9. Assessment Practice Diego Wants Tofind 8+ 9. 2.NSO.2.1Which Doubles Fact Can Help Him?A 5+5=10B6+6=12C7+7= (2024)

Step 1

Given;

Step 2

Two angles are called supplementary when their measures add up to 180 degrees.

Two angles are called complementary when their measures add to 90 degrees.

The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be complementary angles or supplementary angles when they share the common vertex and side.

Answer;

Two angles are called supplementary when their measures add up to 180 degrees.

Two angles are called complementary when their measures add to 90 degrees.

The two angles are said to be adjacent angles when they share the common vertex and side.

If j(x) = 4^(x - 2), the solving the given expression [j(x + h) - j(x)]/h gives;

[j(x + h) - j(x)]/h = (4^(x - 2))(4^(h) - 1)]/h

How to utilize laws of exponents?

We are given the function as;

j(x) = 4^(x - 2)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 4^(x - 2 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [4^(x - 2 + h) - 4^(x - 2)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

4^(x - 2 + h) = 4^(x - 2) × 4^h

Therefore;

[4^(x - 2 + h) - 4^(x - 2)]/h = (4^(x - 2))(4^(h) - 1)]/h

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Given:

[tex]f(x)=|\frac{1-7x}{3}|[/tex]

To find the values of x when f(x)=3, we apply below absolute rule:

If |u|=a, a>0 then, u=a or u= -a

Based on the above rule, our equations would be:

[tex]1-\frac{7x}{3}=3[/tex]

And,

[tex]1-\frac{7x}{3}=-3[/tex]

Next, we find x for 1-7x/3=3:

[tex]\begin{gathered} 1-\frac{7x}{3}=3 \\ \text{Simplify and rearrange:} \\ \frac{7x}{3}=1-3 \\ \frac{7x}{3}=-2 \\ 7x=-2(3) \\ 7x=-6 \\ x=-\frac{6}{7} \end{gathered}[/tex]

Then, we find x for 1-7x/3=-3:

[tex]\begin{gathered} 1-\frac{7x}{3}=-3 \\ \text{Simplify and rearrange} \\ \frac{7x}{3}=1+3 \\ \frac{7x}{3}=4 \\ 7x=4(3) \\ 7x=12 \\ x=\frac{12}{7} \end{gathered}[/tex]

Therefore, the answer is A. The solution set is

[tex]\lbrace-\frac{6}{7},\frac{12}{7}\rbrace[/tex]

We have

Initial mass of Polonium-210

[tex]N_0=10\text{ micrograms}[/tex]

Decay rate, r = 0.502% = 0.00502

Time, t = 190 days

Then, We know that left amount is given by

[tex]N=N_0e^{-rt}[/tex]

Solving

[tex]N=10e^{-0.00502(190)}=10e^{-0.9538}=3.853[/tex]

Answer: 3.853 micrograms

Explanation

the origins mean the center of the cartessian plane, it is the point with coordinate

[tex](0,0)[/tex]

Answer:

the origin is located at the intersection of the vertical and horizontal axes and the distance to all can be measured from this point..(0,0)

The number of integers from 31 to 40 is 10

What are integers?

Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.

From the question, we are to determine the number of integers there are from 31 to 40.

First, we will list all the whole numbers from 31 to 40.

The whole numbers from 31 to 40 are

31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.

All of these numbers are positive whole numbers. Thus, they are integers.

The number of integers listed above is 10.

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Step-by-step explanation:

3x+4x-6=57

7x=63

x=9

AB=3x=3*9

AB=27

First, simplify the expression:

[tex]\begin{gathered} 3\lbrack2x-(3x-4)\rbrack-6(x-3) \\ =3\lbrack2x-3x+4-6(x-3) \\ =3(2x)+3(-3x)+3(4)-6(x-3) \\ =6x-9x+12-6x+18 \\ =6x-9x-6x+12+18 \\ =-3x-6x+12+18 \\ =-9x+12+18 \\ =-9x+30 \end{gathered}[/tex]

Then:

[tex]3\lbrack2x-(3x-4)\rbrack-6(x-3)=-9x+30^{}[/tex]

To find the zero of the given expression, find the zero of -9x+30:

[tex]\begin{gathered} -9x+30=0 \\ \Rightarrow-9x=-30 \\ \Rightarrow x=\frac{-30}{-9} \\ \therefore x=\frac{10}{3} \end{gathered}[/tex]

Therefore, the zero of the given expression is 10/3.

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case, the line passes through the points (1,5) and (9,8)​, then its slope is:

[tex]m=\frac{8-5}{9-1}=\frac{3}{8}[/tex]

Ratio means the quantitative relation between two amounts showing the number of times one value contains or contained in order

example 4 and 6

for example

if we have 4 men and 6 women

we can say the ratio of men to women is 4 to 6

that is 4 : 6

and ratio can also means division

for 4 and 6

= 4 / 6

= 2 / 3

= 2 : 3

that is, for every 2 men we have 3 women

The correct options regarding whether the graph can represent a normal curve are given as follows:

C. Yes, because the graph may not satisfy all of the criteria for a normal curve, but it satisfied at least one of them.D. No, because the graph is not always greater or equal to zero.

