Answers
Answer
Options C and F are correct.
x² + 6x + 9 = 25
(x + 3)² = 25
are both equivalent to
x² + 6x = 16
Explanation
The equations that are equivalent to x² + 6x = 16 will all have to reduce to this exact equation on simplification.
x² + 6x + 9 = 0
Option A is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option B is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option C is corect as it matches the equation given in the quesion.
(x + 3)² = 0
x² + 6x + 9 = 0
Option D is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option E is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option F is corect as it matches the equation given in the quesion.
Hope this Helps!!!
Related Questions
There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water. About how many liters does the tank hold? Round your answer to the nearest whole number. Answer to get 60 points plus brainliest!
Answers
Answer:
379 liters
Step-by-step explanation:
3.79 L / gal * 100 gal = 379 Liters
Kendra's fish tank can hold 379 liters of water under the given conditions.
Given that,
There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3.79 liters = 1 gallon,
Now,
in the fish tank
100 gallon of water = 3.79× 100 liters
= 379 liters
Thus, Kendra's fish tank can hold 379 liters of water under the given conditions.
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Solve g(7) given g(X)= -3x+1
Answers
Step-by-step explanation:
that means we need to calculate the function result with x having a specific value.
for this we replace any appearance of x in the function expression by that specific value, and then we calculate.
g(x) = -3x + 1
g(7) means x = 7, and that gives us
-3×7 + 1 = -21 + 1 = -20
so, g(7) = -20
Answer:
-20
Step-by-step explanation:
Substitute 7 into the function g(x)
Since negatives "rule" positives,
7 * -3 = -21,
-21 + 1 = -20
evaluate the expression 12x-3y when x is -1/4 and y is 3
Answers
Answer:
-12
Step-by-step explanation:
plug in and solve
1. 12(-1/4) - 3(3)
2. -12/4 - 9
3. -3 - 9
4. -12
Jacob is planting shrubs for a landscaping client. He planted more shrubs in the additional region so that the density of shrubs in the new region is equal to the density of shrubs in the rectangular region as shown.
Answers
ANSWER:
52 shrubs
STEP-BY-STEP EXPLANATION:
We know the number of trees planted in a given area, so to calculate the number of total trees, we must calculate the area of the entire figure and thus calculate by means of a proportion
We calculate the total area if we divide the figure in two, as follows:
The area of zone A, which is a rectangle, is calculated as follows:
[tex]\begin{gathered} A_A=b\cdot h \\ A_A=50\cdot20 \\ A_A=1000 \end{gathered}[/tex]The area of zone B, which is a triangle, is calculated as follows:
[tex]A_B=\frac{b\cdot h}{2}[/tex]To calculate the value of the height of the triangle, we apply the Pythagorean theorem on the right triangle that is formed:
Where the hypotenuse is 25 meters and the other leg is 15 meters, just like this:
[tex]\begin{gathered} h^2=a^2+b^2 \\ 25^2=15^2+b^2 \\ b=\sqrt[]{25^2-15^2} \\ b=\sqrt[]{400} \\ b=20 \\ \text{therefore the height is 20 meters, replacing:} \\ A_B=\frac{30\cdot20}{2} \\ A_B=300 \end{gathered}[/tex]Now, the total area would be the sum of both areas:
[tex]\begin{gathered} A_T=1000+300 \\ A_T=1300 \end{gathered}[/tex]Which means that if in an area of 400 square meters (20 * 20) they can plant 16 shrubs, in an area of 1300 square meters they would be:
[tex]\begin{gathered} \frac{16}{400}=\frac{x}{1300} \\ \text{ solving for x} \\ x=\frac{16\cdot1300}{400} \\ x=52 \end{gathered}[/tex]In other words, a total of 52 shrubs can be raised throughout the region.
How do I solve this problem? To find the distance AB across a river, a distance BC=250 is laid off on one side of the river. It is found that B =119 degrees and C=27 degrees. Find AB
Answers
7 John and Raul both bought the same style bike from a store. On
Wednesday, John purchased the bike at a 20% discount off the original
price. On Friday, Raul bought the bike for off the original price.
