To make x² + 6x = 7 a perfect square, we add 16 to the equation.
In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.
The given equation can be shown as:
x² + 6x = 7,
or, x² + 6x - 7 = 0.
To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.
This can be shown as:
x² + 6x - 7 = 0,
or, x² + 2(x)(3) - 7 = 0, where we get b = 3.
Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.
Thus, we add 16 to both sides of the equation, to get:
x² + 2(x)(3) - 7 + 16 = 16,
or, x² + 2(x)(3) + 9 = 16,
or, (x + 3)² = 16, which gives us the required perfect square.
Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.
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Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value of p
Answer:
p = 7
Step-by-step explanation:
(x² + px - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms
= 3x³ +x²(3p - 5) - x(5p + 9) + 15
given the coefficient of the x- term is - 44 , then
-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion
- 5p - 9 = - 44 ( add 9 to both sides )
- 5p = - 35 ( divide both sides by - 5 )
p = 7
During a pumpkin launching contest, two pumpkins are launched at the same time. the path of pumpkin a is modeled by the equation y = –0.01x2 0.32x 4. the path of pumpkin b is modeled by the equation y = –0.01x2 0.18x 5. if x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?
The distance at which pumpkins are the same height.
What do you mean by X and Y coordinates?
The X and Y coordinates are an address that help locate a point in two dimensions of space. The coordinates (x, y) are used to represent any point in the coordinate plane. The x value indicates the point's position in regard to the x-axis, and the y value indicates its position in relation to the y-axis.
SolutionBoth equations' graphs would be at an intersection, which would indicate that their x and y coordinates are identical. The same y coordinate would indicate being at the same height at that precise distance since y refers to the pumpkin's height.
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Answer:
D). the horizontal distance of the pumpkins from the launch site when their heights are the same
Step-by-step explanation:
I took the flipping test nickle
Which equation represents a direct variation?
A.y = 0.5 x
B.x minus y = 5
C.x y = 5
D.y = x + 5
Answer:
A.
Step-by-step explanation:
i'm 99% sure
Answer:
A. y = 0.5x
Step-by-step explanation:
i got it right
Find the fifth term of the sequence.
a) Substituting in n = 2,
[tex]\frac{3(2)^{2}}{2}=6[/tex]
b) Substituting in n = 5,
[tex]\frac{3(5)^{2}}{2}=\frac{75}{2}[/tex]
c) Setting the nth term to be greater than 50,
[tex]\frac{3n^{2}}{2}>50 \\ \\ n^{2} >\frac{100}{3} \\ \\ n>\frac{10}{\sqrt{3}} \\ \\ \lceil n \rceil = 6[/tex]
QUICK HELP PLSSSS
which shape is the cross section of a square pyramid
Answer:
B
Step-by-step explanation:
when a square pyramid is cross sectioned the shape that will appear is the same as that of the base
A right-angled triangle has a hypotenuse of length 8 and another side of length 3.
Find the length of the unknown side g.
Write each step of working as an equation and give the answer to two decimal places
Answer:
The file contains the solution to the above question
a bag of apples and oranges contains twice as many apples as oranges. if there are 15 total pieces of fruit in the bag how many apples are in the bag
Considering the definition of an equation and the way to solve it, there are 10 apples in the bag.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of apples in the bagBeing "or" the number of oranges in the bag, and knowing that:
A bag of apples and oranges contains twice as many apples as oranges.There are 15 total pieces of fruit in the bag.the equation in this case is:
or + apples= 15
or + 2or= 15
Solving:
3or= 15
or= 15 ÷ 3
or= 5
As a bag of apples and oranges contains twice as many apples as oranges, then 2or= 2×5= 10 apples
Finally, there are 10 apples in the bag.
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The product of two powers is 11^8 and their quotient is 11². What are the two powers? Explain.
Answer:
The powers are 3 and 5.
Step-by-step explanation:
When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:
11^a * 11^b = 11^(a+b)
11^a/ 11^b = 11^(a-b)
So, from the information given:
a + b = 8
a - b = 2 Adding:-
2a = 10
a = 5.
and substituting in the second equation
5 - b = 2
b = 3.
A walking path across a park is represented by the equation y=-3x - 3. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 6). Identify the equation that represents the new path.
OA. y=-3x-6
O B. y=x+7
OC. y=3x+15
O D. y=-x+5
166
10
MAR
FREN
10-
10-
10
Answer:
y = (1/3)x + 7
Step-by-step explanation:
The general structure form of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.
The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.
m = 1/3
x = -3
y = 6
y = mx + b <----- Slope-intercept form
6 = (-3)(1/3) + b <----- Insert values
6 = -1 + b <----- Multiply -3 and 1/3
7 = b <----- Add 1 to both sides
Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.
y = (1/3)x + 7
What is the equation of the translated function, g(x), if f(x) = x2?
a.) g(x) = (x – 4)2 + 6
b.) g(x) = (x + 6)2 – 4
c.) g(x) = (x – 6)2 – 4
d.) g(x) = (x + 4)2 + 6
Answer: dfghj
Step-by-step explanation: xcfvghj
Answer: It's D
Step-by-step explanation:
Right on edge 2022
A square has an area of 49 square inches. how long are its sides
Answer:
Step-by-step explanation:
We know that,
Area of a square = l^2
so in this case, we form an equation:
l^2=49 square inches
Now taking square root on both sides
[tex]\sqrt{l}[/tex]^2=[tex]\sqrt{49}[/tex]
l=7 inches
so each side is 7 inches
Hope that helps
Answer:
7 inStep-by-step explanation:
A square has an area of 49 square inches. how long are its sides
A = l²
inverse formula
l = √A
l = √49
l = 7 in
Apply the distributive property to factor out the greatest common factor 15+21
Maria is creating a round stained glass window like the one below. She needs to cut the dark pink glass to the correct size to fit into the frame. At what angle (x) should she cut the glass so that it fits if she knows the arc measure of a is 35º and the arc measure of b is 45º. What does x equal?
Applying the angle of intersecting chords theorem, the value of x is: 40º.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem the following equation is true:
x = 1/2(a + b).
Given the following:
a = 35º
b = 45º
Plug in the values
x = 1/2(35 + 45)
x = 1/2(80)
x = 40º
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Identify m∠EFH.
The figure shows triangle G F H. Angle G is equal to 76 degrees. A measure of angle H is given by the formula 3 times x minus 3 degrees. Side G F lies on ray G F with endpoint G. Angle H F E is an exterior angle and its measure is given by the formula 8 times x plus 8 degrees.
Based on the calculations, the magnitude of m∠EFH is equal to 112°.
How to find the magnitude of m∠EFH?In Geometry, the sum of two (2) non-adjacent interior angles in a triangle is equal to its exterior angle. Thus, we have:
(3x - 3) + 76 = 8x + 8
3x + 73 = 8x + 8
73 - 8 = 8x - 3x
65 = 5x
x = 65/5
x = 13.
From triangle GFH, we have:
m∠EFH = ∠F = 8x + 8
m∠EFH = 8 (13) + 8
m∠EFH = 104 + 8
m∠EFH = 112°.
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What three-dimensional object would be generated by the rotation of the semi circle about the x axis ?
If a semicircle is rotated about the x axis of the graph then the resulting three dimensional shape will be a sphere.
Given a semicircle on a graph.
A semicircle is a half circle .A sphere is a geometrical object that is a three dimensional shape , It is the set of points that are all at the same distance r from given point in three dimensional shape.
Rotation is basically an action of rotating around an object or an axis.
If a semicircle is rotated about x axis then the resulting figure will be a sphere. This is because of the fact that when the semi circle is rotated about the x axis then all the points will be at equal distance in all directions from the center.
Hence if a semicircle is rotated about x axis then the resulting figure will be a sphere.
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Match the vocabulary word with the correct definition.
1. a line segment where two faces meet
edge
2. a three-dimensional figure with one circular base
dimensions
3. to separate something into its basic parts
area
4. units used to measure the volume of a three-dimensional figure
cube
5. a three-dimensional figure with two parallel, congruent, circular bases and a curved surface
decompose
6. a three-dimensional figure made of six congruent squares
composite figure
7. a geometric figure that is made up of two or more basic shapes
base
8. the length of a plane figure; or, a special face of a solid figures
cone
9. the measurement of the space inside a plane figure
cylinder
10. measurements indicating the size and shape of an object, such as length and width
cubic units
Answer:
1. edge
2. cone
3. decompose
4. cubic units
5. cylinder
6. cube
7. composite figure
8. base
9. area
10. dimensions
CSN SOMEONE PLEASE HELP ASAP
If the ADA guidelines state that a
wheelchair ramps angle of elevation
must equal 4.8°. would a
ramp with the
following dimensions be up to code?
Show your work and explain. (Picture is
not drawn to scale.)
3.5 ft
e°
40 ft
The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
How to find the angle of elevation of the ramp?The angle of elevation of the ramp can be found using trigonometric ratios.
Therefore, the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .
Hence,
tan ∅ = opposite / adjacent
opposite side = 3.5 ft
adjacent side = 40 ft
Therefore,
tan ∅ = 3.5 / 40
∅ = tan ⁻¹ 0.0875
∅ = 5.00064459756
∅ = 5 degrees
Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
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Find the polar coordinates in radians from the given rectangular coordinates (-11, -3).
the polar coordinates are:
(√130, 285.3°)
How to find the polar coordinates?For rectangular coordinates (x, y), the polar coordinates are:
[tex]R = \sqrt{x^2 + y^2}[/tex]
For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:
θ = arctan(y/x) + 270°
In this case, we have:
x = -11
y = -3
Then:
[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]
Then the polar coordinates are:
(√130, 285.3°)
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Comparing Ratios Using Fractions
Compare 4:10 and 12:20 using fractions. Which ratio is
smaller? How do you know?
Answer:
4:10
Step-by-step explanation:
4:10 = 4/10 = 2/5
12:20 = 12/20 = 6/10 = 3/5.
So 4:10 is smaller than 12:20 because 2/5 is less than 3/5.
Answer:
4:10
Step-by-step explanation:
First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.
