Solution :
Given a quadratic equation :
[tex]ax^2+bx+c = 0[/tex]
Step 1 : [tex]ax^2+bx+c = 0[/tex]
Step 2 : [tex]ax^2+bx=-c[/tex]
Step 3 : [tex]$x^2+\frac{b}{a}x = -\frac{c}{a}$[/tex]
Step 4 : [tex]$x^2+\left(\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 5 : [tex]$\left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 6 : [tex]$\left(x+\frac{b}{2a}\right)=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 7 : [tex]$x=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)} - \frac{b}{2a}$[/tex]
Step 8 : [tex]$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$[/tex]
Thus the derivation for finding the roots of a quadratic equations.
Answer:
B D A C
Step-by-step explanation:
Edge 2021
Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calculations to find the length of AC.
What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.
12.0 units
12.4 units
15.0 units
15.4 units
Answer:
15.4 units
Step-by-step explanation:
sqrt(5²+4²) = sqrt(41) = 6.4
the other two legs are 5 and 4
so perimeter
= 4+5+6.4 = 15.4 units
Which of the following is true about similar right triangles ?
A. Corresponding angles are not equal.
B. Corresponding trigger number trigonometric ratios are in proportion
C.Corresponding trigonometric ratios are equal
D.Corresponding sides are equal
Answer:
b
Step-by-step explanation:
because its alternation
The option (C) Corresponding trigonometric ratios are equal is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
We have a statement:
Which of the following is true about similar right triangles?
As we know from the definition the two triangles have the same shape, but it is not compulsory to have the same size.
The ratio of the corresponding sides is in the same proportions
The corresponding trigonometric ratios are equal.
Thus, the option (C) Corresponding trigonometric ratios are equal is correct.
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Please help ASAP!!!
A rectangle is formed by placing two identical squares side by side. the area of the rectangle is 892 cm2. What is the perimeter of the square?
Answer:
288 cm^2
Step-by-step explanation:
If you have 2 congruent squares, side by side, the perimeter is 6*sidelength.
We divide 72 by 6 to find sidelength, and get 12.
We square 12 to find the area of a square, and get 144.
Multiply by 2 to find the area of the rectangle, and get 288 cm^2
A plane and a line not in that plane which are parallel to the same line, are parallel to each other. Always, sometimes, or never
Answer:
a line and a plan are considered parallel if they have no points in common if two parallel planes are cut by a third plane then the lines of intersection are parallel
3
JK, KL, and IJ are all tangent to o (not drawn to scale). JA = 8, AL = 11, and
CK = 10. Find the perimeter of AJKL.
Answer:
[tex]P = 58[/tex]
Step-by-step explanation:
The image if the circle and triangle can be found online
Given
[tex]JA = 8[/tex]
[tex]AL = 8[/tex]
[tex]CK = 10[/tex]
Required
The perimeter of JKL
Since the mid-points of the tangents are A, B and C respectively.
[tex]JK = JB + BK[/tex]
Where
[tex]JB = JA = 8[/tex]
[tex]BK = CK = 10[/tex]
So:
[tex]JK =8+10 =18[/tex]
[tex]JL = JA + AL[/tex]
[tex]JL = 8+11 = 19[/tex]
[tex]KL = CL + CK[/tex]
Where
[tex]CL =AL = 11[/tex]
So:
[tex]KL = 11+10 = 21[/tex]
So, the perimeter (P) is:
[tex]P = JK+ KL +JL[/tex]
[tex]P = 18 + 19 + 21[/tex]
[tex]P = 58[/tex]
If you input 3 into the equation below, what is the resulting y-value?
y=9
Answer:
It will still be 9. y=9 is a horizontal line. No matter the x value, the answer will be the same.
Step-by-step explanation:
2x+3y=2
y = 1/2x + 3
What is the solution to the system of equations?
(-2,2)
(0,0.67
(0,3)
(1,0
Answer:(-2,2)
Step-by-step explanation:
2x+3(1/2x+3)=2
⇒7/2x=-7
÷7⇒1/2x=-1
×2⇒x=-2
x=-2 into the equation
⇒2×(-2)+3y=2
⇒3y=6
⇒y=2
Answer:
(-2 , 2)
Step-by-step explanation:
2x + 3y = 2 ---------------(I)
y = (1/2)x + 3 --------------(II)
Substitute y value in equation (I)
[tex]2x + 3*[ \frac{1}{2}x + 3] = 2\\\\2x + 3*\frac{1}{2}x+3*3=2\\\\2x+ \frac{3}{2}x+9=2\\\\2x + \frac{3}{2}x = 2-9\\\\2x + \frac{3}{2}x = -7 \\[/tex]
Multiply the whole equation by 2
[tex]2*2x + 2* \frac{3}{2}x = -7 *2\\\\4x + 3x = -14[/tex]
7x = -14
x = -14/7
x = -2
Plugin x = -2 in equation (I)
2*(-2) + 3y= 2
-4 + 3y = 2
Add 4 to both sides
3y = 2+4
3y = 6
Divide both sides by 3
y = 6/3
y = 2
change from improper fraction to mix number 51/7
Answer:
7 3/7
Step-by-step explanation:
measures of variability,i have realized that
Answer:
Measures of Variability: Range, Interquartile Range, Variance, and Standard Deviation. ... While a measure of central tendency describes the typical value, measures of variability define how far away the data points tend to fall from the center. We talk about variability in the context of a distribution of values.
A light bulb consumes 3600 watt-hours per day. How many watt-hours does it consume in 4 days and 18 hours?
Answer:
17,100
Step-by-step explanation:
A light bulb consumes 3600 watts per day
Therefore the number of watts consumed in 4 days 18 hours can be calculated as follows
3600= 24 hours
x= 1 hour
= 3600/24
= 150 watts in an hour
3600×4
= 14,400
150×18
= 2,700
Total watts
= 14,400+2700
= 17,100
Hence the number if watss produced in 4 days 18 hours is 17,100 watts
Hal earns a B on 75% of his tests. He divides a spinner into 12 equal spaces to model the grades he earns on his tests, with nine of the spaces
representing a B. Which statement about his model is true?
OA. His model cannot be improved.
ОВ.
OC.
His model can be improved the most by dividing the spinner into 15 equal spaces.
His model can be improved the most by using every third space on the spinner to represent a B.
His model can be improved the most by using eight of the spaces to represent a B.
OD
Reset
Next
The true statement is His model can be improved the most by dividing the spinner into 15 equal spaces.
The correct option is (B)
What is data?
As per the situation, he divided the spinner in 12 parts but it would be to score more if he divide the spinner in 15 parts in his b.
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The inequality – x2 - 6 <0 has
Answer:
X es igual a 3
Step-by-step explanation:
x2 - 6 = 0
(3)2 - 6 = 0
What the hcf of 24 and 180
Answer:
12
Step-by-step explanation:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
At Factory Y, a worker's wages for a 40-hour week is $200. She is paid 10% of her regular weekly wages for every hour that she works overtime. At the end of a certain week she received $380. Calculate the number of hours of overtime that she worked.
Answer:
She worked 18 hours of overtime.
Step-by-step explanation:
If she works 40 hours per week and gets $200, subtract $380 - $200 = $180.
If you multiply $180 by 0.1 (which is 10% converted to a decimal), you get 18 which is your final answer.
Help for both??? If you can
Answer:
first : 1808.64 [tex]in^{2}[/tex]
second : 48
Step-by-step explanation:
Area = [tex]\pi[/tex][tex]r^{2}[/tex]
A = [tex]24^{2}[/tex] x 3.14
second:
A = [tex]4^{2}[/tex] x 3
A= 16 x 3
A = 48
What are reciprocals?
Answer:
In mathematics,reciprocal is an expression or function so related to another that their product is unity; the quantity obtained by dividing the number one by a given quantity.
Answer:Rh
Step-by-step explanation:mama
Which equation shows the distributive property? (a) 6 x 3 + 6 x 8 = 6 x (3 + 8) (b) 5 + (22 + 19) = (5 + 22) + 19 (c) 20 x 10 = 10 x 20 (d) 45 + 7 = 7 + 45
help me please
the pythagorean theorem equation
Answer:
(Altitude)^2+(Base)^2=(Hypotenuse)^2
En un océano, hay 3 Islas, cada isla representa un Monomio, si el grado absoluto de cada isla lo representa la cantidad de persona que hay en cada isla, calcular el grado absoluto del océano. En la Primera isla hay 10 personas, en la Segunda isla hay 25 personas y en la Tercera isla hay 8 personas. Nota: Un océano es el polinomio y cada isla es un monomio que está incluido dentro del polinomio.
Answer:
25
Step-by-step explanation:
Un polinomio de grado n se escribe como:
P(x) = aₙ*x^n + ... + a₁*x + a₀*x^0
Donde n es el exponente de mayor del polinomio, y decimos que el grado absoluto de este polinomio es n.
En este caso sabemos que tenemos 3 islas, y cada una de ellas representa un monomio ( un monomio es cada uno de los términos de un polinomio).
Sabemos que el grado de cada isla depende de la cantidad de gente que vive en la isla.
Tenemos una con 10 personas, entonces tendremos un término con un exponente igual a 10.
Tenemos una isla con 25 personas, entonces tendremos un término con un exponente igual a 25.
Tenemos una isla con 8 personas, entonces tendremos un término con un exponente igual a 8.
Recordando que el grado absoluto del polinomio es igual al mayor exponente del polinomio, acá podemos ver que el mayor exponente es 25.
Entonces el grado absoluto del polinomio será 25.
SECTION:B NUMBER PATTERNS
johnny's tile shop has a newly disigned tile. It can be odered in different sizes. size 1 has one white tile in the middle and is surrounded by eight black tiles ; size 2 has four white tiles in the middle and surrounded by twelve black tiles.
draw sizes 3,4 and 5
Answer:
Step-by-step explanation:
Well I am not sure whether to draw it because there are no options of drawing
The requried Tiles of sizes 3, 4, and 5 have been shown in the image.
What is the matrix?A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Here,
To draw the designs for sizes 3, 4, and 5 of Johnny's newly designed tile, we need to follow the same pattern as sizes 1 and 2.
Size 3 has a 7x7 grid of tiles with nine white tiles in the center and 16 black tiles around them,
Size 4 has a 9x9 grid of tiles with 16 white tiles in the center and 20 black tiles around them.
Size 5 has an 11x11 grid of tiles with 25 white tiles in the center and 28 black tiles around them.
Thus, the requried Tiles of sizes 3, 4, and 5 have been shown in the image.
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If a line has a slope of 3, what is the slope of a line perpendicular to it?
Answer:
- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
Here m = 3 , then
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{3}[/tex]
Find the value of x that makes ABCD a parallelogram?
answers
a.) x=30
b.) x=20
c.) x=40
d.) x=60
Answer:
D) x=60
The choose
Step-by-step explanation:
360 =70+70+50+50+2x
360=240+2x
360-240=2x
120=2x
x=120/2
x=60
What is the length of Line segment B C?
Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses?
Answer:
134inches
Step-by-step explanation:
Convert 2feet to inches
1foot= 12 inches
2feet= 12x2inches
=24inches
24inches is to 1 birdhouse
24inches x 6 equals six birdhouses
134inches
Answer:
He will need 162 inches
Step-by-step explanation:
6×2ft is 12 feet. Convert ft into inches for every 1 foot you have 12 inches. A total of 144in. Now multiply 6×3in which equals 18in. Add 144+18=162
graph:y-10=-2(x-10)grgrgrgrggrgrgrgrgrgrrgrrggr
Answer: 14
Step-by-step explanation:
y -1 0 = -6
Ans -2 (x-10) = 14
Hope I could help :)
What percent of all students are middle schools
help plzzzzzzzzzzzzzzzzzzzzz
What is the DMS measure of an angle that is 3.7 radians?
A. 11° 37' 26"
B. 0° 3' 52.5"
c. 211° 59' 39.6"
D. 3° 42' 0"
Last question, so please help me out ASAP!
Answer:
5/18
Step-by-step explanation:
conditional probability formula:
A|B (a given b) = (A∩B)/(B)
so
Moderate|college (moderate given college)= (moderate∩college)/college
moderate∩college= 15
college= 11+15+28= 54
15/54= 5/18
A wooden frame is to be constructed in the form of an isosceles trapezoid, with diagonals acting as braces to strengthen the frame. The sides of the frame each measure 5.3 feet, and the longer base measure 12.7 feet. If the angles between the sides and the longer base each measure 68.4 degrees, find the length of one brace to the nearest tenth of a foot.
Answer:
11.8 ft
Step-by-step explanation:
Since the length of one side, l = 5.3 ft, the longer base b = 12.7 ft and the one brace, d form a triangle with angle between the longer base and side being the angle facing the brace is θ = 68.4°, we use the cosine rule to find the length of thee brace.
So d² = l² + b² -2lbcosθ
So, substituting the values of the variables into the equation, we have
d² = (5.3 ft)² + (12.7 ft)² -2(5.3)(12.7)cos68.4°
d² = 28.09 ft² + 161.29 ft² - 134.62(0.3681)
d² = 189.38 ft² - 49.56 ft²
d² = 139.82 ft²
taking square-root of both sides, we have
d = √139.82 ft²
d = 11.82 ft
d ≅ 11.8 ft to the nearest tenth of a foot.