The solution is 2 roots
The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the quadratic equation be A
where A = ax² + bx + c=0
Let the discriminant of the equation be D
Now , the value of D = 73
To calculate the number of roots a quadratic equation A
We need to compute the discriminant (b² - 4ac).
If the discriminant is less than 0, then the quadratic has no real roots.
If the discriminant is equal to zero then the quadratic has equal roots.
If the discriminant is more than zero then it has 2 distinct roots.
So , the value of D > 0
Therefore , the equation has 2 roots
Hence , the number of roots of the quadratic equation is 2 roots
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Solve the proportion.
W+14/4w+6 =3/4
[tex]\frac{w+14}{4w+6} = \frac{3}{4}[/tex]
So do cross multiplication.
4×(w+14)=4w+56
3×(4w+6)=12w+18
4w+56=12w+18
Carry the 4w to the right side, and the 18 to the left
56-18=12w-4w
38=8w
w=4 3/4
Sorry if this is not what you were asking for.
♡ But anyways, I Hope this helped! ♡
❀ 0ranges ❀
Answer:
[tex] \boxed{ \boxed{ \bold{ \purple{4.75}}}}[/tex]Step-by-step explanation:
[tex] \sf{ \frac{w + 14}{4w + 6} = \frac{3}{4} }[/tex]
Apply cross product property
⇒[tex] \sf{4(w + 14) = 3(4w + 6) }[/tex]
Distribute 4 through the parentheses
Similarly, Distribute 3 through the parentheses
⇒[tex] \sf{4w + 56 = 12w + 18}[/tex]
Move variable to left hand side and change it's sign
Move constant to right hand side and change it's sign
⇒[tex] \sf{4w - 12w = 18 - 56}[/tex]
Collect like terms
⇒[tex] \sf{ - 8w = 18 - 56}[/tex]
Calculate
⇒[tex] \sf{ - 8w = - 38}[/tex]
Divide both sides of the equation by -8
⇒[tex] \sf{ \frac{ - 8w}{ - 8} = \frac{ - 38}{ - 8} }[/tex]
Calculate
⇒[tex] \sf{w = 4.75}[/tex]
Hope I helped!
Best regards!!
The Sides of regular octagon T are three time the length of the sides of regular octagon G
Answer:
According to the statement, the equation is :
Sides of regular octagon T= 3 × the length of sides of regular octagon G
The required equation is x = 3y
Where x is the length of the sides of the octagon T and y is the length of the side of the octagon G.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 5 - 9 is an equation.
We have,
Sides of regular octagon T = x
Sides of regular octagon G = y
Now,
The equation of the sides of regular octagon T is three times the length of the sides of regular octagon G can be written as:
x = 3y
Thus,
The equation is x = 3y.
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Mr. Johnson hired a contractor to build a small deck on the back of his house. The cost of materials alone added to $678.12. When he received the final bill from the contractor, the total amount charged was $1206.12. Verify the accuracy of this bill if labor amounted to 16.5 hours at $32 an hour
Answer:
Yes, the bill is absolutely accurate
Step-by-step explanation:
Cost of materials= $ 678.12
Final bill amount(given)=$1206.12
Rate= $32 per hour for 16.5 hrs
Total amount for 32 hrs = time * rate = 16.5* 32=$528
Therefore, by the problem ,
Cost of materials+ Total amount for 32 hrs = Final bill amount
= 678.12+ 528
=1206.12
Therefore , the final bill amount is 100% accurate as it completely matches with the given bill amount
*ANSWER PLS TY* Find The Volume Of The Pyramid
Answer: A. 1120 in³
Step-by-step explanation:
the formula for the volume of the pyramid: [tex]V=\frac{1}{3} lwh[/tex]
l (length)=16
w (width)=14
h (height)=15
[tex]V=\frac{1}{3} lwh[/tex]
[tex]V=\frac{1}{3} (16)(14)(15)[/tex]
[tex]V=\frac{1}{3} 3360[/tex]
[tex]V=1120[/tex]
Answer:
The answer is option A.
Step-by-step explanation:
Hey there!!
Given,
Length (l)= 16 in.
breadth (b)= 14 in.
height (h)= 15 in.
we have,
[tex]v. of \: pramid = \frac{1}{3} \times a \: of \: base \times height[/tex]
or, volume = {1/3 × (16×14)×15} cubic inch.
by simplifying it we get,
The volume is 1120 cubic inch.
Hope it helps..
Area of a circle- pls pls pls help me- I'll give Brainly answer and big points.
