Answer:
D
Step-by-step explanation:
(ax + b)² = c
step 1 : take square root of both sides
ax + b = ± [tex]\sqrt{c}[/tex]
step 2 : subtract b from both sides
ax = - b ± [tex]\sqrt{c}[/tex]
step 3 : divide both sides by a
x = - [tex]\frac{b}{a}[/tex] ± [tex]\frac{\sqrt{c} }{a}[/tex]
Answer:
D. Take the square root of both sides
Step-by-step explanation:
Given quadratic equation:
[tex](ax+b)^2=c[/tex]
To solve, square root both sides:
[tex]\implies \sqrt{(ax+b)^2}=\sqrt{c}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{n^2}=n, \quad \textsf{assuming }n \geq 0:[/tex]
[tex]\implies ax+b=\pm\sqrt{c}[/tex]
Subtract b from both sides:
[tex]\implies ax=-b\pm\sqrt{c}[/tex]
Divide both sides by a:
[tex]\implies x=\dfrac{-b\pm\sqrt{c}}{a}, \quad a\neq 0[/tex]
The perimeter of a triangle is 44cm. One side is 4cm shorter than the second side and twice as long as the third side. Find the length of each side of the triangle.
The 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
Given that the perimeter of the triangle is 44 cm.
Let us consider a side 's' which is 4 cm shorter than the second side.
That means the second side is 4 cm longer than s, hence the second side is s+4 cm in length.
We also have that the side of length s is of length twice as long as the third side.
Hence, the length of the third side is half that of s so, it is of length s/2.
Hence, at the end 44=s+(s+4)+(s/2)=s(2+1/2)+4
⇒ s(5/2)=40
⇒ s=8*2=16
So, the 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
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Given: AC BD and AC and BD bisect each other.
Prove: BE EC
1) [tex]\overline{AC} \cong \overline{BD}[/tex] and [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]ABCD[/tex] is a parallelogram (a quadrilateral with diagonals that bisect each other is a parallelogram)
3) [tex]ABCD[/tex] is a rhombus (a parallelgoram with congruent diagonals is a rhombus)
4) [tex]\overline{BE} \cong \overline{EC}[/tex] (halves of congruent segments are congruent)
how to get more brancells?
Answer:
Read books, watch documentaries, exercise, anything that benefits your body and mind
Step-by-step explanation:
can you help me with this. step by step
Answer:
B The vertex is at (2,2)
Or could possibly be
C the axis of symmetry is x=2
Lily read 3 books in 4 months. What was her rate of reading in books per month? Express your answer in simplest form.
HELP ASAP!!
What kind of compound inequality is
4x-5≥3
Or
5-x > 8
?
a. hole
b. intersection
c. conjunction
d. union
Answer: D) union
======================================================
Explanation:
Let's solve the first inequality for x.
4x-5 ≥ 3
4x ≥ 3+5
4x ≥ 8
x ≥ 8/4
x ≥ 2
Now solve the other inequality
5 - x > 8
5 > 8+x
8+x < 5
x < 5-8
x < -3
The two solutions we get are x < -3 or x ≥ 2
These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.
Either x is smaller than -3, OR it is 2 or larger
I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.
What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=1x:
a) stretch horizontally by a factor of 2
b) shift left 1 unit
c) shift up 3 units
The expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
How to determine the expression?The function is given as:
[tex]f(x) = \sqrt{x[/tex]
When the function is stretched horizontally by a factor of 2, the rule is:
f'(x) = f(x/2)
So, we have:
[tex]f'(x) = \sqrt{\frac x2[/tex]
When the function is shifted left by 1 unit, the rule is:
f"(x) = f(x + 1)
So, we have:
[tex]f"'(x) = \sqrt{\frac {x - 1}2[/tex]
When the function is shifted up by 3 units, the rule is:
g(x) = f"(x) + 3
So, we have:
[tex]g(x) = \sqrt{\frac {x - 1}2} + 3[/tex]
Hence, the expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
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In question 1, you found the squares of both positive and negative numbers. From the values you entered in the tables, what value or values can you substitute for x in x2 = 9 to make the equation true?
Answer:
x^2=9
so we find the sqare root of both sides
x=square root of 9
x=-3 or 3
Hope This Helps!!!
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate (in ft/min) is the height of the pile changing when the pile is 2 feet high
The rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min. Computed using differentiation.
The sand is falling onto a conical pile, thus we get the pile in the shape of a cone, whose volume is given as:
V = (1/3)πr²h,
where V represents the volume of the cone, r represents its radius, and h represents its height.
In the question, we are given that the rate of piling is 16 ft.³/min, which implies that:
dV/dt = 16 ... (i)
We are also given that the diameter is three times the altitude (height), which can be shown as:
2r = 3h,
or, r = (3/2)h.
Thus, the volume can now be shown as:
V = (1/3)π{(3/2)h}²h,
or, V = (3πh³)/4.
Differentiating this with respect to time, we get:
dV/dt = (3π/4)(3h²)dh/dt.
Now, we need to calculate the rate of change of height, when the height is 2 feet, thus we take h = 2
Using dV/dt = 16 from (i), we can write:
16 = (3π/4)(3(2)²)dh/dt.,
or, 16 = 9π(dh/dt),
or, dh/dt = 16/9π = 0.5659 ft./min.
Thus, the rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min.
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subtract 6x 2 −7x−2 from 6x^{2}-2x+6
Answer:
5x+8
Step-by-step explanation:
The from is the key word
That means the second term is first
6x^2 -2x +6 - (6x^2 -7x -2)
Distribute the minus sign
6x^2 -2x +6 - 6x^2 +7x +2
Combine like terms
5x+8
state the domain and range of the following relation
x^2+y^2=16
The domain and range is [-4, 4] and [0, 4]
What is Domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
x² + y² = 16
y = √16 - x²
For domain under root should not be negative quantity,
16 - x²≥0
16≥x²
So, x≤4 or x≥4
Thus, the domain is [-4, 4]
Range:
y is maximum at x=0, y=4
y is minimum at x=4, y=0
Thus, range = [0, 4]
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find the slope of a line passing through the points A(-2,-7) and B(-2,2)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find the slope of a line passing through (-2,-7) and (-2,2)
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\boxed{\begin{minipage}{6cm} To find the slope, \\ we use the formula below.\end{minipage}}[/tex]
[tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex] | put in the values
[tex]\bf{\dfrac{2-(-7)}{-2-(-2)}}[/tex] | look what happens when I simplify!
[tex]\bf{\dfrac{2+7}{-2+2}}[/tex] | uh-oh
[tex]\bf{\dfrac{9}{0}}[/tex] ...
The operation above is an operation we can't do.
[tex]\bf{Slope=\;Not\;D e f ined}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope=Not\;De fined}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
What is the main benefit of building a connection with your community
Answer: Being connected means greater opportunities to learn from each other, mine each other's wisdom, and help each other thrive. Connecting. By being more closely interconnected, each member of the community is able to enjoy a wider, richer network of resources, wisdom, connections, and support.
There are 10 circles and 6 squares. What is the simplest ratio of squares to total
shapes?
Answer:
The simplest ratio would be 5:3
Step-by-step explanation:
Both 10 and 6 can be divided by 2.
They turn into 5 and 3.
Since you can't make 5 and 3 any smaller, this will be the answer.
5:3
Hope this helped! :D
The dot plots below show the ages of students belonging to two groups of painting classes:
Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer. (10 points)
On the base of visual inspection , it can be said that the Group A has an average lower than the Group B
What is a Dot Plot ?It is the simple form of data visualization , in which the frequency of a data is marked as dots on x and y axis.
The dot plot is given for two groups of 30 people , who go to painting class.
It has been asked that which group most likely has a lower mean age of painting students .
On the base of visual inspection , it can be said that the Group A has an average lower than the Group B
It can be said so as the dots are highest at the age of 19 in Group A , and the whole distribution lies between 9 to 19 age of people ,
while in Group B the age of the people is wide distributed and therefore the average age will be more ,
By calculation it is proved that the average age of Group A is 15.967
and the average age of Group B is 19.7.
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if nm = 8x - 14 and jk = x squared + 1, find JK
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The length of Jk can be either 10 or 26.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Since in a rectangle the opposite sides are equal, therefore, the sides NM and JK will be equal.
JK = MN
8x - 14 = x² + 1
0 = x² - 8x + 15
x = 5, 3
Hence, the length of Jk can be either 10 or 26.
The complete questions are:
Quadrilateral JKMN is a rectangle, if NM= 8x - 14 and JK= x squared + 1, find JK.
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A triangle with side lengths of 5 meters, 7 meters and 9 meters.
Answer:
obtuse triangleStep-by-step explanation:
A triangle with side lengths of 5 meters, 7 meters and 9 meters is
an obtuse triangle
17.
