Given: a quadratic function with vertex (2,3) opening upward .
Find: the given statement is true or false.
Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.
that means graph has no one real solution. hence it will never going to intersect. so this statement is false.
Final answer: the given statement is FALSE.
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]2. Factor completely
2x^2 + 8x + 6
The factors are -3 and -1
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
2x² + 8x + 6
Put it equal to 0 so that we can solve for 'x'
2x² + 8x + 6 = 0
Now, its factors are 6x and 2x
2x² + 6x + 2x + 6 = 0
2x(x + 3) + 2(x + 3) = 0
To cross check your solution is correct or not. You've to just see the the brackets value should be same after taking common. Here the bracket value is (x+3) which is same.
(2x + 2) (x+3) = 0
split the values to solve further,
2x + 2 = 0 | x + 3 = 0
2x = -2 | x = -3
x = -2/2
x = -1
Hence, the factors are -3 and -1
To read more about the Quadratic equation
https://brainly.com/question/1214333
#SPJ13
write the slope-interference form of the equation of each line
The slope interference form of straight line is given by
[tex]y=mx+c[/tex]Here is the slope of the line and c is the y-intercept
Now, from the graph, it is seen that the line passes through the points (0,4) and (3,5)
So,
[tex]\begin{gathered} \frac{y-4}{5-4}=\frac{x-0}{3-0} \\ \frac{y-4}{1}=\frac{x}{3} \\ 3(y-4)=x \\ 3y=x+12 \\ y=\frac{x}{3}+4 \end{gathered}[/tex]So, the required equation is
[tex]y=\frac{x}{3}+4[/tex]
Hi, I am testing the service for Brainly. Can you help me find the median for this set of numbers: 3, 4, 15, 27, 53, 54, 68, 77?
To find the median of a set of numbers, the first step is:
1 - Put the numbers in crescent order
This set of numbers is already in crescent order, so we can skip this step
2 - Count how many numbers there are in the set.
In our set we have 8 numbers, so in this case, the median of the set will be the average value between the two central numbers (that is, the fourth and fifth numbers)
The fourth number is 27, and the fifth number is 53, so the median is the average of these two numbers:
[tex]\text{median = }\frac{(27\text{ + 53)}}{2}=\frac{80}{2}=40[/tex]So the median of this set of numbers is 40.
What is the value of Negative 3mn + 4m minus 3 when m = 2 and n = negative 4?
SOLUTION
STEP 1: Write the given expression
[tex]-3mn+4m-3[/tex]STEP 2: Write the given values
[tex]\begin{gathered} m=2 \\ n=-4 \end{gathered}[/tex]STEP 3: Evaluate the given expression
[tex]\begin{gathered} -3(2)(-4)+4(2)-3=24+8-3 \\ 32-3=29 \end{gathered}[/tex]Hence, the answer is 29
The bases of the prism below are rectangles. If the prism's height measures 3 units and its volume is 198 units^3. solve for x
The volume of a rectangular prism is given by
V=L*W*H
where
V=198 units3
L=6 units
W=x units
H=3 units
substitute given values
198=(6)*(x)*(3)
solve for x
198=18x
x=198/18
x=11 unitsI need help with this answer can you explain it
The solution.
The correct answer is y-intercept at (0,1) and decreasing over the interval
[tex]\lbrack-\infty,\infty\rbrack[/tex]Hence, the correct answer is the last option (option D)
2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
we know that
Applying the Pythagorean Theorem
DE^2=DEx^2+DEy^2
DEx -----> is the distance in the x-coordinate
DEy -----> is the distance in the y-coordinate
DEx=(-5-4)=-9 ------> subtract the x-coordinates
DEy=(-7+3)=-4 -----> subtract the y-coordinates
substitute in the formula
DE^2=(-9)^2+(-4)^2
DE^2=97
[tex]DE=\sqrt[]{97}\text{ units}[/tex]c^2=a^2+b^2
c -----> is the distance DE
a ----> horizontal leg
b ----> vertical leg
we have
a=(-5-4)=-9 ------> subtract the x-coordinates
b=(-7+3)=-4 -----> subtract the y-coordinates
substitute
c^2=(-9)^2+(-4)^2
c^2=97
[tex]c=\sqrt[]{97}\text{ units}[/tex]Do they have the same value? Is +3 equal to -3 and -10 equal to +10? Why?
