A new soup recipe contains 33 percent less sodium per serving than the old soup recipe. The old soup recipe contained x milligrams of sodium per serving. Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?

Answer:

2/5

Step-by-step explanation:

4ounces of coffee in cup  1

4 ounces of cream in cup 2

In the first step  pour 4/2=2 ounces of coffee from cup 1 to cup 2, getting:

2 ounces of coffee in cup 1

2 ounces of coffee and 4 ounces of cream in cup 2

In the second step we pour 2/2=1 ounce of coffee and 4/2=2 ounces of cream from cup 2 to cup 1, getting:

2+1=3 ounces of coffee and 0+2=2ounces of cream in cup 1

so the answer is 2/5

Answer:

Factors: 5x, 3x²y⁵   Not Factor: 10x⁴y³

Step-by-step explanation:

5x is a factor because 15x²y⁶= 5x•3xy⁶

3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y

10x⁴y³ isn't a factor because 15:10=1.5 isn't integer

Answer:

A

Step-by-step explanation:

Aquí, tenemos 2/3 como hombres.

La fracción de mujeres es, por lo tanto, 1-2 /3 = 1/3

Entonces 1/3 de 84 son mujeres Por lo tanto, el número de mujeres es 1/3 * 84 = 28

Answer:

Below.

Step-by-step explanation:

cos2a = 2 cos^2 a - 1

cos^4a =  8cos^4 a - 8cos^2 a + 1

Right side of the identity =

1 /8(3 + 4cos2a + cos4a)​

= 1/8( 3 + 4(2 cos^2 a - 1) + 8cos^4 a - 8cos^2 a+1)

= 1/8 (3 + 8 cos^2 a - 4 + 8 cos^4 a - 8cos^2 a + 1)

= 1/8 (8cos^4 a)

= cos^4 a = the left side.

I realised that I should have derived the identity for cos 4a as well , which i have done in the picture.

The given identity, cos⁴a = 1/8(3 + 4cos2a + cos4a) is proved.

To prove a given identity, say f(a) = f(b), we proceed to simplify any of the expressions among the L.H.S. f(a) and the R.H.S. f(b), to get the other term. If we get the simplified form as the other term, our identity holds and is proved.

We know cos2A = 2cos²A - 1.

Going by the same formula, we derive the value of cos4A.

cos4A = 2cos²2A - 1

or, cos4A = 2(2cos²A - 1)² - 1, putting value of cos2A

or, cos4A = 2(4cos⁴A - 4cos²A + 1) - 1, (expanding (2cos²A - 1)² using the formula of (a-b)² = a² -2ab + b²)

or, cos4A = 8cos⁴A - 8cos²A + 2 - 1, (expanding)

or, cos4A = 8cos⁴A - 8cos²A + 1, (simplifying)

∴ cos4A = 8cos⁴A - 8cos²A + 1.

Given identity to us is, cos⁴a = 1/8(3 + 4cos2a + cos4a).

To prove the identity, we proceed with the R.H.S.:

= 1/8(3 + 4cos2a + cos4a)

We put values of cos2A and cos4A in this expression, to get

= 1/8(3 + 4(2cos²a - 1) + (8cos⁴a - 8cos²a + 1))

Expanding the equation, we get

= 1/8(3 + 8cos²a - 4 + 8cos⁴a - 8cos²a + 1)

Simplifying, we get

= 1/8(8cos⁴a) = cos⁴a = L.H.S.

Hence, the given identity is proved.

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Answer:

13

Step-by-step explanation:

We have:

8a^2 + 2b^2 = 10

Dividing both sides by 2,

=> 4a^2 + b^2 = 5

or (2a)^2 + b^2 = 5

We also have ab = 2

=> (2a + b)^2

= (2a)^2 + 2(2a)(b) + b^2

= (2a)^2 + b^2 + 4ab

= 5 + 4(2)

= 5 + 8

= 13

Answer:

SSS

Step-by-step explanation:

I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)

Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.

Answer:

B

Step-by-step explanation:

you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.

The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

From the question, we are to determine the product of the given polynomials

The given polynomials are

(8x^2-4x-8) (2x^2+3x+2)

Their product can be determined as follows

[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]

[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]

Clear the brackets

[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]

Now, collect like terms

[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]

Simplifying

[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

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Answer:

She is wrong

Step-by-step explanation:

Let us use the scale 1 : 75 to find the length of the gym on the scale drawing.

The scale means that 1 m on the drawing represents 75 m in real life.

Therefore, if the length of the gym is 12.3 cm, then the length of the gym in the scale drawing is:

12.3 / 75 = 0.164 m

Converting to cm:

1 m = 100 cm

0.164 m = 0.164 * 100 = 16.4 cm

She is wrong.

Answer:

12

Step-by-step explanation:

8.3 / .7

Multiply each by 10 to get rid of the decimal

83/7

We know that 84/7 =12 so this is close to 12

Answer:

1/2

Step-by-step explanation:

Cos 60 = [tex]\frac{adjacent}{hypotenuse}[/tex]

1/2 = [tex]\frac{XZ}{4}[/tex]

Multiplying both sides by 4

=> XZ = 2

Sin Y = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin Y = [tex]\frac{2}{4}[/tex]

Sin Y = 1/2

Answer:

The second term becomes the reciprocal and then you multiply the first term by the second term

Answer:

A. second

Step-by-step explanation:

When dividing fractions, we always take the second term and flip that. In other words, we convert the second term into its reciprocal. Remember the phrase "flip the guy, and multiply!" Essentially, the "guy" just refers to the second term.

For example, if we have 1/3 ÷ 2/5, in order to solve this, we flip the second term, which is 2/5 so that it becomes 5/2 and then multiply:

1/3 ÷ 2/5 = 1/3 × 5/2 = 5/6

The answer is thus A.

~ an aesthetics lover

Answer:

The sum of interior angles will be 180 * (6 - 2) = 720°. ∠B = 720 - 170 - 133 - 102 - 117 - 90 = 108°.

The measure of ∠B is 108.

a plane figure with at least three straight sides and angles, and typically five or more.

The sum of interior angles will be 180 * (6 - 2) = 720°. ∠B = 720 - 170 - 133 - 102 - 117 - 90 = 108°.

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Answer:

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part

Answer:

4/5

Step-by-step explanation:

y = 4/5 x -3

This is written in slope intercept form

y =mx + b where m is the slope and b is the y intercept

the slope is 4/5 and the y intercept is -3

195 m^3

Step-by-step explanation:

The equation for the volume of a triangular prism is...

[tex]V=\frac{1}{2}bhl[/tex]

In this equation, b is the base, h is the height, and l is the length. We simply need to plug everything in from the problem into the equation, then solve. To also make this easier, I'm going to change the 1/2 to a 0.5.

[tex]V=0.5*6*13*5[/tex]

[tex]V=[/tex]

195 m^3

Answer:

TRUE

Step-by-step explanation:

if it was b^4 x b^3 then false. but here, would would multiply b^4 by b^3 to make it 12 so true

sorry for bad explanation

Answer:

True

Step-by-step explanation:

If b=2, 2^4 is 16, and 16^3 is 4096.

Also 2^12 is 4096.

So they are equivalent.

Answer:

0.5 or 50%

Step-by-step explanation:

The probability that the winning team is in the Ages 10 - 12 division given that it is in the baseball league:

[tex]P(Y|B)=\dfrac{P(Y \cap B)}{P(B)} \\=\dfrac{2/16}{6/16}\\=\dfrac{2}{6}[/tex]

The probability that the winning team is in the Ages 13 - 15 division given that it is in the baseball league:

[tex]P(Z|B)=\dfrac{P(Z \cap B)}{P(B)} \\=\dfrac{1/16}{6/16}\\=\dfrac{1}{6}[/tex]

Therefore:

[tex]P(Y$ or $Z|B)=\dfrac{2}{6}+\dfrac{1}{6}\\=\dfrac{3}{6}\\\\=0.5[/tex]

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x - 5y = 2

5y = 12x - 2

Divide both sides by 5

y = 12/5x - 1/5

Comparing with the above formula

Slope / m = 12/5

Since the lines are parallel their slope are also the same.

Slope the parallel line = 12/5

Equation of the line using point (2,3) is

[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]

Multiply through by 5

That's

5y - 15 = 12(x - 2)

5y - 15 = 12x - 24

We have the final answer as

Hope this helps you

Answer:

[tex]x \geqslant 0[/tex]

Option D is the right option.

