The standard equation of a vertex is given by:
[tex]f(x)=a(x-h)^2+k[/tex]where (h,k) is the vertex.
Comparing with the given equation after re-arranging:
[tex]f(x)=(x+1)^2+4[/tex]The vertex of the function is (-1, 4)
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
1. Identify the vertex (locator point) of the above parabola2 po(1,2)(3,0)(3,0)(2,1)2. Identify the vertex from the quadratic function y=-5(x-6) 2+82 point
Answer:
(2,1)
Step-by-step explanation:
The vertex of a parabola is it's highest point(if it is concave down), or it's lowest point, if it's concave up.
In this question:
It's concave down, so the vertex is the highest point.
It happens when x = 2, at which y = 1.
So the vertex is the point (2,1)
Find the equation of the line passing through points (6,0) and (-1,14)
Answer:
y = -2x + 12
Step-by-step explanation:
Hope this helps!!
the sum of x and 3/5 is 5/7what is the value of x?
Explanation
the sum of x and 3/5 is 5/7
Step 1
convert the words into math terms
Let
the sum= addition
is= "="
[tex]x+\frac{3}{5}=\frac{5}{7}[/tex]Step 2
to find the value of x, isolate
[tex]\begin{gathered} x+\frac{3}{5}=\frac{5}{7} \\ \text{subtract }\frac{3}{5}in\text{ both sides} \\ x+\frac{3}{5}-\frac{3}{5}=\frac{5}{7}-\frac{3}{5} \\ x=\frac{5}{7}-\frac{3}{5} \\ x=\frac{25-21}{35} \\ x=\frac{4}{35} \end{gathered}[/tex]what are three requirements for fully defining a reference point?
1 - reference point should consist of abstract coordinates.
2- it should be stationary
3- it should be related to all the variables in the frame.
How many ones are between 1 and 1,000,000 (inclusive)?
There are 600,001 ones are between 1 and 1,000,000.
By using the below process we can find the number of ones between 1 and 1,000,000.
The number of times a digit 2 to 9 digit appears in numbers 1 to [tex]10^n = n(10^(^n^-^1^))[/tex].
The number of times the digit 1 appears in numbers in numbers 1 to [tex]10^n = n(10^(^n^-^1^)) + 1[/tex]
Therefore, the number of times a digit 1 appears in numbers 1 to 1,000,000 [tex]= 6(10^(^6^-^1^)) + 1\\= 6(10^5) + 1\\= 600,000 + 1\\= 600,001[/tex]
Therefore, there are 600,001 ones are between 1 and 1,000,000.
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Question 9 of 10 What is the measure of 7 shown in the diagram below? 110- O A. 71• O B. 35.5° X C 32° 39- Z D. 74.50
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Diagram
arc vw = 110 °
angle = 39°
arc xy = ?
Step 02:
We must analyze the diagram to find the solution.
39 = 1/2 ( 110 - arc xy)
39*2 = 110 - arc xy
78 - 110 = - arc xy
- 32 = - arc xy
arc xy = -32 / - 1 = 32
The answer is:
arc xy = 32°
Answer:
Step-by-step explanation:
Answer is C
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
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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]A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table. (a) Make a scatter plot of the data. (b) Find and graph a linear regression equation that models the data. (c) Use the model to predict soft-drink sales if the temperature is 95°F.
ANSWER and EXPLANATION
a) First we have to make a scatter plot. We do this by plotting the calues of High Temperature on the x axis and Number of cans sold on the y axis:
b) We want to find and graph the linear regression equation that models the data.
The linear regression equation will be in the form:
y = a + bx
[tex]\begin{gathered} \text{where} \\ a\text{= }\frac{(\sum ^{}_{}y)(\sum ^{}_{}x^2)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}xy)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \\ \text{and b = }\frac{n(\sum ^{}_{}xy)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}y)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \end{gathered}[/tex]We have from the question that:
x = High Temperature
y = Number of cans added
So, we have to find xy and x^2. We will form a new table:
Now, we will find a and b:
[tex]\begin{gathered} a\text{ = }\frac{(4120)(39090)\text{ - (}554)(297220)}{8(39090)\text{ }-554^2} \\ a\text{ = }\frac{\text{ 161050800 - 164659880}}{312720\text{ - 306916}} \\ a\text{ = }\frac{-3609080}{5804} \\ a\text{ }\cong\text{-62}2 \end{gathered}[/tex][tex]\begin{gathered} b\text{ = }\frac{8(297220)\text{ - (554})(4120)}{5804} \\ b\text{ = }\frac{2377760\text{ - 2282480}}{5804} \\ b\text{ = }\frac{95280}{5804} \\ b\text{ }\cong\text{ 16} \end{gathered}[/tex]Therefore, the linear regression equation is:
y = -622 + 16x
Now, let us graph it using values of x (High Temperature):
That is the Linear Regression Graph.
c) To predict soft drink sales if the temperature is 95 degrees Farenheit, we will put the x value as 95 and find y. That is:
y = -622 + 16(95)
y = 898
The model predicts that 898 cans of soft drinks will be sold when the High Temperature is 95 degrees Farenheit.
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
!!!!!!!???!??!???!!!???!!??!
!!!!!!!???!??!???!!!???!!??! is equal to 111111222122211122211221
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
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)
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.
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 unitshelp 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
7.2. I have a question about advanced trig equations that I really need help with picture included
1) Let's start out isolating the cosine by dividing both sides by 2
[tex]\begin{gathered} 2\cos \mleft(\theta\mright)=\sqrt{3} \\ \frac{2\cos\left(θ\right)}{2}=\frac{\sqrt{3}}{2} \\ \cos \mleft(\theta\mright)=\frac{\sqrt{3}}{2} \\ \end{gathered}[/tex]2) From that we can find two general solutions in which the cosine of theta yields the square root of 3 over two:
[tex]\begin{gathered} \cos (30^{\circ})or\cos (\frac{\pi}{6})\text{ and }cos(330^{\circ}or\frac{11}{6}\pi)=\frac{\sqrt[]{3}}{2} \\ \theta=\frac{\pi}{6}+2\pi n,\: \theta=\frac{11\pi}{6}+2\pi n \end{gathered}[/tex]But not that there is a restraint, so we can write out the solution as:
[tex]\theta=\frac{\pi}{6},\: \theta=\frac{11\pi}{6}[/tex]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]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.
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
"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.
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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)
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
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))=5Do 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
What is the measure of the exterior angle of the triangle? A. 23°B. 149°C. 180°D. 31°
Solution
The diagram below will be of help
From the image above
We know that the sum of angle in a triangle is 180 degrees
That is
[tex]\begin{gathered} 63+86+y=180 \\ 149+y=180 \\ y=180-149 \\ y=31^{\circ} \end{gathered}[/tex]Now, to find x
We also know that the sum of angle in a straight line is 180 degrees
That is
[tex]y+x=180[/tex]We now solve for x
[tex]\begin{gathered} x=180-y \\ x=180-31 \\ x=149^{\circ} \end{gathered}[/tex]Therefore, the value of x = 149 degrees
Option B
Find P (A and B) for the following. P(A) = .65 and P(B) =.69 and P(A and B) =.48P(A and B)
We know that
[tex]\begin{gathered} P(A)=0.65 \\ P(B)=0.69 \end{gathered}[/tex]The probability of the intersection of the two events is:
[tex]P(AandB)=0.48[/tex]Answer:
GIven , P(A) = 0.65 P(B) = 0.69
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.
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]