+3 and -3 do not have the same value
+10 and -10 do not have the same value
Explanation:+3 is a positive number while -3 is a negative number
+3 ≠ -3 (Since one is positive and the other is negative)
The difference between +3 and -3 = 3 - (-3) = 6
Therefore, +3 and -3 do not have the same value
+10 is a positive number while -10 is a negative number
+10 ≠ -10 (Since one is positive and the other is negative)
The difference between +10 and -10 = 10 - (-10) = 20
Therefore, +10 and -10 do not have the same value
Express 1.27times 10^3 in decimal notation
1.27 x 10^3
10^3 is 1000
1.27 x 10^3 = 1.27 x 1000 = 1270
[tex]1.27x10^3\text{ = 1.27}x1000\text{ = 1270}[/tex]Answer:
1270
Multiplying and Dividing Integers 10-16 Name: 1. As a cold front passed through Temple, the temperature changed steadily over 6 hours. Altogether it change -18 degrees. What was the change in temperature each hour for the 6 hours? a.-18 - 6 = -3 degrees b. 18 - 6 = 3 degrees c. 18 + 6 = 24 degrees d. 18 - 6 = 12 degrees 2. Q. Four college roommates rented an apartment together. When they moved out, they were charged $1500 for damages to the carpet and walls. The roommates agreed to equally share the cost. What integer represents how much each person will have to pay?
Given the total change in temperature in 6 hours, it is necessary to divide it by the number of hours
[tex]-\frac{18}{6}=-3[/tex]The change in temperature each hour is -3 degrees
I need help with this problem, please help
Answer:
d.
Step-by-step explanation:
the slope is the factor of x.
a perpendicular slope turns the original slope upside-down and flips the sign.
the original slope is -3/7.
the perpendicular slope is then 7/3.
the only answer option with the correct slope is d.
so, d. must be correct.
let's check that (-2, 2) is on this line :
2 = 7/3 × -2 + 20/3 = -14/3 + 20/3 = 6/3 = 2
2 = 2
correct.
so yes, the point (-2, 2) is on this line, and d. is indeed correct.
f(x) = x ^ 3 + 3x ^ 2 + 4x + 5 and g(x) = 5 , then g(f(x)) =
we have the functions
[tex]\begin{gathered} f\mleft(x\mright)=x^3+3x^2+4x+5 \\ g(x)=5 \end{gathered}[/tex]so
g(f(x))=5Solve for x using trigonometry. Round to the nearest tenth. (hint: One decimal place) 17 x 19
By definition,
sin(angle) = opposite/hypotenuse
From the picture,
sin(x) = 17/19
x = arcsin(17/19)
x = 63.5°
Nadine tried to solve the equation 12x - 19 equals -4 (3 x - 9) - 15 but made a mistake which line shows evidence of Nadines mistake
Answer:
Line 4
Explanation:
The initial expression is:
12x - 19 = -4(3x - 9) - 15
The mistake was made on line 4, the correct steps to solve the expression are:
[tex]\begin{gathered} 12x-19=-4(3x-9)-15 \\ 12x-19=-12x+36-15 \\ 12x-19=-12x+21 \\ 24x-19=21 \\ 24x-19\textcolor{#FF7968}{+19}=21\textcolor{#FF7968}{+19} \\ \textcolor{#FF7968}{24x=40} \\ x=\frac{40}{24}=\frac{5}{3} \end{gathered}[/tex]Because on line 4 they subtract 19 from the right side and the correct step is to add 19 to the right side.
8% of the students at Jemerson Middle School are absent because of illness. If there are 150 students in the school, how many are absent? 12015128
12 students
Explanation
when you have 8% , it means 8 of every 100 students are absent
find the decimal form
[tex]8\text{ \% = }\frac{8}{100}=0.08[/tex]then, to find the 8% of any number, just multiply the number by 0.08
Step 1
If there are 150 students in the school, how many are absent?
