If a(x)=2x-4 and b(x) =x+2, which of the following expressions produces a quadratic function?

"Mitchael owes $8 to his bank, so he decides to add $60 in April at a rate of $2 per day. How many days Mitchael needs in order to get $28 in his account?"

Hello! Remember you have to write clear questions in order to get good and exact answers. The given equation doesn't make any sense so I'll assume the correct one is:

[tex]-8+60x=28[/tex]

So let's write a real world problem you could answer by solving the equation:

"Mitchael owes $8 to his bank, so he decides to add $60 in April at a rate of $2 per day. How many days Mitchael needs in order to get $28 in his account?"

So by isolating x (number of months):

[tex]x=\frac{28+8}{60} \\ \\ x=0.6 \ month \\ \\ \\ Since \ we \ need \ the \ number \ of \ days: \\ \\ April \ has \ 30 \ days, \ so: \\ \\ x-day=0.6\times 30=18 \ days[/tex]

So Mitchael would need 18 days in order to get $28 in his account

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To solve the equation -8+60=28, we follow basic arithmetic by adding the positive payment to the negative debt which gives us 52. This answer indicates an error in the original problem statement, as the expected balance does not match with the calculated one.

A real-world problem that could be answered by solving the equation -8+60=28 might involve a scenario where someone is tracking their financial transactions. Suppose you start with a debt of \(-8 dollars and then receive 60 dollars as a payment of some sort. The question could be to determine how much money you have after receiving the payment. To find out, you would solve the equation to see if your final balance is 28 dollars as expected.

Let's solve this step-by-step:

Add the amount received to the initial debt: \( -8 + 60 \).

Calculate the sum which gives us \( 52 \).

Therefore, after receiving the payment, you have 52 dollars.

To answer the original equation, the final balance should be 28 dollars; however, the solution we found is 52 dollars, indicating there might be a mistake in the original problem statement or the transactions recorded.

Answer:

[tex]x=\pm\sqrt{3}[/tex]  and they are actual solutions

Step-by-step explanation:

we have

[tex]\frac{x^2}{2x-6}=\frac{9}{6x-18}[/tex]

Factor the denominators both sides

[tex]\frac{x^2}{2(x-3)}=\frac{9}{6(x-3)}[/tex]

Simplify

[tex]\frac{x^2}{2}=\frac{9}{6}[/tex]

[tex]x^2=\frac{18}{6}[/tex]

[tex]x=\pm\sqrt{3}[/tex]

Verify

1) For [tex]x=\sqrt{3}[/tex]

[tex]\frac{\sqrt{3}^2}{2(\sqrt{3}-3)}=\frac{9}{6(\sqrt{3}-3)}[/tex]

[tex]\frac{3}{2(\sqrt{3}-3)}=\frac{9}{6(\sqrt{3}-3)}[/tex]

[tex]18=18[/tex] ---> is true

therefore

[tex]x=\sqrt{3}[/tex] ----> is an actual solution

2) For [tex]x=-\sqrt{3}[/tex]

[tex]\frac{-\sqrt{3}^2}{2(-\sqrt{3}-3)}=\frac{9}{6(-\sqrt{3}-3)}[/tex]

[tex]\frac{3}{2(-\sqrt{3}-3)}=\frac{9}{6(-\sqrt{3}-3)}[/tex]

[tex]18=18[/tex] ---> is true

therefore

[tex]x=-\sqrt{3}[/tex]  ----> is an actual solution

therefore

Answer:

The answer is A!

Step-by-step explanation:

Answer:

A.)

Step-by-step explanation:

It has the best graph that matches the table

The Y-axis is the number of students who got that grade

The X-axis is the number grade

To solve the equation (3x+1)+(4x-5)=8x-9, we simplify and solve for x, obtaining x=5 as the solution. Verification by substitution confirms that our solution is correct.

To find the value of X for the equation (3x+1)+(4x-5)=8x-9, we first simplify both sides of the equation by combining like terms. On the left side, we combine the x terms and the constant terms: 3x + 4x + 1 - 5. This simplifies to 7x - 4. The right side of the equation remains as 8x - 9.

