The first three steps for solving the quadratic equation by completing the square are as follows;
1. [tex]\rm 9x^2 +54x = 7[/tex]
2. [tex]\rm 9(x^2 + 6x) = 7[/tex]
3. [tex]\rm 9(x^2 + 6x + 9) = 7 + 81[/tex]
Given
The quadratic equation given as 9x^2 + 54x = 7.
Quadratic equation;The highest power of the degree is 2 is known as a quadratic equation.
To solve using the completing the square method.
The first three steps for solving the quadratic equation by completing the square are given below.
1. Write the equation in a way that the constants are on the right side while the terms with x are on the left.
[tex]\rm 9x^2 +54x = 7[/tex]
2. Make sure that the coefficient of the x^2 term is 1.
[tex]\rm 9(x^2 + 6x) = 7[/tex]
3. Adding a term to both sides that will complete the square on the left side.
This is done by dividing the coefficient of the x term by 2 and squaring it.
The same amount should be added to the right side to balance the equation.
[tex]\rm 9(x^2 + 6x + 9) = 7 + 81[/tex]
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Compare the solution strategies used by Kaleigh and Destiny. What do you notice about the properties each student used? Compare the solution strategies used by Kaleigh and Destiny. What do you notice about the properties each student used?
Kaleigh
4(3x + 2) = 8x + 4
12x + 8 = 81 +4
4x = -4
x = -1
Destiny
4(3x + 2) = 8x + 4
4(3x + 2) 8x + 4
4
4
3x + 2 = 2x + 1
x = -1
Answer:
who's asking?
Step-by-step explanation:
Need answers for 3 and 4 please.
Please help me solve this
Show work
NO LINKS!!!!!
Answer: The first one 5/10 is 0.5 or 50% 5÷10. The second one 5/100 is 0.05 or 500%. The third one 5/1000 is 0.005 or 5000%.
Step-by-step explanation:
All you have to do is divide and you do that for all of them. Also did you know quotient means the answer to a division question. Wow! Also, if you see that all I did was add another zero in the middle of the decimals is because That is Decimal Place value. Here is a picture of that just in case. The last answer for the very bottom one is what I just said about decimal place value so here is the reflection: When dividing by tens using decimals always be sure to use place value. Thank you I was happy to help!
Stanley has $18 to spend on packs of trading cards that cost $1.50 each. The inequality 18≥1.5p represents the number of packs p he can buy. What is the greatest number of whole packs Stanley can buy?
Answer:
Numbers of packs p is 12
Step-by-step explanation:
Data :
Money = $18
Price of a card = $1.5
Equation : 18 ≥ 1.5p
Solve the equation for p
18/1.5 ≥ p
12 ≥ p
Plls help
What is DE
Answer:
DE= 4.24
Step-by-step explanation:
A^2 + B^2 = C^2 Pythagorean theorem
(3)^2 + (3)^2 = C^2
9 + 9 = C^2
18 = C^2
√18 = √C^2
4.24264 = C
The MRA volleyball team decides to raise some extra money for their trip by horganizing a cookie sale. The cost to make the cookies is $45 and the team is charging $0.25 a cookie. How many cookies must be sold to make a profit of at least $100? write an inequality.
Answer:
Inequality:[tex]0.25x\geq 145[/tex]
Answer: At least 580 cookies
Step-by-step explanation:
Lets say they sell x cookies.
Now, that means they will make 0.25x as their income(the price multiplied by the number of cookies).
We know that totally they need to make 100+45 dollars, because that is what will give them a $100 profit. So they need to make $145
Now just set 0.25x equal to $145.
[tex]0.25x=145[/tex], and now solve
[tex]x=145*4[/tex]
[tex]x=580[/tex]
For an inequality, we could just say that:
[tex]0.25x\geq 145[/tex]
Translate the sentence into an equation. The sum of 8 times a number and 9 equals 6. Use the variable y for the unknown number.
Answer:
8y + 9 = 6
Step-by-step explanation:
8 times a number (8y) and 9 (+9) equals 6 (=6)
The graph shows the amount of protein contained in a certain brand of peanut butter.
Which statement describes the meaning of the point on the graph?
A
There are 666 grams of protein per tablespoon of peanut butter.
B
There are 303030 grams of protein per tablespoon of peanut butter
C
There are 666 grams of protein in 303030 tablespoons of peanut butter.
D
There are 303030 grams of protein in 666 tablespoons of peanut butter.
