10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)
Answers
To transform
[tex]x^2+8x+15=0[/tex]Make it a perfect square
since 8x/2 = 4x, then
We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1
[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]Now we will make the bracket to the power of 2
[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]Add 1 to both sides
[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]The answer is C
Related Questions
The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.26 ohms, find the length of a wire of the same material whose resistance is ohms and whose diameter is millimeters.
Answers
Let
R ----> resistance in ohms
L ---> the length of the wire in ft
D ---> the diameter of the wire in mm
In this problem, the equation is of the form
[tex]R=K\frac{L}{D^2}[/tex]we have
L=432 ft
D=4 mm
R=1.26 ohms
so
Find out the value of K (constant of proportionality)
substitute the given values
[tex]\begin{gathered} 1.26=K\frac{432}{4^2} \\ \\ K=\frac{1.26*16}{432} \\ \\ K=0.0467 \end{gathered}[/tex]Part 2
The formula is
[tex]R=0.0467\frac{L}{D^2}[/tex]For
R=1.41 ohms
D=5 mm
substitute in the formula above
[tex]\begin{gathered} 1.41=0.0467\frac{L}{5^2} \\ solve\text{ for L} \\ L=\frac{1.41*25}{0.0467} \\ L=754.8\text{ ft} \end{gathered}[/tex]The answer is 754.8 feetThere are 50 students in a class. Can the teacher make them sit in a rows of having six students in each row? Use divisibility test to answer
Answers
Step 1. There are 50 students and we need to answer of the teacher can make rows of 6 students in each row.
To check if this can be done, divide 50 by 6 and if the residue is 0, there can be rows of 6 and if the residue is not 0 there cannot be rows of 6 students.
Step 2. D
A coach gives 2 water bottles to each player on a basketball team. There are p players on the team. which expression can be used to determine the total number of water bottles that the gives the player on the team?
Answers
If there are p players and every player has 2 water bottles. The total number of water bottles is calculated as:
[tex]\text{Total}=2p[/tex]So, the expression that can be used to determine the total number of water bottles is:
[tex]2p[/tex]Name
1.
Write an expression showing the sum of 8 and a number f.
How do I write this as an expression
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The sum of 8 and a number of f can be written as follow:
8 + f
what digit is in the
Answers
Given x = 7, we have:
[tex]6x=6(7)=42[/tex]Answer: 42
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours?
Answers
Answer:
It would be a lot of bavgeria
Answer:
450000
Step-by-step explanation:
125×(60×60)
=125×3600
=450000
From the time Ryan wakes up, he spends To hour to get ready and 1 hour to travelfrom home to school..How much time does he take to get to school from the time he wakes up?
Answers
Prescription 1: According to the eScience Lab Manual for Lab 1, Experiment 3, you need to prepare 65 mL of a 60% soda/syrup “prescription”.To do this, you can use the 80% soda solution and the syrup solution (0% strength) that you have in inventory.How many mLs of soda solution do you need to create this final solution?
Answers
Let:
x = mL of soda solution
y = mL of syrup solution
The soda solution is 80% strength and the syrup solution is 0% strength, thus the combination of x and y of each solution gives strength of:
80x + 0y
This combination must be 60% strength, thus:
80x + 0y = 60(x + y) [1]
The total amount of solution is 65 mL, thus:
x + y = 65
Substituting in [1]
80x + 0y = 60*65
Operating and simpliifying:
80x = 3900
Dividing by 80:
x = 48.75
I need 48.75 mL of soda solution
A loan of $14,354 was repaid at the end of 16 months. What size repayment check (principal and interest) was written, if a 7.4% annual rate of interest was charged?
Answers
Principal = P = $14,354
Rate = r
Tom is 26 years older than Paul. the product of his ages is 560. How old is Paul?
Answers
Given data:
The given age of Tom is T=P+26.
The expression for the product of their ages is TxP=560.
Substitute (P+26) for T in the second expression.
