The Solution:
Given:
[tex]y=7x^2+bx+c[/tex]Given that the points: (-1,4) and (2,13) are on the graph of the given equation,
We are required to find the values of a and b.
Substitute (x= -1, y = 4) in the equation, we get:
[tex]\begin{gathered} 4=7(-1)^2+b(-1)+c \\ 4=7-b+c \\ -3=-b+c...eqn(1) \end{gathered}[/tex]Substitute (x= 2, y = 13) in the equation, we get:
[tex]\begin{gathered} 13=7(2)^2+b(2)+c \\ 13=28+2b+c \\ -15=2b+c...eqn(2) \end{gathered}[/tex]Solving eqn(1) and eqn(2) simultaneously by the elimination method:
Subtract eqn(1) from eqn(2):
[tex]\begin{gathered} -15--3=2b--b+c-c \\ -12=3b \end{gathered}[/tex]Divide both sides by 3.
[tex]b=\frac{-12}{3}=-4[/tex]Substitute -6 for b in eqn(1).
[tex]\begin{gathered} -3=-b+c \\ -3=-(-4)+c \\ \\ -3=4+c \\ -3-4=c \\ -7=c \\ c=-7 \end{gathered}[/tex]Therefore, the correct answers are:
b = -4
c = -7
To which subset of the real numbers does 22‾√ belong?
Ok
Squared root of 2 is a irrational number because it can not be expressed as a fraction.
So the correct choice is Irrational, the last one.
Karen owns a seafood restaurant. She orders trout from an online retailer.Each pound of trout costs $30, and the company charges a $2 fee forshipping the order. However, if Karen orders 10 or more pounds, the troutcosts only $24 per pound, but the shipping fee is $6.Which piecewise function models the cost of x pounds of trout?○ A. f(x) = {={O B. f(x) ={O c. f(x) = -O D. f(x) =30x + 2, 0< x≤ 1024x+6, x 1024x+6, 0
The piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Let the number of pounds of trout is x and the price is C.
For, x < 10 :
From the question, we have
Each pound of trout costs $30
C = 30x + 2 ....1 )
For, x ≥ 10 :
Each pound of trout costs $24.
C = 24x + 6 ....2 )
Therefore, the piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Piecewise Function :
A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs. A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.
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I would like some help solving this step by step please
you roll a six-sided number cube find theprobabilsty of rolling each of the followingP(1 or 6)
When you roll a six-sided number cube you can get the next set of possible results:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]You have a total of 6 possible results.
From the set of possible results you get the set of presults that are 1 or 6:
[tex]\lbrace1,6\rbrace[/tex]You have 2 results that are 1 or 6
The probability of rolling (1 or 6) is: The number of results that are 1 or 6 divided in the total number of possible results:
[tex]P(1or6)=\frac{2}{6}=\frac{1}{3}[/tex]Then, the probability of rolling (1 or 6) is 1/3Without graphing, find the slope of the line that goes through each pair of coordinate points. (0,5) and (8,2 ) [Choose ] (2,-1) and (6, 1) [ Choose ] (-3,-2) and (- 1,-5) [ Choose]
Answers:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Explanation:
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, the slope of a line that goes through (0,5) and (8,2) is equal to:
[tex]m=\frac{2-0}{8-5}=\frac{2}{3}[/tex]The slope of a line that goes through (2, -1) and (6, 1) is:
[tex]m=\frac{1-(-1)}{6-2}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The slope of a line that goes through (-3, -2) and (-1, -5) is:
[tex]m=\frac{-5-(-2)}{-1-(-3)}=\frac{-5+2}{-1+3}=-\frac{3}{2}[/tex]Therefore, the answers are:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
it is a graph I will send a picture of it
SOLUTION
The image of f(x) is given in the diagram.
