20 POINTS!
Use the graph of the line to answer the questions.

1. What is an equation of the line in point-slope form?

2. How can the point-slope form be written in function notation?

Answer:

55, -150, -78

Step-by-step explanation:

The given inequality is:

[tex]11>\frac{a}{4}-16[/tex]

Adding 16 to both sides, we get:

[tex]11+16>\frac{a}{4}-16+16\\\\ 27>\frac{a}{4}[/tex]

Multiplying both sides by 4, we get:

[tex]27 \times {4}>\frac{a}{4} \times 4\\\\ 108>a[/tex]

Hence, the solution to the inequality is 108 > a or this can be written as a < 108

This means, the values less than 108 are a solution of the given inequality. 108 is not a part of the solution as the inequality symbol says less than 108.

Among the given options following are the values that are less than 108 and thus will satisfy the inequality:

55, -150, -78

Answer:

[tex]\$300[/tex]

Step-by-step explanation:

In this problem we have a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value ( value of the function when the value of x is equal to zero)

b is the base

r is the rate

b=1+r

we have

[tex]f(x)=300(1+0.03)^{x}[/tex]

therefore

The term that represents the amount of money originally deposited in the account is the initial value

For x=0

substitute

[tex]f(0)=300(1+0.03)^{0}[/tex]

[tex]f(0)=\$300[/tex]

Answer:

The correct option is 1.

Step-by-step explanation:

The function is

[tex]f(x)=300(1+0.03)^x[/tex]

We need to find the term that represents the amount of money originally deposited in the account. It means we need to find the initial amount.

Substitute x=0 in the given function, to find the initial value of the function.

[tex]f(0)=300(1+0.03)^(0)[/tex]

[tex]f(0)=300(1)[/tex]

[tex]f(0)=300[/tex]

The term 300 represents the amount of money originally deposited in the account. Therefore the correct option is 1.

for a vertically opening parabola, its axis of symmetry will come from the x-coordinate of its vertex, thus

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-6}{2(1)}~~,~~-7-\cfrac{(-6)^2}{4(1)} \right)\implies (3~~,~~-7-9)\implies (3~~,~~-16) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=3}~\hfill[/tex]

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-3) \\\\\\ y+9=4x-12\implies y=4x-21[/tex]

Answer:

4

because if you cross off one number at a time from each side you are left with 2 number 4s and 4+4/2=4

Let r = range

Range = biggest value minus smallest value

r = 97 - 77

r = 20

Answer:

Range 20

Step-by-step explanation:

First put all the numbers in order from least to greatest

77,79,80,81,83,88,93,94,97,97

To find range you subtract the largest number from the smallest number.

So 97 - 77 = 20

The range is 20

Hope This Helps!! :}

Solving for x:

Start by distributing the numbers outside the parentheses to inside the parentheses:

-1 + 7x + 42 + 6x = 36

Now combine like (similar) terms:

13x + 41 = 36

Subtract 41 from both sides:

13x = -5

Divide both sides by 13:

x = [tex]-\frac{5}{13}[/tex]

Therefore, x = [tex]-\frac{5}{13}[/tex].

Hope this helps! :)

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Round the answer as needed

To find the original number that increased by 130% equals 69, we divide 69 by 2.30, which reveals that the original number is 30.

The student is asking how to find a number that, when increased by 130%, results in 69. To solve this problem, let's represent the original number as x. The increase by 130% of the original number would be x + 1.30x (which equals 2.30x), and this sum is equal to 69. To find x, we divide 69 by 2.30:

x = 69 / 2.30

We calculate this as:

x = 30

Therefore, the number which when increased by 130% equals 69 is 30.

Answer:

[tex]\large\boxed{x>-1}[/tex]

Step-by-step explanation:

In this question, we're trying to solve for x.

In other words, we're going to need to get x by itself in order to get our answer for the inequality.

Solve:

[tex]-2x + 5 <7\\\\\text{Subtract 5 on both sides to get -2x by itself}\\\\-2x<2\\\\\text{Divide both sides by -2}\\\\\text{Since you're dividing by a negative, the} < \text{will flip to} >\\\\x>-1[/tex]

When you're done solving, you should get x > -1

This means that when you solve for x, you should get x > -1

Answer:

Infinite decimals that do not repeat.

Step-by-step explanation:

Repeating decimals can be as fractions where the top and bottom are integers.

Examples: .3333333333333333333333333333333.... can be written as 1/3.

or .19191919191919191919..... can be written as 19/99.

Terminating decimals can also be written as fractions where the top and bottom are integers.

Examples:  .11=11/100 or .161=161/1000

Any number that can be written as a fraction where the top and bottom are integers (bottom integer not 0)

is a rational number.

Repeating decimals are infinite.  So what I think they mean by infinite here is numbers like [tex]\pi[/tex] or [tex]\sqrt{2}[/tex].  There are not rational.  They cannot be written as a fraction where the top and bottom are integers.