Answer: The answer is 12.57 because the formula is The area of a circle is pi times the radius squared (A = π r²). Hope this helps.
Step-by-step explanation:
¿Cuál propiedad de los números complejos se muestra a continuación?
(2+31)+(5 - 41)=(5-41)+(2+31)
A asociativa
B distributiva
C inverso aditivo
D conmutativa
Answer:
D) conmutativa
Step-by-step explanation:
Propiedad conmutativa: Cuando se suman o multiplican dos números, la suma o el producto es el mismo independientemente del orden en que
los números se suman o multiplican.
Se da como:
a + b = b + a
a × b = b × a
Propiedad distributiva: La suma de dos números por un tercer número es igual a la suma de cada número sumado por el tercer número. Se da como:
a × (b + c) = (a × b) + (a × c)
Propiedad asociativa: Se da como:
a + (b + c) = (a + b) + c
a × (b × c) = (a × b) × c
Propiedad inverso aditivo: Se da como
a + (-a) = 0
3/2y-3+5/3 z when y =6 and z= 3
Answer:
Step-by-step explanation:
Plug in the value of y & z in the expression
[tex]\frac{3}{2}y-3+\frac{5}{3}z=\frac{3}{2}*6-3+\frac{5}{3}*3\\\\\\=3*2 - 3 + 5 *1\\\\\\= 6 - 3 + 5\\\\\\= 3 + 5\\\\\\= 8[/tex]
Answer: 11
Step-by-step explanation:
If y=6 and z=3 then your problem will look like this : 3/2(6) - 3 + 5/3(3)
Put both 6 and 3 over 1 to turn them into a fraction and then multiply
3/2 multiplied by 6/1 is 18/2 which reduces to 9
5/3 multiplied by 3/1 is 15/3 which reduces to 5
Then your problem will look like this : 9 - 3 + 5
Follow order of operations and add and subtract from left to right
9 - 3 is 6 and 6 + 5 is 11
So your answer is 11
if band practice is 4:00p.m how many min do i have to untill band practice if its 3:40
Answer:
20 minutes
4:00 - 3:40 = 20 minutes
Answer:
20 minutes
Step-by-step explanation:
в коком году родился пушкин
Answer:
May 26, 1799
Step-by-step explanation:
please help me as soon as possible ...
Your question has been heard loud and clear.
tanθ+tan(60∘+θ)+tan(120∘+θ)
=tanθ+3–√+tanθ1−3–√tanθ+−3–√+tanθ1+3–√tanθ
[tanθ(1−3tan2θ)+(3–√+tanθ)(1+3–√tanθ)
=+(−3–√+tanθ)(1−3–√tanθ)1−3tan2θ
=9tanθ−3tan3θ1−3tan2θ=3tan3θ
Thank you.
Answer: see proof below
Step-by-step explanation:
Use the following identities
tan (A + B) = (tan A + tan B)/(1 - tan A · tan B) --> [tex]\dfrac{tanA+tanB}{1-tanA\cdot tanB}[/tex]
tan 60° = √3
tan 120° = -√3
tan 3A = (3tanA - tan³A)/(1 - 3 tan²A) --> [tex]\dfrac{3tanA-tan^3A}{1-3tan^2A}[/tex]
Proof LHS → RHS
Given: tan Ф + tan(60° + Ф) + tan(120° + Ф)
Sum Difference: tan Ф + (tan 60° + tanФ)/(1-tan60°·tanФ) + (tan 120° + tanФ)/(1-tan120°·tanФ)
(latex) [tex]tan\theta+\dfrac{tan60^o+tan\theta}{1-tan60^o\cdot tan\theta}+\dfrac{tan120^o+tan\theta}{1-tan120^o\cdot tan\theta}[/tex]
Substitute: tan Ф + (√3 + tanФ)/(1-√3·tanФ) + (-√3 + tanФ)/(1+√3°·tanФ)
(latex) [tex]tan\theta+\dfrac{\sqrt3+tan\theta}{1-\sqrt3 tan\theta}+\dfrac{-\sqrt3+tan\theta}{1+\sqrt3tan\theta}[/tex]
Common Denominator: [tan Ф(1-3tan²Ф)+8tanФ]\(1-3tan²Ф)
(latex) [tex]\dfrac{tan\theta(1-3tan^2\theta)+8\theta}{1-3tan^2\theta}[/tex]
Distribute: (tan Ф - 3tan³Ф + 8Ф)\(1 - 3 tan²Ф)
(latex) [tex]\dfrac{tan\theta-3tan^3\theta+8\theta}{1-3tan^2\theta}[/tex]
Simplify: (9Ф - 3tan³Ф)\(1 - 3 tan²Ф)
3(3Ф - tan³Ф)\(1 - 3 tan²Ф)
(latex) [tex]\dfrac{9\theta - 3tan^3\theta}{1-3tan^2\theta}[/tex]
[tex]\dfrac{3(3\theta - tan^3\theta)}{1-3tan^2\theta}[/tex]
Triple Angle Identity: 3 tan 3Ф
3 tan 3Ф = 3 tan 3Ф [tex]\checkmark[/tex]
Two shirt screening companies charge a set up fee and a charge for each shirt made.