Then the image of the function
[tex]f(x)-1\text{ means the f(x) as b}een\text{ shifted vertically down by one unit }[/tex]Thence the image of f(x)-1 is given below as
Therefore the right option is A
Analyze the diagram below and complete the instructions that follow./Find sinA.1/3B.5/14C.4/5D.12/13
As given by the question
There are given that the triangle.
[tex]\begin{gathered} OM^2=3^2+4^2 \\ OM=5 \end{gathered}[/tex][tex]undefined[/tex]if a 3/4 of a cup serving of cereal provides your full daily value of vitamin B6 then what percentage of your daily value of vitamin B6 will you receive in 1/2 of a cup of your cereal
Given
3/4 cup serving of cereal provides 100% of vitamin B6 requirement
The percentage of daily value that would be available in 1/2 of a cup of cereal is:
[tex]\begin{gathered} \text{= }\frac{\frac{1}{2}}{\frac{3}{4}}\text{ }\times\text{ 100 \%} \\ =\text{ }\frac{1}{2}\times\frac{4}{3}\text{ }\times\text{ 100\%} \\ \text{= }\frac{4}{6}\text{ }\times\text{ 100\%} \\ =\text{ 66.67\%} \end{gathered}[/tex]Hence, the percentage of the daily value in 1/2 of a cup is 66.67%
A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts.One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.Write your answer as a fraction. I need help with this math problem
There is a total of 2 + 7 + 11 = 20 shirts
Given the following frequency table of values, iIs the mean, median, or mode likely to be the best measure of the center for the data set? ValueFrequency211220230240250260270280290300310320330340352363371380392404413Select the correct answer below:ModeMeanMedian
Solution
In the dataset given. The distribution is skewed.
The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution)
Thus, the correct answer is median
6. Andre is drawing a triangle that is congruent to this one.He begins by constructing an angle congruent to angleLKJ. What is the least amount of additional informationthat Andre needs to construct a triangle congruent tothis one?
The measure of an angle
The measure of two legs
1) Andre can construct a congruent triangle using SAS congruence, knowing the angle congruent to LKJ and with a compass measure two legs of that triangle
2) Sketching out we have:
Notice that either with a protractor or with a compass we can measure congruent angles and based on SAS congruence we need two congruent legs to determine a SAS congruence.
3) Hence, Andre needs at least:
The measure of an angle
The measure of two legs
The salaries of the employees at four companies are summarized below. Answer the question about them.
Given,
Company A: the range of the salaries is $60000 and the mean salary is $22000.
Company B: the range of the salaries is $58000 and the mean salary is $29000.
Company C: the range of the salaries is $67000 and the mean salary is $27000.
Company D: the range of the salaries is $63000 and the mean salary is $28000.
Required
The company have least average salary and least variability.
a) From the given data, it is clearly seen that the company that have the lowest salary is $22000.
Hence, the company that have the lowest salary is Company A.
b)From the given data, it is clearly seen that the company that have the least salary variability is $58000.
Hence, the company that have the least salary variability is Company B.
Find the median for the scores: 93,69,72,86,72,95,88,74,72,89,89,95,74,79
A set of data is given and it is required to find the median:
[tex]93,69,72,86,72,95,88,74,72,89,89,95,74,79[/tex]Recall that the Median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Hence, to find the median, rearrange the scores either in ascending or descending order.
[tex]69,72,72,72,74,74,79,86,88,89,89,93,95,95[/tex]Next, highlight the two middle numbers since the frequency of the scores is even (14):
[tex]69,72,72,72,74,74,\boxed{79,86},88,89,89,93,95,95[/tex]Find the mean of the two middle numbers to calculate the median for the scores:
[tex]\frac{79+86}{2}=\frac{165}{2}=82.5[/tex]Hence, the median score is 82.5.
The median score is 82.5.
Give an interval over which the function is increasing. Give an interval over which it is decreasing
one interval where the function is increasing is
(-3;1)
one interval where the function is decreasing is
(1;4)
N. Students wanted to determine theheight of the flagpole. They measuredits shadow as 27 ft and the shadow of a 6ft tall student as 2 ft. How tall is theflagpole? Use the digit in the ones placeof your answer for N.