Explanation:

Observe from the graph that the value of X starts at X=0 and the graph is going to the right infinitely.

So the domain of the function should be:

[tex]x \geqslant 0[/tex]

Hope this helps...

Good luck on your assignment..

The domain of the square root function graphed is, x ≥ 0

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The square root function are graphed below in figure.

Now, We know that;

The set of all inputs of the function is called Domain of set.

Hence, By definition of domain of function, we get;

The domain of the square root function graphed is,

x ≥ 0

Thus, The domain of the square root function graphed is, x ≥ 0

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Answer: If point B is on the same line and the same distance from points A and C,  the location is (-1.5, 4,5)

Step-by-step explanation: For point B to be the same distance from the other two points, it must be halfway between them.

for the x-value, find the number that is halfway between 0 and -3. That is -1.5

For the y-value, find the number that is halfway between 4 and 5. That is 4.5

The coordinate for point B is (-1.5, 4.5)

NO

Step-by-step explanation:

Answer:

No it's not

Step-by-step explanation:

The y values are just either 1 or -1 which doesn't make sense

So therefore the answer is no

Hope this helps!

Answer:

Our expressions is f(x) = 3|x-7|-7

Let's calculate the limits in +∞ and -∞

So the right staement is B

As x approaches positive infinity, f(x) approaches negative infinity.

A relation is a function if it has only One y-value for each x-value.

The function f(x) = 3|x − 7| − 7 is a piecewise function, where the absolute value function has two cases depending on the sign of (x - 7).

When (x - 7) is positive, the function becomes 3(x - 7) - 7 = 3x - 28, and when (x - 7) is negative, the function becomes -3(x - 7) - 7 = -3x + 14.

As x approaches positive infinity, both cases approach negative infinity because the dominant term in each case is the linear term (3x or -3x) as x becomes large.

Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches negative infinity.

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Answer:

She traveled 33 miles.

Step-by-step explanation:

11*3 = 33

Answer:

33

Step-by-step explanation:

11mph times 3 hours= 33 miles

Answer:

3x - y = - 7

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (- 2, 1) , thus

y - 1 = 3(x + 2) ← distribute

y - 1 = 3x + 6 ( subtract 6 from both sides )

y  - 7 = 3x ( subtract y from both sides )

- 7 = 3x - y, that is

3x - y = - 7 ← in standard form

The value of angle x is 57.1 degrees.

Here we have given an angle is 38degee and the sides of the triangle are 11cm and 8 cm.

[tex]sin(x)=\frac{opposite side }{hypotenuse}[/tex]

Therefore by using the formula for the attached figure we have

[tex]sin(38^0)=\frac{y}{11}\\\\y=11sin(38^0)\\\\y=6.71[/tex]

Similarly, for the second triangle for the value of x

we have,

[tex]sinx=y/8=6.71/8=0.84\\\\x=sin^-1(0.84)=57.1^0[/tex]

Therefore we get the value of angle x is 57.1 degrees.

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Answer:

add the y coordinates of the two lines and divide by 2

Step-by-step explanation:

½[0+(-12)]

½[0-12]

½[-12)

y co-ordinate of the midpoint is -6

Answer:

The final cost is $43.2

Step-by-step explanation:

We have the following equation:

[tex]C=p(1+r)[/tex]

Where C is the final cost, p is the price before tax and r is the tax rate.

So, to calculated the final cost for a $40 item after 8% tax, we need to replace p by 40 and r by 0.08 and calculate the value of C as:

[tex]C=40*(1+0.08)=43.2[/tex]

Therefore, the final cost is $43.2

Answer: $43.20

Step-by-step explanation: The simplest way to do it (my way) is i first used (1 + r), which is (1 + 8%), that gave me 1.08, then I did the total amount, $40x1.08, which equals $43.20. This may not be the right way to do it, but it is the simplest.

Hope this helped :)

Answer:

If the expression is:

-3x + 12 = -3x + 12, infinite solutions

If the expression is:

-3x + 12 = -3x - 12, no solutions

Step-by-step explanation:

Step 1: Distribute

-3x + 12 = 3x = 12

If both lines have the same slope and same y-int, they are the same line and therefore have infinite solutions.

If both lines have the same slope but different y-int, then they are parallel and therefore have no solutions.