Answer:
The answer is (D): 2 h 52 min
Step-by-step explanation:
write these equations separately as functions:
A(x)=15+0.02m
B(x)=4.69+0.08m
Since we want to find when they are equal, set them equal to each other:
15+0.02m=4.69+0.08m
simplifying this equation gives
10.31+0.02m=0.08m
subtract 0.02m from both sides
10.31=0.06m
divide both sides by 0.06
m=171.833 etc approximately equals 172 minutes
172 min/60=
2 hours and 52 min
Hope this helps!
Answer:
2 h 52 min
Step-by-step explanation:
Let m represent the number of minutes that will make the plans have equal cost. Equating the two plan costs, we have ...
15.00 + 0.02m = 4.69 + 0.08m
10.31 = 0.06 m . . . . . subtract 4.69+0.02m
10.31/0.06 = m = 171.8333... ≈ 172 . . . . minutes at equal cost
There are 60 minutes in an hour, so ...
172 minutes = 120 minutes + 52 minutes = 2 hours + 52 minutes
Plan A will cost the same as Plan B for 2 h 52 min of usage.
Ms. Walker used a coordinate plane to plot her students' scores on a recent quiz. She let x represent the number of correct answers they had on their quiz and y represent the number of points earned. She then plotted the ordered pairs (17, 68), (20, 80), and (24, 96) to represent the data from three students.
What is the slope of the graph in points per question?
Answer:
Slope = 4
Step-by-step explanation:
The x-axis values to represent the number of correct answers.
The y-axis values to represent the number of points earned.
The points on the graph are: (17,68) , (20,80) and (24,96)
The slope(m) of the graph = change in y ÷ change in x
i.e [tex]\frac{80 - 68}{20 - 17}[/tex] = [tex]\frac{96 - 80}{24 - 20}[/tex] = 4
The equation of the straight line graph is;
y=4x
The slope of the graph, representing points earned per correct answer on the quiz, is 4. This is found by dividing the change in points earned by the change in correct answers between any two points on the graph.
Explanation:The slope of a graph in the coordinate plane is the ratio of the change in y (the vertical difference) to the change in x (the horizontal difference) between any two points on the line. In this case, the difference in y (points earned) for the pairs given by Ms. Walker, for example between (20, 80) and (24, 96), is 16. The difference in x (number of correct answers) in the same pairs is 4. Therefore, the slope of the graph, which represents the points per question, is 16 divided by 4: 4 points per question. This means that for each correct answer (each increase in 1 on the x-axis), the number of points earned (y) increases by 4.
Learn more about Slope of Graph here:https://brainly.com/question/17734932
#SPJ3
Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski, Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski Create an
equation to determine at what point the cost of both ski slopes is the same
15x - 75 = 10x - 50
15x - 50 = 10x - 75
15x + 50 = 10x + 75
15x + 75 = 10x + 50
Answer:
15x + 50 = 10x + 75
Step-by-step explanation:
The cost at Black Diamond for ski rental and x hours of skiing is ...
50 +15x
The cost at Bunny Hill for ski rental and x hours of skiing is ...
75 +10x
These costs will be equal when ...
15x + 50 = 10x + 75
Answer:
C: 15x + 50 = 10x + 75
Step-by-step explanation:
The lengths of the sides of triangle ABC are represented in terms of the variable m, where m>6 AB = m - 2 BC = m + 4 AC = m list the angles from smallest to largest.
Answer:
C, B, A
Step-by-step explanation:
From smallest to largest, the side lengths are ...
AB = c = m -2AC = b = mBC = a = m +4The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.
___
Comment on side naming
Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.
Answer:
C, B, A
Step-by-step explanation:
The plane that contains points C and T can also be named plane...
A) CUB
B) BED
C) ACE
D) ABE
Answer:
A) CUB
Step-by-step explanation:
Of the suggested planes, only CUB contains both points C and T.
___
Comments on the other answer choices
BED contains point T, but not C
ACE contains point C, but not T
ABE contains neither C nor T
Answer:
A) CUB
Step-by-step explanation:
BRAINLIEST
find the value of a^n b^n if n=3,a=100,and b=1/4
Answer:
= (100)^3(1/4)^3
= 15,625 i think im not that good at math but i passed
Step-by-step explanation:
Hi there! My name is Zalgo and I am here to help you out on this gracious day. If n=3, a=100 and b=1/4, the equation should look like "100^3 * 1/4^3". The answer would be 15625.
