Maths question and answer: Find the difference between ¼ of #5.00 and 37/½% of #1.50.

Answer:

x < -5

Step-by-step explanation:

3 ( -2x - 4 ) > 18

→ Expand the brackets

-6x - 12 > 18

→ Add 12 to both sides

-6x > 30

→ Divide both sides by -6

x < -5

Answer:

\(\boxed {\boxed {\sf x< -5}}\)

Step-by-step explanation:

We are asked to solve the following inequality for x.

\(3(-2x-4) > 18\)

Solve for x by isolating it and performing the inverse operations.

3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.

\(\frac {3(-2x-4)}{3} > \frac{18}{3}\)

\((-2x-4) > \frac{18}{3}\)

\(-2x-4 > 6\)

4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.

\(-2x-4+4 > 6+4 \\\)

\(-2x > 10\)

x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.

\(\frac {-2x}{-2} > \frac {10}{-2}\)

\(x> \frac {10}{-2}\)

Since we divided by a negative number, the inequality sign must be flipped.

\(x< \frac{10}{-2}\)

\(x < -5\)

The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Answer: c, its da 3rd graph

Step-by-step explanation:

Step-by-step explanation:

a,ar,ar

2

shortest side is 9cm.

answer should be 4 rounded up to the nearest thousandths

Answer:

3.99479 Meters

The algebraic expression -19c - 4c + 9 + 16​ when simplified is -23c + 25

From the question, we have the following parameters that can be used in our computation:

-19c-4c+9+16​

Express properly

So, we have

-19c - 4c + 9 + 16​

Evaluate the like terms

This gives

-19c - 4c + 9 + 16​ = -23c + 25

Hence, the algebraic expression when simplified is -23c + 25

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Answer:6x+3

Step-by-step explanation:

numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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Answer:

Step-by-step explanation:

If you want to find out how many times larger something is than something else, you have to divide. We will set up a problem that looks like this:

\(\frac{2.1*10^8}{4.2*10^2}\)

Diving 2.1 by 4.2 gives us .5; to divide the exponents, we remember that if we divide like bases we have to subtract the exponents. 10 is our base in both cases, so 8 - 2 gives us 6, resulting in:

\(.5*10^6\)

However, this isn't in scientific notation. We need to move the decimal one more place to the right, which in trn reduces the exponent by 1:

\(5*10^5\)

a) The area of the shaded region of the rectangle is A = 84y² - 30y

b) The area of the shaded region of rectangle is A = 78t² + 40t

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the rectangle be represented as ABCD

a)

Now , the length of the rectangle is L = ( 14y - 5 )

The width of the rectangle is W = 6y

And , Area of rectangle is A = L x W

Area of rectangle A = ( 14y - 5 ) ( 6y )

Area of rectangle A = 84y² - 30y

b)

Now , the length of the larger rectangle is L = ( 21t + 8 )

The width of the larger rectangle is W = 4t

And , the length of the smaller rectangle is L = ( 3t - 4 )

The width of the smaller rectangle is W = 2t

And , Area of rectangle is A = L x W

Area of rectangle A = ( 21t + 8 ) ( 4t ) - ( 3t - 4 ) ( 2t )

On simplifying , we get

Area of rectangle A = 84t² + 32t - ( 6t² - 8t )

Area of rectangle A = 78t² + 40t

Hence , the areas of the shaded region of the rectangle are solved

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Answer:

y = -(5/3)x + 64

Step-by-step explanation:

note: if you don't have desmos, I suggest using it cause it helps a lot with graphing

first rearrange 5x - 3y = 12 to get the y by itself (y = mx + b)

m = slope

b = constant

you can start with subtracting 5x by both sides

now you have -3y = 12 -5x

then divide -3 by both sides

y = (12 - 5x) / -3

you can separate it so you have 12/-3 and -5x/-3

12/-3 = -4 and -5x/-3 you can't really solve but you can get rid of the negatives since two negatives make a positive

you should now have y = -4 + (5/3)x

I like to write it as  y = (5/3)x -4  cause its easier to understand

* I always check desmos to make sure I still have the same graph

* The way you flip the line on the graph is by making the slope negative

since we know (5/3) is our slope all we do is make it negative

so (5/3) changes to -(5/3)

* The end number of the equation is where the line sits on the x axis

The way to find this is to start at 30 where the original line intersects and move left over 3 and up 5 then continue until you reach the x axis

when we switch to the other equation we see it sits on 64 on the x axis

y = -(5/3)x + 64

y=0.002x² +0.15x + 2 and y=x set best models the point of intersection of the arrow and the target because it accounts for the fact that the arrow is travelling in a parabolic arc, while the target is located on a straight line.

A parabolic arc is defined by its vertex, focus, and directrix. The arc can be used to describe the trajectory of a projectile, the shape of a satellite dish, or the shape of some suspension bridges.

The equation y=0.002x² +0.15x + 2 models the parabolic arc of the arrow's trajectory and the equation y=x models the straight line of the target.

This equation set is the only one that correctly models both the parabolic arc of the arrow and the straight line of the target.

To better understand why this equation set is the correct answer, let's look at the other equation sets.

The equation set y=-0.002x²+0.15x+2 and y=-x does not work because the equations do not model a parabolic arc and a straight line, respectively.

The equation set y=0.002x²+0.15x + 2 and y=0,2x does not work because the second equation, y=0.2x, does not model a straight line, but rather a line with a slope of 0.2.

Finally, the equation set y=-0.002x² +0.15x+2 and y = 0.2x does not work because the first equation, y=-0.002x² +0.15x+2, does not model a parabolic arc.

Therefore, the equation set y=0.002x² +0.15x + 2 and y=x is the correct answer because it is the only equation set that accurately models both the parabolic arc of the arrow and the straight line of the target.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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Answer:

12 dollars

Step-by-step explanation:

she spent 4 dollars for each of 3 kids so what I did was multiply 3 times 4, and got 12 dollars then she spent 5 dollars on her self which was 17 dollars she spent in the coffee shop.

Answer:

$17

Step-by-step explanation:

Hope this helps!

Answer:

x<1

Step-by-step explanation:

10x + 80 < 90

10x < 90 - 80

10x < 10

x < 1

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hope this helps:)

Answer:

B & D

Step-by-step explanation:

A The variable "x" is canceled  does not apply

B     One solution

C                                                  does not apply

D      One solution

Hope this helps

The instantaneous rate of change of the lightbulb's electric charge, in coulombs per second is : \(Q'(4) = -0.171\).

The instantaneous rate of change of the lightbulb's electric charge at time t is 4 can be calculate by taking the derivative of Q with respect to t and evaluating it at t = 4.

This can be done by using the definition of the derivative:

\(Q'(t) = lim h- > 0 (Q(t + h) - Q(t)) / h.\)

Substituting t = 4, we can find Q'(4) as follows:

\(Q'(4) = lim h- > 0 (Q(4 + h) - Q(4)) / h\)

=\(lim h- > 0 (3e0.7(4 + h)sin(theta) + 0.01sin(4(4 + h)) + 0.02cos(4(4 + h)) - 0.194) / h\)

\(= -0.171.\)

The physical characteristic of matter that causes it to feel a force when exposed to an electromagnetic field is called electric charge. Positive or negative charges can exist in an electric field. Protons are in excess in positively charged matter, while electrons are in excess in negatively charged matter. The Coulomb is the electrical charge unit used in SI (C).

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The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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The equation of the line in slope-intercept form is y = 2x + 4

What is slope how to solve slope equation ?

Slope is a measure of the steepness of a line. It is defined as the ratio of the change in y-coordinates to the change in x-coordinates between any two points on the line. Slope is denoted by the letter m.

The slope formula is:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

To solve for the slope of a line given two points, you can simply plug in the coordinates into the slope formula and simplify.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope is 2, so we have:

y = 2x + b

To find the value of b, we can use the fact that the line passes through the point (2, 8). Substituting these values into the equation, we get:

8 = 2(2) + b

Simplifying the right-hand side, we get:

8 = 4 + b

Subtracting 4 from both sides, we get:

b = 4

So the equation of the line in slope-intercept form is:

y = 2x + 4

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The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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The mass of a piece of metal that has a volume of 12.4 cubic centimeters.

We can set up a proportion with the given masses and volumes:

Mass ₁ / Volume ₁ = Mass ₂ / Volume ₂

We can choose any two sets of masses and volumes from the table to use in the proportion. Let's use the first set of masses and volumes:

2.5 / 2.5 = Mass₂  / 12.4

We can solve for Mass 2 by cross-multiplying and simplifying:

2.5 x 12.4 = 2.5 Mass ₂

31 = Mass ₂

Therefore, the mass of a piece of metal with a volume of 12.4 cubic centimeters is 31 grams. We can round this answer to the nearest tenth of a gram, which gives us 31.0 grams.

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Answer:

Step-by-step explanation:

4/mx

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

-18.3

Step-by-step explanation:

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65