Given:
Shadow of flagpole = 27 feet
Height of the tall student = 6 feet
Shadow of the tall student = 2 feet
Required:
the height of the pole
Explanation:
Both the triangles are similar so the ratio of their corresponding sides are equal
[tex]\frac{height\text{ }of\text{ }flagpole}{height\text{ }of\text{ }student}=\frac{shadow\text{ }of\text{ }flagpole}{shadow\text{ }of\text{ }student}[/tex]Substituting the given values we get
[tex]\begin{gathered} \frac{height\text{ }of\text{ }flagpole}{6}=\frac{27}{2} \\ \\ height\text{ }of\text{ }flagpole=\frac{27\times6}{2}=27\times3 \\ \\ height\text{ }of\text{ }flagpole=81\text{ }feet \end{gathered}[/tex]Final answer:
The height of the flagpole is 81 feet.
Area of a triangle Find the area of the triangle below. Be sure to include the correct unit in your answer. Explanation Check 9 cml 19 cm 10 cm A 0 cm X cm² cm³ ?
Given
To find:
The area of the triangle.
Explanation:
It is given that,
That implies,
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}\times b\times h \\ =\frac{1}{2}\times10\times9 \\ =5\times9 \\ =45cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 45cm
²
Need help with figuring out if this is a system of equations
Given:
The system is:
[tex]\begin{cases}{2x+3y+10z=9} \\ {-x+2y+5z=1} \\ {3x+z=5}\end{cases}[/tex]The solution is (2,3,-1)
Find-:
The (2,3,-1) is the solution of function or not
Explanation-:
The solution is (2,3,-1) which means:
[tex]\begin{gathered} x=2 \\ \\ y=3 \\ \\ z=-1 \end{gathered}[/tex]Check the value for the given expression:
[tex]\begin{gathered} 2x+3y+10z=9 \\ \\ 2(2)+3(3)+10(-1)=9 \\ \\ 4+9-10=9 \\ \\ 3\ne9 \end{gathered}[/tex]So, it is not a solution of system.
the volume of a sphere is 12348 pi in ³ calculate the radius of the sphere
The volume of a sphere is given by the expression:
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]Where V is the volume and r is the radius of the sphere. Solve this expression for r and replace for the given values to find the radius of the sphere, this way:
[tex]\begin{gathered} V=\frac{4}{3}\pi\cdot r^3 \\ 12348\pi=\frac{4}{3}\pi\cdot r^3 \\ \frac{12348\pi}{\pi}\cdot\frac{3}{4}=r^3 \\ 9261=r^3 \\ r=\sqrt[3]{9261} \\ r=21 \end{gathered}[/tex]The radius of the sphere is 21 inches.
Combine like terms and write each expression in standard form
SOLUTION
From the expression
[tex]x^2-5+2x+x^2[/tex]combining like terms we have to bring the x-squares together, we have
[tex]\begin{gathered} x^2+x^2-5+2x \\ 2x^2-5+2x \end{gathered}[/tex]To write in standard form, the 2x should come before the -5, so we have
[tex]2x^2+2x-5[/tex]Hence the answer is
[tex]2x^2+2x-5[/tex]in rst the measure of ∠J=90° the measure of ∠H=69° and Hl=88 feet. find the length of JH to the nearest tenth of a foot
From the information provided, we can construct the following triangle;
The measure of angle J is 90 degrees, the measure of angle H is 69 degrees and line HI measures 88 feet. Therefore to calculate line JH;
[tex]\begin{gathered} \cos \theta=\frac{adj}{hyp} \\ \cos 69=\frac{JH}{88} \\ \text{Cross multiply and you'll have;} \\ 88\times\cos 69=JH \\ 88\times0.35836794\ldots=JH \\ 31.5363\ldots=JH \\ JH\approx31.5ft \end{gathered}[/tex]The answer is 31.5 feet (rounded to the nearest tenth of a foot
For each scenario below, choose the graph that gives the best representation.(A) Carlos is driving on the freeway at a constant speed. He then speeds up to pass a truck, After passing the truck, he exits the freeway and slows down.(B) Rachel is delivering a pizza to Mark's house. She drives at a constant speed toward the house until she hits a traffic jam and has to stop for severalminutes. After, she starts up again and drives at a faster speed than before.
