Write a quadratic function f whose zeros are -2 and 12.

f(x) = 0

Step-by-step explanation:

y+3x=1

y= -3x +1

y= MX+c

m= -3 and c=1

Answer:

232 cars

Step-by-step explanation:

Let's say the number of cars that entered is c.

At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:

64/(88 + c) = 1/5

Cross-multiply:

88 + c = 64 * 5 = 320

c = 320 - 88 = 232

Thus, the answer is 232 cars.

Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.

~ an aesthetics lover

Answer:

232 cars entered between 8 and 9

Step-by-step explanation:

at 9 am there are 64 x 5 vehicles total = 320

320 - 64 - 24 = 232

Step-by-step explanation:

the numbers: 5, 7, 7, 1

the number of numbers:4

mean: the numbers all added then divided by the number of numbers

5+7+7+1=20

20÷4 is 5 so the mean of the date is 5=

the average is 5

True, if A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in Rⁿ.

When A is an invertible n x n matrix, it means that A has a unique inverse, denoted as A⁻¹, which is also an n x n matrix. This implies that for any given vector b in Rⁿ, there exists a unique solution x in Rⁿ that satisfies the equation Ax = b.

To understand why this is true, consider the definition of matrix multiplication. In the equation Ax = b, A is multiplied by x to obtain b. Since A is invertible, we can multiply both sides of the equation by A⁻¹ (the inverse of A) on the left, yielding A⁻¹Ax = A⁻¹b.

Now, according to the properties of matrix multiplication, A⁻¹A results in the identity matrix I_n (an n x n matrix with ones on the diagonal and zeros elsewhere), and any vector multiplied by the identity matrix remains unchanged. Therefore, we get I_nx = A⁻¹b, which simplifies to x = A⁻¹b.

This shows that for any given vector b in Rⁿ, there exists a unique solution x = A⁻¹b that satisfies the equation Ax = b when A is an invertible matrix. Hence, the equation Ax = b is consistent for each b in Rⁿ.

Therefore, the correct answer is True.

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The number 7,656,565 consists of seven digits. To calculate the number of ways these digits can be arranged, we can use the concept of permutations.

The total number of arrangements can be found by considering that each digit can occupy a different position, without repetition. Therefore, the number of ways to arrange the digits in 7,656,565 can be determined.To calculate the number of arrangements, we start by considering that there are seven digits in the number 7,656,565. Each digit can be placed in a different position, without repetition. In other words, we have seven choices for the first digit, six choices for the second digit (as one digit has already been placed), five choices for the third digit, and so on.

Using the concept of permutations, we can calculate the total number of arrangements by multiplying these choices together. Therefore, the number of ways to arrange the digits in 7,656,565 can be found as 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.Hence, there are 5040 different ways in which the digits in the number 7,656,565 can be arranged.

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Answer:

Liliana has 27 candies from her teacher. But her mother didn't want her to eat too much candy, so she took 11 of Liliana's candies.

Step-by-step explanation:

Hope it help, and please give me Brainlest!

Answer:

the answer and explanation is in the picture

please like and Mark as brainliest

hope this helps

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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Answer:

Step-by-step explanation:

Sum of angle in a triangle = 180°

<A+<B+<C = 180

Given <B = 50°

Substituting into the formula

<A+50+<C = 180

<A+<C = 180-50

<A+<C = 130°

Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°

The possible values of <A and <C that will be acute and give a sum of 130° are;

∠A= 58° and ∠C= 72°

∠A= 80° and ∠C= 50°

∠A= 60° and ∠C= 70°

You can see that all the Angles are less than 90° and their sum is 130°

It's important to note that while BNP levels can provide additional information for diagnosing TACO, the diagnosis should be made based on a combination of clinical presentation, symptoms, and other laboratory findings. Consulting with a healthcare professional or hematologist is crucial for accurate diagnosis and appropriate management of transfusion reactions.

Evaluating B-type natriuretic peptide (BNP) levels before and after transfusion can be helpful in establishing a diagnosis for transfusion-associated circulatory overload (TACO). TACO is a transfusion reaction that occurs due to the rapid volume overload caused by transfusion. It primarily affects patients with pre-existing cardiovascular conditions.

