Figure out the height of cliff, when ball hits the ground, the max height of the ball and the seconds the height occur
Answers
The height of the ball, h in meters, is modeled by the next equation:
\(h(t)=-t^2+6t+16\)where t is time in seconds.
a. At t = 0, the height of the ball is equal to the height of the cliff. Substituting t = 0 into the equation, we get:
\(\begin{gathered} h(0)=-0^2+6\cdot0+16 \\ h(0)=16\text{ m} \end{gathered}\)The height of the cliff is 16 m.
b. When the ball hits the ground, h(t) = 0. Then, we need to find the zeros of the polynomial. Using the quadratic formula with a = -1, b = 6, and c = 16, we get:
\(\begin{gathered} t_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t_{1,2}=\frac{-6\pm\sqrt[]{6^2-4\cdot(-1)\cdot16}}{2\cdot(-1)} \\ t_{1,2}=\frac{-6\pm\sqrt[]{100}}{-2} \\ t_1=\frac{-6+10}{-2}=-2 \\ t_2=\frac{-6-10}{-2}=8 \end{gathered}\)In the context of the problem, a negative value has no sense, then t = -2 is discarded.
The ball hits the ground after 8 seconds.
c. The maximum height of the ball corresponds to the vertex of the parabola. The x-coordinate of the vertex, which in this case corresponds to variable time, is computed as follows:
\(t_{\max }=\frac{-b}{2a}\)Substituting with a = -1, and b = 6, we get:
\(\begin{gathered} t_{\max }=\frac{-6}{2\cdot(-1)} \\ t_{\max }=3\text{ seconds} \end{gathered}\)The height of the ball at t = 3 is:
\(\begin{gathered} h(3)=-3^2+6\cdot3+16 \\ h(3)=-9+18+16 \\ h(3)=25\text{ m} \end{gathered}\)The maximum height of the ball is 25 m. This height is reached after 3 seconds.
Related Questions
(7,-1) and (6, 6)
Determine the slope of the line passing through the points whose coordinates
Answers
Answer:
y=-7x+48 slope would be -7
Step-by-step explanation:
Used a Regression Calculator
Can someone help I will mark u brilliant
Answers
Answer:
50
Step-by-step explanation:
We are finding the surface area of a circle here. which is pie r ^2 ( the formula) so the radius is 4. So we do pie 4^2 which equals 50.26548246 which is approximately 50.
Answer:
First, we must know the formula for the area of a circle.
The formula for the area of a circle is;
A = π\(r^{2}\)Where 'π' is pi(22/7 or 3.14), and 'r' is the radius which is being squared.
Plug in what you know;R(radius) = 4 feet.
So,
A = π\(r^{2}\)
Will be;
A = π(4^2) ← what I mean by " ^ ", I mean "to the power of".
Simplify:-
A = 3.14(16)
A = 50.24 feet is the area.
If a customer left a $5 tip for a bill that had a subtotal of $31.25 what percent tip did the customer leave?
Answers
Answer:
16%
Step-by-step explanation:
= (5/31.25)*100=16%
What transformation is represented by the function f(x)=2sin(x−π/2)
up 2
down 2
left π/2
right π/2
down π/2
Answers
Answer:
right π/2
Step-by-step explanation:
The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .
Therefore, the correct answer is right π/2
what are the 6 steps to designing a statistical study
Answers
Answer:
Step 1: Write your hypotheses and plan your research design
Step 2: Collect data from a sample
Step 3: Summarize your data with descriptive statistics
Step 4: Test hypotheses or make estimates with inferential statistics
Step 5: Interpret your results
Step-by-step explanation:
Question is present in the image
Answers
The equation that is equivalent to P = B + Brz is:
r = (P - B) / Bz
To see why, we can rearrange the original equation as follows:
P = B + Brz
P - B = Brz
(P - B) / Bz = r
Therefore, r = (P - B) / Bz is equivalent to P = B + Brz.
