Rightarrow y=5x+0.5.[/tex]
Therefore, c = 0.5 and m = 5.
Thus, the y-intercept of the line is 0.5 and the slope is 5.
A skier is trying to decide whether whether or not to buy a season ski pass. A daily pass cost 67. A season ski pass costs 350. The skier would have to rent skis with either pass for 25 per day. How many days would the skier have to go skiing in order to make the season pass cost the same as the daily pass option.
Write an expression using words to represent the cost of a daily pass. Write the algebraic expression. Write an expression using words to represent the cost of a season pass. Write the algebraic expression
How can you compare the cost of a daily pass with the cost of a season pass algebraically?
Can someone please explain me this
What number must be added to the expression below to complete the square?
x^2+3x
A. 9
B. 9/4
C. 3/2
D. 3
I think it is c or D but it should be C
hope that help
[I don't think it did lol ]
BMK
Use the graph below to answer the following question:
graph of parabola going through negative 4, 4, negative 1, 5, and 1, negative 1
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
Your answer should be
-1
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A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Answer:
9 square inches.
Step-by-step explanation:
We have been given that a rectangle has a length of the [tex]\sqrt[3]{81}[/tex] inches and a width of [tex]3^{\frac{2}{3}}[/tex] power inches. We are asked to find the area of given rectangle.
We know that area of rectangle in length times width of rectangle.
[tex]\text{Area of rectangle}=\sqrt[3]{81}\times 3^{\frac{2}{3}}[/tex]
We can write 81 as [tex]3^4[/tex] as:
[tex]\text{Area of rectangle}=\sqrt[3]{3^4}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can write [tex]\sqrt[3]{3^4}=3^{\frac{4}{3}}[/tex].
[tex]\text{Area of rectangle}=3^{\frac{4}{3}}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:
[tex]\text{Area of rectangle}=3^{\frac{4}{3}+\frac{2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{4+2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{6}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{2}[/tex]
[tex]\text{Area of rectangle}=9[/tex]
Therefore, the area of given rectangle is 9 square inches.