I hope that this helps! :D
"Stay Brainly and stay proud!" - Zalgo
Celine has a bottle that contains 20% milk and the rest water. The bottle has 1 liter of water. Part A: Write an equation using one variable that can be used to find the total number of liters of milk and water in the bottle. Define the variable used in the equation and solve the equation. Hint: 0.2x represents the number of liters of milk in the bottle. (5 points) Part B: How many liters of milk are present in the bottle? Show your work. (5 points)
Answer:
A) 0.2x +1 = x . . . . x is the volume of liquid in the bottle (liters)
B) 0.25 liters of milk are in the bottle
Step-by-step explanation:
It is often convenient to define a variable as the answer to the question. Here, the question says "find the total number of liters of milk and water in the bottle", so that is the definition of our variable, x.
A) The problem statement tells us that 20% of the liquid is milk, so that amount is 0.2x (as the hint says). Then the sum of milk volume and water volume is the total volume:
0.2x + 1 = x . . . . . . . an equation in one variable that can find total volume
We can solve this equation by subtracting 0.2x, then dividing by the coefficient of x.
1 = 0.8x
1/0.8 = x = 1.25 . . . the total number of liters of milk and water is 1.25
__
B) The number of liters of milk is 0.2x, so is 0.2·1.25 = 0.25
There are 0.25 liters of milk in the bottle.
Yesterday, Pablo had 4 4/9 quarts of iced tea, and Rosa had 3 5/12 quarts of iced tea.
How much more iced tea did Pablo have than Rosa?
Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
1. How much more iced tea did Pablo have than Rosa?
= 4 4/9 - 3 5/12 = 40/9 - 41/12 = 40/9 - 41/12 = (40 × 4)/(9 × 4) - (41 × 3)/(12 × 3) = 160/36 - 123/36= 37/36= 37/36 = 1 1/36Pablo has 1 1/36 quarts of ice tea more than Rosa.
2. Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
Iced tea given
= 15% × 4 4/9= 15/100 × 40/9 = 600/900= 2/3Pablo iced tea
= 40/9 - 2/3 = 40/9 - (2 × 3)/(3×3) = 40/9 - 6/9= 34/9= 3 7/9Rosa iced tea
= 41/12 + 2/3 = 41/12 + (2 × 4)/(3 × 4) = 41/12 + 8/12= 49/12= 4 1/12Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.
The relationship between the yearly fee that the local YMCA charges and the fee to bring a friend is modeled by the linear function f (x) = 5x + 795, where x is the number of friends you bring with you each year. If the total fee is $855 one year, how many friends did you bring to the YMCA that year?
Answer:
12 friends
Step-by-step explanation:
Fill in the given number and solve for x.
855 = 5x +795 . . . . . the total fee was 855
60 = 5x . . . . . . . . . . . subtract 795
12 = x . . . . . . . . . . . . . divide by 5
The number of friends you brought was 12.
Identify the slope and y-intercept of the line: PLEASE HELP ME IT WOULD ME SO MUCH THANK YOU!!!!!
y =– (¾)x - 2
Answer:
slope: -3/4y-intercept: -2 . . . . or point (0, -2)Step-by-step explanation:
Slope-intercept form is ...
y = mx + b
Comparing your equation to this pattern, you can see that your equation is already in this form, with ...
m = -3/4b = -2In this form, the coefficient of x (which is m) is the slope of the line. Thus your slope is -3/4. The added constant (which is b) is the y-intercept, the value of y when x=0. Your y-intercept is -2. Expressed as the coordinates of a point, the y-intercept is (x, y) = (0, -2).
Patty deposited $650 in a savings account with two percent simple interest. If she keeps it in the account for one year, how much interest will she earn?
$15
$18
$12
$13
Answer:
$13
Step-by-step explanation:
Depost of 650.00 into a bank account paying 2% simple interest per year. You left the money in for 1 year. Find the interest earned and the amount earned in 1 year.
The interest is $13, and the amount is 663.00.
Answer:
13
Step-by-step explanation:
what is the measure of STY in oo below? 130 310 230 50
ANSWER
B. 310°
EXPLANATION
The sum of angles in a circle is 360°
From the diagram, the measure of arc SY is 50°
The measure of arc STY plus the measure of arc SY is 360°
To find the measure of arc STY, we subtract 50° from 360° to get:
Measure of arc STY
[tex] = 360 \degree - 50 \degree[/tex]
This simplifies to
[tex]310 \degree[/tex]The correct answer is B 310°
Answer:
The correct answer is option B. 310°
Step-by-step explanation:
From the figure we can see that, a circle with center o.
