Factor the trinomial:
5x^2+21x+4

Answer:

$21,000

Step-by-step explanation:

Solve the following fraction problem and choose the correct alternative: Jaime buys a property for $ 84,000 and after one year sells it earning 1/4 of the purchase price. How much was the profit? *

The amount of profit is calculated as

1/4 of the purchase price

Purchase price = $84,000

= 1/4 of $84,000

= 1/4 × $84,000

= $21,000

Therefore, the amount of the profit = $21,000

Answer:

the answer would have to be 1.25

Step-by-step explanation:

Answer:

1 orange= $1.25

2 oranges= $2.50

To show that the third equation equals the second equation minus some multiple of the first equation in each set of three equations, we can use the concept of linear combinations. We have shown that Equation 3 equals Equation 2 minus some multiple of Equation 1.

Let's consider the given set of three equations as follows:

Equation 1: A1x + B1y + C1z = D1
Equation 2: A2x + B2y + C2z = D2
Equation 3: A3x + B3y + C3z = D3

To prove that Equation 3 equals Equation 2 minus some multiple of Equation 1, we need to find constants m and n such that:

Equation 3 = Equation 2 - (m * Equation 1)

Now, let's rearrange the equations to isolate the variables:

Equation 1: A1x + B1y + C1z = D1       (1)
Equation 2: A2x + B2y + C2z = D2       (2)
Equation 3: A3x + B3y + C3z = D3       (3)

To eliminate x, we can multiply Equation 1 by (-A2/A1) and add it to Equation 2:

(-A2/A1) * Equation 1: (-A2/A1) * (A1x + B1y + C1z) = (-A2/A1) * D1
                  => -A2x - (A2/A1) * B1y - (A2/A1) * C1z = (-A2/A1) * D1

Adding this to Equation 2 gives:

(-A2/A1) * Equation 1 + Equation 2:
(-A2x - (A2/A1) * B1y - (A2/A1) * C1z) + (A2x + B2y + C2z) = (-A2/A1) * D1 + D2
Simplifying:
(-A2/A1) * B1y - (A2/A1) * C1z + B2y + C2z = (-A2/A1) * D1 + D2
Rearranging terms:
((B2 - (A2/A1) * B1)y + (C2 - (A2/A1) * C1)z = (-A2/A1) * D1 + D2

We can see that the coefficients of y and z on the left side of the equation match the corresponding coefficients in Equation 3. Similarly, the right side of the equation is (-A2/A1) * D1 + D2.

To eliminate y, we can multiply Equation 1 by (-B3/B1) and add it to Equation 3:

(-B3/B1) * Equation 1: (-B3/B1) * (A1x + B1y + C1z) = (-B3/B1) * D1
                  => -B3x - (B3/B1) * A1y - (B3/B1) * C1z = (-B3/B1) * D1

Adding this to Equation 3 gives:

(-B3/B1) * Equation 1 + Equation 3:
(-B3x - (B3/B1) * A1y - (B3/B1) * C1z) + (A3x + B3y + C3z) = (-B3/B1) * D1 + D3
Simplifying:
-B3x - (B3/B1) * A1y - (B3/B1) * C1z + A3x + B3y + C3z = (-B3/B1) * D1 + D3
Rearranging terms:
((A3 - (B3/B1) * A1)x + (C3 - (B3/B1) * C1)z = (-B3/B1) * D1 + D3

Again, we can see that the coefficients of x and z on the left side of the equation match the corresponding coefficients in Equation 3. The right side of the equation is (-B3/B1) * D1 + D3.

By comparing the coefficients of x, y, and z in Equation 3 with the coefficients in the derived equations, we can find the multiples of Equation 1 needed to subtract from Equation 2 to obtain Equation 3.

Therefore, we have shown that Equation 3 equals Equation 2 minus some multiple of Equation 1.

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The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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Answer:

70

Step-by-step explanation:

To scale anything, you multiply it by 10. Hopefully this helps.

That is not correct.

The order of multiplication matters in multiplication expressions.

The correct order should be:

6 x a x b = a x b x 6

c x a x b = a x b x c

So the original expressions you provided:

6 x c x a=a x b x c

a x b x c = c x a x b

Are not equivalent. The order of the factors matters in multiplication.

The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The domain

On the graph of the function, we can see that:

The x values start from 0 and it extends indefinitely to the right

This means that the domain is x >= 0

The range

On the graph of the function, we can see that:

The y values extend indefinitely on all sides of the coordinate plane

This means that the range is -∝ < y < ∝

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Answer:

b is less than or equal to -6

Step-by-step explanation:

1.  Multiply both sides by -1

2. Simplify

3. Divide both sides by 13

15 is the total number of 17-year-old students in Mr. Greene's class

Let the number of 17-year-old students in Mr. Greene's class is x.