The table shows the total costs for the company Shirt Express. The total costy (in
dollars) for x shirts made by Shirt Custom is represented by the equation y = 8x + 50
Answer:
The correct option is;
Shirt Express charges less per shirt. For the cost to be the same 74 shirts must be ordered
Step-by-step explanation:
1) The given table for Shirt Express can be used to find the equation of the total cost of each made by Shirt Express as follows;
The rate of change of the function m is given as follows;
[tex]m = \dfrac{y_2 - y_1 }{x_2 - x_1}[/tex]
Therefore, we have;
m = (438 - 353)/(50 - 40) = 8.5
Te equation in slope and intercept form is then y - 438 = 8.5(x - 50)
From which we have;
y = 8.5·x - 8.5×50 + 438 = 8.5·x + 13
y = 8.5·x + 13
Therefore, Shirt Express initially charges 13 per shirt which is less than the 50 Shirt Custom charges
2) the cost to be the same, we equate both shirts equations to get;
8.5·x + 13 = 8·x + 50
0.5·x = 50 - 13 = 37
x = 37/0.5 = 74 shirts
Therefore, for the cost to be the same 78 shirts must be ordered
how to do this question plz answer me step by step plzz plz
Answer:
adult cost £7, child cost £2
Step-by-step explanation:
let a represent an adult and c a child , then
2a + 3c = 20 → (1)
a + 4c = 15 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate a
- 2a - 8c = - 30 → (3)
Add (1) and (3) term by term to eliminate a, that is
- 5c = - 10 ( divide both sides by - 5 )
c = 2
Substitute c = 2 into either of the 2 equations and evaluate for a
Substituting into (2)
a + 4(2) = 15
a + 8 = 15 ( subtract 8 from both sides )
a = 7
The cost of an adult ticket is £7 and a child ticket is £2
what property is 16=16
Which of the following are identities? Check all that apply.
Answer:
b
Step-by-step explanation:
thats funny i just did that
Answer: check all the answers except cos(x+y)+cos(x-y)=cos^2 x-sin^2 y
Step-by-step explanation:
took the test and hopefully mine was the same as the image above
The moon has a mass of 7.35x1022, while earth has a mass of 5.97x1024 Kg. What is the combined mass of the moon and earth.
Answer:
6.0435*10²⁴
Step-by-step explanation:
Moon: 7.35*10²²
Earth: 5.97*10²⁴
7.35*10²² = 0.0735*10²⁴
then:
0.0735*10²⁴ + 5.97*10²⁴ = (0.0735 + 5.97)*10²⁴
= 6.0435 *10²⁴
DUE TODAY PLEASE HELP! Find the value of z. A. 50 B. 65 C. 130 D. 110
Answer:
50
Step-by-step explanation:
180 - (65 + 65)
= 180 - 130
= 50
What is the range of the following set of measurements?
"24.35 cm, 22.51 cm, 20.98 cm, 20.98, 30.33 cm, 30.98 cm"
The range is
cm.
Answer:
The range is 10 cm.
Step-by-step explanation:
The range of a set is the difference of the largest and smallest values of the set. Looking at the data, we see that 30.98 cm is the largest value and 20.98 is the smallest value so the range is 30.98 - 20.98 = 10 cm.
Answer:
The answer is
10 cmStep-by-step explanation:
To calculate the range in a given set of data subtract the lowest observation from the highest observation
From the question
The highest measurement = 30.98 cm
The lowest measurement = 20.98 cm
So the range is
30.98 cm - 20.98 cm
We have the final answer as
10 cmHope this helps you
What is the speed of a sailboat traveling 120m in 60s?