[tex]\begin{gathered} (P+26)P=560 \\ P^2+26P-560=0 \\ P^2+40P-14P-560=0 \\ P(P+40)-14(P+40)=0 \\ (P+40)(P-14)=0 \\ P=-40,\text{ 14} \\ P=14 \end{gathered}[/tex]Thus, the age of Paul is 14 years.
Use the graph and the translation (x,y) → (x+2, y + 5) to answer parts a and b below.
Answers
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
Explanations:The translation rule is:
(x+2, y+5)
We are going to get the coordinates of the vertices A, B, and C.
We will also get the coordinates of the vertices A', B', and C' after translation.
A (-9, 5)
B (-1, 0)
C (-5, -2)
After the translation (x+2, y+5)
A' (-9+2, 5+5)
A' (-7, 10)
B' (-1+2, 0+5)
B' (1, 5)
C' (-5+2, -2+5)
C' (-3, 3)
Therefore:
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)find the equation of the line that is parallel of this line and passes through the point (-2, -2)
Answers
solve the problem and show your work below. I have a rectangular garden. i usually grow cucumbers in2/3 of my garden but i want to take 3/4 of the cucumber section to grow radishes. After i make the change, how much of my whole garden will be radishes?
Answers
Given data;
The area in which cucumbers usually grown are 2/3 x.
Here, x is the total area of the garden.
The area of the cucumber taken to grow raddish are,
[tex]\begin{gathered} R=\frac{3}{4}\times\frac{2}{3}x \\ =\frac{1}{2}x \end{gathered}[/tex]Thus, the area of the raddish is 50% of the total area of the garden sfter the changes.
How much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 5% interest compounded continuously.
Answers
The total amount of money that you can deposit in the account would be = $ 8,000
What is interest?Interest is defined as the amount of money that an individual earns from an investment made after a particular period of time.
The formula for calculating simple interest;
simple interest (SI) = Principal×time ×rate/100
The principal amount = $x
time = 5 years
Rate = 5%
simple interest = $2000
From the formula, make principal the subject of formula:
Principal= SI × 100/T ×R
Principal= 2000×100/5 × 5
principal= 200000/25
Principal=$ 8,000.
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I'm working on a practice quiz I'm confused about this question
Answers
In this problem we have to use the Hero formula so first we have to find s:
[tex]s=\frac{a+b+c}{2}[/tex]and then we replace the sides of the triangle:
[tex]s=\frac{12+11+7}{2}=\frac{30}{2}=15[/tex]and with s we can use the formula of A so:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]and replace the data so:
[tex]A=\sqrt[]{15(15-12)(15-11)(15-7)}[/tex]and we simplify it so:
[tex]\begin{gathered} A=\sqrt[]{15(3)(4)(8)} \\ A=\sqrt[]{1440} \\ A\approx37.95 \end{gathered}[/tex]3. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down. (b) What was the equation of your linear function in slope-intercept form? (c) What was the equation of the transformed function in slope-intercept form?
Answers
The required solution,
(a) the graph has been shown,
(b) The slope-intercept equation of linear function is y = x,
(c) The slope-intercept form of transformed equation is y = x + 2 and y = x - 3
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Let's consider a linear function y = x,
The equation of the trasformation in slope-intercept form is given as
For 2 units up
y = x + 2
For 3 units down
y = x - 3
Thus, the required graph has been attached and the solution is determined.
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Line L passes through point (10,−1) and line P is the graph of 5x−7y=8.
If L⊥P , what is the equation of L?
Answers
The equation of line L is [tex]7x+5y=70[/tex].