Now let's check the given options:
x = P/Br + 1/r
This equation is not equivalent to P = B + Brz.
r = (P - B) / Bz
This is the correct equation that is equivalent to P = B + Brz.
r = Bz / (P - B)
This equation is not equivalent to P = B + Brz.
B = P / (rz + 1)
This equation is not equivalent to P = B + Brz.
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 the phone case you want to buy is marked down 25% and you have a 10% off coupon. You pay $27. Can this equation be used to find the original price of the phone case? Explain why the equation does or does not fit the scenario then determine the original price of the phone case.  9/10×0.75C equals 27. 
Answers
The original price of the phone case was $40 according to the given equation.
What does equation mean?In mathematics, an equation is a statement that indicates that two expressions are equal. Equations usually consist of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
According to the given informationYes, the equation 9/10 x 0.75C = 27 can be used to find the original price of the phone case.
Here's why:
The initial price of the phone case is represented by C.
It's marked down by 25%, which means the new price is 0.75C (75% of the original price).
You then apply a 10% off coupon, which means you pay 90% of the new price or 9/10 x 0.75C.
The equation 9/10 x 0.75C = 27 represents the final price you paid for the phone case, so we can solve for C to find the original price.
To solve for C, we can first simplify the left side of the equation:
9/10 x 0.75C = 27
0.675C = 27
Next, we can divide both sides by 0.675 to isolate C:
C = 40
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Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answers
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
Find the value of ab when a = 2/11
and b = 10/11
Answers
Answer:
20/121
Step-by-step explanation:
\(ab=\left(\frac{2}{11} \right) \left(\frac{10}{11} \right) \\ \\ =\frac{(2)(10)}{(11)(11)} \\ \\ =\frac{20}{121}\)
pls help me on algebra here is screenshot
Answers
Answer:
The answer to the question provided is option 2.
Rob collects data about how many customers enter and leave a store every hour. He records a positive number for additional customers entering the store each hour and a negative number for customers leaving the store each hour. Drag and drop the correct choices into the boxes to complete the answers to the questions.
Answers
1) 3:00 to 4:00
The absolute value of the number of people leaving is greater than the absolute value of the number of people entering.2) 103
From 1:00 to 2:00, a total of 14 more people entered, meaning there were 99 people.From 2:00 to 3:00, a total of 8 more people entered, meaning there were 107 people.From 3:00 to 4:00, a total of 4 people left, meaning there were 103 people.The required solution is 4:00 to 5:00 and 87 customers.
It is required to fill in the blanks.
What is arithmetic?The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given:
According to question , Initially, there were 75 customers.
From 1:00 to 2:00, a total of 30 more people entered, meaning there were
75 + 30 - 12
= 93 people.
From 2:00 to 3:00, a total of 14 more people entered, meaning there were
93 + 14 - 8
= 99 people.
From 3:00 to 4:00, a total of 18 people entered, meaning there were
99 + 18 - 30
= 87 people.
4:00 to 5:00 : If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.
Therefore, the required solution is 4:00 to 5:00 and 87 customers.
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The population P(t) of a bacteria culture is given by P(t)=−1,500t2+48,000t+18,000, where t is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 388,500 organisms.
Answers
Using a scale of 1/2 cm = 75 km, how many kilometers would each distance represent? 4 1/2 cm = ____ km, 2 1/4 cm = ___ km , 5 3/4 cm = ____ km. Please Help.
Answers
= 675 km
2 1/4 = 5*75
= 375 km
5 3/4 = 13*75
= 975 km.
The calculation for y=0y=0 corresponds to the
point where the graph crosses the________-axis. This is the point (______)
Answers
The calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
In the question ,
it is given that y=0 ,
When y=0 in a point (x,y) means , that point lies on the x -axis , and it is called as the x intercept .
X intercept is defined as the point where the graph of a line crosses the x-axis .
the point on the x-axis will be (x,0) ,
So , the graph will cross the x-axis when y=0 , and that point will be (x,0).
and the value of x will be called as the x intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
The given question is incomplete , the complete question is
The calculation for y=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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It's 119 miles from Ayville to Beeville. It's another 90 miles from Beeville to Charlwoods. Russell drives 10 miles faster from Beeville to Charlwoods than from Ayville to Beeville. If his combined travel time is 5.4 hours, what are his average speeds?
Answers
Let v be the average speed from Ayville to Beeville.
Let t_1 be the time that Russell took to travel from Ayville to Beevile, and t_2 the time that he took to travel from Beeville to Charlwoods.
Remember the formula that relates the average speed of a moving object with the distance that it traveled and the time that it takes to travel that distance:
\(v=\frac{d}{t}\)Isolate t from the equation:
\(t=\frac{d}{v}\)For the first part of the journey, the distance from Ayville to Beeville is 119 miles. Then:
\(t_1=\frac{119mi}{v}\)For the second part of the journey, the distance from Beeville to Charlwoods is 90 miles, and Russell drives 10 miles per hour faster. Then:
\(t_2=\frac{90mi}{v+10\frac{mi}{h}}\)Since the combined travel time is 5.4 hours, then:
\(t_1+t_2=5.4h\)Substitute the expression for t_1 and t_2:
\(\Rightarrow\frac{119mi}{v}+\frac{90mi}{v+10\frac{mi}{h}}=5.4h\)Add both fractions on the left member of the equation:
\(\Rightarrow\frac{(119mi)(v+10\cdot\frac{mi}{h})+(90mi)(v)}{(v)(v+10\frac{mi}{h})}=5.4h\)Simplify the expression on the numerator:
\(\begin{gathered} \Rightarrow\frac{119mi\cdot v+1190\cdot\frac{mi^2}{h}+90mi\cdot v}{(v)(v+10\frac{mi}{h})}=5.4h \\ \Rightarrow\frac{209mi\cdot v+1190\cdot\frac{mi^2}{h}}{(v)(v+10\frac{mi}{h})}=5.4h \end{gathered}\)Multiply the factors on the denominator:
\(\Rightarrow\frac{209mi\cdot v+1190\cdot\frac{mi^2}{h}}{v^2+10\frac{mi}{h}v}=5.4h\)Multiply both sides of the equation by (v^2+10(mi/h)v):
\(\begin{gathered} \Rightarrow209mi\cdot v+1190\cdot\frac{mi^2}{h}=(5.4h)(v^2+10\frac{mi}{h}v) \\ \Rightarrow209mi\cdot v+1190\cdot\frac{mi^2}{h}=5.4h\cdot v^2+54mi\cdot v \end{gathered}\)Notice that we obtained a quadratic equation for v. Write it in standard form and use the quadratic formula to find the values of v. Recall the following:
\(\begin{gathered} ax^2+bx+c=0 \\ \Rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}\)Then, from the equation for v:
\(\begin{gathered} \Rightarrow209mi\cdot v+1190\cdot\frac{mi^2}{h}=5.4h\cdot v^2+54mi\cdot v \\ \Rightarrow0=5.4h\cdot v^2+54mi\cdot v-209mi\cdot v-1190\cdot\frac{mi^2}{h} \\ \Rightarrow5.4h\cdot v^2-155mi\cdot v-1190\cdot\frac{mi^2}{h}=0 \end{gathered}\)To use the quadratic formula, notice that a=5.4h, b=-155mi and c=-1190(mi^2/h):
\(\begin{gathered} \Rightarrow v=\frac{-(-155mi)\pm\sqrt[]{(-155mi)^2-4(5.4h)(-1190\cdot\frac{mi^2}{h})}}{2(5.4h)} \\ =\frac{155mi\pm\sqrt[]{24,025mi^2+25,704mi^2}}{10.8h} \\ =\frac{155mi\pm223mi}{10.8h} \end{gathered}\)Using only the positive value for the speed, we get that:
\(\begin{gathered} v=\frac{155mi+223mi}{10.8h} \\ =\frac{378mi}{10.8h} \\ =35\frac{mi}{h} \end{gathered}\)Since v is the speed from Ayville to Beevile and the speed from Beevile to Charlwoods is 10 miles per hour faster, then, the average speeds for each part, are:
From Ayville to Beevile: 35 miles per hour.
From Beevile to Charlwoods: 45 miles per hour.
a prescription is written for amoxicillin 75 mg t.i.d. for 10 days. What is the volume of each dose in mL if you dispense amoxicillin 50 mg/mL?
Answers
Each dose of amoxicillin, when dispensed at a concentration of 50 mg/mL, would be 1.5 mL.
To calculate the volume of each dose of amoxicillin in milliliters (mL), we need to know the concentration of the medication and the prescribed dosage.
Given:
Amoxicillin concentration: 50 mg/mL
Prescribed dosage: 75 mg t.i.d. (three times a day) for 10 days
To determine the volume of each dose, we can use the formula:
Volume (mL) = Dosage (mg) / Concentration (mg/mL)
First, let's calculate the dosage for one dose:
Dosage per dose = 75 mg
Now we can calculate the volume of each dose using the concentration of amoxicillin:
Volume (mL) = 75 mg / 50 mg/mL
Volume (mL) = 1.5 mL
Amoxicillin would therefore be administered in 1.5 mL doses at a dosage of 50 mg/mL.
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29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
Answers
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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Coach Matt is making dodgeball teams. He has 16 fifth gradets and 36 sixth graders. To be fair, Coach Matt wants there to be the same number of 5th graders and the same of the sixth graders on each team. Can coach Matt make a teams using all the 5th and 6th graders do the statement that explains why or why not .Here are the choices:1. No. 8 is a factor of 36 but not a factor of 162. Yes. 8 is a common factor of 16 and 363. No. 8 is a factor of 16,but not a factor of 264. Yes. 8 is the greatest common factor of 16 and 36
Answers
We are ask to choose a staement that explain why and why not, in other words, we are to choose the correct statements
The correct statements are;
No. 8 is a factor of 16 but ot 36
Given AC and BD bisect each other at O prove AC is congruent to c
Answers
The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .
Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.
We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.
Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)
Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.
Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD
Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC
Therefore, AC is congruent to c .
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Use Substitution to solve System of equations
y=-4x
6x-y=30
Answers
The solution for the given system of equations is
x = 3
y = -12
What are linear equations in two variables?
Therefore, a linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real values, and a and b are not equal to zero.
Given two linear equations of two variables.
y = -4x .....eq 1
6x - y = 30 .....eq 2
We have to solve them using substitution.
Now,
by substituting eq 1 in eq 2,
6x -(-4x) = 30
6x + 4x = 30
10x = 30
x = 3
from eq 1,
y = -4x = -4*3 = -12
Therefore, x = 3 and y = -12
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Jayden has $0.56 worth of pennies and nickels. He has a total of 20 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Jayden has.
Answers
Answer:
11 pennies and 9 nickels
Step-by-step explanation:
Set up a system of equations where p is the number of pennies and n is the number of nickels:
p + n = 20
0.01p + 0.05n = 0.56
Solve by substitution by rearranging the first equation:
p + n = 20
p = 20 - n
Then, plug this in as p into the second equation, and solve for n:
0.01p + 0.05n = 0.56
0.01(20 - n) + 0.05n = 0.56
0.2 - 0.01n + 0.05n = 0.56
0.2 + 0.04n = 0.56
0.04n = 0.36
n = 9
Then, plug this into the first equation to solve for p:
p + n = 20
p + 9 = 20
p = 11
So, Jayden has 11 pennies and 9 nickels
Which number is composite?
53, 81, 41, 47,31
O41
81
31
47
Pls hurry its a test
Answers
Answer:
81
Step-by-step explanation:
A composite number is a number that can be divisible by more than 1.
81 can be divisible by 1 and 9.
-kiniwih426
Assume: Triangle CDE is a right triangle and Angle D is a right angle. What is the length of the missing side? A) 26 . B) 25 . C) 24 . D) 23 .