Part A-Who received the greater discount on the bike? Show your work.
Part B-If John saved $24, what was the original price of the bike? Show
your work.
Use words, numbers and/or pictures to show your work.
Answers
John recieved the greater discount and the original price of the bike is $120
John purchased the bike at a 20% discount off the original
price.
Let the price of the bike be x
The price at which John purchased the bike is x - 20% of x
= x - (20/100)x
=(80/100)x
Raul brought the bike at original price.
Raul's cost price is x
x is greater than (80/100)x
Raul purchased at a greater price than John, so the greater discount is recieved by John.
John got discount = (20/100) x
He saved = $24
(20/100)x = 24
20x =2400
x = 2400/20
x = 120
The original price is $120
Therefore, John recieved the greater discount and the original price of the bike is $120
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What is the equation of the line that contains the points ( -1 , 1 ) and ( 5 , -3) ?
Answers
ANSWER:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]STEP-BY-STEP EXPLANATION:
The equation of the line in its slope and intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]The slope can be calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points (-1 , 1) and (5 , -3) :
[tex]m=\frac{-3-1}{5-(-1)}=\frac{-4}{5+1}=-\frac{4}{6}=-\frac{2}{3}[/tex]Now, we calculate the value of b, with the help of the slope and the point (-1,1)
[tex]\begin{gathered} 1=-\frac{2}{3}\cdot-1+b \\ b=1-\frac{2}{3} \\ b=\frac{1}{3} \end{gathered}[/tex]Therefore, the equation would be:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]
Sammy is a baker who wants to make profit on his baked goods if it fits him 3.20 or o make a dozen cupcakes how much should he sell them if he wants to make 35% profit
Answers
For there to be a profit,
[tex]\begin{gathered} \\ \text{profit}=\text{ selling price - cost price} \end{gathered}[/tex]From the question,
[tex]\begin{gathered} \text{Cost price = \$3.20} \\ \text{Percentage profit = 35\%} \end{gathered}[/tex]Concept: The formula for the percent profit is given below as
[tex]\text{percentage profit = }\frac{\text{profit}}{\cos t\text{ price}}\times100\text{ \%}[/tex]Assuming the pattern continues, what is S12 for the series −5 − 14 − 23 − 32 − …?A)-104B)-624C)-654D)-663
Answers
The sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
The sequence is:
−5 − 14 − 23 − 32 −
s(12) means the sum of the 12 terms
s(12) = (12/2)[-5 + (12-1)(-9)]
s(12) = 6[-5 -99]
s(12) = 6[-104]
s(12) = -624
Thus, the sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.
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State the number of possible real zeros and turning points of f(x) = x^7 – 6x^6 + 8x^5. Then determine all of the real zeros by factoring. 1) 7 real zeros and 6 turning points; 0, 2, and 42) 7 real zeros and 6 turning points; 0, –2, and –43) 6 real zeros and 5 turning points; 0, 2, and 44) 6 real zeros and 5 turning points; 0, –2, and –4
Answers
Step 1
The given equation is
[tex]f(x)=x^7-6x^6+8x^5[/tex]Required: To find the real zeroes by factorization and the turning points.
Step 2
Find the number of real zeroes
[tex]\begin{gathered} x^7-6x^6+8x^5=0 \\ x^5\mleft(x-2\mright)\mleft(x-4\mright)=0 \\ x^5=\text{ 0} \\ x\text{ = 0 five times} \\ ^{}or\text{ } \\ x-2\text{ = 0} \\ x=\text{ 2} \\ or \\ x-4=0 \\ x=\text{ 4} \\ \text{Therefore, there are 7 real zeroes} \end{gathered}[/tex]Step 3
Find the number of turning points.
[tex]f^{\prime}(x)\text{ = }7x^6-36x^5+40x^4[/tex][tex]\begin{gathered} As\text{ se}en\text{ from the differential, the number of turning points is found by subtracting 1 from the highest power of the function.} \\ \text{Hence, the number of turning points = 7-1 = 6} \\ \text{There are 6 turning points} \end{gathered}[/tex]Therefore, there are 7 real zeroes and 6 turning points; 0, 2 and 4
The answer is option A
What is 4 square root of 4?
