Given function is
[tex]z(x)=1+6x^2+4x[/tex]In the given function, the maximum power of x is 2 and it is of the form
[tex]ax^2+bx+c[/tex]Therefore, it is a quadratic function.
The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x
2
+10x−5 is
The slope of the line passing through the y intercept and the vertex of the quadratic x²+10x-5 is 5.
The provided quadratic equation is,
y = x²+10x-5
The vertex of a quadratic equation,
(-b/2a, -D/4a)
Where,
a = 1,
b = 10,
c = -5,
D = (b²-4ac)
D = (10²-4(-5)(1))
D = 100+20
D = 120,
Putting all the values to find the vertex of the equation,
(-10/2,-120/4)
(-5,-30)
So, the vertex are now known,
To find the y intercept, putting x = 0 and solving the equation for y,
y = (0)²+10(0)-5
y = -5
The y intercept is,
(0,-5)
If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,
M = (d-b)/(c-a)
Now, we know two points,(-5,-30) and (0,-5).
We can now find the slope of line,
M = (-5+30)/(0+5)
M = 25/5
M = 5
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you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?
Given data:
The given principal is P=$3,300.
The given rate of interest is r=3.3%.
The given time is t=20 years.
The expression for the final amount of money is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is 5,478.
In null hypothesis significance testing, if a result is unlikely under the hypothesis, then we infer
support for the _______ hypothesis.
Answer:
Step-by-step explanation:
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.
what is the median value?if another 5 is added, which statement must be true the mean would increase the mean would decrease the median would increaseboth the median and mean will stay the samehow many people made 3 or less trips to the movie
Solution
We have the following data:
0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
And the mean would be:
Mean = 2.958
And the median
Median = 4
Then if we add a 5 then the median would be the same 4
And the mean = 3.04
then the solution is:
The mean would increase
And for the other part of the question
we have:´
4+3+1+2 = 10 people made 3 or less trips to the movie
Write the equation of the quadratic with a directrix of y=-5 and vertex of (-2,-3).
answer step by step, please
The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3
How to write the equation of parabola with directrix of y = -5 and vertex of (-2,-3)Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = -3
P in this problem, is the distance between the vertex and the directrix
P = -3 - -5 = -3 + 5 = 2
p = 2
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -2)² = 4 * 2 (y - -3)
(x + 2)² = 8 (y + 3)
rearranging the equation
8 (y + 3) = (x + 2)²
y + 3 = 1/8 (x + 2)²
y = 1/8 (x + 2)² - 3 (standard vertex form)
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I need help on this also could you check if the first 3 questions are correct
We have two parallel lines intersected by other line.
We have to relate the angles.
We will take the angle with measure 17° as reference (red angle).
The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.
[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.
The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).
The relationship with the red angle is that they are alternate exterior angles.
Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.
Angle <4 and the red angle are corresponding angles.
They have the same measure, so they are congruent.
Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.
Angle <6 and the red angle are vertical angles, so they have the same measure.
Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.
Answer:
Angle <1:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <2:
Measure = 17°
Relationship: Alternate exterior and congruent.
Angle <3:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <4:
Measure = 17°
Relationship: Corresponding and congruent.
Angle <5:
Measure = 163°
Relationship: Linear pair and supplementary.
Angle <6:
Measure = 17°
Relationship: Vertical and congruent.
Angle <7:
Measure = 163°
Relationship: Linear pair and supplementary.
find the equation of the line that contains the point (6,4) and is perpendicular to the line y=3x-5
The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
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a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?
the answer is 1 1/4 cups of vinegar
Step-by-step explanati
Explanation and answer for both Part A and B please
Solve the system of equations below to find it's solution. List the x-coordinate and y-coordinate.y = 2x - 56x - 2y= 20
y = 2x - 5 Eq(1)
6x - 2y= 20 Eq(2)
We are going to use the elimination method to solve the system.
y-2x = -5 Transpose x to the othe side in Eq(1)
2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)
2y - 4x = -10
+ -2y +6x= 20
----------------------
2x = 10 Operating like terms
x= 10/2 Isolating x
x = 5
Replacing x in Eq(1)
y = 2*(5) -5
y= 10 - 5 = 5
The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).
Find the length of the hypotenuse if the length of the legs are 6 inches and 9 inches. Round to two decimal places.The length of the hypotenuse is ___ inches.
The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ \text{Where AC is the hypotenuse, you now have;} \\ AC^2=6^2+9^2 \\ AC^2=36+81 \\ AC^2=117 \\ \text{Add the square root sign to both sides} \\ AC=\sqrt[]{117} \\ AC=10.8166 \\ AC=10.82\text{ (To 2 decimal places)} \end{gathered}[/tex]The answer is 10.82 inches, to 2 decimal places
work out the sale has been decreased
20% of 120
The current amount of the sale is 96
How to find the current amount of the sale ?The sale is 120
It was decreased by 20%
20/100 × 120
= 0.2 × 120
= 24
The amount of the current sale is
120-24
= 96
Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96
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Solve Step by step
8 = x/7 + 9
Answer:
[tex]x=\frac{-1}{7}[/tex]
Step-by-step explanation:
[tex]8=x/7+9\\[/tex]
Subtract 9 from both sides
[tex]-1=x/7[/tex]
Multiply both sides by 7
[tex]\frac{-1}{7} =x[/tex]
Swap the order because you're a smart person
[tex]x=\frac{-1}{7}[/tex]
can someone please help me find the value of x to this equation
SOLUTION
This is a right-triangle problem.