In algebra, we transfer these same skills to expressions involving variables. what elementary skills have you used so far in this course, and how have you extended them?
A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. what is the value of the quantity after 1.2 minutes, to the nearest hundredth?
The value of the quantity after 1.2 minutes, to the nearest hundredth, is 313.56
What is the calculated quantity?A quantity is a measurable attribute of a particular thing or group of objects. One quantity might be more than, less than, or equal to another quantity when comparing them. Quantity is a notion that is used frequently in both mathematics and the sciences.
A quantity cannot be a property that cannot be compared. The conventional format for presenting a quantity is as the product of a magnitude and a unit.
According to the question,
Initial value of the quantity=310
Rate of growth= 8.5% per second
Value of the quantity after 1.2 minutes,
=[tex]310(1+\frac{8.5}{100}) ^{1.2*60}[/tex]
=[tex]310(\frac{108.5}{100})^{72}[/tex]
=313.56
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Answer:
141008.06
Step-by-step explanation:
cannonball is shot into the air. its height can be described by the equation h = -5t2 + 40t, where h is the height in feet and t is the time is seconds. when will the cannonball hit the ground?
Answer:
Step-by-step explanation:
hello :
the cannonball hit the ground when h=0
-5t² + 40t=0 means : -5t(t- 8)=0
t=8
Two random samples were done to determine how often people in a community go to the dentist. the first sample surveyed 10 people as they entered their workplaces. the first sample found that the mean time between visits to the dentist was 7.5 months. the second sample surveyed 50 people as they entered the local grocery store. the second sample found that the mean time between visits to the dentist was 18.1 months. which statements are true? check all that apply. the first sample is likely to be more representative of the population. the second sample is likely to be more representative of the population. the second sample will give a better representation because it is larger. the first sample is not biased. community members probably visit the dentist about once every 18 months.
Answer:
B, C and E
Step-by-step explanation:
If a person stands 40 ft from a tree and the angle of elevation made from their eyes (5 ft above the ground) to the top of the tree is 47°, how tall is the tree? Round your answer to the nearest foot.
Using the given information, the height of the tree is 48 ft
TrigonometryFrom the question, we are to determine the height of the tree
In the given diagram, the height of the tree is (x + 5) feet
First, we will determine the value of x
tan 47° = x / 40
x = 40 × tan47°
x = 42.89 ft
∴ The height of the tree = (42.89 + 5) ft
Height of the tree = 47.89 ft
Height of the tree ≈ 48 ft
Hence, the height of the tree is 48 ft.
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What is one possible value of the
y-intercept of the line passing
through the point (2, 2) and in
between the points (4, 4) and (6, 4)?
Select the correct answer
The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is xfeet, which equation models
this situation?
A 6x²+x-12=0
B. 6x²+x -13=0
C 6x²+x-26=0
D. 36x² +6x-26= 0
Answer:
Step-by-step explanation:
The area for a triangle is
[tex]A=\frac{1}{2}bh[/tex]
Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:
[tex]13=\frac{1}{2} (6x+1)(x)[/tex]
We can get rid of the denominator of 2 by multiplying it on both sides to get:
[tex]26=(6x+1)(x)[/tex] and simplifying a bit:
[tex]26=6x^2+x[/tex]
Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:
[tex]6x^2+x-26=0[/tex] which is choice C
Please help me ASAP!! I really appreciate it
Answer:
a = -1
Step-by-step explanation:
1. Subtract [tex]\frac{2}{3}[/tex] from both sides.
[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]
2. Solve the side after the equal sign.
[tex]6a=-6[/tex]
3. Divide 6 from both sides.
[tex]a=-1[/tex]
4. Hope this helped!
[tex]:)[/tex]
If a school opens at 10 am and closes at 3.30pm. if the lunch interval is of 30 minutes, find the ratio of lunch interval to the total times of class periods.
The ratio of lunch interval to the total times of class periods is 1:10
Given that timing of school opens is 10am , the timing of school closes is 3:30pm and the lunch interval is 30 minutes
We need to find the ratio of lunch interval to the total times of class periods.
Now,
Timing of a school(10.a.mto3.30p.m)=5hours30minutes
Timing for lunch interval=30minutes
Total time of the class periods=5hours30minutes−30minutes
=5hours
=60×5=300 minutes.
Ratio of lunch interval to total time of the class period=30minutes:300 minutes=1:10
Hence the ratio of lunch interval to the total times of class periods is 1:10
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find the area of the diagram
Answer:
13500 ft²
Step-by-step explanation:
Area of rectangle:We can find the width of the rectangle using Pythagorean theorem.
AD² + DC² = AC²
180² + DC² = 195²
32400 + DC² = 38025
DC² = 38025 - 32400
= 5625
DC = √5625
= 75 ft
length = 75 ft
Width = 180 ft
[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]
= 75 * 180
= 13500 ft²
The function f(x) = (0.2)x
O increases for x > 0
O increases for all x
O decreases for all x
O decreases for x > 0
Answer:
Option (3)
Step-by-step explanation:
Since the base of the exponential is less than 1, the function is decreasing for all x.