Answers
Answer:
8
Step-by-step explanation:
4[tex]\sqrt{4}[/tex]
The [tex]\sqrt{4}[/tex] is 2
4x2 = 8
Answer:The square root of 4 is simply just 2 or in other words, 4 = 2.
Step-by-step explanation:
The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number.
3/8 divided by 4/3.5
Answers
1) In this division, we need to turn that decimal number into a fraction:
[tex]undefined[/tex]You go on a hayride to take photographs of landmarks. The map shows your path and two landmarks. Each unit in the coordinate plane corresponds to 10 yards. Approximate your minimum distance from the giant pumpkin. If necessary, round your answer to the nearest tenth.
Answers
Using the distance between a point and a line and the conversion of the units to yards, it is found that the minimum distance from the giant pumpkin is of 8.9 yards.
What is the distance between a points and a line?Suppose that we have a linear function defined according to the following rule, in standard notation:
Ax + By + C = 0.
And a point with coordinates given by:
P(x*,y*)
The shortest distance between the line and the point is given by:
[tex]d = \frac{|Ax^\ast + By^\ast + C|}{\sqrt{A^2 + B^2}}[/tex]
The line of the path in this problem has:
Intercept of 0, as when x = 0, y = 0.Slope of 0.5, as when x increases by 4, y increases by 2.Hence:
y = 0.5x.
-0.5x + y = 0
-x + 2y = 0.
The coefficients are:
A = -1, B = 2.
The giant pumpkin has coordinates given by:
(x*, y*) = (-4, -3).
Hence the distance in units is given by:
d = |(-1)(-4) + 2(-3)|/sqrt(5)
d = 2/sqrt(5)
d = 0.89 units.
Each unit is equivalent to 10 yards, hence the shortest distance in yards is given by:
0.89 x 10 = 8.9 yards.
What is the missing information?The problem is given by the image at the end of the answer.
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Mathew deposits 400800.00 kina with the bank which offers 5½% interest per annum. calculate the interest earned after four years if it is compounded annually?
Answers
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A= future value, P= present value= 400800.00
r= 5.5%=0.055, n =1 , t= 4 years
n= represent the number of times that the interest is compounded each year =1 for this case
Replacing we got:
[tex]A=400800\cdot(1+\frac{0.055}{1})^{4\cdot1}=496520.92[/tex]then we can find the interest in the following way:
[tex]I=A-P=496520.92-400800=95720.919[/tex]A gardening shop receives a shipment of 12 crates of plants. Each crate contains 18 plants. A worker displays all the plants on 24 shelves with the same number of plants on each shelf. How many plants are displayed on each shelf?
A. 6
B. 16
C. 9
D. 36
Thanks!
Answers
Answer:16
Step-by-step explanation:
points on the coordinate plane below which point would lie on both the x-axis and the y-axis ___thats the question
Answers
We see that the unique point that lie on both the x-axis and the y-axis is the pont (0,0)!
Select the conic section that represents the equation.3x² + 3y²-2x + 4 = 0
Answers
Given:
[tex]3x^2+3y^2-2x+4=0[/tex]First, we arrange the equation:
[tex]\begin{gathered} 3x^{2}+3y^{2}-2x+4=0 \\ 3x^2-2x+3y^2+4=0 \\ (3x^2-2x)+3y^2=-4 \end{gathered}[/tex]Further simplification of the given equation will give us a result with an imaginary number, making the equation a nonreal circle, or not a conic section.
A pool fills up 3 gallons of water in one minute. How many pints does it fill in one minute?
Answers
In this problem we have to use the convertion factor that is equal to 1 so:
[tex]\frac{1gal}{8pn}=1[/tex]so we can made the transormation:
[tex]3\text{gal}\cdot\frac{8pn}{1\text{gal}}=24pn[/tex]So in one minute it fills 24 pints
What is the slope of the line that passes through the points (4, -2) and (4, 10)?
