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katrin2010 [14]

3 years ago

13

Ms. Ayala had 152 pencils. She divided the numbers of pencils equally among 13 students. What is the greatest numberof pencils M

s.Ayala could have given each student

2 answers:

uranmaximum [27]3 years ago

8 0

She keeps 9 pecainsle

Alex3 years ago

6 0

Answer:

11

Step-by-step explanation:

she divides the number of pencils equally

so the number of pencils per student is 152/13

which is 11.692...

but she can't give 0.69 of a pencil so she gives only the whole part 11

and she keeps 9 pencils

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Is it possible to draw a triangle with numbers 5,6,11

Tatiana [17]

Answer:

No

Step-by-step explanation:

Let's use the Pythagorean Theorem. For those of you that don't know, it is $a^2 + b^2 = c^2\\$ .

11 is the bigger side in this case, so our formula would go like this: $5^2 + 6^2 = 11^2\\$ .

We now calculate to see if this is true.

25 + 36 $\neq$ 121

Therefore, the answer is wrong.

8 0

3 years ago

Read 2 more answers

Whats the volume of the cylinder? Round your answer to the nearest hundred the top is B the left side of the cylinder is 13cm th

Wittaler [7]

Answer:

The volume of the cylinder is 163.3 m³.

Step-by-step explanation:

Given that,

Height = 13 cm

Base = 4 cm

So, radius = 2 cm

We need to calculate the volume of the cylinder

Using formula of cylinder

$V=\pi r^2h$

Where, r = radius

h = height

Put the value into the formula

$V=\pi\times(2)^2\times13$

$V=163.3\ cm^3$

Hence, The volume of the cylinder is 163.3 cm³.

6 0

3 years ago

Which of the following ordered pairs is a solution to y=2^x

Masja [62]

What are the choices?

7 0

3 years ago

What is the solution to sqrt 17-x=x+3? Show your work.

snow_lady [41]

Answer:

$x=1$

Step-by-step explanation:

Remember:

$(\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2$

Given the equation $\sqrt{17-x}=x+3$ , you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

$(\sqrt{17-x})^2=(x+3)^2$

$17-x=(x+3)^2$

Simplifying, you get:

$17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0$

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

$(x-1)(x+8)=0$

Then:

$x_1=1\\x_2=-8$

Let's check if the first solution is correct:

$\sqrt{17-(1)}=(1)+3$

$4=4$ (It checks)

Let's check if the second solution is correct:

$\sqrt{17-(-8)}=(-8)+3$

$5\neq-5$ (It does not checks)

Therefore, the solution is:

$x=1$

3 0

3 years ago

I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

<em>The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.</em>

2. Determine the zeros.

<em>Factor the polynomials first. </em> $(2x-1)(2x+3)$ <em>This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2</em>

3. Determine the Axis of Symmetry

<em>We can solve this by using the formula of </em> $x=-\frac{b}{2a}$ <em>However, I'll be solving the Axis of Symmetry with Calculus instead.</em>

<em /> $f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$ <em />

<em>Then let f'(x) = 0 to find the Axis of Symmetry.</em>

<em /> $8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$ <em />

<em>Therefore, the Axis of Symmetry is -1/2</em>

4. Determine the vertex.

<em>Substitute the value of Axis of Symmetry in f(x).</em>

<em /> $f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$ <em />

<em>Therefore the vertex is at (-1/2, -4)</em>

5. Does the vertex representing max-pont or min-point?

<em>The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE. </em>

7. Graph f(x)

<em>Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).</em>

<em>--------------------------- </em>End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

<em>The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is. </em>

<em>For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.</em>

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

<em>These are factored forms with different types of operators.</em>

<em>The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)</em>

4. Write in Vertex Form.

$y=a(x-h)^2+k$

<em>The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.</em>

<em>The vertex is at (h,k) and the axis of symmetry is at x = h.</em>

<em>For example, </em> $y=(x-2)^2+3$ <em />

<em>The vertex would be at (2,3) and the axis of symmetry is x = 2.</em>

3 0

3 years ago