Question 7(Multiple Choice Worth 1 points)

(01.02 LC)

Solve for x: −3x − 3= −3(x + 1)

All real numbers
No solution
6
−6

The statistical measurement that informs a CTRS about how well the assessment results compare to what is being measured is Construct validity.

Construct validity assesses how well the assessment measures the intended construct or trait, and compares the results to other tests or measures of the same construct to determine how accurate and reliable the assessment is.

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The range between a drug's effective dose and its toxic dose is called the theurapeutic index.

The therapeutic index, often known as the therapeutic ratio, is a numerical evaluation of a drug's relative safety. The amount of a therapeutic agent that has a therapeutic impact is compared to the amount that has a harmful effect.

A range of doses calibrated between efficacy and toxicity, achieving the maximum therapeutic benefit without producing intolerable side-effects or toxicity, is referred to as the therapeutic window or safety window.

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Answer:

BF = √(12^2 - 8^2) = √(144 - 64) = √80

= 4√5 = about 8.9 cm

Answer:

4

Step-by-step explanation:

4+2(3x-4)=8

4+6x-8 = 8

6x-4 = 8

6x = 12

x = 12/6

x = 2

4(2)-4 = 4

(a) At t = 1 s, the object's position is 0.97 meters.

(b) At t = 2 s, the object's position is -2.54 meters.

(c) At t = 3 s, the object's position is -1.53 meters.

(d) At t = 4 s, the object's position is 8.00 meters.

(e) The object's displacement between t = 0 s and t = 4 s is 8.00 meters.

(f) The average velocity from t = 2 s to t = 4 s is 4.00 m/s.

To find the position of the object at different values of t, we substitute the given values into the equation x = 3.21t - 4.24t^2 + 1.00t^3.

(a) When t = 1 s:

x = 3.21(1) - 4.24(1)^2 + 1.00(1)^3

x = 3.21 - 4.24 + 1.00

x = 0.97 meters

(b) When t = 2 s:

x = 3.21(2) - 4.24(2)^2 + 1.00(2)^3

x = 6.42 - 16.96 + 8.00

x = -2.54 meters

(c) When t = 3 s:

x = 3.21(3) - 4.24(3)^2 + 1.00(3)^3

x = 9.63 - 38.16 + 27.00

x = -1.53 meters

(d) When t = 4 s:

x = 3.21(4) - 4.24(4)^2 + 1.00(4)^3

x = 12.84 - 67.84 + 64.00

x = 8.00 meters

(e) The object's displacement between t = 0 and t = 4 s can be found by subtracting the initial position from the final position:

Displacement = x(final) - x(initial)

Displacement = 8.00 - x(0)

Since the equation x = 3.21t - 4.24t^2 + 1.00t^3 doesn't provide the initial position explicitly, we can assume x(0) = 0 (starting from the origin):

Displacement = 8.00 - 0

Displacement = 8.00 meters

(f) Average velocity from t = 2 s to t = 4 s can be calculated by dividing the displacement by the time interval:

Average velocity = Displacement / Time interval

Average velocity = 8.00 meters / (4 s - 2 s)

Average velocity = 8.00 meters / 2 s

Average velocity = 4.00 m/s

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Answer:

  ∠CBA =90°; ∠CAD =65°; ∠ACD =25°; ∠CBD = 65°

  ∠BWA = 130°; ∠AWD = 50°

Step-by-step explanation:

The diagonals of a rectangle divide the figure into two pairs of congruent isosceles triangles. The figure is symmetrical about both the vertical and horizontal centerlines. Each corner angle of the rectangle is 90°. Of course, the sum of angles in any of the triangles is 180°.

__

The above descriptions tell you ...

  ∠ABD =∠ACD =∠BAC =∠BDC = 25°

  ∠CBA =∠BCD =∠CDA =∠DAB = 90°

  ∠CAD =∠CBD =∠ACB =∠ADB = 90° -25° = 65°

  ∠BWA =∠CWD = 180° -25° -25° = 130°

  ∠AWD = ∠BWC = 180° -65° -65° = 50°

Answer:

n = 3200

Step-by-step explanation:

200 = 1000 - \(\frac{n}{4}\) ( subtract 1000 from both sides )

- 800 = - \(\frac{n}{4}\) ( multiply both sides by 4 to clear the fraction )

- 3200 = - n ( multiply both sides by - 1 )

n = 3200

Answer:

 8

Step-by-step explanation:

Given point S outside a circle and tangents SR and ST, with SR = 8, you want to know the length of ST.

Tangents to a circle from an external point are the same length.

  ST = SR = 8

The length of ST is 8.

<95141404393>

In this problem, we are given a variable resistor R and an 8-Ω resistor in parallel. We are asked to find the rate at which the resistance R is changing when it is equal to 6.0 Ω.

Given that RT = 8R / (8 + R), we can differentiate this equation with respect to time t using the quotient rule. Let's denote dR/dt as the rate of change of R with respect to time. Applying the quotient rule, we have:

dRT/dt = \([ (8)(dR/dt)(8 + R) - (8R)(dR/dt) ] / (8 + R)^2\)

To find the rate at which R is changing when R = 6.0 Ω, we substitute R = 6.0 into the above equation:

dRT/dt = \([ (8)(dR/dt)(8 + 6.0) - (8)(6.0)(dR/dt) ] / (8 + 6.0)^2\)

Simplifying further, we have:

dRT/dt = \([ (8)(dR/dt)(14) - (48)(dR/dt) ] / (14)^2\)

dRT/dt = (112(dR/dt) - 48(dR/dt)) / 196

dRT/dt = 64(dR/dt) / 196

dRT/dt = 16(dR/dt) / 49

Therefore, the rate at which R is changing when R = 6.0 Ω is equal to 16/49 times the rate of change of RT.

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Answer:

I took a screenshot of my answer

Step-by-step explanation:

hope it helps <3

give me a crown please

The answers are (9+12)÷(3+4)÷(2+1)·2 = 2, (9+12÷3)+(4÷2+1·2) = 8, (9+12)÷3+(4÷2)+(1·2) = 11 and (9+12)÷(3+4)÷(2+1·2) = 12.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given are the expressions, we need to put the parentheses to equate the values,

1) 9+12÷3+4÷2+1·2 = 2,

9+12 = 21, 3+4 = 7, 1+2 = 3

(9+12)÷(3+4)÷(2+1)·2 = 21 ÷ 7 ÷ 3 · 2 = 2

(9+12)÷(3+4)÷(2+1)·2 = 2

2) 9+12÷3+4÷2+1·2 = 8

(9+12) = 21, (2+1·2) = 6

(9+12÷3)+(4÷2+1·2) = 21 ÷ 3 + 1 = 8

(9+12÷3)+(4÷2+1·2) = 8

3) 9+12÷3+4÷2+1·2 = 11

9+12 = 21, 4÷2 = 2, 1·2 = 2

(9+12)÷3+(4÷2)+(1·2) = 21 ÷ 3 + 2 +2 = 7 + 2 + 2 = 11

(9+12)÷3+(4÷2)+(1·2) = 11

4)  9+12÷3+4÷2+1·2 = 12

(9+12)÷(3+4)÷(2+1·2) = 12

Hence, the answers are (9+12)÷(3+4)÷(2+1)·2 = 2, (9+12÷3)+(4÷2+1·2) = 8, (9+12)÷3+(4÷2)+(1·2) = 11 and (9+12)÷(3+4)÷(2+1·2) = 12.

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Answer:  Let the points be A(1,1) and B(2,3)

Slope of AB=  

2−1

3−1

​

=2

Product of slope of a line and its perpendicular is −1

⇒ Slope of perpendicular =−  

2

1

​

Mid point of AB is  

(  

2

1+2

​

,  

2

1+3

​

)

(  

2

3

​

,2)

So the equation of perpendicular is  

y−2=−  

2

1

​

(x−  

2

3

​

)

4y−8=−(2x−3)

2x+4y=11

2x+4y−11=0

Step-by-step explanation:

Answer: \(\Large\boxed{6}\)

Step-by-step explanation:

Given expression

\(2(2x^2+xy-z^2)-xy\)

Given information

\(x=2\\\)

\(y=-1\)

\(z=-2\)

Substitute values into the given expression

\(2[2(2)^2+(2)(-1)-(-2)^2]-(2)(-1)\)

Simplify the exponents

\(2[2(4)+(2)(-1)-(4)]-(2)(-1)\)

Simplify by multiplication

\(2[8-2-4]+2\)

Simplify values in the parenthesis

\(2[6-4]+2\)

\(2[2]+2\)

Simplify by multiplication

\(4+2\)

\(\Large\boxed{6}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

\( \red{22}\)

Step-by-step explanation:

Given that,

x = 2

y = ( -1 )

z = ( -2 )

To find the value of given expression, you have to replace x, y and z with 2, -1 and -2 respectively.