We will use the SOHCAHTOA principle.
In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]The final answer is 73.87 degrees.
24. Write the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
[tex]y-y_1=m(x-x_1)[/tex]where m = slope.
[tex]\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}[/tex]Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Step-by-step explanation:
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)
where m = slope.
\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}
y−(−13)=
2
1
(x−0)
y+13=
2
1
(x)
y=
2
1
x−13
Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.
SOLUTION:
Case: System of equations
Given: A table of value of snacks and drinks for Sidney and Erica
Required: Write a system of equations to determine the price of each candy and each drink.
Method:
Step 1: Assume the price of snacks be represented by s and drinks by d
Step 2: Equation for Sidney
[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica
[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]Final answer:
The system of equations is:
[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.
12x^3
Name: Monomial , because it has only 1 term
Degree: 3, exponent of the monomial
Select the correct figures
The correct answer is the figure
There are 175 students enrolled in Blue Bear High School. Twenty-five students train in Karate (T) and 35 students compete with other schools in Karate (C). One hundred students practice martial arts, but not Karate. How many students qualify for a Karate tournament if they train and compete at Blue Bear High School? A. 0 B. 15 C. 60 D. 115
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
As given in the question,
Total number of students enrolled in Blue Bear High School =175
Number of students train in karate = 25
Number of students compete with other school in karate =35
Number of students practice martial arts but not karate=100
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School
= 25 + 35
= 60
Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
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Evaluate 14xy if x=−23 and y=35 . Write your answer as a fraction in simplest form.
Answer: -11270
Step-by-step explanation:
14xy = -11270 x=-23 y=35
14(-23)(35) = -11270
which expression would be easier to simplify if used the associative property to change the group.A.4+(1.2 +(-0.2)b. 85+(120+80)c. (2+3/7)+4/7d. [-40+(60)] +52
The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.
'The other expressions involve more steps.
A table is on sale for $589, which is 24% less than the regular price.
What is the regular price?
Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?
The value of a nickel is 5 cents
The value of the quarter is 25 cents
Since Priam has a total of 9.30 dollars = 930 cents, then
[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5
[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then
[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)
[tex](3q-6)+5q=186[/tex]Add the like terms on the left side
[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides
[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8
[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24
Substitute q by 24 in equation 2 to find n
[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66
He has 66 nickels and 24 quarters
What mathematical symbol goes between the two parentheses to show that you will be using the distributive property?
8 x 57 = (8 x 50) _______ (8 x 7)
Answer: The Answer is the addition symbol
Step-by-step explanation:
8 x 50 = 400
8 x 7 = 56
400 + 56 = 456
8 x 57 = 456
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answer:
I don't know if it is the answer
The mean height of women in a certain country ( ages 20 29) is 64.1 inches .A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches if the standard deviation is 2.52
The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches if the standard deviation is 2.52.
To proceed we, find the z-score of 65 in the distribution, we make use of the formula;
[tex]z=\frac{x-\mu}{(\frac{\sigma}{\sqrt[]{n}})}[/tex]x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.
inserting these values, we have;
[tex]\begin{gathered} z=\frac{65-64.1}{\frac{2.52}{\sqrt[]{70}}} \\ z=0.043 \end{gathered}[/tex]The problem now boils down to finding the probability of the z-score greater than 0.043
From z-score tables. the probability of the z-score greater than 0.043;
[tex]Pr(z>0.043)=0.48285[/tex]Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285
The table below represents the total weight, in pounds, of a set ofstone blocks.<
k=12
1) Gathering the data, and setting this table:
Blocks | Pounds
5 60
6 72
7 84
8 96
2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx
Then we can write:
y =12x
3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.
5 x 12 = 60
6 x 12 =
Assessment
Time Remaining: 2:33:21 | Question 16
Charmaine spent $21 on fruit at the grocery store. She spent a total of $70 at the store. What percentage of the total did she spend on fruit?
%
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When the linear correlation coefficient is 1 there is a perfect positive linear relation between the two variables. Scatter diagram would contain points that all lie on a line with a positive slop.
What is coefficient coorelation?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.
The strength and direction of the linear links between two sets of variables are evaluated using correlation coefficients. Use Pearson's correlation coefficient if both variables are regularly distributed; otherwise, use Spearman's correlation coefficient.
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Can somebody please help me right now??? i’m stuck and i need help with this bad
Answer:
Step-by-step explanation:
The answer is B!