Since the total number of students in the class is 20, the number of 18-year-old students would be 20 - x.

The sum of the ages of the 17-year-old students would be 17x, and

the sum of the ages of the 18-year-old students would be 18(20 - x).

The sum of the ages of all the students is 345.

17x + 18(20 - x) = 345

Apply distributive property

17x + 360 - 18x = 345

-x + 360 = 345

Subtract 360 from both sides:

-x = 345 - 360

-x = -15

x = 15

Therefore, the total number of 17-year-old students in Mr. Greene's class is 15

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I=PRT

$60= 400 ×.05 × t

$60= 20× t

t= 60/20

3=t

Answer:

length is longer

Step-by-step explanation:

length is llonger than dimensions

Answer:

length, is how tall it is....... dimensions is like lenght width and depth

Step-by-step explanation:

a line going up would eb the length,

dimentsions....l lengths...._ width ..... depth /

The value of box/ square is 5, value of circle is 3 and the value of star is 6.

Let box/ square be denoted by x

let the circles be denoted by y

let the stars be denoted by z

now, let us make three linear equation based on the diagram provided

1. x + x = 10

2. y + z= 9

3. y+ x = 8

solving equation 1

x + x = 10

2x = 10

x = 5

Putting the value of x in equation 3

y + x=8

y + 5 = 8

y = 3

Putting the value of y in equation 2

y + z = 9

3 + z= 9

z = 6

Hence , The value of box/ square is 5, value of circle is 3 and the value of star is 6.

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C.

A linear equation is an equation with the maximum degree of one. This means that in a linear equation, no variable has an exponent greater than 1. A linear equation's graph is always a straight line.

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The equation 1.\(5^x\) - x - 2 = 0 then the value of x be -1.44292524676275.

A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

Let the equation \($1.5^x-x-2=0$\)

Lambert form: \($1=-e^{-\ln (1.5) x}(-x-2)$\)

The equation with \($(-x-2) \ln (1.5)=u$\) and \($x=-\frac{u+2 \ln (1.5)}{\ln (1.5)}$\)\($1=-e^{-\ln (1.5)\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)}\left(-\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)-2\right)$$\)

Simplifying the above equation, we get

\($1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$$\)

\($1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$\) in Lambert form: \($e^u u=-\frac{\ln (1.5)}{2.25}$\)

Solve \($e^u u=-\frac{\ln (1.5)}{2.25}: \quad u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$\)

\($$u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$$\)

Substitute back \($u=(-x-2) \ln (1.5)$\), solve for x\($(-x-2) \ln (1.5)=W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right): \quad x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$\)

Therefore, the simplifying x, we get

\($x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}, x=-\frac{W_0\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$\)

Therefore, the value of x be x = -1.44292524676275.

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Answer:

NONE work!!!!!!!!!!

The values of linear transformation are T(1) = 1, T(x) = x, T(x^2) = x^2, T(ax^2 + bx + c) = ax^2 + bx + c.

To find the values of T(1), T(x), T(x^2), and T(ax^2 + bx + c), let's first express each of these polynomials in the standard basis of P3, which is {1, x, x^2}.

1 can be expressed as 1(1) + 0(x) + 0(x^2).

So, T(1) = T(1(1) + 0(x) + 0(x^2)) = 1T(1) + 0T(x) + 0T(x^2) = 1.

x can be expressed as 0(1) + 1(x) + 0(x^2).

So, T(x) = T(0(1) + 1(x) + 0(x^2)) = 0T(1) + 1T(x) + 0T(x^2) = T(x).

x^2 can be expressed as 0(1) + 0(x) + 1(x^2).

So, T(x^2) = T(0(1) + 0(x) + 1(x^2)) = 0T(1) + 0T(x) + 1T(x^2) = T(x^2).

Now, let's consider the polynomial ax^2 + bx + c.

We can express it as a(x^2) + b(x) + c(1).

So, T(ax^2 + bx + c) = T(a(x^2) + b(x) + c(1)) = aT(x^2) + bT(x) + cT(1) = aT(x^2) + bT(x) + c.

Therefore, we have:

T(1) = 1,

T(x) = x,

T(x^2) = x^2,

T(ax^2 + bx + c) = aT(x^2) + bT(x) + c = ax^2 + bx + c.

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Answer:

1.25 cans or 1 1/4

Step-by-step explanation:

5 divided by 4 = 1.25

Answer:

1.25

Step-by-step explanation:

Answer:

(4,-1)

x=4

y=-1

Step-by-step explanation:

Answer:

x = 4 and y = -1

Step-by-step explanation:

hope this helps!

Answer:

i think it is b -8 -2

Step-by-step explanation:

Answer:

in picture

Step-by-step explanation:

Answer:

2x + 24

Step-by-step explanation:

The product of 2 and a number is: 2x

because product means multiply. 2 and a number means 2 times an unspecified number represented as x. 24 more than that product just means to add 24 to the product of 2x.

Answer:2x + 24

Sorry I was gonna do it when it was posted but I was grounded that time sorry. Have a great day!

Answer:

The answer is 225

Step-by-step explanation:

Because you first need to subtract 350-125 and you get 225

Answer:

A

y=3x+11

Step-by-step explanation:

The slope of the line perpendicular to y=-1/3x-4 is 3, and A is the only choice with the slope of 3.

Answer: 9 (3 + x) = 5

Step-by-step explanation: hope this helps

Answer:

9(X) x 3 =5

Step-by-step explanation:

The answer is:

P(not heart) = 77.5% (D)

What is the probability?

Probability is a mathematical concept that describes the likelihood of an event occurring. It is a value between 0 and 1, where 0 means an event is impossible to occur and 1 means an event is certain to occur.

To find the experimental probability of not selecting a heart, we need to determine the number of trials in which Lisa did not select a heart and divide that number by the total number of trials (40). In this case, the number of trials in which a heart was not selected is 40 - 9 = 31.

Hence, the experimental probability of not selecting a heart can be calculated as:

P(not heart) = 31/40 = 0.775

The answer is:

P(not heart) = 77.5% (D)

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The probability of selecting all three purple balls is 0.1429 or approximately 14.29%.

To find the probability that all three balls are purple, we need to use the formula for the probability of the intersection of three events:

P(A and B and C) = P(A) x P(B|A) x P(C|A and B)

where A, B, and C are the events of drawing a purple ball from the bag on the first, second, and third draws, respectively.

The probability of drawing a purple ball on the first draw is:

P(A) = number of purple balls / total number of balls = 9 / 15

After drawing a purple ball on the first draw, there are now 8 purple balls left in the bag out of a total of 14 balls, so the probability of drawing a purple ball on the second draw, given that a purple ball was drawn on the first draw, is:

P(B|A) = number of purple balls left / total number of balls left = 8 / 14

After drawing two purple balls, there are now 7 purple balls left in the bag out of a total of 13 balls, so the probability of drawing a purple ball on the third draw, given that two purple balls were drawn on the first two draws, is:

P(C|A and B) = number of purple balls left / total number of balls left = 7 / 13

Therefore, the probability of drawing three purple balls in a row is:

P(A and B and C) = P(A) x P(B|A) x P(C|A and B) = (9 / 15) x (8 / 14) x (7 / 13) = 0.1429 or approximately 14.29%

So, the probability of selecting all three purple balls is 0.1429 or approximately 14.29%.

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The measure of the exterior angle x of the polygon is x = 105°  .

In the question ,

it is given that ,

in the figure, the measure of external angles are 75° , 90° , 90° and x .

we know that By Polygon Exterior Angle Sum Theorem states that the sum of measure of all exterior angle of a polygon is 360° ,

So , 75° + 90° + 90° + x = 360°

75° + 180° + x = 360°

255° + x = 360°

Subtracting 255 from both the sides , we get

x = 360° - 255°

x = 105°

Therefore , The measure of the exterior angle x of the polygon is x = 105°  .

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The number of square centimeters of the cylinder that Mariah paint in terms of π is 96π square centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

72π = π(6)²h

Height, h = 2 cm.

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

SA = 2π × 6 × 2 + 2π × 6²

SA = 24π + 72π

SA = 96π square centimeters.

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Answer:

Step-by-step explanation:

See attachment

The sum of the remainders is 10. This result is independent of the value of x and holds true for any five consecutive positive integers.

Arbitrary positive integer is any positive integer that is chosen without any particular reasoning or pattern. This can also refer to any number that is randomly chosen or assigned.

Let the original numbers be x, x+1, x+2, x+3, and x+4, where x is an arbitrary positive integer.

Then, their modulo 5 values are x mod 5, (x+1) mod 5, (x+2) mod 5, (x+3) mod 5, and (x+4) mod 5.

Now, let's calculate the sum of these modulo 5 values.

x mod 5 + (x+1) mod 5 + (x+2) mod 5 + (x+3) mod 5 + (x+4) mod 5

= x mod 5 + x mod 5 + 1 + x mod 5 + 2 + x mod 5 + 3 + x mod 5 + 4

= 5x mod 5 + 10

= 0 + 10

= 10

Hence, the sum of the remainders is 10.

This result is independent of the value of x and holds true for any five consecutive positive integers.

This is because when modulo 5 is applied to any set of five consecutive numbers, each number in the set will have an entry in the modulo 5 table, and the sum of the entries in the table is 10.

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