BNP is a hormone released by the ventricles of the heart in response to increased stretching of cardiac muscle cells. Elevated BNP levels indicate heart stress or failure. In the context of transfusion reactions, monitoring BNP levels before and after transfusion can help differentiate TACO from other transfusion reactions that may present with similar symptoms.

If BNP levels are elevated before transfusion and increase further after transfusion, it suggests that TACO is likely the cause of the reaction. This pattern indicates worsening heart stress due to volume overload from the transfusion. By contrast, other transfusion reactions may not have a significant impact on BNP levels.

It's important to note that while BNP levels can provide additional information for diagnosing TACO, the diagnosis should be made based on a combination of clinical presentation, symptoms, and other laboratory findings. Consulting with a healthcare professional or hematologist is crucial for accurate diagnosis and appropriate management of transfusion reactions.

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a) Differential equation (initial value problem) for the mass of the copper sulfate would be dm/dt = 0

b) m(t)=0

What is Differential equation?

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to create a relationship between the two.

a) Solution is flowing out of the tank. This can be expressed mathematically as:

dm/dt = (flow rate of solution into tank) - (flow rate of solution out of tank)

= (2 l/min) - (2 l/min)

= 0

Therefore, the differential equation for the mass of the copper sulfate in the tank is:

dm/dt = 0

This is a simple differential equation with a constant coefficient of 0, and it can be easily solved by integrating both sides of the equation with respect to time.

b. To solve the differential equation, we can write:

m(t) = integral(0, t, dm/dt)

= integral(0, t, 0)

= 0

Since the coefficient of the derivative is 0, the solution to the differential equation is a constant function with a value of 0. This means that the mass of the copper sulfate in the tank will remain constant over time, regardless of the flow rates of the solution into and out of the tank.

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To simplify the expression $4(x^2-2x+2)-7(x^3-3x+1)$, we need to distribute the coefficients and combine like terms.

First, let's simplify the terms within the parentheses:

$x^2-2x+2$ remains unchanged, and $x^3-3x+1$ remains unchanged.

Now, let's distribute the coefficients:

$4(x^2-2x+2)$ becomes $4x^2-8x+8$,

and $-7(x^3-3x+1)$ becomes $-7x^3+21x-7$.

Next, let's combine like terms:

The expression becomes $4x^2-8x+8-7x^3+21x-7$.

Finally, let's rearrange the terms in descending order of exponents:

The simplified expression is $-7x^3+4x^2+13x+1$.

To find the sum of the squares of the coefficients, we square each coefficient and add them up:

$(-7)^2 + 4^2 + 13^2 + 1^2 = 49 + 16 + 169 + 1 = 235$.

Therefore, the sum of the squares of the coefficients of the terms in the simplified expression is 235.

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Given data:

The given equation is y = 2x^2+8x+10 .

The givenn equation can be written in vertex form as,

Thus, the given equation can be written as, 2(x+2)^2 +2, so third option is correct.

Answer:

2nd and 5th options

Step-by-step explanation:

the solution to a system of equations is at the point of intersection of the 2 lines.

If the lines are parallel then they never intersect and will have no solution.

The slopes m of parallel lines are equal.

The options with equal slopes , both - 2 are the

2nd and 5th options

The values of slope and b will create a system of equations with no solution is m= -2 and b= 1/3.

We have two Equation as

y= -2x + 3/2

We know the the lines which are parallel line have same slope.

Also, the parallel lines never intersect then leads to Solution.

And to this inconsistent system, if the linear parameter is not so relevant. So if m=-2 then b may be either equal to -1/3 or -2/3.

So, the No Solution System is

y= -2x+ 2/3

y= -2x - 1/3

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Answer:

500cm.

Step-by-step explanation:

the scale 1:50 means that .........

1cm represents 50cm.

10cm represents ?

crossmultiply .......... 10 × 50 ÷ 1 = 500cm

Answer:

b

b because 30% off of 39.98 is 27.98 and if u do 39.98 minus 11.99 it is 27.99

Answer:

a factor of 4

Step-by-step explanation:

The equation is

\(500 (2) {2}^{t} \)

Which can be simplified to

\(500 (4) {}^{t} \)

Since 4 is the base, the constant factor is 4.

