What is the leading coefficient and the constant of 5x+2-3x^2

Answer:

The Coordinates of Point C are C(5,2)

The slope of CD is 3

The possible coordinates of point D(a,b) are (6, 5) and (4, -1)

Step-by-step explanation:

According to the Question,

Now, Let The Coordinates of Point C are C( x , y ) .

        The Coordinates of Point C are C( x , y ) =  [tex]\frac{(10)}{2} , \frac{(4)}{2}[/tex] ⇒C(5, 2).

       Thus, The slope of CD is [tex]\frac{-1}{The slope of AB}[/tex]  =  [tex]\frac{-1}{\frac{-1}{3} }[/tex]  ⇔  3.

       ⇒ √{ (b - 2)² +(a - 5)² } = √10

      on squaring both sides we get,

       ⇒ a² - 10a + 25 + b² - 4b + 4 = 10

       ⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)

     ⇒Thus,  (b - 2)/(a - 5) = 3

     ⇒ b - 2 = 3a - 15

     ⇒ b = 3a - 13 ⇔⇔ (Equation 2)

 ⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19

 ⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19

 ⇒10a² - 100a + 240 = 0

 ⇒a² - 10a + 24 = 0

 ⇒(a - 4)(a - 6) = 0

 ⇒a = 4 or a = 6

Now,

Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).

Answer:

152 cups were ordered.

Step-by-step explanation:

Let the number of small size cups = x

And the number of medium size cups = y

Total number of cups used = 63

Therefore, first equation will be,

x + y = 63 -------(1)

Brewers emptied = 147 oz

Quantity of coffee in a small cup = 8 oz

Total amount of coffee in small cups = 8x

Quantity of coffee in a medium cup = 12 oz

Total amount of coffee in medium cups = 12y

Therefore, second equation will be,

8x + 12y = 147 -------(2)

Multiply equation (1) with 12 and subtract is from equation (2)

(8x + 12y) - (12x + 12y) = 147 - 756

-4x = -609

x = 152.25

Therefore, 152 cups of small size coffee were ordered.

Answer:

20mins

Step-by-step explanation:

3/4 * 60 = 45 mins

1/4 * 60 = 15mins

15mins + 10mins = 25 mins

45 - 25 = 20mins

Answer:

They are not similar

Step-by-step explanation:

Angles dont match

Answer:

The independent variable (IV) is the depths at the Altantic Ocean and the dependent variable (DV) is the water temperatures.

Step-by-step explanation:

The IV is what is changed between the groups of the study.

The DV is what is being measured for the groups.

You can say that the DV depends on the IV because changes and differences in the DV depends on the changes for the IV.

I hope this helps! :)

Answer:

3 : 8

Step-by-step explanation:

[tex]\frac{x}{1} = \frac{3y}{8}[/tex]

cross multiply

8x = 3y

x = 3/8

x : y = 3 : 8

Answer:

Step-by-step explanation:

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.766 = x /3

0.766*3 = x

2.298 = x

2.30  = x

Answer:

$22.50

Step-by-step explanation:

Answer:

$95 is the markup

Step-by-step explanation:

Add 45+50=95

[tex]\longrightarrow{\green{\frac{5}{6}}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{1}{2} + \frac{1}{3} [/tex]

Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.

The L. C. M for 2 and 3 is 6.

Now, multiply the L.C.M. with both numerator & denominator.

[tex] = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} [/tex]

[tex]= \frac{3}{6} + \frac{2}{6} [/tex]

Now that the denominators are equal, we can add them.

[tex]= \frac{3 + 2}{6} \\ \\ = \frac{5}{6} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Point C has the coordinates: (-5, -2)

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

a) Since there are 2 #1 in the spinner, the probability of landing on a 1 is 2/8 or 1/4

b) Since there is only one #2, the probability is only 1/8.

c) Probability of landing on #3 is 2/8 or 1/4.

d) Probability of landing on a #4 is 1/8

e) Just like the case of #1 & #3, there are 2 chances out of eight that it will land on a #5 so the probability is 2/8 or 1/4

Answer:

C

Step-by-step explanation:

Slope

Y-intercept = -4

Knowing the slope is 3 and the y-intercept is -4, the answer should be y=3x-4.

Answer:

Step-by-step explanation:

1) Vertically opposite angles are equal.

x + 30 = 180 - 2x

Add '2x' to both sides

x + 30  +2x = 180

3x + 30 = 180

Subtract 30 from both sides

3x = 180 - 30

3x = 150

 x = 150/3

x = 50

2)  Let the angle be x

It's complement angle = 90 - x

[tex]x = \frac{2}{3}(90-x)\\\\x = \frac{2}{3}*90 - \frac{2}{3}*x\\\\x =2*30 - \frac{2}{3}x\\\\x +\frac{2}{3}x = 60\\\\\frac{3}{3}x+\frac{2}{3}x=60\\\\\frac{5}{3}x =60\\\\x = 60*\frac{3}{5}\\\\x = 12*3\\x = 36[/tex]

The angles are : 36 , 54

3) Let the angle be x

It's supplement = 180 - x

[tex]x = \frac{1}{5}(180-x)\\\\x =\frac{1}{5}*180 - \frac{1}{5}x\\\\x + \frac{1}{5}x= 36\\\\\frac{5}{5}x +\frac{1}{5}x = 36\\\\\frac{6}{5}x = 36\\\\x = 36*\frac{5}{6}\\\\x = 6*5 = 30\\[/tex]