Answer:

Rational numbers do NOT include:

infinite decimals

Step-by-step explanation:

Answer:

domain {-1,1.3}

Step-by-step explanation:

The domain is the input values, or in this case the first or x values

domain {3,1,-1,-1}

We do not put the same value twice

domain {3,1,-1}

We like to put them in numerical order

domain {-1,1.3}

Answer:

[tex]y = - \frac{3}{20} {x}^{2} [/tex]

Step-by-step explanation:

The given parabola has focus at:

[tex](0, - \frac{5}{3} )[/tex]

and directrix at

[tex]y = \frac{5}{3} [/tex]

This is a vertical parabola that opens downwards.

The equation is of the form;

[tex] {x}^{2} = - 4py[/tex]

p is the distance from the vertex to the directrix.

Since the vertex is at the origin, we have

[tex]p = \frac{5}{3} [/tex]

We plug this value into the equation to get:

[tex] {x}^{2} = - 4( \frac{5}{3} )y[/tex]

[tex] {x}^{2} = - \frac{20}{3} y[/tex]

We solve for y to obtain:

[tex]y = - \frac{3}{20} {x}^{2} [/tex]

The 3rd option is correct.

Answer:

16 possible hair/clothing combinations

Step-by-step explanation:

1) Brown-dress; 2)Brown-jumpsuit; 3)Brown-pajamas ; 4)Brown-Jeans; 5)Black-Dress; 6)black jumpsuit; 7)black pajamas; 8)black jeans; 9)blonde dress; 10)blond jumpsuit; 11)blonde pajamas; 12)blond jeans; 13)red dress; 14)red jumpsuit; 15)red pajamas; 16)red jeans

Or just multiply 4x4 because there were four of each.

That's true: if a triangle has two congruent angles, then it's an isosceles triangle.

An isosceles triangle has two congruent sides, which are opposite to the congruent angles, and a base, which is the side opposite to the non-congruent angle.

Answer:

165.347 pounds ..

Step-by-step explanation:

The weight of patient is given in kilograms which is

W = 75 kilo grams.

In order to convert the weight into pounds we have to multiply or divide 75 with some number.

There are 2.20462 pounds approximately in one kilogram.

So the weight in pounds will be:

Weight in pounds = 75 * 2.20462

= 165.3465 pounds

= 165.347 pounds ..

Answer:

15.86 inches

Step-by-step explanation:

Area of rectangle = length times width

l = ∛81 inches

w = 3 2/3 inches

= l x w

= ∛81 x 3 2/3

= 15.86 inches

Step-by-step explanation:

Let's say x is the length of the first piece.

The second piece is 2x.

The third piece is 2x.

So the total length is:

x + 2x + 2x = 279

5x = 279

x = 55.8

That means 2x = 111.6.

So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.

Answer:

Piece 1 : 55.8 ft

Piece 2: 111.6 ft

piece 3: 111.6 ft

Step-by-step explanation:

From the question we can see that the total length of the rope is 279 ft and as mentioned it is cut into three pieces. Since the first piece has no length we can give it a variable of x . Piece two is twice as long as piece one, so we can give it a value of 2x . Lastly, piece three is the same as piece two, so it would also be 2x.

So we can now say the following:

[tex]x + 2x + 2x = 279ft[/tex]  .... now we can solve for x.

[tex]5x = 279[/tex]

[tex]x = 55.8 ft[/tex]

So we can see that piece one is 55.8 ft long . Now we can use this value to find pieces two and three.

[tex]2x = P2[/tex]

[tex]2(55.8) = P2[/tex]

[tex]111.6 = P2[/tex]

So pieces two and three are 111.6 ft long

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

depending on the space you're considering, it would be SOMETIMES true. But usually, the 2 lines would be parralel.

What i'm saying is, that in an euclidian space, the 2 lines would be parallel. In another kind of space, the two lines could be anything...

for example: look at how longitude and lattitude are represented on a globe : they are "lines"... 2 sets of perpendicular lines...

Now look at what happens in the poles : all lines intersect! (therefore, they're not parallel, and not necessarily perpendicular either)

Answer:

[tex]\displaystyle =9[/tex]

Step-by-step explanation:

The slope formula is

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle y_2=7\\\displaystyle y_1=(-2)\\\displaystyle x_2=(-6)\\\displaystyle x_1=(-7)[/tex]

[tex]\frac{7-(-2)}{(-6)-(-7)}=\frac{9}{1}=9[/tex]

Therefore, the slope is 9, and the correct answer is 9.

Hope this helps!

Answer:

The correct answer would be true.  Reversing the statement clause and inserting a "not" in a if- then statement will also make the new statement true. For example, "If I eat this, then give me five dollars". The reverse would be " If I do not eat this, then do not give me five dollars". Both sentences mean the same.