Answers
Answer:
Length of base DE = 24 units
Step-by-step explanation:
Given:
In given triangle, right angle at D
SO,
Perpendicular of given triangle = 32 unit
Hypotenuse of given triangle = 40 unit
Find:
Length of base DE
Computation:
Using Pythagoras theorem
Base = √Hypotenuse² - Perpendicular²
Length of base DE = √Hypotenuse of given triangle² - Perpendicular of given triangle²
Length of base DE = √40² - 32²
Length of base DE = √1,600 - 1,024
Length of base DE = √576
Length of base DE = 24 units
Dot Plots and Histograms-Quiz-Level F
Briana is learning to play the guitar. At the end of each week, she records the number of days
she practiced. Her data is shown below.
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
OFReady
Which dot plot displays the data distribution?
1
2
2
3
4
Number of Days
3
Number of Days
:
5
6
7
567
0
+
0
1
2
3
4
Number of Days
2
5
...
3
4
Number of Days
5 6
..
Answers
The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with
Two dots at 0
One dot at 2
Two dots at 3
Four dots each at 4, 5, and 6
One dot at 7
A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.
The data can be presented as follows;
2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6
The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.
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The dot plots below show the numbers of bird feeders in 16 different sections of two bird sanctuaries, Bird Paradise and Bird Safari.
What is the difference between the median numbers of bird feeders at the two bird sanctuaries?
A. 1
B. 2
C. 1.4375
D. 3
Answers
We can respond to that by addressing the problem at hand Median of Bird Paradise - Median of Bird Safari is the difference between the medians.
What is the median?The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three different metrics are employed in mathematics. The terms are median, mode, and mean. The term "measures of central tendency" refer to these three metrics.
The mean of the provided data provides the average value. A median identifies the midpoint of the provided data. The given data's repeated value is determined by mode.
In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.
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At Dela's Deli, Dela fills containers with homemade vinaigrette salad dressing. The table shows the amount of vinegar and olive oil used for the dressing.
Number of containers Vinegar (tsp) Olive Oil (tsp)
1 4 12.5
6
At this rate, how much vinegar and olive oil will be used to make 6 containers of salad dressing?
Dela will use 10 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 10 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Answers
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
We have,
Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.
So, for 6 containers
= 4 x 6
= 24 teaspoons of vinegar
and, = 12.5 x 6
= 75 teaspoons of olive oil
Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
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Which of the following are steps in practical problem solving?
Answers
Answer:
Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.
Step-by-step explanation:
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What is the solution to the system graphed below? PLS ANSWER ASAP
Answers
The system of equations has its solutions to be (0, 3)
How to determine the solution to the system of equations?From the question, the system of equations is represented on the graph
On the graph, we have the following representations
Two lines of different colorsBoth lines intersect at a pointSay the functions are f(x) and g(x)
To determine the solution to the system of equations, we set both equations equal
i.e. f(x) = g(x)
This in other words mean that we determine the coordinates of the points where the graphs intersect
In this case, they intersect at point (0, 3)
This represents the solution
Hence, the solution to the system of equations is (0, 3)
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Which pair of complex factors results in a real-number product? 15(–15i) 3i(1-3i) (8 + 20i)(–8 – 20i) (4+7i)(4-7i)
Answers
Answer:
(4 + 7i)(4 - 7i)
Step-by-step explanation:
Factors of the form of a conjugate pair always produce a real number
(a + bi)(a - bi) ← produce a real number product ( a and b are real ), that is
(a + bi)(a - bi) ← expand using FOIL
= a² - bi² ( i² = - 1)
= a² + b² ← a real number
Thus
(4 + 7i)(4 - 7i)
= 16 - 49i²
= 16 + 49 = 65
Answer:
the correct answer is the last one, (4+7i)(4-7i)
Step-by-step explanation:
Solve for b b+4.22=7.08
Answers
Steps to solve:
b + 4.22 = 7.08
~Subtract 4.22 to both sides
b = 2.86
Best of Luck!