Given,
Line L passes through point (10,-1)
Equation of line P = [tex]5x-7y=8[/tex]
Line L is perpendicular to line P
First find the slope of line P, for that convert the equation into the general form [tex]y=mx+c[/tex]
Where, m=slope
[tex]5x-7y=8\\\\5x-8=7y\\\\y=\frac{5}{7}x-\frac{8}{7}[/tex]
Comparing with general form,
[tex]m=\frac{5}{7}[/tex]
Any line perpendicular to it should have slope in the form [tex]-\frac{1}{m}[/tex]
So, the slope of line L becomes [tex]-\frac{7}{5}[/tex]
Equation of line L can be written as [tex]y-y1=m(x-x1)[/tex]
Where, (x1,y1) is the point through which line passes and 'm' is the slope of line L
[tex]y-(-1)=-\frac{7}{5}(x-10)\\\\5(y+1)=-7x+70\\\\5y+5=-7x+70\\\\7x+5y=70[/tex]
Thus, the equation of line L is [tex]7x+5y=70[/tex]
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drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.{{x|x\geq7}}AnswerAnswer,AnswerAnswer
Answers
In order to write this set in interval notation, first let's understand what the set represents.
This set includes all numbers that are greater than or equal to 7.
That is, the smaller number in the set is 7, and the greater value doesn't exist, so we can use positive infinity to represent that the set only grows.
Since number 7 is included in the set, we use square brackets, and since positive infinity is not included in the set (because it's not a number that is in the set), we use parenthesis, so the interval notation is:
[tex]\lbrack7,\text{inf)}[/tex]Find the slope of the line that passes thru the points (1,2) & (7,7)
Answers
Determine the slope of line passing through points (1,2) and (7,7).
[tex]\begin{gathered} m=\frac{7-2}{7-1} \\ =\frac{5}{6} \end{gathered}[/tex]So slope of the line is 5/6.
Diameter = 9 ftMarci purchased the rug shown. To the nearest hundredth, what area of floor space will the rug cover? (1 = 3.14)A)28.26 ft?B)58.54 ft?C) 63.59 ft2D)254.34 ft2
Answers
Given:
a.) A rug with a diameter of 9 ft.
Since the rug appears to be a circle, we will be using the following formula:
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex]Where,
D = diameter
We get,
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex][tex]\text{= }\frac{\pi(9)^2}{4}[/tex][tex]\text{= }\frac{81(3.14)}{4}[/tex][tex]\text{ Area = }63.585\text{ }\approx63.59ft.^2[/tex]Therefore, the rug will cover 63.59 ft.^2 of the floor area. The answer is letter C.
I’m confused the other answer is QUANTITATIVE sorry that it’s in capital but I don’t really get it
Answers
answer is
discrete and quantitative
Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. C a You can enter your results and check your work in the table below. 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?!
Answers
Answer:
c = 14
a = 7√3
Explanation:
To find the value of c, we will use the sin(30) because sin(30) is equal to the opposite side over the hypothenuse. So:
[tex]\sin (30)=\frac{7}{c}[/tex]Additionally, sin(30) is also equal to 0.5, so we can replace this value and solve for c:
[tex]\begin{gathered} 0.5=\frac{7}{c} \\ 0.5c=7 \\ c=\frac{7}{0.5} \\ c=14 \end{gathered}[/tex]Therefore, the length of the hypotenuse (c) is 7.
Now, we can calculate the length of the other leg using the Pythagorean theorem, where:
[tex]a=\sqrt[]{c^2-7^2}^{}[/tex]So, replacing the value of c by 14, we get:
[tex]\begin{gathered} a=\sqrt[]{14^2-7^2} \\ a=\sqrt[]{196-49} \\ a=\sqrt[]{147} \\ a=\sqrt[]{49\cdot3} \\ a=7\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of the other leg (a) is 7√3
A line segment, ST, has endpoints S(-7,-3) and T(-1,-1). Which of the following equations represents the perpendicular bisector of the line segment? A. y = 2x - 15 B. y = -3x - 14 C. y = 6x - 14 D. y = -3x - 20
Answers
SOLUTION
The given points are: (-7,-3) and (-1,-1)
The slope of the line segment is:
[tex]\begin{gathered} m=\frac{-1-(-3)}{-1-(-7)} \\ m=\frac{-1+3}{-1+7} \\ m=\frac{2}{6} \\ m=\frac{1}{3} \end{gathered}[/tex]Recall that the product if solpes of perpendicular line give -1.
The the slope of the perpendicula bisector is:
[tex]\begin{gathered} m_1=\frac{1}{\frac{1}{3}} \\ m=3 \end{gathered}[/tex]Therefore the slope of the perpendicular bisector is -3.
Recall that the perpendicular bisector passes through the center of a line segment.
Hence the perpendicular bisector will pass through:
[tex]\begin{gathered} (\frac{-7-1}{2},\frac{-3-1}{2}) \\ =(\frac{-8}{2},\frac{-4}{2}) \\ =(-4,-2) \end{gathered}[/tex]Using the point slope form, the equation of the perpendicular bisector is:
[tex]\begin{gathered} y-(-2)=-3(x-(-4)) \\ y+2=-3x-12 \\ y=-3x-12-2 \\ y=-3x-14 \end{gathered}[/tex]Therefore the required equation is:
[tex]y=-3x-14[/tex]Suppose that 73% of the residents in a particular community speak English as their primary language.a. What is the probability that exactly seven out of eight random residents in this community will speak English as their primary language?
Answers
Explanation
The question can be solved using the probability distribution formula, which can be seen below.
[tex]P_x=nCxp^xq^{n-r}[/tex]Part A
From the image we can see that n=8 and p=0.73 while q= 1-0.73 = 0.27
Therefore for;
[tex]\begin{gathered} P(7)=8C7(0.73)^7(0.27)^1 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1 \\ =0.23862 \end{gathered}[/tex]Answer: 0.2386
Part B
[tex]\begin{gathered} Pr(x\ge7)=Pr(7)+Pr(8)=8C7(0.73)^7(0.27)^1+8C8(0.73)^8(0.27)^0 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1+\frac{8!}{8!0!}\times(0.73)^8(0.27)^0 \\ =0.23862+0.08064 \\ =0.31926 \end{gathered}[/tex]Answer: 0.3193
Part C: Out of a random number of 40 people in the community, the expected number of people that speak English as a lnaguage will be;
[tex]\frac{73}{100}\times40=29.20[/tex]Answer: 29.20
Cuts iy ucaly cal-VUMU Problem Sandy has a garden in her backyard. The drawing shows How many bags of fertilizer will Sandy need to cover the dimensions of her garden. A bag of fertilizer covers 3 her garden? square feet The area of the garden is feet Sandy will need garden bags of fertilizer to cover her 4 ft. 6 ft.
Answers
Determine the area of the garden by using the following formula for the area of a triangle:
A = b·h/2
where
b: base = 4 ft
h: height = 6 ft
replace the previous values of the parameters into the formula for A:
A = (4 ft)(6 ft)/2
A = 12 ft²
next, take into account that:
1 bag of fertilizer = 3 ft² of garden
then, you have:
number of bags of fertilizer = (12 ft²)/(3 ft²) = 4 bags
Answer:
Determine the area of the garden by using the following formula for the area of a triangle:
A = b·h/2
where
b: base = 4 ft
h: height = 6 ft
Replace the previous values of the parameters into the formula for A:
A = (4 ft)(6 ft)/2
A = 12 ft²
Next, take into account that:
1 bag of fertilizer = 3 ft² of garden
then, you have:
number of bags of fertilizer = (12 ft²)/(3 ft²) = 4 bags
Step-by-step explanation:
word problem using a two-step near inequallyPablo wants to rent a boat and spend less than $47. The boat costs $6 per hour, and Pablo has a discount coupon for $7 off. What are the possible numbers ofhours Pablo could rent the boat?Use t for the number of hours.Write your answer as an inequality solved fort
Answers
Answer:
Pablo could rent the boat for less than 9 hours.
t < 9
Explanation:
Since Pablo wants to spend less than $47 to rent a boat and we're told that the boat costs $6 per hour and Pablo has a discount of $7 off, we can go ahead and represent this as an inequality as shown below using t to represent the number of hours;
[tex]6t-7<47[/tex]To solve for t, let's add 7 to both sides;
[tex]6t<54[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}<\frac{54}{6} \\ t<9 \end{gathered}[/tex]From the above, we can see that Pablo could rent the boat for less than 9 hours in order to spend less than $47.
