Find the ratio a:b, if it is given that a+b=4a

Helpppp

Answer:

x = - 3, x = 2

Step-by-step explanation:

Given

x² + x - 6 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)

The factors are + 3 and - 2, since

3 × - 2 = - 6 and 3 - 2 = + 1, hence

(x + 3)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

(-6,0) is the ordered pair for this solution, you might want to double check though

-6,0 is the answer just substitute the numbers and boom

[tex]x=y^2-1\implies y=\pm\sqrt{x+1}[/tex]

We want to find [tex]a[/tex] such that

[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=\int_a^02\sqrt{x+1}\,\mathrm dx[/tex]

On the left,

[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=-1}^{x=a}=4(a+1)^{3/2}[/tex]

and on the right,

[tex]\displaystyle\int_a^02\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=a}^{x=0}=4-4(a+1)^{3/2}[/tex]

For the areas to be equal, we need

[tex]4(a+1)^{3/2}=4-4(a+1)^{3/2}\implies(a+1)^{3/2}=\dfrac12[/tex]

[tex]\implies a=\dfrac1{2^{2/3}}-1\approx-0.370[/tex]

To find the value of 'a' for which the line x = a splits the region into two equal areas, integrate the curve starting from -sqrt(a+1) to sqrt(a+1) and set it equal to the area of the region between the curve and the y-axis.

This question pertains to the concept of finding the area under curves in Calculus. To solve this problem, we need to set up an equation that represents the given situation and solve for 'a'. The line 'x = a' splits the region into two equal areas, meaning the area on the right of the line is equal to the area on the left of the line.

Starting from the x-axis, the curve 'x = y^2 - 1' intersects the line at y = sqrt(a+1) and y = -sqrt(a+1). Thus, we want the integral from -sqrt(a+1) to sqrt(a+1) of the curve to be equal to the area of the region between the curve and the y-axis. Formulate and solve the intergral problem to get the desired value of 'a'.

Additionally, this problem might involve the use of numerical methods like the Simpson's rule or midpoint rule to get an accurate result.

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Answer:

Step-by-step explanation:

f⁻¹(x) is the inverse of f(x).

y = 4x − 9.  To find the inverse, switch x and y and solve for y.

x = 4y − 9

x + 9 = 4y

y = (x + 9) / 4

So the inverse function is:

f⁻¹(x) = (x + 9) / 4

ANSWER

[tex]{f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]

EXPLANATION

The given function is

f(x)=4x-9

Let

y=4x-9

Interchange x and y.

x=4y-9

Add 9 to both sides,

x+9=4y

Divide both sides by 4

[tex] \frac{x + 9}{4} = y[/tex]

[tex]y = \frac{x + 9}{4} [/tex]

Therefore,

[tex] {f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]

Answer:

Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.

Step-by-step explanation:

Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.

The cube of a number (n) divided by two can be mathematically represented as n³/2.

The cube of a number is achieved when you raise that number to the power of 3. If we have a number, let's denote it as 'n', and we cube it, and we get n³. Now, if you are to divide the cube of a number by two, the formula would be n³/2. For example, if n = 2, the cube of 2 is 8, divided by two equals 4.

The cube of a number divided by two means that you take a number raise it to the power of 3, and then divide the result by 2. For example, if the number is 4, the cube of 4 is 4 × 4 × 4 = 64. Dividing 64 by 2 gives you a result of 32.

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Answer:

- 4 + 7i

Step-by-step explanation:

Solving (3+5i) - (7-2i)

= 3 + 5i - 7 + 2i

=3 - 7 + 5i + 2i

= - 4 + 7i

So, (3+5i) - (7-2i) is equivalent to - 4 + 7i

Answer: 3

Step-by-step explanation: 1/2 times, the height which is 3 and times 2 equals the base which is 3.

Final answer:

The problem involves finding the values of x and y in a parallelogram, using given segment lengths. Without an additional equation, we can only express one variable in terms of the other, resulting in the equation 4 = 3x + 2y.

Explanation:

The question is asking us to find the values of x and y in a parallelogram DEFG, where we know the lengths of some segments inside the parallelogram, specifically DH, HF, GH, and HE. As properties of a parallelogram dictate that opposite sides are equal in length, and segments DH and HF form one side, while segments GH and HE form the opposite side, we conclude that DH + HF must equal GH + HE.

Setting up the equation (x + 2) + (2y) = (4x - 3) + (4y + 1), we combine like terms, which gives us x + 2y + 2 = 4x + 4y - 2. Upon further simplification, by subtracting x and 2y from both sides, we get 4 = 3x + 2y. This equation allows us to express one variable in terms of the other.

Finding a specific value for x and y would require additional information, such as another equation involving x and y to solve this system of equations. Without this, we are limited to only expressing one variable in terms of the other.

Answer:

504

Step-by-step explanation:

To find the average of a series of numbers one must add them all then divide by the amount of numbers.

So....

516+497+501+528+476= 2,518

then...

2,518/5 = 503.6

6> 5 so you would round UP

ROUNDED : 504

Answer:

The answer is D.

Step-by-step explanation:

A. 8^3 x 8^2 < 8^4

8^3 = 512    8^2 = 64       512 x 64 = 32768

8^4 = 4096                  32,768 < 4096 is NOT true

B. 4^4 x 4^4 = 4^16

4^4 = 256       256 x 256 = 65536

4^16 = 4294967296

256 = 4294967296   is NOT true

C. 2^2 • 2^6 < 2^8

2^2 = 4     2^6 = 64    64*4 = 256

2^8 = 256             256 < 256   is NOT true

D. 3^3 • 3^3 > 3^5​

3^3 = 27    27*27 = 729

3^5 = 243

729 > 243 IS true

Answer:

1) 15/32

2) 2

Step-by-step explanation:

1) 3 /8  / 5/4

= 3 · 5 /8 · 4

= 15 /32

2) 4/5 * 2 1/2

First solve --> 2 1/2 = 2 · 2 + 1 /2

= 5 /2

Then solve: 4 /5  * 5 /2

= 4 · 5 /5 · 2

= 20 /10

= 2 · 10 /1 · 10

= 2

Answer:

A = 28 in²

Step-by-step explanation:

Equation for the area of a parallelogram: A = b * h

Plug in: A = 7 in * 4 in

Solve: A = 28 in²

Answer:

its 28

Step-by-step explanation:

Answer:

Here's what I get.

Step-by-step explanation:

You have two conditions.

1. The club must raise at least $500, and that comes from the sale of lemonade and water.

Let c = cans of lemonade

and b = bottles of water

Then the first condition is

(1) 2c + 1.50b ≥ 500

2. The club can accept a maximum of 360 cans and bottles

Your second condition is

(2) c + b ≤ 360

Your system of inequalities is

[tex]\left[ \begin{array}{rcl}2c + 1.50b & \geq & 500\\c+b & \leq&360\\\end{array}\right][/tex]

Answer:

4 ounces of flour will make 1 cake.

Step-by-step explanation:

16 ounces = 1 pound

16 ounces divided by 4 cakes = 4 ounces for 1 cake

Jesse needs ⅔ pound or 0.125 pounds (2 ounces) of flour to make one cake, calculated by dividing the half-pound bag of flour by the number of cakes it can produce (4 cakes).

Jesse is baking cakes for a bake sale and needs to know how much flour is needed for one cake.

From the information provided, we know that a ½ pound bag of flour is enough to make 4 cakes.

To determine how much flour is needed for one cake, we use a simple division.

To find the amount of flour per cake, we divide the total amount of flour by the number of cakes that can be made from it. That gives us:

½ pound flour ÷ 4 cakes = ⅔ pound flour per cake.

Therefore, Jesse needs ⅔ pound (which is 0.125 pounds or 2 ounces) of flour to make one cake.

The correct answer is (D) because 3 multiple 1/3, the 3 go with 3 and we get the 1. And 9 multiple 1/3, the 9 go with 3 and we will go 3 multiple 1 and we will get 3.

Answer:

92 squre feeeet you willllll paintttttttttttttttttttttt

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think 33 : this i got by multiplying 75 by 45%

or 166: i got this by dividing 75 by 45%

The total points for 75 positive behaviors points are 33.45.

We have given that,

n order to go on the field trip, you must accrue 75 positive behavior points. You found out that you have 45% of the points necessary to go.

We have to determine the points.

Positive behavior strategies are evidence-based, proactive approaches to changing challenging student behavior.

We have 75 are the positive points so we have,

[tex]75\times 0.45=33.75[/tex]

Therefore we get the total points are 33.45.

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Answer:

The correlation coefficient is 0 which implies no association between the number of apples eaten per week and the times sick in a year.

Step-by-step explanation:

The correlation coefficient between paired data gives information on the strength and the direction of the relationship between the paired data sets. The coefficient of correlation can imply strong or weak association as well as positive or negative association between data sets.

In the data given, the number of apples eaten per week can be used to explain the number of times an individual falls ill per year. This implies that the number of apples eaten per week is our explanatory or independent variable while times sick in a year is our response or dependent variable.

We can use Ms.Excel to compute the correlation coefficient between these two variables;

The first step is to enter the data in two adjacent columns in an excel workbook. We then type;

=CORREL

In an empty cell and enter the data arrays. This is an in-built function that computes the correlation coefficient.

Ms. Excel returns a correlation coefficient of 0. The correlation coefficient of 0 implies no association between the number of apples eaten per week and the times sick in a year.

Answer:

c

Step-by-step explanation:

Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets is 0.23.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that a dot plot shows how many pets each customer owned before entering Jeremy's Pet Store today.

Based on this data we need to find the reasonable estimate of the probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets.

The total number of customer enter  Jeremy's Pet Store is 13.

Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets= 3/13

=0.23

Hence, Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets is 0.23.

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To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion and solve for the unknown variable. The answer is approximately 156 minutes.

To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion using the given information. Since Petra jogs 2 miles in 24 minutes, the rate at which she jogs is 2 miles / 24 minutes. We can use this rate to find out the time it would take her to jog 13 miles.

Set up the proportion: 2 miles / 24 minutes = 13 miles / x minutes. Cross multiply and solve for x to find the answer.

2 miles / 24 minutes = 13 miles / x minutes
2x = 24 × 13
2x = 312
x = 156

So, it would take Petra approximately 156 minutes to jog 13 miles at the same rate.

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Answer:

a² + 4 a + 4

Step-by-step explanation:

( a + 2 ) ( a + 2 )

Expand brackets

a² + 2 a + 2 a + 4

Simplify

a² + 4 a + 4

[tex]\text{Hey there!}[/tex]

[tex]\text{(a + 2)(a + 2)}[/tex]

[tex]\text{In order for you to solve this, you need to DISTRIBUTE}[/tex]

[tex]\text{a(a) = a}^2[/tex]

[tex]\text{a(2) = 2a}[/tex]

[tex]\text{2(a) = 2a}[/tex]

[tex]\text{2(2) = 4}[/tex]

[tex]\text{Next, combine your like terms: 2a \& 2a}[/tex]

[tex]\text{2a + 2a = 4a}[/tex]

[tex]\text{Everything else stays the same because they aren't like terms}[/tex]

[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is:a^2+4a+4}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Step-by-step explanation:

[tex]\log_{12}\left(\dfrac{\frac{1}{2}}{8w}\right)=\log_{12}\left(\dfrac{1}{16w}\right)\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_{12}(16w)^{-1}\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-1\log_{12}(16w)\qquad\text{use}\ \log_a(bc)=\log_ab+\log_ac\\\\=-\left(\log_{12}16+\log_{12}w\right)=-\log_{12}2^4-\log_{12}w\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-4\log_{12}2-\log_{12}w[/tex]

Answer: [tex]=-17[/tex]

Step-by-step explanation:

 The first thing you must remember is the mulplication of signs. You know that:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

You can observe that the number inside the parentheses is positive (+) and the sign that is outside the parentheses is negative (-), therefore, when you multiply these signs you get a negative sign (-). Then you get:

[tex]-6-(11)=-6-11[/tex]

Now, you need to add these numbers. And the result obtained is:

[tex]=-17[/tex]

Answer:

It’s -17

Step-by-step explanation:

I just got it right in the quiz

Answer: OPTION D

Step-by-step explanation:

We know that the function [tex]y=log(x)[/tex] is not defined for values of x less or equal than zero, therefore its domain is [tex](x|x>0)[/tex] and the range is all real numbers.

In this case we have the function [tex]y=log(x-2)+1[/tex], then [tex]x-2[/tex] must be greater than zero.

Then:

[tex]x-2>0\\\\x>2[/tex]

Therefore, the domain of the function is:

[tex]x>2[/tex] or [tex](2, \infty)[/tex]

And the range is:

All real numbers.

Answer:

the answer is D the other guy was right i just tried it.

Step-by-step explanation:

- "Let's see how many packs of each item we can make and what's left over. That's the remainder.

287 = 6(287/6) = 6(47) + 5

143 = 3(143/3) = 3(47) + 2

341 = 7(341/7) = 7(48) + 5

So on that 48th pack we have 5 people markers so need 1 more and 2 dice, so we need one more. We have enough teleport markers for the 48th pack.

Choice A."

540:4500*100 =

(540*100):4500 =

54000:4500 = 12%

(a+3)(a-2)

a^2-2a+3a-6

a^2+a-6

Answer is a^2+a-6

You must FOIL (first, outside, inside, last)

First (The first number/variable of each parentheses must be multiplied together)

(a + 3)(a - 2)

[tex]a^{2}[/tex]

Outside (The outside number/variable of each parentheses must be multiplied together)

(a + 3)( a - 2)

-2a

Inside (The inside number/variable of each parentheses must be multiplied together)

(a + 3)(a - 2)

3a

Last (The last number/variable of each parentheses must be multiplied together)

(a + 3)( a - 2)

-6

Now add/subtract each FOIL answer according to its sign

[tex]a^{2}[/tex] - 2a + 3a - 6

Combine like terms

[tex]a^{2}[/tex] + a - 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Check the picture below.

so, let's notice, is really just a 2x20 rectangle with a quarter of a semicircle with a radius of 11.

[tex]\bf \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \implies A=\pi 11^2\implies A=121\pi \implies \stackrel{\textit{one quarter of that}}{\boxed{A=\cfrac{121\pi }{4}}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\underline{\textit{area of the figure}}}{\stackrel{\textit{rectangle's area}}{(2\cdot 20)}+\stackrel{\textit{circle's quart's area}}{\cfrac{121\pi }{4}}\qquad \approx \qquad 135.03\implies \stackrel{\textit{rounded up}}{135}}[/tex]

Answer:

i think its A

Step-by-step explanation:

The correct steps are:

start with

[tex]x^2+8x+15=0[/tex]

Add 1 to both sides:

[tex]x^2+8x+16=1[/tex]

The left hand side is a perfect square:

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

Answer:

Option D

Step-by-step explanation:

The given expression is x² + 8x + 15 = 0

We have to solve it further to transform into the form ( x - p )² = q

x² + 8x + 15 = 0

[ x² + 8x + 15 ] + 1 = 0 + 1

x² + 8x + 16 = 1

( x + 4 )² = 1

Option D is the answer.