Next, we set the simplified left side of the equation equal to the right side: 7x - 4 = 8x - 9. To solve for x, we can subtract 7x from both sides to get x on one side of the equation, resulting in -4 = x - 9. Adding 9 to both sides gives us x = 5 as the solution.

To verify, we substitute x=5 back into the original equation: (3(5)+1)+(4(5)-5) = 15 + 1 + 20 - 5 = 31, and on the right side, 8(5) - 9 = 40 - 9 = 31, which confirms our solution since both sides equal 31.

Answer:

Step-by-step explanation:

zxy or xyz or z×x×y

Final answer:

The mathematical expression for 'the product of z, x, and y' is simply 'zxy' or 'z  times x  times y', which indicates that the three variables are being multiplied together to form a product.

Explanation:

To translate "the product of z, x, and y" into a mathematical expression, we represent multiplication using either the multiplication sign (times) or simply by juxtaposition (placing the variables next to each other). Thus, the product of the variables z, x, and y is represented as z  imes x  imes y or simply as zxy. This expression shows that z, x, and y are being multiplied together to give a Mathematical Result.

In mathematics, when expressions are evaluated and produce the same value, they are known as equivalent expressions. For example, the expression (5 - 3xy) is evaluated by following the order of operations, which in this case involves subtracting the product of 3 and xy from 5. If x, y, and z are treated as three independent variables, it is also possible to represent their product in the form of a Multiple or Product, like so: xyz.

Answer:

28-c3+6=0

Collect like terms

28-6=c3

22=c3

Divide both sides by 3

22/3=c3/3

C=7

To evaluate the expression 28-c3+6, you must know the value of 'c'. Assuming c3 means c cubed, then you would calculate 'c' cubed, subtract it from 28 and then add 6. Without a value for 'c', we cannot compute a definitive answer.

To solve this mathematical expression, we must first understand what c3 means. In this case, 'c' and '3' are variables and without a given value for 'c' we cannot fully evaluate it. However, if we assume that 'c3' means 'c' cubed then, we can proceed with that understanding. Cubing a number means multiplying it by itself twice. For example, if c=2, then c cubed would be 2*2*2=8.

Next step is to follow the rules of the order of operations, often remembered by the acronym PEMDAS - Parentheses, Exponents, Multiplications and Divisions (from left to right), Additions and Subtractions (from left to right).

Therefore, given the expression 28-c3+6, you would first calculate 'c' cubed and then perform the remaining operations from left to right. If 'c' was 2, your expression would look like this: 28-8+6. Following PEMDAS, subtraction comes before addition, so you subtract 8 from 28 which is 20 and then add 6 to that, giving a result of 26. But remember, without knowing the true value of 'c', we cannot definitively solve the expression.

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Answer:

0.073

Step-by-step explanation:

The question is about growth function and you are asked to find out the growth rate. Growth function has a format of

y = a(1+r)^t

Where

y= future value = S(t)

a= current value = 273

r= growth rate

t= time =t

Since its a growing function, the r will be positive. If its decay function then the r will be negative. As you can see, the growth rate value is located inside the parentheses. The growth rate of the function should be:

(1+r)= (1.073)

r= 1.073- 1

r= 0.073

The 42 inches fishing rod is fit into the box.

Explanation:

Length of the box = 40 inch

Width of the box = 10 inch

Height of the box = 10 inch

Let us first find the diagonal of the base of the box and 'd' be the diagonal.

Diagonal formula:

[tex]d^2=l^2+w^2[/tex]

   [tex]=40^2+10^2[/tex]

   [tex]=1600+100[/tex]

[tex]d^2=1700[/tex]

Let r be the length from a bottom corner to the  opposite top corner.

To find r:

Using Pythagoras theorem,

[tex]r^2=s^2+h^2[/tex]

    [tex]=1700+10^2[/tex]

    [tex]=1700+100[/tex]

[tex]r^2=1800[/tex]

Taking square root on both side of the equation,

[tex]r=\sqrt{1800}[/tex]

r ≈ 42.43 inch

The length of the longest tube that will fit in the box is 42.43 inches.

Hence the 42 inches fishing rod is fit into the box.

To determine if the fishing rod will fit, compare the length of the fishing rod to the length of the box and check the other dimensions for a comfortable fit.

To determine if the fishing rod will fit inside the box, we need to compare the length of the fishing rod to the dimensions of the box. Since the fishing rod is 42 inches long, we need to check if 42 inches is less than or equal to the length of the box. If it is, then the fishing rod will fit.

Step 1: Compare the length of the fishing rod (42 inches) to the length of the box. If 42 inches is less than or equal to the length of the box, go to Step 2. Otherwise, the fishing rod will not fit.

Step 2: Check the other dimensions of the box to ensure that the fishing rod can fit without any issues. If the fishing rod can fit comfortably inside the box, then it will fit.

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Answer:

Its 111ft. tall if thats what your asking.

Step-by-step explanation:

100+11=111

The answer is: [tex]83.66^\circ[/tex]. The angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].

To solve the problem, we need to find the angle of elevation that the ladder makes with the ground when it is resting on top of the hook and ladder truck. We are given that the ladder is 100 feet long and its base is 11 feet from the ground.

We can use trigonometry to solve for the angle of elevation (θ). The tangent of the angle of elevation is the ratio of the opposite side (height from the ground to the top of the ladder) to the adjacent side (the distance from the base of the ladder to the point on the ground directly below the top of the ladder).

Let's denote:

- The length of the ladder as [tex]\( L \)[/tex], which is 100 feet.

- The distance from the base of the ladder to the point on the ground directly below the top of the ladder as [tex]\( d \)[/tex], which is 11 feet.

- The height from the ground to the top of the ladder as [tex]\( h \)[/tex].

Using the Pythagorean theorem, we can find [tex]\( h \)[/tex]:

[tex]\[ h^2 + d^2 = L^2 \][/tex]

[tex]\[ h^2 + 11^2 = 100^2 \][/tex]

[tex]\[ h^2 = 100^2 - 11^2 \][/tex]

[tex]\[ h^2 = 10000 - 121 \][/tex]

[tex]\[ h^2 = 9879 \][/tex]

[tex]\[ h = \sqrt{9879} \][/tex]

[tex]\[ h \approx 99.39 \text{ feet} \][/tex]

Now, we can find the angle of elevation using the tangent function:

[tex]\[ \tan(\theta) = \frac{h}{d} \][/tex]

[tex]\[ \theta = \arctan\left(\frac{h}{d}\right) \][/tex]

[tex]\[ \theta = \arctan\left(\frac{99.39}{11}\right) \][/tex]

[tex]\[ \theta \approx \arctan(9.03545455) \][/tex]

[tex]\[ \theta \approx 83.66^\circ \][/tex]

Therefore, the angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].

The final answer is:

[tex]\[ \boxed{83.66^\circ} \][/tex]

The complete question is:

A 100 ft ladder rests on top of a hook and ladder truck with its base 11 feet from the ground. When the angle of elevation of the ladder is 81°, how high up the building will the ladder reach?

Answer:

There will be 8 columns

Step-by-step explanation:

So first you get 48 and divide it by 6 then you get 8 as your answer

Final answer:

To determine the number of columns in a 48-bead array with 6 rows, divide the total beads by the number of rows, which results in 8 columns.

Explanation:

The student has arranged 48 beads into an array with 6 rows. To find out how many columns there are, we divide the total number of beads by the number of rows. Therefore:

Divide 48 by 6.

48 ÷ 6 equals 8.

Thus, there are 8 columns of beads.

Each row has the same number of beads, so with 6 rows and 8 columns, we can visualize the array as a rectangle where every row contains 8 beads.

Answer:

if you want to solve for t: t = 6s / 5

if you want to solve for s: s = 5t  / 6

Step-by-step explanation:

To solve the equation 3 + 4n/n = 7b for n, you can cancel out the n in the numerator and denominator. Then, subtract 3 from both sides of the equation and divide by 7 to solve for b.

To solve the equation 3 + 4n/n = 7b for n, we need to isolate n on one side of the equation. First, we can simplify the equation by canceling out the n in the numerator and denominator, as they are dividing each other. This leaves us with 3 + 4 = 7b. Next, we can subtract 3 from both sides of the equation to get 4 = 7b - 3. Finally, we can divide both sides of the equation by 7 to solve for b: 4/7 = b.

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Answer:

Therefore the results from adding the equation in this system is

[tex]7x=-35[/tex]

Step-by-step explanation:

Given:

Equations as

[tex]11x-3y=-17[/tex]         .......................1

[tex]-4x+3y=-18[/tex]         .......................2

To Find :

Result when adding equation 1 and 2 = ?

Solution

On adding equation 1 and 2 the "3y" term will get cancel and the like terms will combine that is add (11x and -4x ) and ( -17 and - 18)  as shown below

           11x     -    3y    = -17

           -4x    +   3y     = - 18

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

           7x     + 0        =  - 35

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

Therefore the results from adding the equation in this system is

[tex]7x=-35[/tex]

Answer:

C

Step-by-step explanation:

did test

Answer:

[tex]average\ speed = 36\ mi/hr[/tex]

Step-by-step explanation:

Given:

Each city is exactly 120 miles from the other two.

Average rate from city A to city B = 60 mi/hr

Average rate from city B to city C = 40 mi/hr

Average rate from city c to city A = 24 mi/hr

We need to find the Dale's average rate for the entire trip.

Solution:

First we find the total time and total distance by following way.

Time taken to travel from A to B = [tex]\frac{Distance}{Speed} = \frac{120}{60}= 2\ hr[/tex]

Time taken to travel from B to C = [tex]\frac{Distance}{Speed} = \frac{120}{40}= 3\ hr[/tex]

Time taken to travel from C to A = [tex]\frac{Distance}{Speed} = \frac{120}{24}= 5\ hr[/tex]

So, total time taken = [tex]2+3+5=10\ hr[/tex]

Total distance =  120 + 120 + 120 = 360 miles

Using average speed formula.

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

[tex]average\ speed = \frac{360}{10}[/tex]

[tex]average\ speed = 36\ mi/hr[/tex]

Therefore, the average rate for the entire trip [tex]average\ speed = 36\ mi/hr[/tex]

Answer:

si amuigos  hasta luego to es bien cien nueve

Step-by-step explanation:

The answer is: 5 x ^2 + 2 x − 2

Answer:

x = 15

Step-by-step explanation:

Step 1:  Distribute

3x - 5(x) - 5(2) = -40

3x - 5x - 10 = -40

Step 2:  Combine like terms

-2x - 10 = -40

Step 3:  Add 10 to both sides

-2x - 10 + 10 = -40 + 10

Step 4:  Divide both side by -2

-2x / -2 = -30 / -2

x = 15

Answer:

20%

Step-by-step explanation:

If 120 = 100%

  144 = x

By cross multiplication,

120x = 144 * 100

120x = 14400

x = 14400/120

x = 120%

The percentage increase is 20%

Step-by-step explanation:

By angle bisector property:

[tex] \frac{w}{30} = \frac{15}{18} \\ \\ \therefore \: w = \frac{15 \times 30}{18} \\ \\ \therefore \: w = \frac{15 \times 30}{6 \times 5} \\ \\ \therefore \: w = 3 \times 5\\ \\ \huge \orange{ \boxed{ \therefore \: w = 15}}[/tex]

Answer:825000

Step-by-step explanation:

Answer:825000

Step-by-step explanation:

825*1000

7.0267

Step-by-step explanation:

The clue here is that the decimal point follows after the "and"

