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3 years ago

Is 2(2x-4)+8y+10-2y an expression to be simplified or an equation to be sovled? check all that apply

1 answer:

8 0

I’m pretty sure the answers are B, C, and D because it is an expression because their is not equal signs, so that crosses out E, F, and G. But I’m not really sure, but all I can tell you is that it is most likely not E, F, and G

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The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate t

Doss [256]

Answer:

First Case:

$\displaystyle p=\frac{5}{2}\text{ and } d=-2$

Second Case:

$\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}$

Step-by-step explanation:

We know that the first three terms of an arithmetic series are:

$6p+2, 4p^2-10, \text{ and } 4p+3$

Since this is an arithmetic sequence, each subsequent term is d more than the previous term, where d is our common difference.

Therefore, we can write the second term as;

$4p^2-10=(6p+2)+d$

And, likewise, for the third term:

$4p+3=(6p+2)+2d$

Let's solve for d for each of the equations.

Subtracting in the first equation yields:

$d=4p^2-6p-12$

And for the second equation:

$2d=-2p+1$

To avoid fractions, let's multiply the first equation by 2. Hence:

$2d=8p^2-12p-24$

Therefore:

$8p^2-12p-24=-2p+1$

Simplifying yields:

$8p^2-10p-25=0$

Solve for p. We can factor:

$8p^2+10p-20p-25=0$

Factor:

$2p(4p+5)-5(4p+5)=0$

Grouping:

$(2p-5)(4p+5)=0$

Zero Product Property:

$\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}$

Then, we can use the second equation to solve for d. So:

$2d_1=-2p_1+1$

Substituting:

$\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}$

So, for the first case, p is 5/2 and d is -2.

Likewise, for the second case:

$\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}$

So, for the second case, p is -5/4, and d is 7/4.

By using the values, we can determine our series.

For Case 1, we will have:

17, 15, 13.

For Case 2, we will have:

-11/2, -15/4, -2.

8 0

3 years ago

HELP PLS PLS PL SPLSLSSPPS

erma4kov [3.2K]

Answer:

x ≈ 73.3

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos39° = $\frac{adjacent}{hypotenuse}$ = $\frac{57}{x}$ ( multiply both sides by x )

x × cos39° = 57 ( divide both sides by cos39° )

x = $\frac{57}{cos39}$ ≈ 73.3 ( to the nearest tenth )

8 0

3 years ago

If it takes 10 minutes for the ingredients to properly mix two minutes for the pills to travel down the bill today I have in sev

arsen [322]

Complete question is;

If it takes 10 minutes for the ingredients to be properly mixed, 2 minutes for the pills to travel down the belt to the oven, 7 Minutes in the oven and another 3 minutes down the belt to the drum how many total minutes does it take for the pills to arrive at the drum

Answer:

22 minutes

Step-by-step explanation:

This is basically asking us to add the times given.

Because the end product is the pills.

And it is a process of producing the pills and transporting it to the drum.

Now;

- 10 minutes for mixing the ingredients

- After mixing, 2 minutes to travel from the belt to the oven

- Spends 7 minutes in the oven

- spends 3 minutes to move through the belt to the drum.

Total time taken = 10 + 2 + 7 + 3 = 22 minutes

4 0

3 years ago

According to these three facts, which statements are true?

Yanka [14]

Q1) We have the following statements:

1. Circle W has center (−3, 0) and radius 8.

We can write this statement as the following equation:

 $(x-h)^2+(y-k)^2=r^2 \therefore (h,k)=(-3,0) \ and \ r=8 \\ \\ \therefore (x+3)^2+y^2=64$

The graph of this equation is shown in Figure 1.

2. Circle V is a translation of circle W, 2 units down.

To do this translation we add two units to the y-coordinate, so:

 $(x+3)^2+(y+2)^2=64$

The graph is shown in Figure 2.

3. Circle V is a dilation of circle W with a scale factor of 2.

To do this dilatation we multiply both the center and the radius by the scale factor of 2, thus:

 $(x+3)^2+y^2=64 \\ (h,k)=(-3,0) \\ (h_v,k_v)=2\times (-3,0)=(-6,0) \ and \ r_v=8\times2=16 \\ \\ (x+6)^2+y^2=256$

This circle is shown in Figure 3

So let's analyze each statement.

Q1.1) The center of circle V is (−5, 0).

This is false. From the statement 2 we know that the new center is (-3, -2) and from 3 the new center is (-6, 0).

Q1.2) Circle V and circle W are similar.

Since all circles have the same shape even though they may be different sizes, then all circles are similar. Therefore, it is true that circle V and circle W are similar.

Q1.3) The radius of circle V is 16.

From the statement 3 we can affirm that this is true. By applying the dilatation with a scale factor of 2 we find out that the radius of the new circle is in fact equal to 16.

Q1.4) Circle V and circle W have the same center.

From the statement 2 we know that the new center is (-3, -2) and from 3 the new center is (-6, 0). On the other hand, the center of circle W is (-3, 0). From this, it follows that this statement is false.

Q2) Suppose x is any positive number.

We have two concentric circles as follows:

$x\ \textgreater \ 0 \\ \\ Circle \ 1: Center \ (0,0) \ and \ radius \ 2x \\ \\ Circle \ 2: Center \ (0, 0) \ and \ radius \ 10x$ 

Q2.1) Why is circle 1 similar to circle 2?

If we perform a dilatation, that is, a resizing of one circle, centered on the shared center, until both circles overlap, it will be true that the circles will always overlap no matter what size they are, thus, they are similar. In fact, as we said in above all circles are similar.

Q2.2) Circle 2 is a dilation of circle 1 with a scale factor of 0.2.

Suppose that:

 $x=2$

Then circle 1 is given by the following equation:

 $x^2+y^2=4$

If we dilate this circle with a scale factor of 0.2 then:

 $Circle \ 1: x^2+y^2=4 \\ Diameter \ 1=2r=2\times 2=4 \\ \\ (h,k)=(0,0) \\ (h_v,k_v)=0.2\times (0,0)=(0,0) \ and \ r_v=0.2\times 2=0.4 \\ \\ Circle \ 2:x^2+y^2=0.16 \\ Diameter \ 2=2\times 0.4=0.8 \\ \\ So: \\ \\ Diameter \ 1 \neq Diameter \2$

So the statement both circles have congruent diameters is false.

Q2.3) Circle 2 is a dilation of circle 1 with a scale factor of 5.

We have the same equation for circle 1:

 $x^2+y^2=4$

$Circle \ 1: x^2+y^2=4 \\ \\ Dilatation: \\ (h,k)=(0,0) \\ (h_v,k_v)=5\times (0,0)=(0,0) \ and \ r_v=5\times 2=10 \\ \\ Circle \ 2:x^2+y^2=100$

Two circles have the same area if they have the same radius. Given that this is no applied to our circles, the statement circle 1 and circle 2 have equal areas is false.

8 0

3 years ago

For a wedding, a pastry chef is increasing the cake recipe by 4 and ½ times. How much butter is needed? Flour?

BaLLatris [955]

Answer:

Butter: 18/4 cups

Flour: 36 cups

Step-by-step explanation: I think this is right.

4 1/2 = 9/2

9/2 x 1/4 = 18/4 x 1/4 = 18/4

1 1/3 = 4/3

9/2 x 4/3 = 27/6 x 8/6 = 216/6 = 36

8 0

3 years ago