And an arc SY with central angle 50°
To find the measure of arc STY
From the figure we can write,
arc SY + arc STY = 360
measure of arc STY = 360 - measure of arc SY
= 360 - 50 - 310°
Therefore the correct answer is option B. 310°
In this triangle, cosA/cosB is equal to what? (the triangle is below)
Answer:
CosA/CosB =1
CosA = Adjacent side/Hypotenuse
=AC/AB = 3/4.24
Cos B = Adjacent side/Hypotenuse
= BC/AB = 3/4.24
CosA/CosB = (3/4.24)/(3/4.24) = 1
The value of CosA/CosB = 1
Answer:
1
Step-by-step explanation:
trust lol
Define what an inverse function is in terms of domain and range.
and
Define what a function is in terms of domain and range.
Answer:
Step-by-step explanation:
Let's start with a function first. The domain of a function is all the x values that are covered by the graph of the function; the range is all the y values that are covered by the graph of the function.
In order to graphically find the inverse of a function, you literally switch the x and y variables and replot them. For example if a point on your function is
(3, -1), then the point on its inverse is (-1, 3). Because of this, you interchange the domains and the ranges. Therefore, the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.
The domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
Let the function be f(x).
Let the domain of the function f(x) is (a, b) and the range of the function f(x) is (c, d).
The inverse function of f(x) will be f⁻¹(x).
Then the domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ2
HELP ME PLEASE MATH
Which graph represents the following system of inequalities?
y > 5x-1, because it is just a greater than sign, the shaded area would be to the left of a dotted line.
y ≤ x +3, because the sign is less than or equal to, the line is solid and the shaded area would be to the right.
Combine the shaded areas would make Graph B. the correct answer.
PLS HELP SHOW ALL YOUR WORKING OUT
BRAINLIEST
Find the inverse of the function. f(x) = the cube root of quantity x divided by six. - 7
Answer:
[tex]f^{-1}(x)=6(x+7)^{3}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]
Let
[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]
Exchanges the variable x for y and y for x
[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]
Isolate the variable y
[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]
elevates to the cube both members
[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function
Let f(x)=14/7+2e^−0.6x . What is f(3) ? Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(3)=1.9[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]
we know that
f(3) is the value of the function for the value of x equal to 3
so
substitute the value of x=3 in the function
[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]
Answer:
1.9
Step-by-step explanation:
fX)=14/7=2e^-0.6x = 1.9
4. Which relation is a function?
A.{(0; -9), (-9, -2), (0, -3)}
B.{(0, -9), (-9,0), (-3, -3)}
C.{(0, -9), (-2, -3), (-2, 0), (-3,-2)}
D.{0,-9, -2, -3}
Answer:
It's B.
Step-by-step explanation:
That is B because there are no duplicate x-values in the ordered pairs.
D is a set of numbers, not a function.
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1 /4 square foot. How many squares is the wall divided into?
Answer:
96 squares
Step-by-step explanation:
The number of squares is ...
(wall area)/(square area) = (24 ft²)/(1/4 ft²) = 24×4 = 96 . . . . squares
Answer:
96 squares
Step-by-step explanation:
given T(-5,8,3) and M(-2,-1,-6) find the ordered triple that represents TM. Then find the magnitude of TM.
Answer:
TM = (3,-9,-9)
The magnitude of TM = 3√19
Step-by-step explanation:
Given T=(-5,8,3) and M = (-2,-1,-6)
TM is the difference between the vector M and the vector T
So,
TM = M - T = (-2,-1,-6) - (-5,8,3) = (-2+5 , -1-8 , -6-3) = (3,-9,-9)
The magnitude of TM = The distance of TM = [tex]\sqrt{3^2+(-9)^2+(-9)^2}=\sqrt{9+81+81}=\sqrt{171} = \sqrt{9*19} =3\sqrt{19}[/tex]
So, TM = (3,-9,-9) and |TM| = 3√19
Elizabeth attempts a field goal by kicking a football from the ground with an initial vertical
velocity of 64 ft/s. How long will the football be in the air?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]
Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.
please help:Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]
Final answer:
The coordinates of the midpoint are (1.35, 2.85).
Explanation:
The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).
An air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu). The unit has a maximum variance of y Btu. If x is the air conditioning unit’s actual capacity, which graph could be used to determine variance levels that would cause a unit to be rejected because of its cooling capacity?
Answer:
ITS 100% A
Step-by-step explanation:
Answer:
Option 2.
Step-by-step explanation:
Let as consider x be the air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).
It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).
We need to find the graph that could be used to determine the variance levels that would cause a unit to be rejected because of its cooling capacity.
It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.
[tex]y\leq |x-6000|[/tex]
The related equation of this inequality is
[tex]y=|x-6000|[/tex]
It is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000).
The related curve is a solid V-shaped curve because the points on curve included in the solution set.
The shaded region lie below the curve because the sign of inequality is ≤.
Therefore the correct option is 2.
