I am needing help with problems 1 and 2. I’m definitely stuck and confused on where to start
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Solution
1.
We need to write y = x^2 -2x - 5 in vertex so as to be able to determine the vertex and the axis of symmetry.
To do that, we need to write in the form y = a(x - h)^2 + k -----(1)
[tex]\begin{gathered} y=x^2-2x-5=x^2-2x+(-\frac{2}{2})^2-(-\frac{2}{2})^2-5 \\ \\ \Rightarrow y=x^2-2x+1-1-5 \\ \\ \Rightarrow y=x^2-2x+1-6 \\ \\ \Rightarrow y=(x-1)^2-6\text{ -----\lparen2\rparen} \end{gathered}[/tex]Comparing equation (2) with equation (1)
here a = 1, h = 1, k = -6.
Therefore, the vertex is: (1, -6)
The axis of symmetry is: x = h
Therefore, the axis of symmetry is x = 1.
Question 2)
The height function is given as;
[tex]H(t)=-16t^2+16t+32[/tex]To find out how long Jason will hit the water, we need to set H(t) = 0;
[tex]\begin{gathered} \Rightarrow-16t^2+16t+32=0 \\ \\ \Rightarrow-16(t^2-t-2)=0 \\ \\ \Rightarrow t^2-t-2=0 \\ \\ \Rightarrow(t-2)(t+1)=0 \\ \\ \Rightarrow t=2,t=-1 \end{gathered}[/tex]since negative time is not lucid, t = 2 is cogent.
Therefore, it will take 2 seconds for Jason to hit the water.
Related Questions
graph the following line passing through -1 and 4 whose slope is m equals 1/4
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Answer:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]From the question, we're told that the slope, m, is 1/4 and the line passes through -1 and 4, so our x1 = -1 and y1 = 4, let's substitute these values into the above equation to determine the equation of the line;
[tex]\begin{gathered} y-4=\frac{1}{4}\lbrack x-(-1)\rbrack \\ y-4=\frac{1}{4}(x+1) \\ 4y-16=x+1 \\ 4y=x+17 \\ y=\frac{1}{4}x+\frac{17}{4} \end{gathered}[/tex]So the line will have a y-intercept at 17/4. See below the graph of the line;
The function d(t)= 300,000t represents the distance (in kilometers) that light travels t seconds How long does it take light to travel 12 million kilometers?
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The function for the distance travelled is d(t) = 300,000t.
Determine the time taken by light to travel 12 million km.
[tex]\begin{gathered} 12000000=300000\cdot t \\ t=\frac{12000000}{300000} \\ =\frac{120}{3} \\ =40 \end{gathered}[/tex]So light takes 40 seconds to travell 12 million km.
Answer: 40 seconds
i need help can you help
Answers
we know that
when you calculate the unit rate, if the numerator is greater than the denominator, then tghe unit rate is greater than 1
so
Verify each case
4 miles : 3 1/3 hour -------->
4 > 3 1/3
uniyt rate is greater than 1
1/3 mile : 2 3/8 hours
1/3 < 2 3/8
unit rate is less than 1
2 1/2 miles : 3 hours
2 1/2 < 3
unit rate is greater than 1
so
Verify each case
You earn $900 per week and earn a 5% commission on sales each week. What are the possible amounts (in dollars)that you must sell each week to earn at least $1050 per week? Write a linear inequality and solve.
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$3000 or more
Explanation:Amount earned weekly = $900
let the number of sales = y
Amount in commission per sales = 5% = 0.05
At least $1050 means the minimum amount of sales per week:
It is represented as ≥ 1050
The linear inequality:
Amount earned weekly + Amount in commission per sales(number of sales) ≥ 1050
900 + 0.05(y) ≥ 1050
900 + 0.05y ≥ 1050
subtract 900 from both sides:
900 - 900 + 0.05y ≥ 1050 - 900
0.05y ≥ 150
divide both sides by 0.05:
0.05y/0.05 ≥ 150/0.05
y ≥ 3000
Hence, the possible amounts (in dollars) that you must sell each week to earn at least $1050 per week is $3000 or more (atleast $3000)
a parking lot is constructed in the shape of a parallelogram if the base is 200 in the height is 120 ft and a diagonal with its 140 what is the area of the parking lot
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We can draw the following picture:
then, we can see that the parallelogram consists in 2 equal triangles:
The area of a triangle is
[tex]A_T=\frac{b\cdot h}{2}[/tex]By substituting the given values into the area formula, we get
[tex]\begin{gathered} \\ A_T=\frac{200\cdot120}{2} \\ A_T=\frac{24000}{2} \\ A_T=12000ft^2 \end{gathered}[/tex]Therefore, the area of the parallelogram is twice the area of one triangle:
[tex]A_{\text{parallelogram}}=2\cdot A_T[/tex]which gives:
[tex]\begin{gathered} A_{\text{parallelogram}}=2\cdot12000 \\ A_{\text{parallelogram}}=24000ft^2 \end{gathered}[/tex]that is, the answer is 24000 ft^2
please help me ASAP!!!!!!!
