1. Use the given conditions to write an equation for the line in​ point-slope form and general form. Passing through (−4,4) and parallel to the line whose equation is 7x−9y−8=0 Question content area bottom Part 1 The equation of the line in​ point-slope form is enter your response here. ​(Type an equation. Use integers or fractions for any numbers in the​ equation.) Part 2 The equation of the line in general form is enter your response here=0. ​(Type an expression using x and y as the variables. Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]

Step 2: Separate into possible cases.

[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]

Step 3: Solve for x in both cases.

[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]

[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]

Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

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Answer:

yyjyidsksjsjsosiddhdoehsudidhdhsjidjsjsjejsksksksjsjsjdd

Using proportions, it is found that his net pay is of $158,040.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

His first discount is for the retirement account, hence the taxable amount is:

T = 240000 - 20500 = $219,500.

He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of  $219,500, hence:

N = 0.72 x 219500 = $158,040.

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Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

y+(4/2)^2 = x^2+4x+(4/2)^2

y+4 = x^2 + 4x + 4

y+4 = (x+2)^2

y = (x+2)^2 - 4

This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)

There are 32 subsets of the set h.

We have given that h={A,E,I,O,U},

We should count the elements of the set, then put that number as the exponent of 2.

A set A is a subset of another set B if all elements of set A are elements of set B. In other words, set A is contained inside set B.

Remember that 2 should always be the base in finding the number of subsets: 2^5=32

Therefore there are 32 subsets of the set h.

Here set h is denoted by small h but the set is always denoted by capital letters.

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The expression that is equivalent to the given expression is [tex]3\sqrt[6]{z}[/tex]

From the question, we are to determine which of the expressions is equivalent to the given expression

The given expression is

[tex]6\sqrt{z} \div \sqrt[3]{8z}[/tex]

The expression can be simplified as

[tex]6\sqrt{z} \div \sqrt[3]{8z}[/tex]

[tex]\frac{6\sqrt{z}}{\sqrt[3]{8z}}[/tex]

[tex]= \frac{6 \times \sqrt{z}}{\sqrt[3]{8} \times \sqrt[3]{z}}[/tex]

[tex]= \frac{6 \times z^{\frac{1}{2} } }{2 \times z^{\frac{1}{3} }}[/tex]

[tex]= 3\times z^{\frac{1}{2} -\frac{1}{3}}[/tex]

[tex]= 3\times z^{\frac{1}{6}}[/tex]

[tex]= 3\times\sqrt[6]{z}[/tex]

[tex]= 3\sqrt[6]{z}[/tex]

Hence, the expression that is equivalent to the given expression is [tex]3\sqrt[6]{z}[/tex]

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Answer:

has no x^2 term

Step-by-step explanation:

Has no x^2 term   <====== that would make it an exponential function, not linear

Answer:

x = 95°

y = 40°

z = 95°

Step-by-step explanation:

Answer:

07698+96965#5_(-&)!:86539'6";

The solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The given equation will be solved as:-

= 3x² + 8x - 10  

Using the formula of factors:-

x = [tex]\dfrac{-b\pm\sqrt{b^-4ac}}{2a}[/tex]

x = [tex]\dfrac{-8\pm\sqrt{64-(-120)}}{2\times 3}[/tex]

x = [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

Therefore the solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

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The answer to the question is 5 units up.

Answer:

x=3

Step-by-step explanation:

6x-3x=16-7

3x=16-7

3x=9

x=3

Answer:

u = 10 ft

Step-by-step explanation:

cuboid volume = w × h × l

width * hight * length

560 = 7 × 8 × u

u = 10 ft

Answer:

u = 10 ft

Step-by-step explanation:

Volume of a rectangular prism = lwh

where:

Given:

Substitute the given values into the formula and solve for h:

⇒ 560 = 8 × 7 × u

⇒ 560 = 56u

⇒ 56u ÷ 56 = 560 ÷ 56

⇒ u = 10 ft

Therefore, the height of the prism is 10 ft.

Answer:

4/9, 49%, 4,9

Step-by-step explanation:

4/9=0,444444

49%=0,49

4,9=4,9

A function assigns the values. The value of g(x) can be filled as 4, 6, 9, and 13.5, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

The value of g(x) can be found by substituting the value of x as given in the function. Therefore, the values will be,

A.) x = -1

[tex]g(-1) = 6(\dfrac32)^{-1}\\\\g(-1) = 4[/tex]

B.) x = 0

[tex]g(0) = 6(\dfrac32)^0\\g(0) = 6[/tex]

C.) x = 1

[tex]g(1) = 6(\dfrac32)^1\\\\g(1) = 9[/tex]

D.) x = 2

[tex]g(2) = 6(\dfrac32)^2\\\\g(2) = 13.5[/tex]

Hence, the value of g(x) can be filled as 4, 6, 9, and 13.5, respectively.

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Answer:

Option 1

Step-by-step explanation:

Angle bisector:

  Angle bisector is a line that divides the angle into two equal angles.

⇒ ∠KLM = ∠MLN

Answer:

4x10 8x5

Step-by-step explanation:

Answer:

0.5774

Step-by-step explanation:

1) Input tan(30) into a calculator to get 0.5773502692...

2) To count 4 decimal places, we start after the decimal point. This means that we end it at the first 3. Additionally, we round 3 up to 4 because of the digit after it which is 5.

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is the tangent of 30, rounded to 4 decimal places?

.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

First, let's focus on this phrase - "tan 30"

.

What in the world could that possibly mean?

"tan" is the tangent, which is one of the six trig ratios.

.

The simplest way to find the tangent of 30 degrees is ... with a calculator!

[tex]\bf tan\quad 30 \approx 0.5774[/tex]

The answer has been rounded to 4 decimal places, like you asked.

Since the fifth decimal place was more than 5, I added 1 to the fourth decimal place - 0.5774, and not 0.5773.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf tan 30\approx 0.5574. \quad Hope\;you\;will\;have\;a\;fantabulous\;day![/tex]

~ [tex]\boxed{\bf aesthetic\;\not{101}}[/tex]~

Answer:

C will be your answer.

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Answer:

the area of rectangle is 270 cm and its length is 18 cm

the breath of the perimeter of given rectangle respectively

used concept

area of rectangle l into b where is is v is breadth of the rectangle perimeter of rectangle 2 into l + b where I and b stands for same as the

solution

let's the length of rectangle is equal to l is equal to 18 cm

breath of rectangle is is equal to b is equal to

area of rectangle is equal to 270 CM

now according to the question and l into b is equal to a

18 into b is equal to 1070

b is equal to 270 upon 18

b is equal to 15 CM

p no no perimeter of the rectangle is equal to 2 into l + b

2 multiply 18 + 15

2 X 33

is equal to 66 cm

therefore the breath and the perimeter of rectangle are 15 cm and 66 respectively

Answer:

-1

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis.

Answer:

[tex]\huge\boxed{\sf y-intercept = -1}[/tex]

Step-by-step explanation:

Here,

Since, this is the point where x = 0 and where the line passes through the y-axis.

[tex]\rule[225]{225}{2}[/tex]

Reason:

I'm assuming that the swimmer travels along the 50 meter side

Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.

The slope- intercept is y> (1-4x) / 5 and y< 2x + 6

A  statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4x – 5y < 1  and 1/2y – x < 3

Solving

4x – 5y < 1

-5y < 1- 4x

-y < (1-4x) / 5

y> (1-4x) / 5

Now, the second inequality,

1/2y – x < 3

1/2y< 3+x

y< 2x + 6

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Answer:

The sea lion dives 24 feet.

Step-by-step explanation:

A seal (S) dives 15 feet.

A sea lion (SL) dives 6 feet less than 2 times the seal's dive.  That can be expressed as:

SL = 2S -6

Since we know S = 15, we can say:

SL = 2*(15) - 6

SL = 24 feet

The sea lion dives 24 feet.

Answer:

  f(-2) = 0

Step-by-step explanation:

The value of the function for a particular x-value can be read from the graph.

The graph is a map showing the value of f(x) for each value of x for which the function is defined. The x-values are identified by the numbers on the horizontal x-axis. The corresponding function values are found by referencing the vertical y-axis.

To find the function value f(x) for x=-2, we locate the vertical grid line marked with -2 at the x-axis. We then locate the point on the graph of the function where it crosses that vertical grid line. Tracking horizontally from that point to the vertical y-axis, we can read the function value from the vertical scale.

The attachment has a red arrow pointing to the intersection of the graph with the grid line x=-2. That point of intersection lies on the x-axis, where the y-value is 0. That means ...

  f(-2) = 0

__

Additional comment

On this graph, the axis crossing point (x=0, y=0) is not labeled. It is halfway between x=-1 and x=1. Similarly, it is halfway between y=-1 and y=1. Based on this and on experience with similar graphs, you can assume that the axis crossing has coordinates (x, y) = (0, 0).

The time it takes = 3 hours 12 minutes

Rate is a ratio which compares two quantities of different units.

Analysis:

Speed = 5 miles/hour

distance covered = 16 miles

speed taken = distance covered/time taken

time taken = 16/ 5 = 3.2 hours = 3 hours 12 minutes

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Answer:

1 7

_

8

Step-by-step explanation:

5 x 3 = 15

5 + 3 = 8

=1 7

_

8

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

To solve the problem substitute the value of n as 5 in each expression and then simplify to check if it equals to 16 or not.

A.) (25/n) + 7

      = (25/5) + 7

      = 12

This is not the required expression.

B.) 30 - 3n

      = 30 - 3(5)

      = 15

This is not the required expression.

C.) 7+ (45/n)

       = 7 + (45/5)

       = 7 + 9

       = 16

This is the required expression.

D.) n² - 114

       = (5)³ - 114

       = 125 - 114

       = 11

This is not the required expression.

Hence, the correct option is C.

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Answer:

Equation of parabola is (x+1)²=20(y-3)

Step-by-step explanation:

And the graph above

(x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.

Two or more expressions with an Equal sign is called as Equation.

Given, focus : (-1, 3)

directrix : x + 5 = 0 or x=-5

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

√(x+1)²+(y-3)²=|x+5|

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

√(x+1)²+(y-3)²=|x+5|

squaring both sides,

(x+1)²+(y-3)²=(x+5)²

(x+1)²=20(y-3)

Hence,  (x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.

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Answer:

x² - 4x + 3 = 0

Step-by-step explanation:

given roots x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation is then the product of these factors , that is

(x - a)(x - b) = 0

given

roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then

(x - 3)(x - 1) = 0 ← expand factors using FOIL

x² - 4x + 3 = 0