Given:
Given the word problem, we can deduce the following information:
a)
1. Carlos is driving on the freeway at a constant speed.
2. He then speeds up, and exits the freeway and slows down.
Based on hte given information, the graph should have a constant or horizontal line at the first part, increases as he speeds up on the second part, and decreases as he slows down.
Thus the graph should be:
b)
1. Rachel is delivering at a constant speed toward the house until she hits a traffic jam and has to stop for several minutes.
2. She starts up again and drives at a faster speed than before.
So based on the given information, the graph should have a horizontal line at the first part since Rachel is driving at a constant speed. Next, the line should be increasing and higher than the horizontal line since Rachel is driving at a faster speed than before.
Therefore, the graph is:
I’m not sure how to solve this I just know I have to get 5 with an exponent of 7 I think
this is an addition of powers .
on sunday , Margos dad gives 5c, we will represent it as 5^1
therefore: sunday 5^1
Monday 5^1 x ( 5^1)
because bases are the same , we add exponents
this means that 5^1(5^1) = 5^2
Tuesday 5^2(5^1) = 5^3
wednesday 5^3(5^1) = 5^4
thursday 5^4( 5^1)= 5^5
Friday 5^5(5^1)= 5^6
saturday 5^6 (5^1)= 5^7
50 points!
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6[tex]\sqrt{2}[/tex] ) can be [tex]x\sqrt{2}[/tex] while AB and CB are x. Because 6[tex]\sqrt{2}[/tex] is equal to [tex]x\sqrt{2}[/tex], you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = [tex]x\sqrt{3}[/tex]. CB is equal to 6 so 2x = 6, x = 3.
A travel agency polled its customers about their favorite kind of vacation. The results of the survey are shown in the given two-way frequency table.
Vacation Preferences
Seaside Mountain Historical Sightseeing Total
Female 38 36 32 17 123
Male 43 52 23 19 137
Total 81 88 55 36 260
What is the marginal relative frequency of customers who prefer sightseeing vacations?
A.
0.47
B.
0.21
C.
0.14
D.
0.89
The marginal relative frequency of customers who prefer sightseeing vacations is (C) 0.14
The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
[tex]Marginal relative frequency = \frac{sightseeing(total)}{Total}[/tex]
= 36/260
= 0.1385
≅ 0.14
Hence, marginal relative frequency of customers who prefer sightseeing vacations is 0.14.
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Fill in the table using function rule
Y=6x+2
Using our equation y = 6x + 2, we were able to write out values for our table of function.
Function TableA function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.
Since we have our equation, we can proceed to find what values of y we would have when x is in a certain condition.
Using from -2 to + 5, we can have a good table of function.
When x = -2
y = 6x + 2
y = 6(-2) + 2 = -10
When x = -1
y = 6(-1) + 2 = -4
When x = 0
y = 6(0) + 2 = 2
When x = 1
y = 6(1) + 2 = 8
When x = 2
y = 6(2) + 2 = 14
When x = 3
y = 6(3) + 2 = 20
When x = 4
y = 6(4) + 2 = 26
When x = 5
y = 6(5) + 2 = 32
Using the values above, we have a good function table and can proceed to plot a graph if needed.
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Question 60 state wether the triangle is an isosceles triangle,right triangle, neither of these or both.
Given:
The points of the triangle:
[tex]P_1=(7,2);P_2=(-4,0);P_3=(4,6)[/tex]Required:
To find out if the given triangle is an equilateral triangle or an isosceles triangle or both or none of these.