[tex]\begin{gathered} \text{absent}=\text{total}\cdot0.08 \\ \text{absent}=150\cdot0.08 \\ \text{absent}=12 \end{gathered}[/tex]so, 12 students are absent
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answer: [tex]\frac{5}{2\sqrt{5x+3\\} }[/tex]
Step-by-step explanation:
First, use the chain rule to quickly find the answer so that you can check after you go through the ridiculous process that is the bane of every calculus 1 student's existence.
f(x) = (5x + 3)^(1/2)
(d/dx) (5x + 3)^(1/2) =
(1/2)(5x + 3)^(-1/2) * (5) =
5/[2(5x+3)^(1/2)]
Now, we enter the first gate of hell:
f'(x) = the limit as h approaches 0 of [(f(x+h) - f(x))/h]
lim as h -> 0 of [(5(x+h)+3)^(1/2) - (5x+3)^(1/2)/h]
lim as h -> 0 of [(5x+5h+3)^(1/2) - (5x+3)^(1/2) / h]
Multiply numerator and denominator by the conjugate of the numerator, which is (5x+5h+3)^(1/2) + (5x+3)^(1/2).
lim as h -> 0 of
[√(5x+5h+3) - √(5x+3) ] [√(5x+5h+3) + √(5x+3) ]
______________________________________
h[√(5x+5h+3) - √(5x+3) ]
Simplify the numerator via FOIL:
5x+5h+3 + √(5x+5h+3)√(5x+3) - √(5x+3)√(5x+5h+3) - (5x+3)
The remaining radicals in the numerator cancel each-other, giving us:
5x + 5h + 3 - 5x - 3
Simplify Further:
5h
Now that we have simplified our numerator, let's continue:
lim as h -> 0 of (5)(h)/[(h)((5x+5h+3)^(1/2) + (5x+3)^(1/2))]
The h in the numerator cancels the h in the denominator.
lim as h -> 0 of 5/[(5x+5h+3)^(1/2) + (5x+3)^(1/2)]
Now, we directly substitute h with 0 in the equation.
5/[ (5x+3)^1/2 + (5x+3)^(1/2) ]
In the denominator, both sides of the addition sign are the same, so we can simplify it further to:
5/[ 2(5x+3)^(1/2) ]
This is the same answer we received using the chain rule, so it is correct!
Find the area of the compound shapes on the coordinate plane below.
Answer
Part A: 100 square units
Part B: 39 square units
Part C: 48 square units
Explanation
Part A
Scale: 1cm represent 2 units on x-axis and 1cm represents 5 units on y-axis.
Firstly, we convert the figure into two composite plane shapes, that is, a rectangle and a triangle.
Area of composite shapes = area of rectangle + area of triangle
= Length x Width + 1/2(base x height)
= 10 x 8 + 1/2(10 x 4)
= 80 + 20
= 100 square units
Part B
Scale: 1cm represent 3 units on x-axis and 1cm represents 1 unit on y-axis.
Convert the figure into two composite plane shapes, that is, a rectangle and a trapezium.
Area of composite shapes = area of rectangle + area of trapezium
= Length x Width + 1/2(sum of parallel sides)(perpendicular height)
= 3 x 9 + 1/2(3 + 9)(2)
= 27 + 1/2(24)
= 27 + 12
= 39 square units
Part C
Scale: 1cm represent 2 units on x-axis and 1cm represents 2 units on y-axis.
Convert the figure into two composite plane shapes, that is, a trapezium and a triangle.
Area of composite shapes = area of trapezium + area of triangle
= 1/2(sum of parallel sides)(perpendicular height) + 1/2(base x height)
= 1/2(4 + 8)(6) + 1/2(4 x 6)
=1/2(12 x 6) + 1/2(24)
= 36 + 12
= 48 square units
For the parabola given by 4y – 9 = x2 – 6x, find the vertex and focus.
Solution
Gievn the equation below
[tex]4y-9=x^2-6x[/tex]To find the vertex and focus of the given equation, we apply the parabola standard equation which is
[tex]4p(y-k)=(x-h)^2[/tex]Where p is the focal length and the vertex is (h,k)
Rewriting the equation in standard form gives
[tex]\begin{gathered} 4y-9=x^2-6x \\ 4y=x^2-6x+9 \\ 4y=x^2-3x-3x+9 \\ 4y=x(x-3)-3(x-3) \\ 4y=(x-3)^2 \\ 4(1)(y-0)=(x-3)^2 \end{gathered}[/tex]Relating the parabola standard equation with the given equation, the vertex of the parabola is
[tex]\begin{gathered} x-3=0 \\ x=3 \\ y-0=0 \\ y=0 \\ (h,k)\Rightarrow(3,0) \\ p=1 \end{gathered}[/tex]Hence, the vertex is (3,0)
The focus of the parabola formula is
[tex](h,k+p)[/tex]Where
[tex]\begin{gathered} h=3 \\ k=0 \\ p=1 \end{gathered}[/tex]Substitute the values of h, k and p into the focus formula
[tex](h,k+p)\Rightarrow(3,0+1)\Rightarrow(3,1)[/tex]Hence, the focus is (3, 1)
help me please im not understanding on the right side it says: to the total number of people present. Express as a simplified ratio
ANSWER
4 : 9
EXPLANATION
The total number of people present is the number of females plus the number of males:
[tex]125+100=225[/tex]The ratio of number of males to total number of people is:
[tex]\frac{100}{225}[/tex]We have to simplify this fraction. Both 100 and 225 are divisible by 5:
[tex]\begin{gathered} 100\colon5=20 \\ 225\colon5=45 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}[/tex]And then again, 20 and 45 are divisible by 5:
[tex]\begin{gathered} 20\colon5=4 \\ 45\colon5=9 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}=\frac{4}{9}[/tex]We can't simplify more than that, so the ratio is 4 : 9
For the point P(24,14) and Q(31,17), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
STEP 1
Identify what is given and establish what is required.
We are given the coordinates of two points P and Q on the cartesian and are asked to find their midpoint M assuming a straight line is drawn from P and Q
Midpoint between two points is given as:
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2_{}}{2} \\ \text{Where} \\ x_1,y_{1\text{ }}are\text{ the coordinates of point 1} \\ x_2,y_{2\text{ }}are\text{ the coordinates of point }2 \end{gathered}[/tex]STEP 2
Employ formula while putting the appropriate variables.
We select point P as our point 1 as in the formulae and
We select point Q as our point 2 as in the formulae
This gives us:
[tex]\begin{gathered} M=\frac{24+31}{2},\frac{14+17}{2} \\ M=\frac{55}{2},\frac{31}{2} \\ M=27.5,15.5 \end{gathered}[/tex]Therefore, our midpoint M is(27.5, 15.5)
the sum of two numbers is 24 . one number is 3 times the other number . find the two numbers
We are given that the sum of two numbers is 24. If "x" and "y" are the two numbers then we have that:
[tex]x+y=24[/tex]We are also given that one number is three times the other, this is expressed as:
[tex]x=3y[/tex]Now, we substitute the value of "x" from the second equation in the first equation:
[tex]3y+y=24[/tex]Now, we add like terms:
[tex]4y=24[/tex]Now, we divide both sides by 4:
[tex]y=\frac{24}{4}=6[/tex]Therefore, the first number is 6. Now, we substitute the value of "y" in the second equation:
[tex]\begin{gathered} x=3(6) \\ x=18 \end{gathered}[/tex]Therefore, the other number is 18.
what does this mean i dont get it pls help :)
Answer:
Left circle: 6x + 2y
Bottom middle circle: 5x
Bottom right rectangle: 3x + y
Step-by-step explanation:
According to the question, the expression in each circle is the result of the sum of the two rectangles connected to it.
The expression in the left circle is the sum of the expressions in the rectangles above and below it:
⇒ (4x + 3y) + (2x - y)
⇒ 4x + 3y + 2x - y
⇒ 4x + 2x + 3y - y
⇒ 6x + 2y
Therefore, the expression in the left circle is 6x + 2y.
The expression in the right circle is the sum of the expressions in the rectangles above and below it, however the expression in the rectangle below this circle is missing.
To find the missing expression, subtract the expression in the rectangle above the circle from the expression in the circle:
⇒ (4x + 5y) - (x + 4y)
⇒ 4x + 5y - x - 4y
⇒ 4x - x + 5y - 4y
⇒ 3x + y
Therefore, the expression in the lower right rectangle is 3x + y.