A sailboat traveling 120m in 60s is 20.
three times a number n plus 16
Answer:
3n+16
Step-by-step explanation:
three times: (3) a number n +16
(3)n+16 or 3xn+16
3n+16
Calculate the value of 0.1×0.06
0.006
Step-by-step explanation:0.1 × 0.06 =
= 1/10 × 6/100
= 6/1000
= 0.006
What is 6,129,999 rounded to the nearest thousand
Answer: 6,130,000
Step-by-step explanation:
No work needed
please do the steps solve the equation for d: 1/6d-8=5/8 2. Solve the equation for x: 3x-4+5x=10-2z 3. Solve the equation for c: 7(c-3)=14 4. Solve the equation for m: 11(m/22+3/44)=87m+m 5. Solve the equation for k: ck+5k=a
Step-by-step explanation:
1. 1/6d - 8 = 5/8
1/6d -8 + 8 = 5/8 + 8
1/6d = 69/8
1/6d / 1/6 = 69/8 / 1/6
d = 51.75 or [tex]51\frac{3}{4}[/tex]
2. 3x - 4 + 5x = 10 - 2z
8x - 4 = 10 - 2z
8x - 4 + 4 = 10 - 2z + 4
8x = 14 - 2z
8x / 8 = (14 - 2z) / 8
x = [tex]\frac{14 - 2z}{8}[/tex]
3. 7(c - 3) = 14
7(c - 3) / 7 = 14 / 7
c - 3 = 2
c - 3 + 3 = 2 + 3
c = 5
4. 11(m / 22 + 3 / 44) = 87
m / 22 + 3 / 44 = 87 / 11
m / 22 + 3 / 44 = 348 / 44
m / 22 = 345 / 44
m = 172.5
5. ck + 5k = a
k(c + 5) = a
k = [tex]\frac{a}{c+5}[/tex]
Find the exact value of cos A in simplest radical form
Answer:
2√6/7
Step-by-step explanation:
The following data were obtained from the question:
Cos A =?
Hypothenus = 14
Adjacent = √96
Cos A = Adjacent /Hypothenus
Cos A = √96/14
Cos A = √(16 × 6)/14
Cos A = (√16 × √6)/14
Cos A = 4√6/14
Cos A = 2√6/7
Therefore, the value of Cos A is 2√6/7
Find the measure of b. A. 80 B. 70 C. 40 D. 20
Answer:
40°
Step-by-step explanation:
e = 20°
d = 20°
c = 140°
b = 40°
If one angle in the circle is 20° then the measure of b is 40°.
What is alternate exterior angle?Alternate exterior angles are those angles which are formed when two parallel lines are intersected by a transversal line and angle formed outside is known as alternte exterior angles.
How to find angle?When we observe the angles then we can say that d and 20° angles are alternate exterior angles. We can say that b=2d.So we have to put the value of d in the above formula to get the value of b.
b=2*20
=40°
Hence if one angle in the circle is 20° then the measure of b is 40°.
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Find the slope that passes through (9, 4) and (7, 7) simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer:
m= =3/2
Step-by-step explanation:
(9,4) (7,7)
m= y2-y1/x2-x1
m=7-4/7-9
=3/-2
=-3/2
Help!!!!!!!!!!!!!!!!!!!!!!
6. A number decreased by half of the number is four.
Answer:
number between 12 and 14
Step-by-step explanation:
Start with given compound inequality, Add 4 to all sides ,combine terms on the left side ,combine terms on the right side, multiply all by 2, multiply ,so the number is between 12 and 14 which makes it possible to be 12,13,or 14
pls help!!
will give the brainliest!
need explanation!
Urgent!!
Answer:
38.89%
Step-by-step explanation:
the whole p8e chart is 360° as a perfect circle would be,
so : 360° - ( 66° + 144° ) = 360° - 210° = 140°
140° of the pie chart was cast in favor of candidat C.
(140° ÷ 360°) × 100 = 38.89%
A model of an airplane is 19 in. long. The actual plane is 152 ft. long. What is the scale of the model?
Answer:
1 in : 8 ft or 1 : 96
Step-by-step explanation:
The scale is the ratio of model dimensions to actual dimensions:
19 in : 152 ft = 1 in : 8 ft = 1 in : 96 in = 1 : 96
__
The scale can be expressed in mixed units as 1 in : 8 ft, or it can be expressed as the pure ratio 1 : 96.
Complete the space by dividing, 12 x ____ = 84: *
Answer:
7
Step-by-step explanation:
variable = 84/12
= 7
84 ÷ 12 = 7
Verification
12 × 7 = 84
Complete the space by dividing, 12 x 7 = 84: *