Explanation:
To find if the triangle is an equilateral triangle or an isosceles triangle we will have to first find the length of the sides by distance formula.
Distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)_^2+(y_2-y_1)^2}[/tex]So applying the distance formula on side P₁P₂
Substituting the value of P₁ and P₂ in the distance formula we get
[tex]P₁P₂=\sqrt{(-4-7)^2+(0-2)^2}=\sqrt{(-11)^2+(-2)^2}=\sqrt{121+4}=\sqrt{125}=5\sqrt{5}[/tex]Now lets find the length of P₂P₃
Substituting the value of P₂ and P₃ in the distance formula we get
[tex]P₂P₃=\sqrt{(4-(-4))^2+(6-0)^2}=\sqrt{(4+4)^2+6^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]Now lets find the length of P₁P₃
Substituting the value of P₁ and P₃ in the distance formula we get
[tex]P₁P₃=\sqrt{(4-7)^2+(6-2)^2}=\sqrt{(-3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]S now we have the length of all three sides, that is
[tex]\begin{gathered} l(P₁P₂)=5\sqrt{5} \\ \\ l(P_2P_3)=10 \\ \\ l(P₁P_3)=5 \end{gathered}[/tex]If we add any two sides of triangle then it is greater than the third side so it is a triangle.
[tex]\begin{gathered} 5\sqrt{5}+5>10 \\ 5+10>5\sqrt{5} \\ 5\sqrt{5}+10>5 \end{gathered}[/tex]So it is a valid triangle. But the length of all the sides of triangle are different.
In equilateral triangle all the sides are same.
In isosceles triangle any sides are same.
Since here none of the sides are same so it is neither an equilateral triangle nor an isosceles triangle. It is a Scalene triangle with all three sides different.
Final answer:
The answer is none of these.
Given that events "A" and "B" are independent, P(A) = 0.80, and P(A and B) = 0.24, what is P(B)?
Answer:
P(B)=0.3
Explanation:
Given two independent events, A and B:
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Substitute the given values:
[tex]\begin{gathered} 0.24=0.8\times P(B) \\ \text{ Divide both sides by 0.8} \\ \frac{0.24}{0.8}=\frac{0.8\times P(B)}{0.8} \\ P(B)=0.3 \end{gathered}[/tex]The probability of event B is 0.3.
2x+y=21;y=-2x+21please hurry I need this straight away use any method
Answer:
(k, -2k+21) where k is any integer
Explanation:
Given the following simultaneous equation;
2x+y=21 ..... 1
y=-2x+21 ..... 2
Subtitute equation 2 into 1:
2x + (-2x+21) = 21
2x -2x+21 = 21
0x = 21-21
0x = 0
x = 0/0
Since the variables cannot be determined, we will subtitute x = k
Substitute x = k into equation 2;
From 2: y = -2x+21
y = -2k+21
Hence the solution to the system of equation is (k, -2k+21) where k is any integer
I WILL GIVE BRAINLIEST
Juan bought three and three-fourths pounds of pineapple and three and three-eighths pounds of strawberries for a fruit salad. After eating one and fifteen-sixteenths pounds of the fruit salad, how much was left?
five and three-sixteenths pounds
five and three-eighths pounds
five and nine-sixteenths pounds
seven and twenty-one sixteenths pounds
Salad was left (A) Five and three-sixteenths pounds.
Fraction is the comparison between numbers or mathematical quantities.
Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds
Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds
So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds
Juan eats = (1+15/16) = 31/16 pounds
Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds
Hence the correct option is (A).
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How do you solve linear equations in algebra ?-3y>-3-4x
Given linear equations in algebra: -3y >-3-4x
The above is an inequality.
To solve linear equation with two variables we need two equations.
Only one equation is given. The only other explanation is to solve for any of the variables by making it the subject of formula.