Rewrite 4x = y +6 in slope-intercept form.

2. and 3. are already in slope intercept form.

1. y=4x-2

4. y=3x-2

Final answer:

Jack is 64 years old and Jill is 46 years old. These ages satisfy the conditions that the digits of Jack's age reversed are Jill's age, the sum of their ages is 11 times the difference, and Jack is older than Jill.

Explanation:

The puzzle presented by Jack and Jill to their son, Junior, involves figuring out their ages with a given set of clues:

If you reverse the digits in Jack's age, you get Jill's age.

The sum of both Jack's and Jill's ages is equal to 11 times the difference in their ages.

Jack is older than Jill.

Let's denote Jack's age as 10a + b and Jill's age as 10b + a, where a and b are the tens and units digits of Jack's age, respectively. Based on the clues:

10a + b + 10b + a = 11(a - b)

This simplifies to:

Without the third clue, there would be multiple solutions. However, the third clue tells us that Jack is older than Jill, meaning a > b. The possible ages for Jack (from 10-99) that have a digit twice the size of the other would be: 31, 42, 53, 64, 75, 86, and 97. The age of 97 can be discounted as being unrealistic, leaving us with a smaller set of possibilities.

By trial and elimination, we find that Jack is 64 years old and Jill is 46 years old, which fits all the given clues and is a plausible answer.

Final answer:

90,708,501 cubic feet .

Explanation:

The volume of a pyramid is calculated by using the formula V = (1/3) × (base area) × (height). Since Becky learned that the Great Pyramid of Giza has a square base with each side measuring 751 feet, we can calculate the base area as follows: base area = side × side = 751 feet × 751 feet. We then multiply this area by the height of the pyramid, which is 481 feet, and divide by 3 to find the volume. The calculation is as follows:

base area = 751 ft × 751 ft

Volume = (1/3) × base area × height

Volume = (1/3) × (751 × 751) ft² × 481 ft

Volume = 90,708,501 ft³

Answer:

one solution : x = -1

Step-by-step explanation:

look this solution :

The solutions of the given rational equation are negative one and three.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The rational equation is given below.

[tex]\rm \dfrac{1}{x-4} + \dfrac{x}{x-2} = \dfrac{2}{x^2-6x+8}[/tex]

By solving the equation, then we have

[tex]\begin{aligned} \dfrac{1}{x-4} + \dfrac{x}{x-2} &= \dfrac{2}{x^2-6x+8}\\\\ \dfrac{x- 2 + x(x - 4)}{(x-4)(x - 2)} &= \dfrac{2}{x^2-6x+8}\\\\\dfrac{x^2 -4x + x - 2}{x^2 - 6x + 8} &= \dfrac{2}{x^2-6x+8}\\\\x^2 - 3x - 2 &= 2\\\\x^2 - 3x - 4 &= 0\end[/tex]

Then the solution of the equation will be

          x² - 3x - 4 = 0

    x² - 4x + x - 4 = 0

x(x - 4) + 1 (x - 4) = 0

       (x - 4)(x + 1) = 0

                       x = -1, 4

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Answer:

24 minutes.

Step-by-step explanation:

This question shows up in a great many places in math or physics, so it is a pretty good question to learn how to do.

First you should note that answer will be under 40 minutes.

1/40 + 1/60 = 1/TimeTotal

The common denominator on the left is 120 minutes

3/40*3 + 2/60*2 = 1/timetotal

3/120 + 2/120      = 1/ timetotal

5/120 = 1/time total  Now to use to the key stop

What you do now is you always turn the left side over. You do the same thing to total time.

120/5 = total time

24 = total time

What this means is that if you let both pipes run for 24 minutes, they will fill the tank working together.

Answer:

D. Only one

Step-by-step explanation:

Lines are perpendicular if they intersect to form a right angle (90°).

The perpendicular postulate tells you that when you have a line and a point not on the line, then there is only one perpendicular line that can be drawn through the point to the line.