1. Lines p and q are intersected by line r, such that line p is parallel to line q. If m<1=7x - 36 and m<2 = 5x+12, what is the m<1
Answers
We are given a figure in which line r intersects two parallel lines p and q.
The angles labeled as ∠1 and ∠2 are known as same-side interior angles.
Same-side interior angles are supplementary meaning that their sum is equal to 180°.
So we can write,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ (7x-36)+(5x+12)=180\degree \end{gathered}[/tex]Now let us solve this equation for x.
[tex]\begin{gathered} 7x+5x-36+12=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ x=\frac{204}{12} \\ x=17\degree \end{gathered}[/tex]Now we can find the exact value of the angle ∠1
[tex]\angle1=7x-36=7(17)-36=119-36=83\degree[/tex]Therefore, angle ∠1 = 83°
which equation can be used to determine the cost c
Answers
c = 8t + 12 (option C)
Explanation:
The equation will be in the form of equation of line:
y = mx + c
where y = cost
m = slope, x = change for calls, c = intercept
m = change for calls/change in lenght of call
m = slope = (28-20)/(2-1) = (36 -28)/(3-2)
m = 8/1 = 8
So we know the rate of change is 8
for t = 1, = 8 *1 = 8
for t = t , 8*t =8t
The option in the question with 8t is c = 8t + 12
To confirm if the option is correct, we use any of the value of time:
when t = 2
c = 8(2) + 12 = 16 + 12
c = $28
This is correct from the table. Hence, the equation can be used to determine the cost c is c = 8t + 12 (option C)
22. QRST is a rectangle. If RU = 3x - 6 and UT = x + 9, find x and the length of QS.RUx= 5QS =TS
Answers
We are given two lengths of the rectangle:
RU=3x-6
UT=x+9
These two lengths are shown in the following diagram:
Since this is a rectangle, the lengths of RU and UT must be equal:
[tex]RU=UT[/tex]Thus
[tex]3x-6=x+9[/tex]We need to solve this equation for x.
We start by subtracting x to both sides of the equation:
[tex]\begin{gathered} 3x-x-6=9 \\ 2x-6=9 \end{gathered}[/tex]Now, add 6 to both sides:
[tex]\begin{gathered} 2x=9+6 \\ 2x=15 \end{gathered}[/tex]Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]We have the value of x: x=7.5
Now we have to find the length of QS. Since QS and RT are diagonals of the same rectangle, they have to be equal:
[tex]RT=QS[/tex]This means that we can find RT by adding RU and UT, and the result will be equal to QS:
[tex]QS=RU+TU[/tex]substituting the given expressions for RU and TU:
[tex]QS=3x-6+x+9[/tex]And now, substitute x=7.5 and solve for QS:
[tex]QS=3(7.5)-6+7.5+9[/tex][tex]\begin{gathered} QS=22.5-6+7.5+9 \\ QS=33 \end{gathered}[/tex]Answer:
x=7.5 and QS=33
Replace * with a digit that allows you to reduce the fraction. If there are two * in thesame fraction, replace them with the same digit. Find all possible values of * in eachfraction.6*2/1*0
Answers
There are 10 possible digits that we can replace. These are from 0 - 9.
Let's start replacing with 0 first. The fraction will be 602/100 and can be reduced to 301/50.
If we replace * with 1, the fraction will be 612/110 and be reduced to 306/55.
If we replace * with 2, the fraction will be 622/120 and be reduced to 311/60.
If we replace * with 3, the fraction will be 632/130 and be reduced to 316/65.
We can use all the digits from 0 - 9 to replace * and it will allow us to reduce the fraction because the numerator and denominator ends in 2 and 0 respectively.