Lincoln stands on the top of a building and fires a gun upwards. The bullet travels
according to the equation h = -16t² + 384t + 50, where h is the height of the bullet off
the ground in metres at t seconds after it was fired.
a) How far is Lincoln above the ground when he shoots the gun?
b)How high does the bullet travel vertically relative to the ground?
c)How long does it take the bullet to reach its greatest height?
d)After how many seconds (round to nearest 100th) does the bullet hit the ground?
please help asap!
Answer:
a) 50 meters
b) 2354 meters
c) 12 seconds
d) 24.13 seconds
Step-by-step explanation:
Hello!
a) How far is Lincoln above the ground when he shoots the gun?We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.
Equation: [tex]h = -16t^2 + 384t + 50[/tex]
Plug in 0 for t:
[tex]h = -16t^2 + 384t + 50[/tex][tex]h = -16(0)^2 + 384(0) + 50[/tex][tex]h = 50[/tex]The height at which Lincoln shot the bullet is 50 meters.
We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.
Standard form of a Parabola: [tex]y = ax^2 + bx + c[/tex]
The y-intercept is the "c" value.
Given our equation: [tex]h = -16t^2 + 384t + 50[/tex]
The c-value is 50. This proves that the y-intercept is 50.
b)How high does the bullet travel vertically relative to the ground?We want to find the highest point of the graph. To do that, we can find the vertex.
We can utilize the Axis of Symmetry (AOS) to find the Vertex.
First, find the AOS using the formula: [tex]AOS = -\frac{b}{2a}[/tex]
a = -16b = 384Plug it into the formula:
[tex]AOS = -\frac{b}{2a}[/tex][tex]AOS = -\frac{384}{2(-16)}[/tex][tex]AOS = \frac{384}{32}[/tex][tex]AOS = 12[/tex]Plug in 12 for t in the equation:
[tex]h = -16t^2 + 384t + 50[/tex][tex]h = -16(12)^2 + 384(12) + 50[/tex][tex]h = -2304 + 4608 + 50[/tex][tex]h = 2304+50[/tex][tex]h = 2354[/tex]Therefore, the highest point of the bullet is 2354 meters.
c)How long does it take the bullet to reach its greatest height?We answered this in the last question. The t-value when h is at its highest is 12.
d)After how many seconds (round to nearest 100th) does the bullet hit the ground?We have to solve for the values of t when h is 0 (when it touches the ground).
Set the equation to 0, and solve using the quadratic formula.
Quadratic formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-384\pm\sqrt{384^2 - 4(-16)(50)}}{2(-16)}[/tex][tex]x = \frac{-384\pm\sqrt{147456 +3200}}{-32}[/tex][tex]x = \frac{-384\pm\sqrt{150656}}{-32}[/tex][tex]x = \frac{-384\pm388.14}{-32}[/tex][tex]x = -\frac{4.14}{32}, x = \frac{772.14}{32}[/tex]We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.
[tex]x = \frac{772.14}{32}[/tex][tex]x = 24.13[/tex]It takes approximately 24.13 seconds for the bullet to hit the ground.
Can someone please help me with this?
Answer: -5
Step-by-step explanation:
When x = 8, y = -5.
Try It #2
Use function notation to express the weight of a pig in pounds as a function of its age in days d.
Based on the weight of the pig and the age in days, the function notation would be w = f (d).
What function expresses the pig's weight in days old?The function will take the form of:
y = f(x)
y will be the weight and x will be the age of the pig in days.
The function would therefore be:
w = f (d)
In conclusion, the function notation to express the pig's weight is w = f (d).
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Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.
No, it isn't true that blending problems arise when one must decide which of two or more ingredients is to be chosen to provide a product.
Given sentence "Blending problems ...............................supply a product."
We have to answer whether the given sentence is true or false.
We can say that the given sentence is fake. the sole objective functions allowed for applied math problems maximizing profits and minimizing costs.
Blinding problems are a typical application of mixed integer applied mathematics. They involve blending several resources or materials to make one or more products similar to a requirement. Mixed integer linear programs are linear problems during which some variables are required to require integer values.
Hence the given statement is fake regarding arise of blending problems.
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Question is incomplete because it should includes:
State whether the statement is true or false.
Which equation matches the statement below?
Three times the difference of a number "n" and five is sixteen more than double the number "r
O 3(5-n)=2n+16
O 3(n-5)=16+2n
3(n-5)=2n+16
3n-5=2n+16
Answer:
3(n-5)=2n+16
Step-by-step explanation:
3 lots of 'n' and 5 means 3 times both values so these values are put into a bracket with a common multiplier (ie. the 3)
3(5 - n)
16 more than 2 lots of 'n' means that n has to be doubled. n + n = 2n. add 16 to this and we have
2n + 16
if these values are both equal (hence why they are in an equation) then all that is needed is for them to be set equal alongside each other.
3(n-5) = 2n+16
:)
What is the value of x for these problems? Pls help I’m so desperate
Answer:
First Question x = [tex]17\sqrt{2}[/tex] Second Question x = 36
Step-by-step explanation:
First Question:
Since The triangle is isosceles, [tex]17^2 +17^2=x^2[/tex] (Pythagoras)
[tex]x=17\sqrt{2}[/tex]
Second Question
This is half an equilateral triangle, so [tex](\frac{1}{2}x)^2+(18\sqrt{3})^2=x^2[/tex]
[tex]\frac{3}{4}x^2=972[/tex]
[tex]x^2=1296[/tex]
[tex]x=36[/tex] (cannot be negative)
A kennel has 3 black puppies and 4 brown puppies. If someone is randomly choosing puppies, what is the probability they choose a black and a brown puppy?
A)0.2449
B)0.2857
C)0.7846
D)0.5
The probability they choose a black and a brown puppy is 0.2857 (option B)
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability they choose a black and a brown puppy = (number of black puppies / total number of puppies) x ( (number of brown puppies / total number of puppies - 1)
3/7 x 4/6 = 0.2857
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The total surface area of this cuboid is 112^2
Find the value of x
length = 10cm
width = 2cm
Hight = x
The value of x is 3
How to solve for x?The given parameters are:
Length = 10cm
width = 2cm
Height = x
The surface area is calculated as;
Area = 2 *(lw + lh + wh)
So, we have:
2 * (10 * 2 + 2x + 10x) = 112
Evaluate the like terms and divide by 2
20 + 12x = 56
Subtract 20 from both sides
12x = 36
Divide by 12
x = 3
hence, the value of x is 3
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Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area
(angle of sector ) p2
360
Sector Area = [?] cm2
Round to four decimal places.
The area of the sector rounded to 4 decimal place is 78.6396 cm²
How to find the area of a sector?area of sector = ∅/ 360 × πr²
Therefore,
r = radius∅ = 46 degrees.Hence,
area of a sector = 46 / 360 × 3.14 × 14²
area of a sector = 46 / 360 × 3.14 × 196
area of a sector = 46 / 360 × 615.44
area of a sector = 28310.24 / 360
area of a sector = 78.6395555556
Hence,
area of a sector = 78.6396 cm²
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Match the concept with its definition and characteristics. i. A set of instructions (codes) that perform a specific task. ii. A calculation where the result is placed into a variable. iii. The computer programming equivalent of a recipe in cooking iv. A formula to calculate a new value based on other values and operations.
1. Algorithm 2. Expression 3. Equation
First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.
Given four definitions of equation, expression, algorithm but mixed.
We have to match the definitions with appropriate term.
We know that expression is a combination of numbers, symbols, fraction, coefficients, indeterminants mostly not found in equal to form. It exhibits a behaviour only.
Algorithm is a computer programming to do a specific task in a predetermined way.
Equation is a relationship between two variables expressed in equal to form. In this we have to put the value of variables and the equation gives us a value.
Hence First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.
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Gotta need answers fast like asap, it’s geometry, just fill the blanks pls
Two or more triangles are said to be congruent if and only if they have equal lengths of sides and equal measures of angles.
Thus, the required proof is as shown below:
STATEMENTS REASONS
1. ΔABC and ΔDEC with AB ≅ DE;
BC ≅ EC; <1 ≅ <2 Given
2. <1 and < ABC; < 2 and <DEC are sup Sum of angles on a straight line
3. <ABC ≅ <DEC Congruent angles of similar triangles
4. ∴ΔABC ≅ ΔDEC Side-Angle-Side (SAS) postulate
5. ∴<ACB ≅ <DCE CPCTC postulate
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A line passes through the two points (0, -2) and (9, 1). what is the y y -coordinate of the point on this line whose x x -coordinate is 12? a. -6 b. 0 c. 2 d. 4
Answer: 2
Step-by-step explanation:
The slope of the line is
[tex]\frac{-2-1}{0-9}=\frac{1}{3}[/tex]
So, the equation of the line is [tex]y=\frac{1}{3}x-2[/tex].
Substituting in x=12,
[tex]y=\frac{1}{3}(12)-2=2[/tex]
Slope BC and DE are both -0.4 what is their relationship