Final answer:

From a point not on a given line, only one perpendicular line to the given line can be drawn, as it is the shortest and unique path between the point and the line.

Explanation:

The question relates to the geometric concept of drawing perpendicular lines to a given line from a point outside of that line. According to geometric principles, through a point not on a given line, you can draw only one perpendicular line to the given line. This is because the perpendicular line is the shortest path between a point and a line, and only one unique shortest distance exists, as any other line from the point to the given line will be longer. Therefore, if you were given a point and a line that the point is not on, you could take a ruler or a straight edge and draw exactly one line that crosses the original line at a 90-degree angle, demonstrating a perpendicular connection.

Answer:

C.) Linear

Step-by-step explanation:

The line of best fit is a straight line.

Linear also make sense because the more nickles minted in a year, the more chance for a nickle to be from that year.

Answer:

A

Step-by-step explanation:

Given 2 sides and the included angle use the Cosine rule to solve for x

x² = 1.6² + 1.1² - (2 × 1.6 × 1.1 × cos78° )

    = 2.56 + 1.21 - ( 3.52 × cos78° )

   = 3.77 - 0.7318

   = 3.0382

Take the square root of both sides

x = [tex]\sqrt{3.0382}[/tex] = 1.7 → A

Answer:

625 mm

Step-by-step explanation:

$50 worth in dimes is 500 dimes. 500 dimes times 1.25mm per dime = 625mm

Answer:

3 /2

Explanation:

If two lines are perpendicular , when you multiply the gradients together you get -1

The slope of a line is 2/3 What is the slope of a line that is perpendicular to this line?

Answer:

-3/2

Answer:

Final answer is [tex]F\left(1\right)=0.2625[/tex].

Step-by-step explanation:

Given function is [tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex].

Now we need to use that function [tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex] to find the value of F(1).

F(1) means value of functino F(t) at t=1, So plug t=1 into given function.

[tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex]

[tex]F\left(1\right)=\frac{2.1}{2^3(1)}[/tex]

[tex]F\left(1\right)=\frac{2.1}{8(1)}[/tex]

[tex]F\left(1\right)=\frac{2.1}{8}[/tex]

[tex]F\left(1\right)=0.2625[/tex]

Hence final answer is [tex]F\left(1\right)=0.2625[/tex].

Answer:

The solution is [tex]F(1) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given function is [tex]2\times \frac{1}{2^{3t}}[/tex]

We need to find the value of function [tex]F(t) = 2\times \frac{1}{2^{3t}}[/tex] at t = 1

Replace t with 1 in [tex]F(t) = 2\times \frac{1}{2^{3t}}[/tex]

[tex]F(1) = 2\times \frac{1}{2^{3(1)}}[/tex]

[tex]F(1) = 2\times \frac{1}{2^{3}}[/tex]

[tex]F(1) = 2\times \frac{1}{8}[/tex]

[tex]F(1) = \frac{2}{8}[/tex]

[tex]F(1) = \frac{1}{4}[/tex]

Therefore, the solution is [tex]F(1) = \frac{1}{4}[/tex]

Answer:

I don't understand the question take a snip it or take a picture of the question

Step-by-step explanation:

Answers= 12, 30 and 10.

Explanation: 12-5 is 7

30-5 is 25

15-5 is 10

ANSWER

{x|x<0} and {x|x>0}

EXPLANATION

If the two inequalities have an intersection,then it has a solution.

If the two inequalities have no intersection, then there is no solution.

The inequality {x|x<0} and {x|x>0} has no intersection, there is no solution.

The inequalities

{x|x≤0} and {x|x≥0},

{x|x≤0} or {x|x≥0}

both have intersection, therefore have solutions.

