Guided Practice #1
Damaya is baking pies. For every 2 cups of flour, she uses 3
cups of sugar. How many cups of sugar will she need if she
uses 12 cups of flour? Model your answer on the double
number lines below.
0
O.
G
E

Las soluciones para los dos primeros ejercicios son:

Vamos a ver la primer operacion, está es:

10² + 6³ - [4*(5 - 2)]²

Primero se resuelve lo que esta adentro del parentesis, en este caso:

5 - 2 = 3

Reemplazamos eso:

10² + 6³ - [4*(3)]²

Luego se resuelve lo que está dentro de los corchets:

4*3 = 12

Reempazamos eso para obtener:

10² + 6³ - [12]²

Ahora podemos resolver los exponentes, recordar que el exponente nos dice cuantas veces debemos multiplicar un número por si mismo, entonces:

10² = 10*10 = 100

6³ = 6*6*6 = 216

[12]² = 12*12 = 144

Reemplazando eso obtenemos:

100 + 216 - 144 = 316 - 144 = 172

Veamos tambien el siguiente problema:

-3² + (-2)⁴ + - 4³ + (-2)⁴

Apliquemos los exponentes, primero tenemos:

-3²

Notar que el exponente se le aplica solamente al 3, no al signo, entonces:

-3² = -(3)² = -3*3 = -9

En cambio, en:

(-2)⁴

El exponente si se le aplica al signo, entonces:

(-2)⁴ = (-2)*(-2)*(-2)*(-2) = 4*4 = 16

Los otros dos terminos dan:

- 4³ = -4*4*4 = -64

(-2)⁴ = 16

Reemplazando eso en la expresión:

-3² + (-2)⁴ + - 4³ + (-2)⁴ = -9 + 16 - 64 + 16 = -41

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Answer:

see explanation

Step-by-step explanation:

the y- intercept 8 occurs when time = 0

that is it was 8° F when recording began at time = 0

Answer: I hope this helps.

Step-by-step explanation:

Answer:

[tex]\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\[/tex]

Answer:

25 and 32

Step-by-step explanation:

32 - 25 = 7

32 x 25 = 800

Answer:

5

Step-by-step explanation:

PEMDAS

14-8+6+4-11

14-8=6

6+6=12

12+4=16

16-11=5

Answer:

B. 0,3

Step-by-step explanation:

[tex]\texttt{Identify the zeros of the function}:f(x)=x^2-3x[/tex]

The roots are the x values in which where the graph intersects the x-axis. In order to solve, we will need to find the roots by replacing y with 0. In the end, we will solve for x.

= 0,3

The width of each column is 3.375.

According to the statement

We have to find that the width of the each column.

So, For this purpose, we know that the

Width is the the horizontal measurement taken at right angles to the length.

In other words, It is the distance from one side to the other side which measures across a particular shape or object whose lengths are forming right angles with the sides as in the case of a rectangle.

From the given information:

A production assistant must divide a page of text into two columns. If the page is 6 3/4 inches wide.

Then

width of the page = 27/4 inches

And the number column is divided into page = 2

Then

The width of column = width of the page/ column in a page

The width of column = 27/4/ 2

The width of column = 6.75/ 2

The width of column = 3.375.

So, The width of each column is 3.375.

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Answer:

5 days.

Step-by-step explanation:

The food will last her 5 days.
[tex]3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1-\frac{5}{8}[/tex][tex]=\frac{3}{8}[/tex]

Answer:

Carl and Alex are wearing hats.

Step-by-step explanation:

If Bob doesn't isn't wearing a hat, then Carl is, so Carl clearly is wearing a hat.

Now let's look at Alex. If he wasn't wearing a hat, then Bob would be wearing one. (If Alex doesn't wear a hat, then Bob wears

a hat). The logical conclusion is that Alex must be wearing a hat as well.

Answer:

no

Step-by-step explanation:

quadruple means by 4, so it would be 400%

Answer:

160

Step-by-step explanation:

If 80% of the frogs in a pond are spring peppers, and there are 200 frogs in the pond, to find how many spring peppers are in the pond, find 80% of 200.

[tex]\begin{aligned} \sf \implies 80\% \textsf{ of }200 & = \sf 80\% \times 200\\\\& = \sf \dfrac{80}{100} \times 200\\\\& = \sf \dfrac{80}{100} \times \dfrac{200}{1}\\\\& = \sf \dfrac{80 \times 200}{100 \times 1}\\\\& = \sf \dfrac{16000}{100}\\\\& = \sf 160\end{aligned}[/tex]

Therefore, there are 160 spring peppers in the pond.

Answer: 7x -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

400,000

Answer:

y=8

Step-by-step explanation:

10.19 feet is the radius of a circle with a circumference of 64 feet.

A line that is bent such that its ends meet and all of its points are equally spaced from the middle. We gathered in a circle around the hearth. Something shaped like or like a circle.

Dimensional terms include circumference, diameter, radius, chord, segment, tangent, point of contact, arc, angles on major and minor arcs, angle of center, and sectors. A circle's circumference is the distance that surrounds it.

A curving line makes up the shape of a circle. It is spherical, and every point along the curved line is equally spaced from the center. Due to its two-dimensional nature, this shape is flat.

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Answer:

0.2

Step-by-step explanation:

Answer: 2000

Step-by-step explanation:

The pattern is multiplying by 10. Therefore, 200 x 10= 2000

Answer:

80,000,000

Step-by-step explanation:

76,161,555 is higher then 75,000,000 so it must round up.

Answer: 80,000,000

Step-by-step explanation:

since it's the ten million place you look at place value behind which is the millions place you see if the number is above or below 5. For this instance, since 6 is larger or above 5 you would round up. So, instead of 76,161,555 it would be 80,000,000

The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.

A function is defined as a expression containing one or more variables.

Technically speaking, a function is a means of linking a set of inputs to a set of outputs.

The height of the ball  at any time t is given by the function:

[tex]h(t)=-16t^2+38t+2[/tex]

Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.

Let us substitute the values:

[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]

This is in the form of a quadratic equation in t.

Solving by using the quadratic formula:

We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Therefore for the above quadratic equation:

[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]

Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.

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==========================================================

Explanation:

Point L is at the location (-4, 2)

Translate 3 units to the left to arrive at (-7,2)

Then translate 4 units up to get (-7,6) which leads to choice A

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

The rule of "translate 3 units left, 4 units up" can be condensed into the notation of [tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)[/tex]

Let's apply this rule to point M(1,2)

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)\\\\(1,2)\to(1-3,2+4)\\\\(1,2)\to(-2,6)\\\\[/tex]

This further confirms what choice A is saying since it mentions M'(-2,6)

I'll let you check the other points in choice A.

Answer:

the Answer is c yo I know it bro

Answer: C

Step-by-step explanation:

x^2 + 6x + 8 = (x + 2 )(x + 4 )

The solution by substitution of values to 4 ) is ( - 8 ) / 14 and 6 ) is - 213 .

4 ) Using substituition

By replacing values of c and d in given equation

( 5 [tex]c^{2}[/tex] - [tex]d^{2}[/tex] + 3 ) / ( 2 c - 4 d )

c = - 1 and d = - 4

( 5 [tex]( - 1 )^{2}[/tex] - [tex]( - 4 )^{2}[/tex] + 3 ) / ( 2 ( - 1 ) - 4 ( - 4 ) )

= ( 5 - 16 + 3 )  / ( - 2 + 16 )

= ( - 8 ) / 14

6 ) Using substituition

By replacing values of x and y in given equation

3 [tex]| x + y |^{2}[/tex] - [tex]( x y )^{2}[/tex]

x = 3 and y = - 5

3 [tex]| 3 + ( - 5 ) |^{2}[/tex] - [tex]( 3 * ( - 5 ) )^{2}[/tex]

( 3 * 4 ) - 225

= - 213

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Answer: 309.73

Step-by-step explanation:

The first mistake in solving the given algebraic expression is; Line 3

We are given the algebraic expression as;

6(2y + 6) = 4(9 + 3y)

The first step would be to use distributive property of algebra to expand the bracket to get;

12y + 36 = 36 + 12y

The next step will be to use subtraction property of equality to subtract 36 from both sides to get;

12y = 12y

Now, since the coefficients of the variable is the same on both sides, then it means the equation has no solution and as such the conclusion is that the first mistake is in line 3.

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The rounding off a number of 493 is 490 and The rounding off a number of 917 is 920.

Rounding off number:

1)Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding.

2)Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4.

The given numbers are 493 and 917

The rounding-off number of 493 is

⇒493, The last number is 3, need to decrease and round off⇒490

The rounding-off number of 917 is

⇒917, The last numberis 7, need to increase and round off⇒920

Therefore, The rounding off a number of 493 is 490 and The rounding off a number of 917 is 920.

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Answer:

2

Step-by-step explanation:

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