Step-by-step explanation:

Answer:

its true

Step-by-step explanation:

Answer:The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2

Step-by-step explanation:

Answer:

A. x-9 and x+9 because these are perfect squares. 9 times -9 is -81. x times x is x^2. 9 + -9 is 0

Answer:

45

Step-by-step explanation:

Um, If we say that all the numbers are 44, and now we add 50, then we will get 270. Find the mean of 270. We get 45.

Final answer:

To find the new average after adding 50 to a set of 5 numbers with an average of 44, multiply the average by the number of elements, add the new number, then divide by the total number of elements to get the new average of 45.

Explanation:

The average of a set of 5 numbers is 44. To find the sum of the original set, multiply the average by the number of elements: 44 x 5 = 220. When 50 is added, there are now 6 numbers in the set. To find the new average, divide the new sum (220 + 50 = 270) by the total number of elements (6) to get 45 as the new average.

Answer:

24 cm2 is the answer or option d

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+2x-8x-16=0\\\\x(x+2)-8(x+2)=0\\\\(x+2)(x-8)=0\iff x+2=0\ \vee\ x-8=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x-8=0\qquad\text{add 8 to both sides}\\x=8[/tex]

Answer:

2 and -8

Explanation is Apex

The answer is:

There is a total of 48 overripe fruit.

To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.

Let be "x" the number of oranges, so:

[tex]Oranges=x\\Apples=x+32[/tex]

Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:

[tex]OverripeApples=\frac{1}{3}(x+32)\\\\OverripeOranges=\frac{3}{5}(x)[/tex]

Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:

[tex]\frac{1}{3}(x+32)=\frac{3}{5}(x)[/tex]

[tex]\frac{1}{3}(x)+\frac{1}{3}(32)=\frac{3}{5}(x)[/tex]

[tex]\frac{1}{3}(32)=\frac{3}{5}(x)-\frac{1}{3}(x)[/tex]

[tex]\frac{1}{3}(32)=\frac{3x*3-1*x}{15}=\frac{9x-5*x}{15}=\frac{4x}{15}[/tex]

[tex]\frac{32}{3}=\frac{4x}{15}[/tex]

[tex]\frac{32*15}{3}=4x[/tex]

[tex]\frac{480}{3}=4x[/tex]

[tex]160=4x[/tex]

[tex]\frac{160}{4}=x[/tex]

[tex]40=x[/tex]

Therefore, we have that there are 40 oranges and 72 apples (40+32).

Now, calculating the number of overripe oranges and apples, we have:

[tex]OverripeApples=\frac{1}{3}(72)=24\\\\OverripeOranges=\frac{3}{5}(40)=24[/tex]

Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.

Have a nice day!

To find the total weight of the shipment where [tex]\frac{1}{5}[/tex] weighs 25 pounds, we use the equation [tex]\frac{1}{5}[/tex]W = 25 and solve for W, leading to a total weight of 125 pounds.

The question is asking us to write an equation that represents the situation where [tex]\frac{1}{5}[/tex] of a shipment of books weighs 25 pounds.

To find the total weight of the shipment, we should set this up as an equation where the total weight of the shipment is represented by W. Since [tex]\frac{1}{5}[/tex] of the shipment weighs 25 pounds, we can write the equation as [tex]\frac{1}{5}[/tex] W = 25.

To find the weight of the whole shipment, we need to multiply both sides of the equation by 5, which will give us

W = 125 pounds.

When converting units such as pounds to ounces, we use the unit equivalence 1 pound = 16 ounces.

If the weight of the books needed to be in ounces, we could convert 125 pounds by multiplying

125 x 16 = 2000 ounces

Answer:

50 degrees

Step-by-step explanation:

all inside angles in every triangle can be added up to equal 180 degrees.

this is a right angle, so one has to be 90 degrees

on the bottom right it's marked 140 degrees on the outside, in order to find the inside angle, you need to subtract 140 from 180, which gives you 40 degrees

180-90=90

90-40=50

so the answer is 50

if that's not clear enough leave a comment, hope this helps!

Answer:

50°

Step-by-step explanation:

Inside angles of a triangle = 180°

The triangle shown is a right triangle.

Therefore, it is 90°

180 - 90 = 90

90 - 40 = 50

Answer = 50°

Answer:

B = 135

A = 60

C = 75

Hope this helps

Answer:

∠B = 135°

∠A = 60°

∠C = 75°

Step-by-step explanation:

Since, Straight Line PQ always has angle 180°

∴ ∠PBS = 180 - ∠ABC

             = 180° - 45° = 135° = ∠B

Since, ∠RAS and ∠BAC are vertically opposite to each other.

So, ∠RAS = ∠BAC

Also ∠RAS = 60°

∴ ∠BAC = 60° = ∠A

The straight line ∠PCQ always has angle 180°.

∴ ∠PCR = 180 - ∠RCQ

⇒ ∠PCR = 180 - 105° = 75° = ∠C