For example,

One and one thousandth = 1 + 1/1000 = 1.001

One and two hundred sixty-three thousandths = 1+ 263/1000 = 1.263

Hence;

seven and two hundred sixty-seven ten thousandths= 7+ 267/10000= 7.0267

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Answer:

1. B. x = 11

2. E. [tex]m\angle BEF=140^{\circ}[/tex]

3. D. 4.3 in

4. D. 40.8 ft

Step-by-step explanation:

1. By Angle Addition Postulate,

[tex]m\angle KLM=m\angle KLV+m\angle VLM[/tex]

Since

[tex]m\angle KLV=34^{\circ}\\ \\m\angle KLM=14x+19\\ \\m\angle VLM=12x+7,[/tex]

then

[tex]14x+19=34+12x+7\\ \\14x-12x=34+7-19\\ \\2x=22\\ \\x=11[/tex]

2. By Angle Addition Postulate,

[tex]m\angle FED=m\angle DEB+m\angle BEF[/tex]

Since

[tex]m\angle FED=14x+8\\ \\m\angle DEB=22^{\circ}\\ \\m\angle BEF=13x-3,[/tex]

then

[tex]14x+8=22+13x-3\\ \\14x-13x=22-3-8\\ \\x=11[/tex]

Therefore,

[tex]m\angle BEF=(13\cdot 11-3)^{\circ}=(143-3)^{\circ}=140^{\circ}[/tex]

3. The area of trapezoid is

[tex]A_{trapezoid}=\text{Midsegment}\times \text{Height}[/tex]

From the diagram,

[tex]\text{Smaller base}=1.2\ in\\ \\\text{Bigger base}=4.2\ in,[/tex]

then

[tex]\text{Midsegment}=\dfrac{1.2+4.2}{2}=2.7\ in[/tex]

Since the area of trapezoid is [tex]11.6\ in^2,[/tex] then

[tex]11.6\ in^2 =2.7\ in\times \text{Height}\\ \\\text{Height}=\dfrac{11.6\ in^2}{2.7\ in}\approx 4.3\ in[/tex]

4. Use formula for the area of the circle to find the radius of the circle:

[tex]A_{circle}=\pi r^2[/tex]

So,

[tex]132.7=\pi r^2\\ \\r^2=\dfrac{132.7}{\pi}\\ \\r=\sqrt{\dfrac{132.7}{\pi}}\ ft[/tex]

Now, find the circumference of the circle:

[tex]C=2\pi r\\ \\C=2\pi \cdot \sqrt{\dfrac{132.7}{\pi}}=2\sqrt{132.7\pi}\approx 40.8\ ft[/tex]

Do 4x^2 = 16x

16x+6 = 40

     -6    -6

16x = 34

/16    /16

x=2.125

Rounded to the nearest hundredth is, 2.13

IF THIS IS HELPFUL PLS GIVE ME BRAINLIEST AND ANSWER MY MATH PROBLEM.

Answer:

-2.92 and 2.92

i took the test

Hence, After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse. Hence, At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.

Answer:

the answer is the ship is traveling at 21.25 MPH, started 10.5 miles from lighthouse and after 11 hours will be 244.25 miles from the lighthouse.

Step-by-step explanation:

Answer:

is

47 degree fahrenheit

The high temperature in degrees Fahrenheit was [tex]\( 59^\circ \)[/tex] Fahrenheit.

To convert a temperature from Celsius to Fahrenheit using the formula  F = 1.8C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius, you simply plug in the value of C and solve for F.

Given that the high temperature in the mountain city was [tex]\( 15^\circ \)[/tex] Celsius, we can plug this value into the formula:

F = 1.8 * 15 + 32

F = 27 + 32

F = 59

So, the high temperature in degrees Fahrenheit was [tex]\( 59^\circ \)[/tex]Fahrenheit.

The interest that he gains after 3 years is $9282.

Step-by-step explanation:

⇒ SI = (44200 × 7 × 3)/100

⇒ SI = 442 × 7 × 3

⇒ SI = $9282