The set of all numbers of the form a+b*sqrt(2), where a and b are integers, is countable.

This can be proven by first showing that sqrt(2) is irrational, which implies that the function f(a; b) = a + b*sqrt(2) is one-to-one and onto from the set Z Z = {(a,b)} to the set of numbers {a+b*sqrt(2)}.

This reduces the proof to showing that Z Z is countable. Z Z is a subset of Z x Z and Z x Z is countable, as it can be put into a one-to-one correspondence with the set of natural numbers. Thus, there is a bijection between Z x Z and the set of numbers {a+b*sqrt(2)}, which implies that the set of numbers a+b*sqrt(2) is countable.

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Answer: D, 1.01

1.01 is in between 0.62 and 1.05

Answer: D-1.01

Step-by-step explanation:

The inequality is 130x + 7500 ≤ 23000.

Let's assume "x" represents the number of 130-kilogram crates that can be loaded into the shipping container.

The total weight of the crates can be calculated by multiplying the weight of one crate (130 kilograms) by the number of crates (x). The total weight should not exceed the maximum weight capacity of the container, which is 23000 kilograms.

Additionally, there are other shipments already loaded into the container, weighing a total of 7500 kilograms. So, we need to consider the weight of these shipments as well.

Therefore, the inequality that represents the situation is:

130x + 7500 ≤ 23000

This inequality ensures that the weight of the crates (130x) plus the weight of the other shipments (7500) does not exceed the maximum weight capacity of the container (23000).

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Answer:

I'm pretty sure its C

Hope that helps :)

a) The volume V of the solid is (112/3) π r² h.

b) The volume V of the solid is 9.333π.

a) To find the volume V of the right circular cone, we can use the formula:

V = (1/3) π (base radius)² height

Given that the base radius is 4r and the height is 7h,

V = (1/3)  π (4r)²  7h

V = (1/3) π 16r² 7h

V = (112/3) π r² h

Therefore, the volume V of the solid is (112/3) π r² h.

b) To find the volume V of the solid obtained by rotating the region bounded by the curves about the line y = 2, we can use the disk method. The volume of each disk is given by the formula:

dV = π (outer radius)² dx

The outer radius is the distance from the curve y = 2 to the axis of rotation y = 2.

In this case, the curve y = 2x intersects y = 2 at x = 1. So the outer radius is 1 - x.

To find the limits of integration, we set the two curves equal to each other:

2x = 2

x = 1

Therefore, the limits of integration are x = 1 and x = 3.

Now, V = ∫[1, 3] π  (1 - x)² dx

On solving the integration we get

V = π * (9 + 1/3)

V = π * (27/3 + 1/3)

V = π * (28/3)

V ≈ 9.333π

So, the volume V of the solid is approximately 9.333π.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Additional requirements in figure :-

Mark point :-

Draw a straight line from E to AB .

And the point line joins mark it as "F" .

It will generate quadrilateral FBCD.

we get to know In quadrilateral left angle is 90°

How ?

{

proof :

As three angles are given 90° So third angle will also be 90°

Reason:

→ Sum of interior angles = 2 (no. of angles - 2 × 180°

→Sum of interior angles = (4-2 × 180°)

→Sum of interior angles = (2 × 180°)

→Sum of interior angles = 360°

}

✿Now let the left angle be x

we know :

Area of rectangle = Length × Breadth

STEPS :

Now let's find EF :

To find A

F :

In triangle AFE:

We know :

Area of triangle =( Height × Base)/2

Steps :

To find area of figure :

______________________

~WindyMint

Answer:

\(\displaystyle 62\:in.^2\)

Step-by-step explanation:

▽ \(\displaystyle \frac{hb}{2} = A, \frac{1}{2}bh = A, or\:\frac{1}{2}hb = A\)

▯ \(\displaystyle hb = A\)

All edges meet at right angles, therefore resulting in this:

\(\displaystyle 62 = 56 + 6 \Rightarrow 62 = 7 \times 8 + 4 \times 1\frac{1}{2}\)

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Answer:

The starting height of the chairlift

Answer:

its c

Step-by-step explanation:

just trust me

Answer:

7/20

Step-by-step explanation:

ok so it has 30 members, 7 are seniors it's possible. if there is multiple choice just let me know if it is not on there.