The expression in the bottom middle circle is is the sum of the expressions in the rectangles to its left and right:
⇒ (2x - y) + (3x + y)
⇒ 2x - y + 3x + y
⇒ 2x + 3x - y + y
⇒ 5x
Therefore, the expression in the bottom middle circle is 5x.
Determine the slope by using the slope formula and add two points on the line check your answer by drawing a right triangle and labeling the rise and run right numbers in simplest form select undefined if Applicable
Answer:
The slope is -2
Explanation:
The slope can be calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
Replacing (x1, y1) by ( 0, -1) and (x2, y2) by (1, -3), we get:
[tex]m=\frac{-3-(-1)}{1-0}=\frac{-3+1}{1}=\frac{-2}{1}=-2[/tex]Now, we can check the answer using the following drawing
Since rise over run is also equal to 2/(-1) = -2. We can say that the slope is -2.
I am trying to create a study guide and I need step by step explanation on this question please
Answer:
[tex]-5a^3[/tex]Explanation:
We are given the expression:
[tex]\begin{gathered} \frac{10a^6}{-2a^3} \\ We\text{ can simplify the expression further to become:} \\ =\frac{10}{-2}\times\frac{a^6}{a^3} \\ =-5\times a^3 \\ =-5a^3 \\ \\ \therefore\frac{10a^6}{-2a^3}\Rightarrow-5a^3 \end{gathered}[/tex]Having simplified the expression, the answer obtained is: -5a^3
"People who are generous help those in need however they can."
To which theory of ethics is the person who made this statement likely appealing?
Conventionalism
Virtue-based ethics
Kantian deontology
Egoism
Answer: Conventionalism
Step-by-step explanation:
The person who made the statement, "People who are generous help those in need however they can," is appealing to virtue-based ethics.
What is Virtue ethicsVirtue ethics is a way of thinking about what is right and wrong. It focuses on becoming a good person and practicing good qualities.
This focuses on helping people develop good qualities such as being generous, caring, and kind. In this situation, the statement means that being kind and helping people who need it is seen as doing the right thing.
Learn more about ethics from
https://brainly.com/question/9520498
#SPJ2
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149 millimeters, and a standard deviation of 8 millimeters.
If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.3 millimeters? Round your answer to four decimal places.
The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949
Given,
In the question:
According to the given problem the mean diameter μ= 149 mm (population mean) and the standard deviation is σ = 8mm
random sample size, n= 50 steel bolts is selected
Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 3.3mm
Let z = (x-μ) / (σ/√n ) ....(1)
using formula (1) and when the sample mean differs from the population mean by more than 1.8mm
z = (3.3 - 149) /(8/√50 )
⇒z = -2.575
The probability that the sample mean will differ from the population mean by more than 1.8 mm
P( z > -2575) = 1 - P(z< -2.575) = 1 - 0.0051 = 0.9949
Hence, The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949.
Learn more about Probability at:
https://brainly.com/question/11234923
#SPJ1
3. If you ordered a pizza to share with others, which of the following sets ofnumbers would best describe the part of the pizza you ate.a. Integerb. WholeC. Naturald. Rational
rational, because you've split the pizza
So for example if you cut the pizza into 12 pieces to one of your friends you gave 1/12
A gift box is 12 inches long 8 inches wide and 2 inches high how much wrapping paper is needed to wrap the gift box
Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box is equal to the total surface area of the box.
[tex]\begin{gathered} \text{length l =12 inches} \\ \text{width w = 8 inches} \\ \text{ height h = 2 inches} \end{gathered}[/tex]The total surface area of the box can be calculated using the formula;
[tex]undefined[/tex]Surface are of the wood cube precision =0.00The weight of the woo cube precision =0.00 The volume was 42.87 in3
Given:
The volume of the cube is 42.87 cubic inches.
The volume of a cube is given as,
[tex]\begin{gathered} V=s^3 \\ 42.87=s^3 \\ \Rightarrow s=3.5 \end{gathered}[/tex]The surface area of a cube is,
[tex]\begin{gathered} SA=6s^2 \\ SA=6\cdot(3.5)^2 \\ SA=73.5 \end{gathered}[/tex]Answer: the surface area is 73.5 square inches ( approximately)