Angles are  30 , 150

4) Ratio = 7 : 3

The angles are = 7x , 3x

7x + 3x = 180

10x = 180

x = 180/10

x = 18

7x = 7 * 18 = 126

3x = 3 * 18 = 54

Angles are 126 , 54

1. Intersecting lines are lines that cross each other. When two lines intersect, the opposite angles are equal.

Given: x + 30° and 180° - 2x are vertically opposite angles

⇒   x + 30° = 180° - 2x

⇒   3x = 150°

⇒   x = 50°

2. Let the complement be : C

Given : The other angle is two third of its complement

[tex]\sf{\implies Other \ angle = \dfrac{2}{3} \times C}[/tex]

Two angles are said to be Complementary if their sum is equal to 90°

[tex]\sf{\implies C + \dfrac{2C}{3} = 90}[/tex]

[tex]\sf{\implies \dfrac{5C}{3} = 90}[/tex]

[tex]\sf{\implies 5C = 270}[/tex]

[tex]\sf{\implies C = 54}[/tex]

[tex]\sf{\implies Other \ angle = \bigg(\dfrac{2}{3} \times C\bigg) = \bigg(\dfrac{2}{3} \times 54\bigg) = 36 }[/tex]

Answer: The size of the angle which is two third of its complement is 36°

3. Let the supplement be : S

Given : The other angle is one fifth of its supplement

[tex]\sf{\implies Other \ angle = \dfrac{1}{5} \times S}[/tex]

Two angles are said to be Supplementary if their sum is equal to 180°

[tex]\sf{\implies S + \dfrac{S}{5} = 180}[/tex]

[tex]\sf{\implies \dfrac{6S}{5} = 180}[/tex]

[tex]\sf{\implies 6S = 900}[/tex]

[tex]\sf{\implies S = 150}[/tex]

[tex]\sf{\implies Other \ angle = \bigg(\dfrac{1}{5} \times S\bigg) = \bigg(\dfrac{1}{5} \times 150\bigg) = 30 }[/tex]

Answer: The size of the angle which is one fifth of its supplement is 30°

4. Two supplementary angles are in the ratio 7 : 3

Let the supplementary angles be : 7S and 3S

Two angles are said to be Supplementary if their sum is equal to 180°

⇒   7S + 3S = 180°

⇒  10S = 180°

⇒   S = 18°

First Angle : 7S = (7 × 18) = 126°

Second Angle : 3S = (3 × 18) = 54°

C. 270

Hope this helps! :)

Answer:

A.)90 degrees

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

cos(71)x19=6.1

6.1 =6

Answer:

ladder is 20 feet long.So answer is option c.

Step-by-step explanation:

let the length of a ladder be x

take 71 degree as reference angle

using sin rule

sin 71 =opposite/hypotenuse

0.94=19/x

x=19/0.94

x=20.21

x=20 feet

900Answer:900

Step-by-step explanation:

Answer:

No because they are not proportional. 2•3=6 but 4•3 does not equal 11.

Answer:

the answer choices oh uhm I think i

The total of the two cars is 0.46 + 0.34 = 0.8

The total of all probabilities needs to equal 1

The probability of not buying either car is 1 - the sum of the two probabilities

1-0.8 = 0.20

The probability of not buying either car is 0.20

Answer:

D

Step-by-step explanation:

7.17 x 10(4) = 71,700

8.17 x 10(5) = 817,000

Any numbers between 71,700 and 817,000 is obv the answer

I did the math

A 69,200

B 7,200,000,000

C 7,570

D 80,530

Pretty obv that D be the only one that is inbetween 71,700-817,000

(excuse my spelling pls)

9514 1404 393

Answer:

  x = 0

Step-by-step explanation:

When there is no linear term in the equation, the axis of symmetry is x=0.

__

The values 'a' and 'c' represent a vertical scale factor and a vertical translation, respectively. They do not change the axis of symmetry from that of the parent function, which is x=0.

Answer:

35º

Step-by-step explanation:

u = 180 - 145

u = 35

Answer:

55 =x

Step-by-step explanation:

x+15=2x-40

Subtract x from each side

x-x+15=2x-x-40

15 = x-40

Add 40 to each side

15+40 = x-40+40

55 =x

Answer:

x = 55

Step-by-step explanation:

x+15=2x-40

take away x from both sides and add 40 on both sides to get the like terms on each side

55 = x

Answer:

h = 5

Step-by-step explanation:

6/8 - h/8 = 1/8

Multiply each side by 8 to clear the fractions

8*(6/8 - h/8) = 1/8*8

6 - h = 1

Subtract 6 from each side

6-h-6 = 1-6

-h = -5

Multiply each side by -1

h = 5

Answer:

[tex]h = 5[/tex]

Step-by-step explanation:

Solve the equations:

[tex] \frac{6}{8} - \frac{h}{8} = \frac{1}{8} [/tex]

Reduce fractions to the lowest term by canceling the greatest common factor:

[tex] \frac{3}{4} - \frac{h}{8} = \frac{1}{8} [/tex]

Rerreange unknown terms to the left side of the equation:

[tex] - \frac{h}{8} = \frac{1}{8} - \frac{3}{4} [/tex]

Find the common denominator and write the numerator above common denominator:

[tex] - \frac{h}{8} = \frac{1 - 6}{8} [/tex]

Calculate the sum or difference:

[tex] - \frac{h}{8} = \frac{ - 5}{8} [/tex]

Reduce the greatest common factor on both sides of the equation:

[tex] - h = - 5[/tex]

Divide both sides of the equation by the coefficient variable:

[tex]h = 5[/tex]

Answer:

i think its yz but not sure

Step-by-step explanation:

Write the additive inverse of [tex]\frac{ - 1}{3} [/tex].

➼ The additive inverse of [tex] \frac{ - 1}{3} [/tex] is [tex]\frac{+ 1}{3} [/tex].

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

210 IS THE POSSIBLE ANSWER