Answer:

x = [tex]\frac{-3}{k}[/tex]

Step-by-step explanation:

Given

kx + 7 = 4 ( isolate the term in x by subtracting 7 from both sides )

kx = - 3 ( divide both sides by k )

x = [tex]\frac{-3}{k}[/tex] = - [tex]\frac{3}{k}[/tex]

Answer:

The value of the equation for x is [tex]x=\frac{-3}{k}[/tex]

Step-by-step explanation:

Consider the provided equation.

[tex]kx+7=4[/tex]

We need to solve the equation for x.

Subtract 7 from both the sides.

[tex]kx+7-7=4-7[/tex]

[tex]kx=-3[/tex]

Divide both sides of the equation with k.

[tex]\frac{kx}{k}=\frac{-3}{k}[/tex]

[tex]x=\frac{-3}{k}[/tex]

Hence, the value of the equation for x is [tex]x=\frac{-3}{k}[/tex]

Answer:

54 kilometers

Step-by-step explanation:

87x6 or 522km - 78x6km or 468 = 54

The falcon can fly 54km further than the goose.

How to find the difference between the distance traveled by the falcon and the goose?

Speed of the falcon = 87km/hr

Speed of the goose = 78km/hr

speed = [tex]\frac{distance}{time}[/tex]

distance = speed*time

Distance traveled by falcon in 6 hours = 87*6 km = 522km

Distance traveled by goose in 6 hours = 78*6 km = 468 km

How much further the falcon fly

= Distance traveled by falcon - Distance traveled by goose

= (522 - 468 )km

=54km

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The answer is:

The second option:

[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]

From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).

So,

Working with the length of the box:

Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(8-(x+x))=(8-2x)[/tex]

Now,

Working with the width of the box:

Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(6-(x+x))=(6-2x)[/tex]

Now that we already know the length and the width of the box, we must remember that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:

[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]

Have a nice day!

Answer: The second option!

Step-by-step explanation:

3Ac?????????????????

Okay!

The most important part of this problem is knowing which inequality sign to use

Greater than >

Less Than  <

Equal to .. =

Greater or equal to ≥

Less than or equal to  ≤

Charlotte needs AT LEAST 5,000 votes, meaning she has to have 5,000 votes or more

That means we use this sign →  ≤

Now lets set up an equation to find how many more we need

5,000  ≤  3,187 + X

solve for X

1,813 ≤ X

Hope I helped :) Sorry for the long explanation

Answer:

Vertex = (-1,4).

Step-by-step explanation:

Given equation is [tex]y=-(x-1)(x+3)[/tex].

Now we need to find the vertex of the graph of given function [tex]y=-(x-1)(x+3)[/tex].

To find that we can rewrite given function into vertex form

[tex]y=-(x-1)(x+3)[/tex]

[tex]y=-(x^2+3x-1x-3)[/tex]

[tex]y=-(x^2+2x-3)[/tex]

[tex]y=-(x^2+2x+1-1-3)[/tex]

[tex]y=-((x+1)^2-1-3)[/tex]

[tex]y=-((x+1)^2-4)[/tex]

[tex]y=-(x+1)^2+4[/tex]

Now compar this equation with [tex]y=a(x-h)^2+k[/tex]

we get: h=-1, k=4

Hence vertex is (h,k) or (-1,4).

Final answer:

The vertex of the graph of the function y = -(x-1)(x+3) is at the point (-1, -2).

Explanation:

The vertex of the graph of the function y = -(x-1)(x+3) can be found by rewriting this function in vertex form or by calculating the axis of symmetry and the value of the function at that point. Since the function is in factored form, we need to find the axis of symmetry which is the average of the x-values of the roots (x-intercepts). In this case, the roots are x = 1 and x = -3.

To find the axis of symmetry, we take the average of 1 and -3, which gives us:

((1) + (-3))/2 = (-2)/2 = -1

Now, we plug x = -1 into the function to find the y-coordinate of the vertex:

y = -((-1)-1)((-1)+3) = -(1)(2) = -2

Therefore, the vertex of the graph of the function is at (-1, -2).

Answer:

[tex]\large\boxed{y=-(x+5)^2+4}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of an quadratic equation}\\\\f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=\dfrac{-b}{2a}\\\\k=f(k)=\dfrac{-(b^2-4ac)}{4a}\\=================================[/tex]

[tex]\text{We have:}\\\\y=-x^2-10x-21\\\\a=-1,\ b=-10,\ c=-21\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)-21=-25+50-21=4\\\\y=-(x-(-5))^2+4=-(x+5)^2+4[/tex]

Final answer:

The vertex form of the quadratic equation  [tex]y = -x^2 - 10x - 21[/tex]is  [tex]y = -(x + 5)^2 + 4[/tex], with the vertex being (-5, 4).

Explanation:

To find the vertex form of the quadratic equation  [tex]y = -x^2 - 10x - 21[/tex], we need to complete the square. Here's a step-by-step guide:

Start with the given quadratic equation:  [tex]y = -x^2 - 10x - 21.[/tex]

Factor out the coefficient of the  [tex]x^2[/tex]term from the first two terms:  [tex]y = -(x^2 + 10x) - 21.[/tex]

Find the number that completes the square for the expression [tex]x^2 + 10x.[/tex]This is  [tex](10/2)^2 = 25.[/tex]

Add and subtract this number inside the parentheses, then group the perfect square and the constant terms: y = -[tex](x^2 + 10x + 25 - 25) - 21.[/tex]

Rewrite the equation, recognizing the perfect square trinomial:  [tex]y = -[(x + 5)^2 - 25] - 21.[/tex]

Combine the constant terms: [tex]y = -(x + 5)^2 + 4.[/tex]

The vertex form of the equation is  [tex]y = -(x + 5)^2 + 4[/tex], where the vertex of the parabola is (-5, 4).

The square root of 44 is 6.633249581

If you were going to round to the nearest whole number, it would be seven.

Hope that helps!

The value square root of 44 is 6.63 thus nearest integer of the square root of 44​ will be 7.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep it as it is.

As per the given,

The square root of 44​ = √44

√44 = 6.633249581

Since 6 > 5 so it will round up to the nearest integer.

6.633249581 → 7

Hence "The value square root of 44 is 6.63 thus nearest integer of the square root of 44​ will be 7".

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Answer:

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

Step-by-step explanation:

The given logarithmic equation is

[tex]\log_{3x+4}(4096)=4[/tex]

We take antilogarithm to get:

[tex]4096=(3x+4)^4[/tex]

We write the left hand side as a power.

[tex]8^4=(3x+4)^4[/tex]

Since the exponents are the same the bases are also equal.

[tex]8=3x+4[/tex]

[tex]8-4=3x[/tex]

[tex]4=3x[/tex]

Divide both sides by 3;

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

Answer:

75

Step-by-step explanation:

Henry started with 20 convertibles and 5 trucks.

His aunt bought him x miniature trucks.

Now, his convertibles represent 1/5 of his collection.  How many trucks did her aunt buy?

So, if his convertible represent 1/5 of his collection now, that means his collection is 5 times larger than the number of convertibles.  We know he has 20 convertibles... so the collection now counts 100 (5 * 20) items.

Out of 100 items, we remove the 20 convertibles to get a total of 80 trucks.

Then we subtract the initial 5 trucks... so, his aunt bought him 75 trucks.

His aunt bought 75 trucks

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

Let :

Number of Additional Miniature Trucks from Henry's Aunt = X

Initial Number of Convertibles = 20

Initial Number of Trucks = 5

Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertible.

[tex]\frac{1}{5}( 20 + 5 + x ) = 20[/tex]

[tex]\frac{1}{5}( 25 + x ) = 20[/tex]

[tex]( 25 + x ) = 20 \div \frac{1}{5}[/tex]

[tex]25 + x = 20 \times \frac{5}{1}[/tex]

[tex]25 + x = \frac{20 \times 5}{1}[/tex]

[tex]25 + x = \frac{100}{1}[/tex]

[tex]25 + x = 100[/tex]

[tex]x = 100 - 25[/tex]

[tex]x = \boxed {75 ~ \texttt{trucks}}[/tex]

Henry's aunt bought him 75 trucks

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent

Answer: [tex]1.38\frac{g}{cm^3}[/tex]

Step-by-step explanation:

You need to remember the formula for calculate the density:

[tex]density=\frac{mass}{volume}[/tex]

In this case:

[tex]density_{(rock)}=\frac{mass_{(rock)}}{Volume_{(rock)}}[/tex]

You know that:

[tex]mass_{(rock)}=15.5g[/tex]

And when it is placed in a graduated cylinder, the volume is displaced from 25.0 mL to 36.2 mL.

Then, the volume of the rock is:

[tex]Volume_{(rock)}=36.2mL-25.0mL=11.2mL[/tex]

Since [tex]1mL=1cm^3[/tex], you can rewrite the volume as:

[tex]Volume_{(rock)}=11.2cm^3[/tex]

Substituting values into the formula, you get that the density of the rock is:

[tex]density_{(rock)}=\frac{15.5g}{11.2cm^3}=1.38\frac{g}{cm^3}[/tex]

Answer: the answer is 12 dollars

Step-by-step explanation: turn the percent 15 into a decimal, then just multiply .15*80 to get your answer

Answer: $12

Step-by-step explanation: 80$ is the cost. you're taking 15% of the cost. 15% of the cost is .15 of 80$. .15 x 80 is 12

Answer:

y = √-2x+7

y = -√-2x+7

Answer:

x² + y² - 4x + 1 = 0

Step-by-step explanation:

The equation of a circle in general form is

x² + y² + 2gx + 2fy + c = 0

Given

(x - 2)² + y² = 3 ← expand the squared factor

x² - 4x + 4 + y² = 3 ( subtract 3 from both sides )

x² + y² - 4x + 1 = 0 ← in general form

Answer:

d=5.39 units

Step-by-step explanation:

Given A (-3, -2)  

T= (x+5, y-3)

T= (-3+5, -2-3)

T=(2,-5)

Applying the translation on;

A( -3,-2)

A' (-3+2, -2+ -5)

A'= (-1, -7)

Distance

d= [tex]\sqrt { X2-X1)^2 + (Y2-Y1)^2[/tex]

A = (-3,-2)     and  A'(-1, -7)

d=√ (-1--3)² + (-7--2)²

d=√ (2)²+(-5)²

d=√4+25

d=√29

d=5.39 units

Answer:

The coordinates of point N are (-13 , -20)

Step-by-step explanation:

* Lets revise how to find the mid-point of a segment

- If a line has two endpoints(x1 , y1) and (x2 , y2), then we can find

 the mid-point (x , y) of it by using this rule

 x = (x1 + x2)/2  and y = (y1 + y2)/2

* Now lets solve the problem

∵ The line segment is MN

∵ M is (3 , 4)

∵ The mid-point is (-5 , -8)

- Let M is (x1 , y1) and N is (x2 , y2)

- Let the mid-point is (x , y)

∴ x1 = 3 , y1 = 4

∴ x = -5 , y = -8

∵ x = (x1 + x2)/2

∴ -5 = (3 + x2)/2 ⇒ multiply both sides by 2

∴ -10 = 3 + x2 ⇒ subtract 3 from both sides

∴ x2 = -13

∵ y = (y1 + y2)/2

∴ -8 = (4 + y2)/2 ⇒ multiply both sides by 2

∴ -16 = 4 + y2 ⇒ subtract 4 from both sides

∴ y2 = -20

∴ The coordinates of point N are (-13 , -20)

Answer:

(-13 , -20) TRUST me

Step-by-step explanation:

X = 50

To solve this equation you would use 2x-5=95

Then you would solve and X = 50