Write your answer in simplest form.
Answers
The slope of the line that passes through the points (4, -2) and (4, 10) is 0. The slope of a line is 0 if it is horizontal. This function is constant.
What is slope?The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.
If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.
The slope of a line is 0 if it is horizontal. This function is constant.
A line's slope is ambiguous if it is vertical.
In other terms, the rise is (y2 y1) = y. The rise of a road between two points is the difference in the altitude of the road at those two sites, say y1 and y2. The run, or (x2 x1) = x, is the difference in distance from a given point measured along a level, horizontal line for relatively small distances where the Earth's curvature may be disregarded. Here, the ratio of the altitude change to the horizontal distance between any two places on the line is used to define the slope of the road between the two points.
In mathematical language, slope m of the line is
slope = [tex]\frac{x-x1}{y-y1} =\frac{4-4}{-2+10} = 0[/tex]
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pls help this is due today and i have no idea what i am doing
(this isnt math but i didnt see music)
Why is it important for musicians to transcribe music?
Why do you think Beethoven’s story is unique (special)?
What are some ways that we can get better at active listening?
Below is a picture of a musical staff. What is a musical staff? What do the top lines and the bottom lines represent?
an image showing both staffs
What is a musical form? How does it make music more interesting?
Answers
Answer: look at explanation
Step-by-step explanation:
1. It helps you learn and listen to minor details in music better.
2. He had a handicap (partially deaf/deaf) but still managed to overcome and lay his mark in the music world.
3. Pay attention, eye contact, listen, pay attention to nonverbal cues, and show that you are listening
4. A foundation on which notes are drawn on. The lines represent a sound in music. A musical form is the structure of musical compositions. It makes music more interesting because it makes it organized and not jumbled up.
6A. Solve h(0)=100-16(0) to the 2nd power and What does the output represent 6B. Solve h(2)=100-16(2) to the 2nd power and does our equation predict that the ball has to hit the ground at 2 seconds. Explain
Answers
I think is confused
6A.- h(0) = 100 - 16(0)^2
= 100 - 0
h(0) = 100
h(0) = 100 ft
The result is the value starting height 100 ft
6B.- h(2) = 100 - 16(2)^2
h(2) = 100 - 64
h(2) = 36 ft
No, the equation does ot predict that the ball is going to hit the ground after 2 seconds because the height was 32 ft, that is the height necessary to hit the ground.
Given the following information, which is the best description of the data?Range—5, from 12 to 17Mode—14Median—14.5Mean—15The data is around 13.The data is around 12.The data is around 15.The data is around 17.
Answers
we have that
the best description of the data is
The data is around 15Which function is the inverse of fix) = V5767O A.(-40) =3622 + 2. for = > 0O B.1-1(0) =652 + 2, for = ≥ 0O C.+ 2. for I > 0O D.f-11) = 6522. for r > 0
Answers
Given:
The function is
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]Required:
Find the inverse of the function.
Explanation:
The given function is:
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]Put
[tex]f(x)=y[/tex][tex]y=\frac{\sqrt{x-2}}{6}[/tex]Interchange x and y.
[tex]x=\frac{\sqrt{y-2}}{6}[/tex]Take the square on both sides.
[tex]x^2=\frac{y-2}{36}[/tex][tex]\begin{gathered} 36x^2=y-2 \\ y=36x^2+2 \end{gathered}[/tex]Substitute
[tex]y=f^{-1}(x)[/tex][tex]f^{-1}(x)=36x^2+2[/tex]Final Answer:
Option A is the correct answer.
The ratio of two cars, the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5. The new version of the Flash added 14 miles per gallon and now the ratio is 24:27 .
What is the miles per gallon of the Thunderbolt?
The Thunderbolt gets
miles per gallon.
Answers
If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is 15.27 miles per gallon
The ratio the Thunderbolt and the Flash, in terms of their miles per gallon = 6:5
Then the miles per gallon of the Thunderbolt and the Flash is 6x and 5x respectively
The new version of the Flash added 14 miles per gallon
New ratio of the cars = 24:27
Therefore the equation is
5x+14 = 27x
27x-5x = 14
22x = 14
x = 7/11
The miles per gallon of the Thunderbolt = 24x
= 24×7/11
= 15.27 miles per gallon
Hence, If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is 15.27 miles per gallon
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A student buys 5 books for $47.85. If all of the books are the same price, the cost of each book is
Answers
Answer: $9.57
Step-by-step explanation: 47.85/5 = 9.57. Therefore each book costs $9.57.
4to the fitth power times 4 negative 7 expnent
Answers
Answer:
-16,777,216
Step-by-step explanation:
4 to the fifth power =1024
-4 to the seventh power = 16, 384
1024 × -16, 384 =
- 16,777,216
Please help me with this question
Answers
Step-by-step explanation:
substitution means to use one equation to express one variable only in terms of the other variable and constants.
let's use
6f + 11b = 317
for that purpose.
6f = 317 - 11b
f = (317 - 11b)/6
now we use that my substituting "f" by its identical expression in b in the second equation :
7(317 - 11b)/6 + 5b = 221
to avoid handling fractions we multiply everything by 6 :
7(317 - 11b) + 30b = 1326
2219 - 77b + 30b = 1326
893 - 47b = 0
893 = 47b
b = 893/47 = 19 cents
f = (317 - 11b)/6 = (317 - 11×19)/6 = (317 - 209)/6 =
= 108/6 = 18 cents
a piece of fudge is 18 cents.
a piece of bubble gum is 19 cents.
find the coordinates of of the point at -270 degrees on circle radius 3.6 centered at the origin
Answers
Answer: [tex](0, 3.6)[/tex]
Step-by-step explanation:
When rotating -270 degrees, which is the same as 90 degrees, we are going to the topmost point of the graph.
Since the radius is 3.6, this point has coordinates [tex](0, 3.6)[/tex].
Select the vector along which a translation of the plane would map point A to its image T(A).
Answers
The vector along which a translation of the plane would map point A to its image T(A) is: C. vector MN.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.
In this context, we can reasonably infer and logically deduce that vector MN is a translation of the given plane which would map point A to its image point T(A) because they both move in the same direction.
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Only about 16% of all people can wiggle their ears. Is this percent different for millionaires? Of the 342 millionaires surveyed, 58 could wiggle their ears. What can be concluded at the α = 0.01 level of significance?For this study, we should use Select an answerThe null and alternative hypotheses would be: H0: ? Select an answer (please enter a decimal) H1: ? Select an answer (Please enter a decimal)The test statistic ? = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 3 decimal places.)The p-value is ? α Based on this, we should Select an answer the null hypothesis.Thus, the final conclusion is that ...The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the populaton proportion is significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 16%.Part a options:- a. t- test for a population mean- z-test for a population proportionPart b options:(left box): u; ?; p(right box): >; =; =/; >Part c options:t; zPart e options:<; >Part f options:ACCEPT, REJECT, FAIL
Answers
Part a:
In this study, we have only a reference value of 16% (the proportion of people that can wiggle ears) and a population of 342 millionaires whose results we want to compare with this reference value. Since there is a relativelly high number of millionaries that were surveyed, we should use the z-test for a population proportion.
Part b:
It p is the sample proportion, the null hypothesis, in this case, is given by:
[tex]H_0:p=0.16[/tex]Therefore, the alternative hypothesis is given by:
[tex]H_1:p\ne0.16[/tex]Part c:
According to the data, the z-score is given by:
[tex]z=\frac{\frac{58}{342}-\cdot0.16}{\sqrt{\frac{1}{342}\cdot\frac{58}{342}(1-\frac{58}{342})}}\approx0.473[/tex]Part d:
According to the normal table, the p-value related to z-score given by:
0.638
Part e:
Therefore, we can check that this p-value is > a
Part f:
Based on this, we should ACCEPT the null hypothesis.
Part g:
Thus, the final conclusion is that the data suggest the population proportion is not significantly different from 16% at a = 0.01, so there is statistially significant evidence to conclude that the population proportion of millionaries who can wiggle their ears is equal to 16%.