Let us solve it now.

\(2(2x² + xy-z²)-xy \\ 2((2 \times 2 ^{2}) + (2 \times - 1 ) - ( { - 2}^{2})) - (2 \times - 1 )\)

You have to solve this equation according to the BODMAS theorem.

That is,

B = brackets

O = of

D = division

M = multiplication

A = addition

S = subtraction

\(2((2 \times 2 ^{2}) + (2 \times - 1 ) - ( { - 2}^{2})) - (2 \times - 1 ) \\ 2((2 \times 4) - 2 - ( - 4)) - ( - 2) \\ 2(8 - 2 + 4) + 2 \\ 2(6 + 4) + 2 \\ 2 \times 10 + 2 \\ 20 + 2 \\ 22\)

The concentration of bicarbonate (HCO3-) in the lake is approximately 10^(-4) M.

To find the concentration of bicarbonate (HCO3-) in the lake, we need to consider the equilibrium reactions involving CO2, H2CO3, and HCO3-.

The first step is to write the equilibrium equation for the dissociation of H2CO3:

H2CO3 ⇌ H+ + HCO3-

Since the concentration of dissolved CO2 is fixed at 1.2 x 10-5 M, we can assume that the concentration of H2CO3 is also 1.2 x 10-5 M.
Next, we need to consider the acid dissociation constant (Ka) for the dissociation of H2CO3. However, in this case, we are given the pKa values. To convert pKa to Ka, we use the equation Ka = 10^(-pKa).

So, for the first dissociation reaction, Ka1 = 10^(-pKA1) = 10^(-6.33).
Now, we can set up an expression for the equilibrium constant (Keq) for the dissociation of H2CO3:

Keq = [H+][HCO3-] / [H2CO3]
Since the concentration of H2CO3 is given as 1.2 x 10-5 M, we can substitute this value into the equation:
Keq = [H+][HCO3-] / (1.2 x 10-5)

Now, let's consider the second dissociation reaction of HCO3-:
HCO3- ⇌ H+ + CO3^2-

This reaction has a pKa2 value of 10.33, so we can convert it to Ka2 using the equation Ka2 = 10^(-pKa2).
Now, we can write the equilibrium constant expression for the second dissociation reaction:
Keq2 = [H+][CO3^2-] / [HCO3-]

Since we are interested in finding the concentration of HCO3-, we can rearrange this equation to solve for [HCO3-]:

[HCO3-] = [H+][CO3^2-] / Keq2

We can substitute the expression for Keq2 into the equation:
[HCO3-] = [H+][CO3^2-] / (10^(-pKa2))

At this point, we need to make an assumption that the concentration of CO3^2- is negligible compared to the concentration of HCO3-. This is a reasonable assumption since the pH of the lake is 4.0, indicating an acidic environment. Therefore, we can assume that [CO3^2-] ≈ 0.

With this assumption, the equation simplifies to:
[HCO3-] ≈ [H+]

Since the lake's pH is 4.0, we can calculate the concentration of H+ using the equation pH = -log[H+]:
[H+] = 10^(-pH)

Substituting the given pH value into the equation:
[H+] = 10^(-4)

Now, we can substitute this concentration of H+ into the equation for [HCO3-]:
[HCO3-] ≈ [H+] ≈ 10^(-4)

Therefore, the concentration of bicarbonate (HCO3-) in the lake is approximately 10^(-4) M.

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Answer:

x = 2, P = 22 cm, A = 21 cm²

Step-by-step explanation:

The 2 legs of the triangle are congruent , then

6x - 4 = 8 ( add 4 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

perimeter = 8 + 8 + 6 = 22 cm

Area = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here b = 6 and h = 7 , then

A = \(\frac{1}{2}\) × 6 × 7 = 3 × 7 = 21 cm²

Answer:

x = 2

Perimeter = 22 cm

Area = 21 cm²

Step-by-step explanation:

=> We know that the 2 side lengths of the given triangle are congruent, because of the congruency mark theorems, therefore to solve for x first, we can say;

6x - 4 = 8

6x = 8 + 4

6x = 12

x = 12/6

x = 2

Now that we know the side lengths of the triangles are 8, 8 and 6, we can find the perimeter;

Side 1 + Side 2 + Side 3 = Perimeter

8 + 8 + 6 = Perimeter

22 = Perimeter

Lastly to find the Area of the triangle, follow the formula of;

A = 1/2 (b * h)

A = 1/2 (6 * 7)

A = 1/2 (42)

Area = 21

Hope this helps!

Answer:

B

Step-by-step explanation:

Isosceles has two of the same lengths

Isosceles is also an acute angle, since the angles are less than 90 degrees.

Hope this helped!

Step-by-step explanation:

First, we factorize that

  3x³− 12x

 = 3(x³− 4x)

 = 3X(X− 4)

Hence volume =  3X(X− 4)

We know that,

the volume of a cuboid is length x breadth x height

possible dimensions are

                 length = 3,

                 breadth = X,

                  height = X− 4.

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Answer:

disagree because the outcome of the problem would be incorrect

Answer:

Step-by-step explanation:
I got you.

1.
The six-sided figure can be broken down into a rectangular prism with dimensions 35 x 20 x 30 and a right triangular pyramid with base 35 x 15 and height 30.

The rectangular prism has a total floor area of 35 x 20 = 700 square feet.

The right triangular pyramid has a base area of 0.5 x 35 x 15 = 262.5 square feet and a total floor area of 262.5 + 700 = 962.5 square feet.

So the total floor area of the six-sided figure is 962.5 square feet.

To find the cost to cover the floor with wax, we multiply the floor area by the cost per square foot:

962.5 * $1.38 = $1322.35

So the wax will cost $1322.35 to cover the floor.

2.
The shape for the quilt block can be divided into two right triangles and a rectangle. The rectangle has a length of 13 inches and a width of 5.18 inches, so its area is 13 * 5.18 = 67.34 square inches. The two right triangles each have a base of 5 inches and a height of 6 inches, so their area is 0.5 * 5 * 6 = 15 square inches each. The total area of the two right triangles is 15 * 2 = 30 square inches. The total area of the quilt block is 30 + 67.34 = 97.34 square inches.

So the area of the shape for the quilt block is 97.34 square inches.

3.
The area of a parallelogram is given by the formula: Area = base * height.

So the area of this parallelogram is:

22.5 feet * 19.25 feet = 432.0625 ft^2

So the area of the parallelogram is 432.0625 square feet or approximately 432 and 6/16 square feet.

4.
An isosceles trapezoid has two equal sides that are parallel to each other. In this case, the two equal sides are perpendicular to the height and are equal to 4 + 7 = 11 meters each. The average of the two parallel sides is the formula for the top base of a trapezoid, so the top base is (3 + 11)/2 = 7 meters.

The area of a trapezoid is given by the formula: Area = (bottom base + top base) * height / 2.

So the area of this trapezoid is:

(3 + 7) * 6.2 / 2 = 33.4 m^2

So the area of the trapezoid is 33.4 square meters.

5.
The area of a rhombus is given by the formula: Area = (diagonal 1 * diagonal 2) / 2.

In this case, the base of the rhombus is equal to one of its diagonals, and the height is equal to the other diagonal. So the area of this rhombus is:

(16 * 15.5) / 2 = 124 cm^2

So the area of the rhombus is 124 square centimeters.

6.
he total area of the figure can be found by dividing it into two parts: a parallelogram and a triangle.

The parallelogram can be found by using the formula for the area of a parallelogram: Area = base * height. In this case, the base is 4 inches and the height is 2.3 inches, so the area of the parallelogram is: 4 * 2.3 = 9.2 square inches.

The triangle can be found by using the formula for the area of a triangle: Area = (base * height) / 2. In this case, the base is 2.5 inches and the height is 3 inches, so the area of the triangle is: (2.5 * 3) / 2 = 3.75 square inches.

The total area of the figure is the sum of the areas of the parallelogram and triangle: 9.2 + 3.75 = 12.95 square inches.

So the total area of the figure is approximately 12.95 square inches.

7.
The figure can be broken down into two triangles and a rectangle. The area of one triangle is (1/2)bh = (1/2)(22)(34) = 308. To find the area of the other triangle, use the Pythagorean theorem to find the length of the remaining side. The two remaining sides are 43 and 18, and the hypotenuse is the side connecting the two vertices, so we have:

a^2 + b^2 = c^2

43^2 + 18^2 = c^2

1,849 + 324 = c^2

2,173 = c^2

c = 46.7

The area of this triangle is (1/2)bh = (1/2)(46.7)(34) = 786.2

The rectangle has a base of 43 and a height of 34, so its area is 43 * 34 = 1,462

The total area of the figure is 308 + 786.2 + 1,462 = 2,556.2 square meters.

So the answer is 2,556.2 m2.

14÷3= 4.6666666...

so 4 cookies for each one... with 2 cookies left

Answer:

-(6y + 2z) - 7z - (12z + 32y)7,956

Step-by-step explanation:

The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

If g(x) is the inverse of f(x), 2 is the value of f(g(2)).

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

Given

\(&x \rightarrow f(x) \\\)

\(&-6 \rightarrow 1 \\\)

\(&-3 \rightarrow 2\)

\($$g(x)=f^{-1}(x)\) inverse

To find the value of f(g(2)).

For two functions f(x) and g(x) where f(x) and g(x) are inverse; f(g(x))=x

So, by comparison: f(g(2)) = 2.

Therefore, the inverse of the function f(g(2)) = 2.

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The statement that the sales tax on a good that has been purchased is a function of the selling price in a given state, is TRUE.

The sales tax on an item that is purchased is calculated on the selling price of the item and then added to the item so that the person purchasing the item can pay for the sales tax as well.

Because the sales tax is based on the selling price, it is therefore a function of the selling price with the given state being the percentage of the sales tax.

For instance, a 4% sales tax on a good that is $10 is:

= 4% x 10

= $0.40

This sales tax is based on the selling price and so is a function of it.

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Answer:

z=104 degrees

Y=26

Step-by-step explanation:

180-76=104

Z=104 degrees

3y-2=76

 3y=78

y=26

Answer:

40

Step-by-step explanation:

A way to do this would be to think of it as a graph.

To find out how many different playgrounds you can build with 10 swing sets and 2 different slides, you can multiply 10 by 2 to get 20.

Taking this number, you can multiply it by 2 (for the seesaw) to get the total amount of different playgrounds.

Multiply 20 by 2 will get you 40.

He can make a total of 40 different playgrounds.

Answer:

The answer is in the picture below

Step-by-step explanation:

Answer: Diffusion

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer:

5 gg

Step-by-step explanation:

Let us treat the number of gigabytes of data she can use (at max) per month as x.

We can say that \(54.5 + 5x = 74\) will always be deducted from her and $5x per month for the extra data she uses.

    \(54.5 + 5x = 74\)

⇒  \(5x = 74 - 54.5\)

⇒  \(5x = 25.5\)

⇒  \(x = 25.5 / 5\)

⇒ \(x = 5.1\)

As she can only buy a fixed number of data, which cannot be a decimal, let us take the number directly below 5.1 - which is 5 - as the answer.

Caroline can use up to 5gg of data

The answers are 13) 24°, 14) 25° and 15) 20°

Given that are right triangles we need to find the reference angles,

Using here the concept of trigonometric ratios,

Sin = ratio of perpendicular to hypotenuse.

Cos = ratio of base to hypotenuse.

Tan = ratio of perpendicular to base.

So,

13) Sin? = 24/59

? = Sin⁻¹(24/59)

? = 24°

14) Cos? = 30/33

? = Cos⁻¹(30/33)

? = 25°

15) Tan? = 10/27

? = Tan⁻¹(10/27)

? = 20°

Hence the answers are 13) 24°, 14) 25° and 15) 20°

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