15. Your research problem should have a positive impact on the field.
a. Timely c. Novel
b. Significant d. Supported by Literature
16. It is the question that a researcher wants to answer or a problem that wants to be
solved.
a. Researchable c. Novel
b. Timely d. Research Problem
pls help
Answer:
15: significant 16: research problem
How do I answer this?
Answer:
2k³ is the GCF.
Step-by-step explanation:
GCF of [tex]10k^{3} ,6k^{3}[/tex]
Finding the factors:
=10k³[Factoring 10k³]
=2×5×k×k×k
=6k³[Factoring 6k³]
=2×3×k×k×k
Common factors in 10k³ and 6k³.
=2×k³
=2k³
GcF
[tex]\\ \tt\hookrightarrow 2(k)(k)(k)[/tex]
[tex]\\ \tt\hookrightarrow 2k^3[/tex]
HELPPPPP MEEEEE PLEASEEEE
Answer:
I don't know sooooooooop
mark me as brainliest ok understood
A map uses a scale
of 1.5 cm = 25 mi.
If two cities are 150 miles
apart, how far apart will
they be on the map?
225
Correct answer will have the brainliest answer look at the image pls.
Answer:
2nd option
Step-by-step explanation:
A=wl=2.75·2.25=6.1875
2 1/4= 2.25
2 3/4= 2.75
PLEASE HELP ME TO UNDERSTAND
Answer:
x > 0Step-by-step explanation:
The denominator is positive for any value of x.
So we solve the numerator:
5ˣ - 1 > 05ˣ > 15ˣ > 5⁰x > 0Abigail and Spencer calculate the slope of the line between the points (3,-1) and (5,4) in different ways. Abigail calculates the slope by dividing -1 - 4 with 3 - 5. Spencer divides 4 - (-1) by 5 - 3. When they check their work with their mutual friend Lauren, she says that they are both wrong and shows them her work. She calculates -1 - 4 and divides by 5 - 3. Who is correct among these three friends? Who is incorrect? Why?
You must show all of your work to receive credit.
Miss Robbins needs a border for a bulletin board
that has a length of 90 centimeters and a width of
75 centimeters. How many centimeters of border
does she need?
Answer:
330 cm
Step-by-step explanation:
90 x 2 =180
75 × 2 = 150
180 +150 = 330
Please give me right answer fast need it by tonight
graph the equation.
- 5/4 (x-1)(x+3)
Answer:
Step-by-step explanation:
So, to graph a parabola we must have at least 3 points, the x intercepts and the turning point. Currently the equation is in x intercept form which means that we know straight away (assuming the equation =0) that the x intercepts are:
(1,0) and (-3,0)
Now we have to find the turning point and we can do this by putting the equation into turning point form:
-5/4([tex]x^{2} +2x-3[/tex])
-5/4(([tex](x+1)^{2} -3-1[/tex])
-5/4[tex](x+1)^{2}+5[/tex]
Now we can figure out the turning point which is:
(-1,5)
Graph those three points and you should get a parabola shape
Someone help me with this pls
Answer:
x° = 55°
Step-by-step explanation:
An exterior angle is equal to the sum of the remote interior angles:
x° = 21° +34°
x° = 55°
If the ratio of homes without children to homes with children is about 8:7 if there is 4125 homes how many are without children
Answer:
2200
Step-by-step explanation:
8+7=15 4125/15=275 275x8=2200
The sides of One World Trade Center in New York City form
eight isosceles triangles, four of which are 200 ft long at their base BC. The
length AC of each sloping side is approximately 1185 ft.
The value of ∠BAC in the isosceles triangle is 9.7°
Cosine rule
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
a² = b² + c² - 2bc*cos(A)
where a, b, c are the sides of the triangle and A, B, C are the angles opposite the sides.
AB = AC = 1185 (isosceles), BC = 200, let ∠BAC = x°, hence:
200² = 1185² + 1185² - 2(1185)(1185)cos(x)
2(1185)(1185)cos(x) = 2808450
cos(x) = 0.9857
x = 9.7°
The value of ∠BAC in the isosceles triangle is 9.7°
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The table shows the results of a survey about students' preferred subjects in middle
school. What is the probability that a randomly selected student from the survey is a
7th grader that prefers English? Write your answer as a fraction and NOT as a
decimal.
Answer:
19/149
Step-by-step explanation:
38/298 = 19/149
7th graders who prefer English out of all students
7. Arrival of the Normandy Train
Claude is waiting to meet the train from Normandy at Gare Saint-Lazare in Paris. He
tells Marie the hour of the train's arrival and he tells Jean at which minute it arrives. He
also tells them both that the train arrives between 0600 and 1000.
They consult the timetable and find the following services between those times:
0620, 0639, 0650; 0717, 0746; 0825, 0839; 0917, 0925, 0950.
Marie then says, “I don't know when Claude's train arrives, but I'm sure that neither does
Jean."
Jean replies, “I didn't know his train, but now I do."
Marie responds, “Now I do as well!"
When is Claude's train and how do you know?
Answer:
0839
Step-by-step explanation:
First of all, let's cancel 0620 and 0746, because they dont have any other number that has the same last 2 digits as them. Jean would've immediately known the train number if it was one of these two.
Now, when Marie says "I'm sure that neither does Jean", it means she is guaranteed Jean doesn't know the train number. It mean she couldnt've gotten 06 or 07, as 0620 and 0746 have it.
We're left with 0825,0839,0917,0925 and 0950
When Jean replies he knows the train number, it means he couldnt've gotten 25, as it's repeated.
And when Marie responds she knows as well, she couldnt've gotten 09, as it's also repeated.
We can cancel 0825,0917,0925 and 0950
So, the train number is 0839
A B (2x + 53) 10. The figure shows a trapezium ABCD where AB // DC. Find the value of x and of y. D C x 5x² 2.237 A B 11. The figure shows a kite ABCD where AB = AD. RC - and the diagonals AC and BD intersect
Answer:
x = 30
y = 114
Step-by-step explanation:
considering DC || AB the sum of angle <D and angle <A must be equal to 180 because they are supplementary:
5x + x = 180 add like terms
6x = 180 divide both sides by 6
x = 30
Same goes for angle <C and angle <B:
y + 2.2x = 180 we know the value of x is 30
y + 2.2*30 = 180
y + 66 = 180 subtract 66 from both sides
y = 114
The data set shows the number of people who attended a concert over a period of 10 days.
12, 35, 27, 55, 22, 23, 60, 49, 15, 66
What is the mean of this data set?
Round the answer to the nearest tenth.
29.8
35.2
36.4
40.4
Answer:
40.4
Step-by-step explanation:
I took the test
Given Data set of people who attend the concert has a mean of 36.4.
What is the mean?the sum of the values by adding them all up. Divide the sum by the number of values in the data set is known as the mean.
Given The data set shows the number of people who attended a concert over a period of 10 days.
12, 35, 27, 55, 22, 23, 60, 49, 15, 66
the Sum of the given data set = 364
from the general formula of the mean
mean = (sum of data)/ number of data
Given the number of data = 10
Thus
Mean = 364 / 10
Mean = 36.4
therefore, the Mean of the given Data set is 36.4.
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Select the three equations that match the model.
9+?=14
?=14-9
9=14-?
all others do not work
Find the product of (x 5)(x − 5). X2 − 10x 25 x2 10x 25 x2 − 25 x2 25.
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x+5)(x-5) = x^2 - 25[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is obtained as:
[tex](x+5)(x-5) = x(x - 5) + 5(x - 5) \\\\(x+5)(x-5) = x^{1+1} - 5x + 5x - 25 = x^2 - 25[/tex]
Thus,
The product of [tex](x+5)(x-5) = x^2 - 25[/tex]
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In recent days, Rudy has worn a brown shirt on 5 days and shirts in other colors on 5 days. Considering this data, how many times would you expect Rudy to wear a brown shirt in the next 12 days?
Answer:
6
Step-by-step explanation:
5/10
1/2
then 6 trust me
Suppose the measure of <4 was 105º. Which
answer choice below represents is the measure of
<1?
A. 180°
B. 105°
C. 75°
D. 15°
Answer:
C
Step-by-step explanation:
Angle 1 and angle 4 sit on the same straight line which means
<1 + <4 = 180
We are given that <4 = 105 degrees. So the equation above becomes.
<1 + 105 = 180 Subtract 105 from both sides
<1 = 180 - 105
<1 = 75
Mr. McKinney is planning to purchase new carpet for his large family room. The dimensions of the room are shown in the diagram. How much carpet will he need?
Answer:
204 ft²
Step-by-step explanation:
Let's split the room to make it look like there are two squares.
We can make it to where one square is 14 ft long and 10 ft wide.
The other square can be 16 ft long and 4 ft wide
Find the areas of those two squares by multiplying width and length
14 x 10 = 140
16 x 4 = 64
Add those two together
140 + 64 = 204
Answer:
a
Step-by-step explanation: