3a+15=55-5a
Solve in detail

The two roots of the quadratic function f(b) = b² - 75 are:

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.

We have

Remember that the root of a function is the value of x when the value of the function is equal to zero.

In this problem

The roots are the values of b when the function f(b) is equal to zero.

So,

For f(b)=0

\(b^2-75=0\)

\(b^2=75\)

Square root both sides

\(b=(+/-)\sqrt{75}\)

Simplify

\(b=(+/-)5\sqrt{3}\)

\(b=5\sqrt{3}\) and \(b=-5\sqrt{3}\)

Therefore

\(\rightarrow\bold{b = 5\sqrt{3}}\)

\(\rightarrow\bold{b=-5\sqrt{3}}\)

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Answer:

Plot points at (0,1) and (-3,3) and draw a line going through both points.

Step-by-step explanation:

Let's start by graphing the y intercept.

y=mx+b

m is the slope. b is the y intercept. Since the equation is y=-2/3x+1, we can conclude the y intercept is 1. We graph a point at (0,1).

If you didn't know the y intercept is where the line intercepts the y-axis.

Now, from the point (0,1) we go up 2 and to the left 3 as it is a negative slope. We reach (-3,3). Plot a point there. Then draw a line going through both points. There's your line!

Answer:can you show a picture of it??

Step-by-step explanation:

Answer:

697.7

Step-by-step explanation:

Answer:

The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s

Step-by-step explanation:

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0  

⇒  x2 - 10x + 5x - 50 = 0  

⇒ x (x - 10) + 5 (x - 10) = 0

⇒  (x+5) (x-10) = 0

⇒   (x+5) (x-10) = 0  

⇒ x =  -5 or 10  

⇒ x = 10 (x = -5 , rejected)

Answer:

x = 33.45

Step-by-step explanation:

We need to find the value of x in the given expression i.e.

\(\sin(42)=\dfrac{x}{50}\)

Multiplying both sides by 50. So

\(\sin(42)\times 50=\dfrac{x}{50}\times 50\\\\x=\sin(42)\times 50\\\\x=33.45\)

So, the value of x is equal to 33.45.

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". The percentage can be calculated by dividing the value by the total value and then multiplying the result by 100.01

First, determine the total amount of lavender solution needed for the 18 ounces of perfume.

This is 18 ounces x 12% = 2.16 ounces.

Next, determine the amount of lavender solution in the 15% solution. This is 2.16 ounces / 0.15 = 14.4 ounces.

Subtract the amount of lavender solution in the 15% solution from the total amount needed. 2.16 - 14.4 = 0.76 oz

Determine how many ounces of the 6% solution are needed. This is 0.76 oz / 0.06 = 12.67 oz

Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.

Hence, Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.

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=break your pencil lead while writing, and = feel overly stressed.

=put together a swing set correctly, and =read the directions.

These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).

=make an error on your income tax return, and =file Form 1040 long.

These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.

=have a salad with dinner, and =work on a home project.

These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.

Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

XZ = 28

Explanation:

The trapezoid is isosceles because it has two equal sides WZ and XY.

The diagonals of isosceles trapezoids have the same length. So, WY is equal to XZ and we can write the following equation:

WY = XZ

15x - 2 = 9x + 10

Then, solving for x, we get:

15x - 2 = 9x + 10

15x - 2 + 2 = 9x + 10 + 2

15x = 9x + 12

15x - 9x = 9x + 12 - 9x

6x = 12

6x/6 = 12/6

x = 2

Therefore, the value of XZ is equal to:

XZ = 9x + 10

XZ = 9(2) + 10

XZ = 18 + 10

XZ = 28

So, the answer is XZ = 28

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

26.5

Step-by-step explanation:

cut the shape into 3 shapes

area of a retangle is = L*W=  5*4 = 20

Area of a triangle =  a= h*b/2 = 3*3/2 = 4.5

Area of a triangle = a= h*b/2 = 2*2/2 =2

Answer:

670,000

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

670,000

Step-by-step explanation:

Here's a tip to help you remeber

5 or more let it score

4 or less let it rest

That means that if the last number is 5 or if it's greater than 5 it will round up. But if it's 4 or less than 4 it will round down.

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer:

16 boxes will be needed for 122 books.

Step-by-step explanation:

Given that,

Each box can hold 8 books.

We need to find the number of boxes needed for 122 books. It can be calculated as follows :

\(\dfrac{122}{8}\) = 15.25

It means 15 boxes can be filled and 16 boxes will be needed for 122 books.

Answer:

e + 2/ 5  = 4

Hope this helps, and be sure to report the answer that had a link

Step-by-step explanation:

Answer:

9 54 divided by 9 = 6  72 - 18 = 54

Step-by-step explanation:

The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.

To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).

The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.

Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.

So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.

Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)

Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.

Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.

Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.

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Answer:

17+21+14+17+12+15+16 / 7 and the answer is 16

Step-by-step explanation:

STEP N0#1 add all the data/ numbers together

STEP NO#2 divide the sum you got by the number of data points/ number

the number you get after dividing is the mean

Step-by-step explanation:

(a) 3pq / 4r² × 2rs / 6q²......first start by expanding the expression

It will be ;

3 × p × q / 4 × r × r X 2 × r × s / 6 × q × q

so now ,cancel out like terms. The q on top can cancel out with the q down same thing happens to r

so you'll get something like ;

3 × q / 4 × r X 2 × s / 6 × q ......so now divide , like 3 into 6 and 2 into 4 ,then you'll get something like;

qs / 4q

that's the answer

(b)15 ab² / 8 c²d ÷ 3ab / 4cd.......start by changing the sign from ÷ to × and then 3ab and 4cd will switch places

15ab² / 8c² d × 4cd / 3ab.....expand the expression

15 ×a×b×b / 8×c×c×d X 4×c×d / 3×a×b

then cancel like terms and you'll get;

15b / 8c X 4/3.....then divide 3 into 15 and 4 into 8

5b / 2c

hope this helps

7:

To find 6% of 45.50=

0.06x45.50= 2.73

and than 17% of 45.50

0.17x45.50= 7.735

so add 2.73 and 7.735= 10.465

than add 10.465 to $45.50 = $55.965 So the answer is $55.965.

8:

again the same thing but with the different numbers.

0.06x105.75= 6.345

0.20x105.75= 21.15

21.15+6.345= 27.495

so than 105.75-27.495= $78.255

9:

same thing again

146.75x0.25= 36.6875

0.09x146.75= 13.2075

But this time add the tax (13.2075)= 146.75+13.2075= 159.9575

but than you subtract the discount which is 25% so 159.9575-36.6875=123.7

So that is the price! $123.7

I hope that helps!

Answer:

No, i dont agree as 1/3 in percentage is 33%

33+50=88

100-88=12

Meaning that he used 12% of the tickets in the batting cage.

The required (x + 1) / (x + 4) is a simplified value of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
= x² + 3x + 2 / x² + 6x + 8

Factorize the expression

=  (x + 2)(x + 1)/ (x + 4)(x + 2)
= (x + 1) / (x + 4)

Since the common factor in the numerator and denominator is (x + 2) it gets canceled.

Thus, the required (x + 1) / (x + 4) is a simplified value of the given expression.

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The probabilities, we need to understand the context. Assuming we are working with a fair six-sided die, where each face has an equal chance of landing, here are the probabilities:

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Answer:

slope measures the rate of change in the dependent variable as the independent variable changes

Step-by-step explanation:

i don't know hope it helps a little

Answer on Question #54875

–

Math

–

Statistics

and Probability

A normal population has a mean of 0.1 and standard deviation 2.1. Find the probability that the

mean of a sample of size 900 will be negative.

Solution

In accordance with the given problem, we have the following data:

μ

=

0

.

1

,

σ

=

2

.

1

and

n

=

900

. It is known that

푥

~

M

(

μ

,

σ

2

)

and

z

~

N

(

0

,

1

)

Answer:the answer is 19.10 or 20

Step-by-step explanation: