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3 years ago

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Jessica has some markers. She has 5 more black markers than blue markers. She has 4 times as many red markers as black markers.

She has 8 blue markers.
How many markers does Jessica have altogether?

1 answer:

abruzzese [7]3 years ago

4 0

The answer is 73 because , 5+8=13 black times 4=52 red so

8 blue + 13 black + 52 red = 73 markers in all

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2. Three points of a parallelogram are (4, 3), (-4, 3), and (2, 3). Find the coordinates of the 4th point to complete the parall

antiseptic1488 [7]

Parallelograms have equal and parallel opposite sides

<em>The coordinates of the 4th point is (-2,3)</em>

Let the parallelogram be ABCD, such that:

$A = (4,3)$

$B =(-4,3)$

$C = (2,3)$

A and B have the same y-coordinates, while their x-coordinates are additive inverse

This means that:

The y-coordinates of point C and point D will be the same, while their x-coordinates will be additive inverse.

<u>For point C</u>

We have:

$x = 2$

$y = 3$

<u>For point D</u>

The coordinates would be:

$x =- 2$

$y = 3$

Hence, the coordinates of D is (-2,3)

Read more about parallelograms at:

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2 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

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2 years ago

In the function f(t) = sin(t), what is the effect of multiplying t by a coefficient of 2?

liubo4ka [24]

Answer:

"changes the period to pi"

Step-by-step explanation:

f(t) = Sin(t),

Here, t is the period, by definition.

Multiply t by a number that is GREATER THAN 1, makes the period shorter and compressed.

Multiplying t by a number that is between 0 and 1 makes the period expanded.

For the first, if we multiply the period by a, the period becomes $\frac{2\pi}{a}$

Since the problem tells us to multiply by 2, we know the period becomes compressed and becomes :

$\frac{2\pi}{2}=\pi$

Third answer choice is right.

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3 years ago

Simplify (2*4)−1.

EastWind [94]

The simplification form of the number expression (2⁴)⁻¹ is 1/2⁴ option (B) one over two raised to the fourth power is correct.

<h3>What is an integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number expression is:

= (2⁴)⁻¹

Using the properties of the integer exponent:

= 1/2⁴

The above number is one over two raised to the fourth power

Thus, the simplification form of the number expression (2⁴)⁻¹ is 1/2⁴ option (B) one over two raised to the fourth power is correct.

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2 years ago

What is -2(-y) in expanded form

damaskus [11]

Answer:

2y

Step-by-step explanation:

$(-2)(-y) = (-1)(2)(-1)(y) = (-1)^2\ccdot 2y = 2y$

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2 years ago