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When you study the Domain of a quatient of two polynomial functions, have in mind that you need to worry about the zeros in the function that goes in the DENOMINATOR.
In your case, the only zero you fear is that coming from the function:
g(x) = x - 8
and this function has a zero at the point x = 8
Then the quotient f/g is NOT defined at x=8 (meaning that x = 8 is NOT in the Domain of the quotient f/g.
Then the only correct answer is: The second one that states that the Domain is All Real numbers except for x = 8 because the denominator is ZERO.
Find the 10thterm of the following geometric sequence,1, 3,9, 27, ...
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Given:
1, 3,9, 27, ...
To determine the 10th of the given geometric sequence, we use the formula:
[tex]a_n=a_1\cdot r^{n-1}[/tex]where:
an=nth term of the sequence
r=common ratio
a1=first term of the sequence
We can get the common ratio by observing that:
Based on the given geometric sequence, we let:
n= 10
a1=1
r=3
We plug in what we know:
[tex]\begin{gathered} a_n=a_1\cdot r^{n-1} \\ a_{10}=1\cdot(3)^{10-1} \\ \text{Simplify} \\ a_{10}=1(3)^9 \\ a_{10}=19683 \end{gathered}[/tex]Therefore, the 10th term of the given geometric sequence is 19683.
The question and answer options are in the image below
Answers
1) Looking at the graph, we can see that the length of MN is 3 units.
2) Notice that according to the question, each unit represents 3", so MN is 9" inches long.
2.2) Since the scale factor is greater than 1, (it's 3) then we'll have an image M'N' thrice larger than the Pre-image, so we can write out the following:
[tex]\begin{gathered} MN=9in \\ k=3 \\ M^{\prime}N^{\prime}=27in \end{gathered}[/tex]3) Hence, the answer is M'N' is 27 inches long
a city's metropolitan area covers 6,500 square miles and is home to 2,695,000 people. what is the population density of this metropolitan area?
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Answer:
414.62 people/mi²
Explanation:
The population density is calculated as the number of people divided by the area of the city. So, it is equal to
[tex]\frac{2,695,000\text{ people}}{6,500mi^2}=414.62people/mi^2[/tex]Therefore, the answer is 414.62 people/mi²
As a scuba diver descends deeper into the ocean, the water pressure increases. If a represents the depth (in feet)of the diver, then the relationship P = 15 +0.434x gives the water pressure P in psi (pounds per square inch).Use this formula to answer the question.Oxygen will become toxic at approximately 104.5 psi, resulting in death. At what depth will this pressure bereached? (Round to the nearest foot.)Atfeet, oxygen will become toxic.
Answers
206 ft
1) In this scenario, we need to plug into that equation the figure that makes the Oxygen toxic and solve for x, since x stands for the depth.
2) So, we can write this:
[tex]\begin{gathered} P=15+0.434x \\ \\ 104.5=15+0.434x \\ \\ 15+0.434x=104.5 \\ \\ -15+15+0.434x=104.5-15 \\ \\ 0.434x=89.5 \\ \\ \frac{0.434x}{0.434}=\frac{89.5}{0.434} \\ \\ x\approx206 \end{gathered}[/tex]3) Thus. at approximately:
[tex]206\:ft[/tex]What is the number of terms in this expression? m/5+4×5
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m / 5 + 4- 6
using the order of operation
PEMDAS
m/5 + 4 - 6
division first
m/ 5 + ( 4 - 6)
m/5 + (-2)
= m/5 - 2
find the lcm
the lcm is 5
m - 10 / 5
The answer is m - 10 / 5
What is a collection of fact or information?VariablesDataQuantitativeQualitative
Answers
factor the expression 6h-18
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6(h-3).
1) Let's find the GCD between 6, and 18
6h-18 As the GCD is 6 we can write
6(h -3) If we distribute we got the initial expression back.
2) Then the answer is 6(h-3).
For the dilation, is the image J'K'L' M' an enlargement or reduction of JKLM? What is the scale factor?yAJK'K-2OM-3The image is a(n)The scale factor n =M'24L'
Answers
Solution
The image below contain the solution
Brief Explanation
Obviously, the image is a reduction
The scale factor is
[tex]\frac{1}{2}=0.5[/tex]Lucia already knew 1 appetizer recipes before starting culinary school, and she will learn 3 new appetizer recipes during each week of school. After how many weeks of culinary school will Lucia know a total of 40 appetizer recipes?
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w e can writhe a equation
[tex]y=3x+1[/tex]where y is the total of recipes and x the weeks
y=40 according to the text
so, we can replace y and solve x to know the weeks
[tex]\begin{gathered} 40=3x+1 \\ 40-1=3x \\ x=\frac{39}{3} \\ x=13 \end{gathered}[/tex]so she will know 40 appetizer recipes on 13 weeks
Find the distance between (-9,-8) and (5,1) rounded to the nearest tenth.Select One Answer:A. 4.1B. 18.0C. 8.1D. 16.6
Answers
Answer:
Explanation:
The formula for calculating the distance between two points is expressed as;
[tex]\sqrt[\square]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given the coordinates (-9, -8) and (5, 1)
[tex]\begin{gathered} D\text{ = }\sqrt[\square]{(5-(-9))^2+(1-(-8))^2} \\ D\text{ = }\sqrt[\square]{(5+9)^2+(1+8)^2} \\ D=\sqrt[\square]{14^2+9^2} \\ D\text{ = }\sqrt[\square]{196+81} \\ D\text{ = }\sqrt[\square]{277} \\ D\text{ = 16.6} \end{gathered}[/tex]Hence the distance bet
7. Jackie is buying a printer for $100 and the ink cartridges cost $35 each. If x stands for
the number of ink cartridges bought, then the total cost, C, is modeled by
a. C= 100x + 35
b. C = 35x + 100
c. C= 100 + 35 + x
d. C= 100x + 35x
Answers
Answer:
100 + 35x
Explanation:
Given the following
Initial cost of phone = $100
Monthly payment = $35
Payment after x months minus initial cosst = 35 * x = 35x
Total money after x-months = Initial payment + Payment after x months
Total money after x-months = 100 + 35x
wehre x is the number of months
Hence the required expression will be 100 + 35x
Which expression is equivalent to 3a2 + 6a + 5a2?
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 34° = ____
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Answer:
sin 34° = 0.56
Explanation:
Using the calculator, we get that:
sin 34° = 0.56
Holly is planning a high school reunion a local hotel rents a hall for 300 and charges 65 per guest Write a linear equation. Total cost y X for number of guest
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ANSWER:
y=300+65x
STEP-BY-STEP EXPLANATION:
We have that the total cost, is given of a fixed cost and a variable cost, just like this:
let y be the total cost
let x be the number of guest
[tex]y=300+65x[/tex]1 - Two Way Tables 1. Fill out the table about Mrs. Bowles music collection. In her collection there are: 84 cassettes and CDs in total 58 total popular cassettes and CDs 2 classical cassettes out of 50 total cassettes Cassettes CDs Totals Classical Pop Totals
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The table below gives the image of the completed table
The ones circled in red are the values given from the question
The other values are obtained by either subtracti
Maria has a jewelry box and wants to increase its size. She finds one with four times the length, width, and height. How many times bigger will the volume of the new box be?
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To get the scale factor of how much bigger the new box be, we let the dimensions of the smaller box equal to 1, and then get the volume.
[tex]\begin{gathered} \text{Smaller box Volume} \\ l=1 \\ w=1 \\ h=1 \\ V_{\text{small box}}=l\times w\times h \\ V_{\text{small box}}=1\times1\times1 \\ V_{\text{small box}}=1\text{ cubic units} \end{gathered}[/tex]Then we multiply all the dimensions with four, and get the volume, then divide it by the volume of the smaller box.
[tex]\begin{gathered} \text{Bigger box} \\ l=1\times4=4 \\ w=1\times4=4 \\ h=1\times4=4 \\ V_{\text{big box}}=4\times4\times4 \\ V_{\text{big box}}=64\text{ cubic units} \\ \\ \text{Divide it by the original box} \\ 64\div1=64 \end{gathered}[/tex]Therefore, the volume of the new box will be 64 times bigger.
XZWWhich of the following statements is correct?
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SOLUTION
Since side XY is parallel to side VW, then
Then, angle XYZ at Z is equal to angle WVZ at Z
Also angle XYZ at X is equal to angle WVZ at W (alternate angles)
Angle XYZ at Y is equal to angle WVZ at V (alternate angles)
Therefore the two triangles are similar by angle-angle similarity.
Option A is the correct answer
The graph below represents the value of a car, inthousands of dollars, with respect to the number ofyears since it was purchased.Based on the graph, what was the initial value of thecar (in thousands of dollars)?A.0B.10C.12D.15
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we can look at the graph and observe that
y axis= value in thousands of dollars
x axis= time in years
the car was bought at the price of 12 thousands of dollars, and after that the value was going down
The accompanying diagram shows two cables ofequal length supporting a pole. Both cables are 14meters long, and they are anchored to points in theground that are 14 meters apart.14 mPole14 m14 mWhat is the exact height of the pole, in meters?Your answer
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As shown in the figure:
The two cables and the ground like as an equilateral triangle
The length of each side = 14 m
The pole is perpendicular to the ground
So, there are two right angle triangle
From the left side triangle:
hypotenuse = 14 m
And the length from the cable to the pole = 14/2 = 7 m
Let the height of the pole = h
Using Pythagorean theorem:
[tex]\begin{gathered} 14^2=7^2+h^2 \\ h^2=14^2-7^2=196-49 \\ h^2=147 \\ h=\sqrt[]{147}=\sqrt[]{3\cdot49}=7\sqrt[]{3} \end{gathered}[/tex]So, the height of the pole = 7√3 meters.
5) Write the equation of the line below using the rise over run method. Write theequation in slope-intercept form.
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First we need to find the slope of the line. Using the rise over run method, we can see that the change in the y axis (rise) is negative, and if we see the difference in y axis is 3 units between the points (-2, 4) and (-1, 1). The run is the change in the horizontal axis. We can see that the difference is 1.
Then:
Rise = -3
Run = 1
[tex]\text{slope}=\frac{-3}{3}=-3[/tex]The slope is -3.
The equation of a line given a point and the slope is:
[tex]y-y_0=m(x-x_0)[/tex]Where m is the slope and x1, y0 are the coordinates of a point.
If we take the point (-1, 1), and the slope = -3:
[tex]y-1=-3(x-(-1))[/tex]Now if we solve for y, we get the equation of the line in slope-intercept form:
[tex]\begin{gathered} y=-3(x+1)+1 \\ y=-3x-3+1 \\ y=-3x-2 \end{gathered}[/tex]The equation of the line in spoe intercept form is:
[tex]y=-3x-2[/tex]12% of yesterday's customers purchased premium grade gasoline from Jasco. If 24 customers bought premium grade gasoline how many customers were there altogether.
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Given:
The percentage of customers who purchased gasoline is g = 12%.
The number of customers who purchased gasoline is n = 24.
The objective is to find a total number of customers altogether.
Explanation:
Consider the total number of customers altogether as x.
The value of x can be calculated as,
[tex]\begin{gathered} \frac{1\text{2 \%}}{100\text{ \%}}=\frac{24}{x} \\ x=\frac{100}{12}\times24 \\ x=200 \end{gathered}[/tex]Hence, the total number of customers altogether is 200.
Choose Yes or No to tell whether the pairs of angles are congruent.
Answers
From the diagram
Correspond angles are congruent YES
Alternate interior angles are congruent YES
Same side interior angles are congruent YES
Select all solids whose cross sections are dilations of some two- dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1. Cylinder Cube Triangular Prism Cone Triangular Pyramid
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Ok, so:
Let's look at the cone:
The cone has a relation with the equation of dilating the cylinder by 1/3, as this:
V cone = (1/3) * pi (r)^2 * h
V cylinder = pi * (r)^2 * h
Then, the cross-section of the cylinder being dilated by 1/3 (which is between 0 and 1) gives the cone.
So, cone is a solid whose cross sections are dilations of some two- dimensional shape.
Ok, then, the volume of a triangular prism is given by:
V = 0.5 * b * a * h, where h is ths height, b and a are its sides.
The volume of a triangular pyramid is given by:
V = 1/3 ( Base area * height).
If we do not know the Base area, we can write it like b*a.
So, these two equations has a relation, as this:
(0.5 b*a*h) / (1/3 b*a*h) = 1.5
This means that if we multiply the volume of the triangular pyramid by 1/1.5, the result is 0.5
Then, the cross-section of the triangular pyramid being dilated by 1/1.5 (which is between 0 and 1) gives the triangular prism.
So, the answer would be Cone and triangular prism.
What are two advantages of displaying data in a chart? O A. It allows the data to be organized in meaningful ways. B. It makes it easier to see and work with the data. C. It increases the number of words needed to describe the data. D. It makes it harder to make sense of the data.
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Charts are used to represet data.
There are different types of charts being used, pie chart, bar chart and so on.
In a chart, the datas are visualized in an easier way rather than expressing in long descriptions.
It makes it easier to see and work with the data.
Therefore Answers A and B is correct
