Answer:
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
[tex]x = - \frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
The solutions of the given quadratic equation are real and equal.
Step-by-step explanation:
The given quadratic equation is
[tex]4x^2+12x+9 = 0[/tex]
The coefficients a, b and c are as follow:
[tex]a = 4 \\\\b = 12\\\\c = 9[/tex]
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
Bonus:
The solution of this quadratic equation is given by
[tex]x=\frac{-12\pm\sqrt{(144 - 144)}}{8} \\\\x=\frac{-12\pm\sqrt{0}}{8} \\\\x=\frac{-12\pm 0}{8} \\\\x=\frac{-12 + 0}{8} \: and \: x=\frac{-12 - 0}{8}\\\\x= -\frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
Therefore, the solutions of the given quadratic equation are real and equal.
Pencils are sold in boxes of 10 Erasers are sold in boxes of 14 A teacher wants to buy the same number of pencils and erasers work out the smallest number of boxes of each item she should buy
Answer:
7 boxes of pencils and 5 boxes of erasers.
Step-by-step explanation:
The least common denominator of these two numbers are 70. 7×10 and 14×5. So she is purchasing the same quantity of both.
(x-2)^2 + (y-3)^2=25 up 2units
[tex](x-2)^2+(y-3)^2=25[/tex]
We are given this equation. The equation of a circle with radius r and center (h,k) takes the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center of the circle in the given equation is (2,3). Up 2 units would increase the y-value of the center by 2.
Thus, the center of the new circle will be (2,5). Putting this new center into the equation gives us:
[tex](x-2)^2+(y-5)^2=25[/tex]
Let me know if you need any clarifications, thanks~!
Select the correct answer. Simplify the expression. What classification describes the resulting polynomial? (3x2 − 11x − 4) − (2x2 − x − 6) A. quadratic trinomial B. linear binomial C. quadratic binomial D. linear monomial
Answer:
A : quadratic trinomial
Step-by-step explanation:
Given
(3x² - 11x - 4) - (2x² - x - 6)
Distribute both parenthesis, noting the second is distributed by - 1
= 3x² - 11x - 4 - 2x² + x + 6 ← collect like terms
= x² - 10x + 2 ← this is a quadratic with 3 terms, thus quadratic trinomial → A
Hope helped.. Mark BRAINLIEST
Thanks!!
Answer:
A. quadratic trinomial
Step-by-step explanation:
[tex](3x^2-11x-4)-(2x^2-x-6)[/tex]
Remember that polynomials are closed to subtraction, therefore, linear binomial and linear monomial can't be an option.
[tex]3x^2-11x-4-2x^2+x+6[/tex]
[tex]x^2-10x+2[/tex]
We got a quadratic equation. Once it has the c term, it is a quadratic trinomial.
WILL GIVE BRAINLIEST
find the value of r so that the line passes through the points (10, r) and (4, -3) and has the slope of 4/3
Answer:
r=9⅓
Step-by-step explanation:
(10,r). (4,-3)
(x¹,y¹) (x²,y²)
gradient=y²-y¹
x²-x¹
4= -3-r
3 4-10
multiply both sides by 3(4-10)to remove the denominators.
3(4-10)× 4 = -3-r ×3(4-10)
3 4-10
(4-10)×4= (3-r)×3
16-40=9-3r
put the liketerms together
note* signs(- +) change when they cross the equal sign(=)
3r=4+40-16
3r=28
divide both sides by 3
r=28/3.
r=9⅓
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items? y squared = 4 x squared minus 100 y = negative x squared + 50 x minus 300 x = negative y squared minus 400 x squared = negative 6 y squared + 200
Answer:
B. y= -x^2+50x-300
Step-by-step explanation:
A. y^2=4x^2-100
B. y= -x^2+50x-300
C. x=-y^2-400
D. x^2=-6y^2+200
we are to find profits (y) when the company sells x items
Option A can be used to calculate the profit (y) squared
Option B can be used to calculate profits (y)
Option C can be used to calculate items sold(x)
Option D can be used to calculate items sold squared(x^2)
We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B
Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is
B. y= -x^2+50x-300
the amplitude of the graph is the midline is y =
Answer:
Amplitude of 2, midline is y=4
Answer:
y=4.
Step-by-step explanation:
I hope this helps!
The graph of y=√X is translated 3 units to the right and slid 5 unitsdown, what would be the resulting equation?
Answer: [tex]y=\sqrt{x-3}-5[/tex]
Step-by-step explanation:
The vertex form of a square root equation is: [tex]y=a\sqrt{x-h}+k[/tex] where
a is the vertical stretchh is the horizontal shift (positive is right, negative is left)k is the vertical shift (positive is up, negative is down)Input: h = 3 (3 units right) and k = -5 (5 units down) into the vertex form:
[tex]y=\sqrt{x-(3)}+(-5)\\\\y=\sqrt{x-3}-5[/tex]
The resulting equation is: [tex]h(x) = \sqrt{x - 3} - 5[/tex]
-------------------------------
This question is solved using the translation concept.
Translating a function f(x) a units to the right is the same as finding f(x - a).Translating a function f(x) a units down is the same as finding f(x) - a.-------------------------------
Original function:
[tex]f(x) = \sqrt{x}[/tex]
-------------------------------
Translated 3 units to the right
This is f(x - 3), so:
[tex]g(x) = f(x - 3) = \sqrt{x - 3}[/tex]
-------------------------------
Translating 5 units down
This is g(x) - 5, so:
[tex]h(x) = g(x) - 5 = \sqrt{x - 3} - 5[/tex]
Which is the resulting equation.
The image at the end of this answer compared the graph of the original function, in red, with the translated, in blue.
A similar question is given at https://brainly.com/question/23630829.
3 ( 1 - 20 ) + 10 = 4
Answer:
3(1 - 20) + 10 = 4
3 * (-19) + 10 = 4
-57 + 10 = 4
-47 = 4
Since the two are not equal, this statement is false/invalid.
Hope this helps!
HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture included)
Answer:
Option (D)
Step-by-step explanation:
In the given triangle ABC,
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
72° + 85° + m∠C = 180°
m∠C = 180 - 157
m∠C = 23°
By applying Sine rule in the triangle,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302[/tex]
[tex]\frac{\text{Sin72}}{a}=0.06302[/tex]
a = [tex]\frac{\text{Sin72}}{0.06302}[/tex] = 15.09
[tex]\frac{\text{Sin85}}{b}=0.06302[/tex]
b = [tex]\frac{\text{Sin85}}{0.06302}[/tex]
b = 15.81
Therefore, option (D) will be the answer.
U
480
S
d
T
b
R.
C
P
1549
Q
Answer:
a = 26°
b = 48°
c = 26°
d = 106°
a culinary student decorates a 8-in. -diameter round cake. What is the approximate are of the top of the cake?
Answer:
The top of the cake is 25.12 in²
Step-by-step explanation:
Hello!
So you are dealing with a circumference question! And because the diameter is 2x the radius, we know the radius is actually 4.
Lets write out the circumference formula and use that to help us.
c = 2[tex]\\\pi[/tex] x r
pi is 3.14....
But lets use 3.14
c = 2(3.14) x 4
Plus this into a calculator and we get 25.12 as the answer.
Answer:
≈50.265 [tex]in^{2}[/tex]
Step-by-step explanation:
You first have to find the radius since the formula for the area of a circle is A=[tex]\pi r^{2}[/tex].
Since the radius is half the diameter, just divide 8 by 2 which will give you 4.
r=4
Now plug in the radius into the formula and simplify.
A=[tex]\pi 4^{2}[/tex]
[tex]A=\pi 16[/tex]
≈50.265 [tex]in^{2}[/tex]
Find the value of x if 12x=34^2 - 26^2
Answer:
[tex]\boxed{\sf x =40}[/tex]
Step-by-step explanation:
[tex]\sf 12x=34^2 - 26^2[/tex]
Solve the square.
[tex]\sf 12x=1156-676[/tex]
[tex]\sf 12x=480[/tex]
Divide both sides by 12.
[tex]\displaystyle \sf \frac{12x}{12} =\frac{480}{12}[/tex]
[tex]\sf x =40[/tex]
f(x) = (x + 1)2
What is the domain of f?
Choose 1 answer:
All real values of x such that x = -1
All real values of such that > -1
All real values of x such that I + 0
All real values of x such that 2 > 0
غم عصتلحينلحصعالم
Answer:
all real numbers
Step-by-step explanation:
f(x) = (x + 1)^2
There is no restriction on x, so the domain is:
all real numbers
Hey loves!!! This is my last question(for now).Please help.
Answer:
35 degrees.
Step-by-step explanation:
m < TSK = 180 - 22 - 123
= 180 - 145
= 35.
Tia measured the daily high temperature in Kats, Colorado for each of the 30 days in April. She then created both a dot plot and a box plot to display the same data (both diagrams are shown below). Which display can be used to find how many days had a high temperature above 15∘ C15, degrees, start text, C, end text
*see attachment below showing the dot plot and box plot created by Tia
Answer:
Dot plot
Step-by-step explanation:
In a dot plot, the temperature of a day is represented by 1 dot. There are 30 dots on the box plot shown in the attachment that was made by Tia.
This dot plot display makes it easier to find how many days had a temperature that is higher than 15°.
Thus, from the dot plot, we have:
2 dots representing 2 days having a temperature of 16°C each
2 days also have daily temperature of 17°C
2 days have temperature of 18°C as well, and
1 day has temperature of 19° C.
Therefore, the number of days that had a temperature above 15°C is 7 days.
Answer:
Dot Plot, Box Plot
Step-by-step explanation:
I got the other guy's answer wrong but mine is right =)
What is the equation of a line that is parallel to y=2/3x+4 and passes through the point (3,7)
Answer:
y=2/3x+5
Step-by-step explanation:
Parallel lines share the same slope so we already know the slope: 2/3.
Now we need to find the y-intercept for the equation. To do that, replace 4 with b. We have y=2/3x+b.
To find out what b is, we need to plug in the x and y values we are given into the current equation. We get 7=2/3(3)+b.
7=2+b
5=b
Now we can put all the information we have together.
y=2/3x+5
From the top of a vertical cliff 75.0m high, forming one bank of a river, the angles of depression of the top and bottom of a vertical cliff which forms the opposite bank are 22° and 58° respectively. Determine the height of the second cliff and width of the river
Answer:
a. 46.9 m b. 56.1 m
Step-by-step explanation:
a. Width of the river
The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.
Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from
tan58° = 75.0 m/d
d = 75.0/tan58° = 46.87 m ≅ 46.9 m
b. Height of the second cliff
Now, the difference in height of the two cliffs is gotten from
tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°
h = dtan22° = 18.94 m
So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m
PLEASE HELP!!! URGENT!
Answer:
(D) [tex]p^{2} -9p+18[/tex]
Step-by-step Explanation:
Assuming that the equation [tex]x^{2} -2[/tex] = p, we can convert the equation into this.
[tex]p^{2} +18=9p[/tex]
We can convert [tex]9x^{2} -18[/tex] into 9p because [tex]x^{2} -2[/tex] × 9 = [tex]9x^{2} -18[/tex]
Now we simplify this equation.
We can subtract 9p from both sides of the equation.
[tex]p^{2} +18-9p = 0[/tex]
Re-ordering the equation gets us:
[tex]p^{2} -9p+18[/tex]
So, (D) [tex]p^{2} -9p+18[/tex] is equivalent to the original expression of [tex](x^{2} -2)^{2} + 18 = 9x^{2} -18[/tex]
Solve. x2+5x−2=0 Enter your answers, as exact values, in the boxes. x = or x =
Answer:
[tex]x=\frac{-5+\sqrt{33} }{2}[/tex]
[tex]x=\frac{-5-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
Using the quadratic formula in which a=1, b=5 and c=-2
[tex]x_1=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\x_2=\frac{-b-\sqrt{b^{2}-4ac } }{2a}\\x_1=\frac{-5+\sqrt{5^{2}-4(1)(-2) } }{2(1)}\\x_1=\frac{-5+\sqrt{33} }{21}\\x_2=\frac{-5-\sqrt{25+8 } }{2}\\x_2=\frac{-5-\sqrt{33} }{2}[/tex]
HELPP I NEED THIS ASAP!! 10 points
The graph shows a Y in meters of shark from the surface of another name for a certain amount of time x in minutes
Part A : Describe how you can use similar triangles to explain why do you suppose the graph between point a and B is the same as the slope of the graph between points a and C?
Part B:What are the initial value to and slope of the graph what do they represent?
Answer:
(∠C) ≅ (∠B)
∴ tan(∠B) = tan(∠C) and
Slope AB = Slope BC
Step-by-step explanation:
Part A:
To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;
The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)
The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)
The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal
Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C
Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)
The slope AB = tan(∠B)
Slope BC = tan(∠C)
(∠C) ≅ (∠B)
Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.
Determine the value of x.
Answer:
B. 6sqrt(2).
Step-by-step explanation:
Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.
In this case, x = 6.
So, the hypotenuse is B. 6sqrt(2).
Hope this helps!
The shaded figure is a rhombus.
The area of the shaded section is 60 square units. What is the value of x?
Answer:
6
Step-by-step explanation:
the value of x is 6
so the answer is 6
Answer:
answer is 8
Step-by-step explanation:
Write an expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at
the top
Answer:
ΔE =12.3 - (-9.6) which is equivalent to 21.9 feetStep-by-step explanation:
Give the distance covered by Vivian at the bottom of the elevation to be -9.6 feet and the distance covered by Vivian at the top of the elevation to be 12.3 feet, Vivian's change in elevation will be expressed as the difference in the elevation at the bottom and the elevation at the top.
Let the initial elevation Ei = -9.6 feet
Final elevation Ef = 12.3 feet
Change in elevation ΔE = Ef - Ei
Change in elevation ΔE =12.3 - (-9.6)
Change in elevation ΔE = 12.3 + 9.6
Change in elevation ΔE = 21.9 feet
Hence the expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at the top is ΔE =12.3 - (-9.6) which is equivalent to 21.9 feet
Answer:
12.3 – (-9.6)
Step-by-step explanation:
Its the answer they provided
Which three-dimensional figure is formed by the rotation given?
Answer: The bottom right
Step-by-step explanation: Take a peek at the pic :)
A car rental agency advertised renting a car for $24.95 per day and $0.26 per mile. If Brad rents this car for 3 days, how many whole miles can he drive on a $200 budget ?
Answer:
481 whole miles
Step-by-step explanation:
Total cost would be 3 x 24.95 + 0.26m, where m is the miles driven.
Total cost has to be under or equal to $200, so
3 x 24.95 + 0.26m <= 200
74.85 + 0.26m <= 200 ( 3 x 24.95)
0.26m <= 125.15 ( subtract 74.85)
m <= 481.35 ( divide 0.26)
The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set?
Answer:
[tex](\frac{2}{3},\infty)[/tex]
Step-by-step explanation:
Set builder notation is a mathematical notation used to write the elements of a set stating the conditions that the elements of the set must satisfy. A solution set is also a way of defining solutions to equations and inequalities. A solution set contains a set of all variables for which the equation is true.
The notation {x l x > two-thirds} is a set of all real numbers greater than 2/3, it can also be represented as:
[tex](\frac{2}{3},\infty)[/tex]
Answer:
c) (two-thirds, ∞)
Step-by-step explanation:
edg2020
Colin has a pad with x pieces of paper on it. For his first class, he wrote on 5 fewer than half of the pieces of paper in the pad. He used 2 more sheets in his second class than in his first. How many sheets are left for his third class? ill give brainliest to the first answer
Answer:
Colin has 8 sheets left for his third class.
Step-by-step explanation:
Given that:
Total Number of pieces of papers = [tex]x[/tex]
Number of pieces of papers used for 1st class = 5 fewer than half of the pieces in the pad
Writing the equation:
[tex]\text{Number of pieces of papers used for 1st class =} \dfrac{x}{2} -5 ...... (1)[/tex]
Also, Given that number of pieces of papers used for the 2nd class are 2 more than that of papers used in the 1st class.
[tex]\text{Number of pieces of papers used for 2nd class =} \dfrac{x}{2} -5+2 = \dfrac{x}2 -3 ...... (2)[/tex]
Now, number of pieces of papers left for the third class = Total number of pieces of papers in the pad - Number of pieces of papers used in the first class - Number of pieces of papers used in the first class
[tex]\text{number of pieces of papers left for the third class = }x-(\dfrac{x}{2}-5)-(\dfrac{x}{2}-3)\\\Rightarrow x-\dfrac{x}2-\dfrac{x}2+5+3\\\Rightarrow x-x+5+3\\\Rightarrow 8[/tex]
So, the answer is:
Colin has 8 sheets left for his third class.
Which explains whether AFGH is congruent to AFJH?
Answer:
Hey there!
FGH is congruent to FHJ because of the ASA postulate, stating that in congruent triangles, two angles and one side must be congruent.
Hope this helps :)
arithmetic sequences (nth term)
Tick the arithmetic sequences.
In order for a sequence to be arithmetic the relations between their numbers must be the sum of a common ratio, therefore to determine which ones are arithmetic sequence we need to satisfy the following expression:
[tex]a_n - a_{n-1} = a_{n-2} - a_{n-3}[/tex]
The expression just mean that the subtraction of consecutive terms should be equal for position in the sequence.
"1, 5, 9, 13...":
[tex]13 - 9 = 5 - 1\\4 = 4[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"6, 10, 15, 21...:
[tex]21 - 15 = 10 - 6\\6 = 4[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"2, 3, 5, 8...:
[tex]8 - 5 = 3 - 2\\3 = 1[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"2, -4, 8, -16...:
[tex]-16- 8 = -4 - 2\\-24 = -6[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"-1, 2, 5, 8...:
[tex]8 - 5 = 2 -(- 1)\\3 = 3[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"73, 66, 59, 52...:
[tex]52 - 59 = 66 - 73\\-7 = -7[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"6, 1, -4, -9...:
[tex]-9 - (-4) = 1 - 6\\-5 = -5[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"1, 2, 4, 8...:
[tex]8 - 4 = 2 - 1\\4 = 1[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
Find the first five terms of the patterns with these nth terms.
For [tex]3n + 3[/tex]:
[tex]3*1 + 3 = 3 + 3 = 6[/tex]
[tex]6 + 3 = 9[/tex]
[tex]9 + 3 = 12[/tex]
[tex]12 + 3 = 15[/tex]
[tex]15 + 3 = 18[/tex]
(6, 9, 12, 15, 18)
For [tex]9n - 7[/tex]:
[tex]9*1 - 7 = 9 - 7 = 2[/tex]
[tex]2 + 9 = 11[/tex]
[tex]11 + 9 = 20[/tex]
[tex]20 + 9 = 29[/tex]
[tex]29 + 9 = 38[/tex]
(2,11,20,29,38)
Write down a formula for the nth term of these patterns. The first term is n = 1.
The nth term of any arithmetic sequence is: [tex]a(n) = a(1)*(n - 1)*r[/tex]
Therefore we need to identify r in each sequence.
For (9,15,21,27,33):
[tex]r = 15 - 9 = 6[/tex]
[tex]a(n) = 1*(n - 1)*6 \\a(n) = 6*n - 6[/tex]
For (-2,-8,-14,-20,-26):
[tex]r = -8 - (-2) = -6[/tex]
[tex]a(n) = 1*(n - 1)*(-6)\\a(n) = -6*n + 6[/tex]
20 × 20 - 4
solve and show work
Answer:
20×20-4
=400-4
=396
hope it helps u....
plz mark as brainliest...
Answer:
396Step-by-step explanation:
Using BODMAS rule:
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Now, let's solve:
[tex]20 \times 20 - 4[/tex]
Multiply the numbers
[tex] = 400 - 4[/tex]
Calculate the difference
[tex] = 396[/tex]
Hope this helps...
Best regards!!