The parabolas y = -x² and y= -x² - 4x + 6 are graphed below. What are the y-values of the solutions to this system of equations?

y= 1,9
y= 1,6
y= -0,6
y= -3,1

Answer:

Expression that can be used to produce vector b from vector a        

=        T× magnitude of vector a × vector 'a'

Step-by-step explanation:

Given question is based on the concept of vectors

Vectors:-  Vectors is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication

To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector 'b' with increased magnitude from a given vector 'a'.

its clear from  the question that only the magnitude of  vector a is increased to produce another vector b

hence we multiply any constant ('T') with the magnitude of vector a to increase its magnitude.

and finally multiply the increased magnitude with the vector 'a' itself to get the answer.

so, the final expression that can be used to produce vector b from vector a is =  T× magnitude of vector a × vector 'a'.

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Answer: 18x+24

Step-by-step explanation:

[tex]f(x+3)=3(x+3)^2 + 5\\\\f(x+3)=3(x^2 + 6x+9)+5\\\\f(x+3)=3x^2+18x+27+5\\\\f(x+3)=3x^2 + 18x+32[/tex]

[tex]\therefore f(x+3)-[f(x)+3]=(3x^2 +18x+32)-[3x^2 +5+3]\\ \\=3x^2 +18x+32-3x^2 - 8\\\\=\boxed{18x+24}[/tex]

If function f(x) = 3x² + 5 then the value of f(x + 3) - [f(x) + 3] is 18x + 24.

Given the function f(x) = 3x² + 5.

We have to find the value of f(x + 3) - [f(x) + 3]

First we have to find the value of f(x + 3) - [f(x) + 3]

f(x + 3) = 3  (x + 3) ² + 5f(x + 3)

           = 3(x ² + 6x + 9) + 5f(x + 3)

           = 3x ² + 18x + 27 + 5f(x + 3)

           = 3x ² + 18x + 32

Now substitute these values and find the value of f(x + 3) - [f(x) + 3].

f(x + 3) - [f(x) + 3] = (3x² + 18x + 32) - [3x ^ 2 + 5 + 3]

                           =3x ²  + 18x + 32 - 3x ² - 8

                           =18x + 24

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Answer:

B AND E

Step-by-step explanation:

hope that helpsndbwbe

Answer:

[tex]-\frac13[/tex]

Step-by-step explanation:

Just the slope, so we can simply apply the definition, as variation in y over the variation in x

[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]

Answer:

0.222

Step-by-step explanation:

Y2-Y1 ÷ X2-X1

4-2 ÷ -7-2

2÷-9

0.222

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given the roots of the polynomial, therefore, the following details can be written as,

Therefore, the polynomial will become,

P(x) = (x-2)²(x-0)²(x+2)¹

      = (x²+4-4x) (x)² (x+2)

       = (x²+4-4x) (x³+2x²)

       = x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³

       = x⁵ - 2x⁴ - 4x³ + 8x²

Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

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Answer:

21x²

Step-by-step explanation:

hopefully A is a typo

Answer: A (if it's just a typo)   or   [tex]21x^{2}[/tex]

Step-by-step explanation:

Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.

12 + 9 = 21

[tex]21x^{2}[/tex]

Answer:

Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.

Answer:

A pentagon has 5 sides.

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 5 - 2) x 180

Sum of the interior angles = 540°

STEP 2: Find one interior angle:

one interior angle = 540 ÷ 5 = 108°

STEP 3: Find the sum of interior angles of a decagon

A decagon has 10 sides

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 10 - 2) x 180

Sum of the interior angles = 1440°

STEP 4: Find one interior angle:

one interior angle = 1440 ÷ 10 = 144°

STEP 5: Find the ratio:

Pentagon : Decagon = 108 : 144

Simplify:

Pentagon : Decagon = 3 : 4

Answer: The ratio is 3 : 4

Answer:

AB : y=1/5x+12

CB : y=-3x+10

CD : y=1/2x-1

DA : y=-2x+1

Answer:

x = 31.5, y = 41.7, z = 48

Step-by-step explanation:

use the rule that cos (x)  = adjacent/hypotenuse:

you know that x (the angle) = 42 and the adjacent side = 35, so:

cos (42) = 35/y

y = 35/cos(42)

y = 47.1

then, to find x:

use the fact that tan (x) = opposite side/adjacent side

so tan (42) = x/35

x = 35tan(42)

x = 31.5

finally, you know all 3 angles of the triangle have to add up to 180, so to find z you can do:

z + 90 + 42 = 180

z + 132 = 180

z = 48

Answer:

Slope-intercept form: y = 3x - 1

Step-by-step explanation:

We are given that a line passes through the point (-5, -16) and has a slope of 3

We want to write the equation in point-slope form, and simplify it to slope-intercept form (if it is possible to do so).

First, point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

We have both the slope and a point, but let's label the values of everything to avoid confusion + mistakes:

m = 3

[tex]x_1=-5\\y_1=-16[/tex]

Now substitute into the formula (remember: we have NEGATIVE numbers, and the formula uses SUBTRACTION):

[tex]y--16=3(x--5)[/tex]

The equation can be simplified

[tex]y+16=3(x+5)[/tex]

We can also write this in slope-intercept form

Start by distributing 3 to both x and 5 (multiply both x and 5 by 3)

[tex]y+16=3x + 15[/tex]

Subtract 16 from both sides

y = 3x - 1

Answer:

The graph is translated 5 units left and 2 units down

Step-by-step explanation:

transformation =

initially the equation of graph  [tex]y=\sqrt{x-2} = f(x)[/tex]

after transformation the equation becomes [tex]y = \sqrt{x+3} -2 = g(x)[/tex]

transformation done [tex]f(x) = \sqrt{x-2}[/tex]  → [tex]g(x) = \sqrt{x+3} -2[/tex]

it depends on the value of h. The horizontal shift is described as:

g(x) = f(x + h) - The graph is shifted to the left h units.

g(x) = f(x - h) - The graph is shifted to the right h units.

if h=0,  means that the graph is not shifted to the left or right

The vertical shift depends on the value of k. The vertical shift is described

as:

g(x) = f(x) +k    - The graph is shifted up k units.

g(x) = f(x)- k     - The graph is shifted down k units.

so here in the question the graph is shifted 5 units left and then 2 units down

you can see the graph of initial equation and transformed equation below.

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The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

The expression is given as:

[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]

Open the inner bracket

[tex]\frac{x^3 -y^3}{(x - y}[/tex]

Apply the difference of two cubes to the numerator

[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]

Cancel out the common factors

[tex]x^2+xy+y^2[/tex]

Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

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Answer: 6 years ago

Step-by-step explanation: Since Chad is 34 years younger than Johann, Chad is currently 26. 60 divided by 3 (since the question says three times) is 20, and 26 (Chad’s current age) minus 20 is 6. So, 6 years is the correct answer.

Answer:

  21 years

Step-by-step explanation:

Let x represent the number of years since Johann was 3 times Chad's age. The given relation can be written as the equation ...

  (60 -x) = 3(34 -x)

__

Solving this, we have ...

  60 -x = 102 -3x . . . . . eliminate parentheses

  2x = 42 . . . . . . . . . add 3x-60

  x = 21 . . . . . . . . .divide by 2

21 years ago, Johann was 3 times as old as Chad.

_____

Additional comments

Their ages then were 39 and 13.

If you recognize the age difference is 60-34 = 26 years, and that J will be 3×C when C's age is half that difference, then you know C was 13 at that time. That was 34-13 = 21 years ago.

The number of students is 33.2 million

Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.

Given:

In 2019= 16.6 million

% decrease = 5%

So,

% decrease= x - 16.6/ x

5% = x- 16.6/x

0.05= (x-16.6)/x

0.05x = x-16.6

-0.05 x = -16.6

x= 16.6/0.05

x= 16600000/0.05

x= 332,000,000

x= 33.2 million.

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The shaded area for the inequality y > -3-(5/4)x is given below.

The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.

The given inequality is -5x-4y<12

solving this inequality for y

-5x-4y<12

⇒ -4y<12+5x

⇒y > (12+5x)/(-4)

⇒y > -3-(5/4)x

the line y= -3-(5/4)x has y intersection at (0,-3) and  x intersection at (-12/5,0).

The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).

Therefore the shaded area for the inequality y > -3-(5/4)x is given below.

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[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: 5x = 3x + 12[/tex]

[ by vertical opposite angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 5x - 3x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 12 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 6[/tex]

Therefore, the correct choice is D. 6

Answer:

48 cm²

Explanation:

Let the breadth be b, then the length is 3b

P = 2(Length + Breadth)

32 = 2(3b + b)

32 = 2(4b)

8b = 32

b = 4

Breadth is 4 cm

Length: 3b = 3(4) = 12 cm

Area of rectangle:

Length × Breadth

12 × 4

48 cm²

Given :-

To Find :-

Solution :-

Using formula;

Where;

We have;

By putting all values in formula we get;

→ 2(3x + x) = 32

→ 2(4x) = 32

→ 2 × 4x = 32

→ 8x = 32

→ x = 32/8

After dividing 32 with 8, we get;

→ x = 4

Hence;

Now, using formula;

Where;

We have;

By putting all values in formula we get;

→ Area of rectangle = 12 × 4

By multiplying 12 with 4, we get;

→ Area of rectangle = 48 cm²

Answer:

B) 8cm, 15cm, 17cm

Step-by-step explanation:

We will use angle sum property for this question. (Angle sum property means the addition of the 2 smallest sides have to be larger or equal to the biggest side)

We will try it with all the options.

Option A) 5+8=13. Which is not greater then 17 so it cant be a right triangle.

Option B) 8+15=23. Which is greater then 17 so it can be a right triangle

Hope I helped

The baby is 111.3 ounces or 6.96 pounds lighter than an average baby.

Weight is the measurement of Gravitational force on an object.

It can be zero as in the space.

It is given in the question that

A baby weighed only 8.7 ounces at birth

weight of an average baby is 7lb 8 ounces

1 lb = 16 ounce

an average baby weight = 7 * 16 +8 = 120 ounces

The baby weight is just 8.7 ounces

so the baby is 120-8.7 = 111.3 ounces lighter than an average baby.

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Answer:

175

Step-by-step explanation:

Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)

For the given problem, the average queue length is:

Average queue length = (50 * 35) / (1 - 50 * 35)

= 175

Answer:

x = 9/2

Step-by-step explanation:

√2x + √2x = 6

2√2x = 6

2√2x/2 = 6/2

√2x = 3

(√2x)² =( 3)²

2x = 9

x = 9/2

Answer:

x = 4.5

Explanation:

[tex]\rightarrow \sf \sqrt{2x} + \sqrt{2x} = 6[/tex]

add following

[tex]\rightarrow \sf 2\sqrt{2x} = 6[/tex]

divide both sides by 2

[tex]\rightarrow \sf \sqrt{2x} = 3[/tex]

square both sides

[tex]\rightarrow \sf 2x = 3^2[/tex]

simplify the following

[tex]\rightarrow \sf 2x = 9[/tex]

divide both sides by 2

[tex]\rightarrow \sf x = 4.5[/tex]

The composite function is given as follows:

[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]

The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

The composite function is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

Hence the composite function is:

[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]

For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:

[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]

[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]

Hence the domain is:

[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

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Step-by-step explanation:

sin(x/2) = sqrt((1 - cos(x))/2)

cos(x/2) = sqrt((1 + cos(x))/2)

tan(x/2) = sin(x/2)/cos(x/2)

sin(x) = 15/17

so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.

via Pythagoras we get the 3rd, horizontal side :

17² = 15² + side²

289 = 225 + side²

64 = side²

side = 8

cos(x) = 8/17

sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =

= 0.514495755...

cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =

= 0.857492926...

tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =

= 3/5 = 0.6

Answer:

The answer is 1.5.

Step-by-step explanation:

I don't have one