Suppose you had been in charge of designing the study. what sample size would be needed to construct a margin of error of 2% with 95% confidence? use the prior point estimate of p* = 0.15 for this calculation. round up to the nearest whole number. (for example, 144.1 would round to 145)
Answer:
1225
Step-by-step explanation:
hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).
(When I say conf here I am referring to the confidence level as a decimal).
All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.
A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence and this can be determined by using the formula of margin of error.
Given :
A margin of error of 2% with 95% confidence.The prior point estimate of p* = 0.15.The following calculation can be used to determine the sample size needed to construct a margin of error of 2% with 95% confidence.
[tex]\rm MOE = z \times \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]0.02=1.96\times \sqrt{\dfrac{0.15\times 0.85}{n}}[/tex]
[tex]\left(\dfrac{0.02}{1.96}\right)^2= \dfrac{0.15\times 0.85}{n}[/tex]
[tex]n = \dfrac{(1.96)^2\times 0.15 \times 0.85}{(0.02)^2}[/tex]
[tex]n = 1224.51[/tex]
n = 1225 (round off)
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence.
For more information, refer to the link given below:
https://brainly.com/question/23012921
Ribbon costs $0.45 per foot . A sewing project calls for 20. 5 feet of ribbon to the nearest cent that will be the cost of the ribbon for the project
To find the total cost of the ribbon, multiply the length needed (20.5 feet) by the cost per foot ($0.45), which equals $9.225. Round this to the nearest cent to get $9.23.
To calculate the cost of the ribbon needed for a sewing project, you multiply the length of the ribbon required by the cost per foot. In this case, the project calls for 20.5 feet of ribbon and the ribbon costs $0.45 per foot. The formula to use is: Total Cost = Length in Feet x Cost Per Foot. Now, let's do the math:
Total Cost = 20.5 feet x $0.45/foot = $9.225.
To round to the nearest cent, the total cost would be $9.23.
I did this problem and I was told I did it wrong how do I fix it??
Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Answer:
A=Pe^rt
P= princible (1300)
e= (2.71828)- function on a graphing calculator
r = interest rate (.05 or 5%)
t = time (10 years)
A = 1300e^.05(10)
A = 1300e^.5
A = 2143.337652
A = 2143
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]\bf A=1300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=1300(1.05)^{10}\implies \stackrel{\textit{rounded up}}{A=2118}[/tex]
1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
Answer: Option C
"The sides opposite and adjacent to theta are the same length."
Step-by-step explanation:
By definition the tangent of an angle [tex]\theta[/tex] is written as:
[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]
Where:
"opposite" is the side opposite the [tex]\theta[/tex] angle
"adjacent" is the side that contains the angle [tex]\theta[/tex] and the angle of 90 °.
In this case we know that
[tex]tan(\theta) = \frac{opposite}{adjacent} = 1[/tex]
If [tex]\frac{opposite}{adjacent} = 1[/tex] then [tex]opposite = adjacent[/tex]
Finally the answer is the option C
"The sides opposite and adjacent to theta are the same length."
Answer:
C. The sides opposite and adjacent to theta are the same length.
Step-by-step explanation:
Given : tanθ = 1
recall tanθ = [tex]\frac{opposite}{adjacent}[/tex]
the only way for [tex]\frac{opposite}{adjacent}[/tex] to equal 1, is that the numerator is the same value as the denominator,
hence the answer is
C. The sides opposite and adjacent to theta are the same length.
Suppose that y varies inversely with x, and y = 2 when x = 4. What is an
variation?
Answer:
xy=8
Step-by-step explanation:
The equation for inverse variation is
xy = k where k is the constant of variation
4*2 = k
8=k
The equation is
xy=8
A parabola with a vertical axis has its vertex at the origin and passes through point (7,7). The parabola intersects line y = 6 at two points. The length of the segment joining these points is
A. 14
B. 13
C. 12
D. 8.6
E. 6.5
Answer:
[tex]\boxed{\text{B. 13}}[/tex]
Step-by-step explanation:
1. Find the equation of the parabola
The vertex is at (0, 0), so the axis of symmetry is the y-axis.
The graph passes through (7, 7), so it must also pass through (-7,7).
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 0),
h = 0 and k = 0
The equation is
y = ax²
2. Find the value of a
Insert the point (7,7).
7 = a(7)²
1 = 7a
a = ⅐
The equation in vertex form is
y = ⅐x²
3. Calculate the length of the segment when y = 6
[tex]\begin{array}{rcl}6 & = & \dfrac1{7}x^{2\\\\42 & = & x^{2\\x & = & \pm \sqrt{42}\\\end{array}[/tex]
The distance between the two points is the length (l) of line AB.
A is at (√42, 6); B is at (-√42, 6).
l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0
[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]