What are the characteristics of a normal curve?

The characteristics of a normal curve are defined as follows:

Single peak at the center of the distribution, which is also the mean of the distribution.The function is symmetric.The values of the tails at the distribution are close to 0.The values are all equal or greater to zero.

In the context of this problem, these two first options are satisfied. However, the distribution contains negative values, meaning that the graph is not always greater or equal to zero.

Hence, options C and D are correct.

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The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)

How to find the velocity of a body under simple harmonic motion

Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:

y = y' + Δy · cos ωt (1)

Where:

y' - Initial positionΔy - Amplitudeω - Angular frequency.t - Time

The equation for the velocity of the body in simple harmonic motion is found differentiating (1):

v = - ω · Δy · sin ωt (2)

If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:

v = - 1 · 5 · sin (2π / 3)

v = - 5 · sin (2π / 3)

v = - 5 · √3 / 2

v = - 5√3 / 2

The velocity is equal to - 5√3 / 2.

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The correct option regarding the minimum height reached by the toy is:

A height of -1.76 inches at 5.647 seconds.

How to find the minimum value of the function?

The function for the height of the toy in the spring after x seconds is modeled as follows:

y = -cos(x) + 2cos(x)sin(x)

It is a trigonometric function, hence there is no rule to find the minimum value of the function as there is for a quadratic function, for example.

Since there is no rule, we have to sketch the graph of the function in the given domain of 0 < x < 6.

Using a graphing calculator, the graph of the function is given at the end of the answer, with minimum point at (5.647, -1.76), hence the correct option is:

A height of -1.76 inches at 5.647 seconds.

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1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.

2) The sets that positive integers belong to among the available are;

possibilities

Choices A, B, C, and D

1) There are two basic categories into which numbers are often divided:

- Rational numbers

- Irrational numbers

The four examples above are all different categories of rational numbers.

Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.

Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.

In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers

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Answer:

use ASA

Step-by-step explanation:

since D=B, AB║CD

angle DEC=AEB (vertical angles)

AE=EC (given)

Answer:

1

Step-by-step explanation:

when there is no number, they are always 1.

1 multiplied by itself is always 1, so 1/1 is 1.

Hope this helps!

btw, brainliest if correct, ty!

Answer/Step-by-step explanation:

Simplify

x⁻⁵

-------

y³

Since the x on top has a negative exponent it must go down to the denominator.

So the answer would be:

1

-------

x⁵y³

I hope this helps!

According to the secant-tangent theorem, we have the following expression:

[tex](x+3)^2=10.8(19.2+10.8)[/tex]

Now, we solve for x.

[tex]\begin{gathered} x^2+6x+9=10.8(30) \\ x^2+6x+9=324 \\ x^2+6x+9-324=0 \\ x^2+6x-315=0 \end{gathered}[/tex]

Then, we use the quadratic formula:

[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

Where a = 1, b = 6, and c = -315.

[tex]\begin{gathered} x_{1,2}=\frac{-6\pm\sqrt[]{6^2-4\cdot1\cdot(-315)}}{2\cdot1} \\ x_{1,2}=\frac{-6\pm\sqrt[]{36+1260}}{2}=\frac{-6\pm\sqrt[]{1296}}{2} \\ x_{1,2}=\frac{-6\pm36}{2} \\ x_1=\frac{-6+36}{2}=\frac{30}{2}=15 \\ x_2=\frac{-6-36}{2}=\frac{-42}{2}=-21 \end{gathered}[/tex]Hence, the answer is 15 because lengths can't be negative.

Jason, this is the solution:

Walter's daily wage = $ 50

Tips = 15% of the total cost of the dinner he serves

Tuesday earnings = $ 170

Therefore,

Tips = 170 - 50

Tips = 120

For finding the cost of the dinners, we use Direct Rule of Three, as follows:

Percentage Cost

15 120

100 x

_____________________

120 * 100 = 15 * x

12,000 = 15x

Dividing by 15 at both sides:

15x/15 = 12,000/15

x = 800

The total cost of the dinners Walter serverd on Tuesday was $ 800

Hence, the coordinates of other point (x, y) are (0,6).

i.e. (x, y) → (0,6)

Let AB be the segment where

The coordinate M(2, 9) and C(4, 12)

and we have to find the point E.

Let us assume the other point is (x, y)

As we know that

The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.

Mid - point formula:

m = [tex]\frac{x_{1}+x_{2} }{2}[/tex]

n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]

So,

Substituting M(2, 9) into C(4, 12):

2 = [tex]\frac{4+x_{2} }{2}[/tex]

9 = [tex]\frac{12+y_{2} }{2}[/tex]

Solve the Equation:

[tex]x_{2} = 0\\y_{2} = 6[/tex]

Express solutions in ordered pairs:

(0,6)
Hence, the coordinates of other point (x, y) are (0,6).

i.e. (x, y) → (0,6)

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The solution to the equation g(x) = 6x - 9 whenx = -8b is g(-8b) = -48b - 9

How to evaluate the value of the function?

From the question, the equation of the function is given as

g(x) = 6x - 9

Also, we have the value of the variable to be

x = -8b

So, we substitute -8b for x in the equation of the function

g(x) = 6x - 9

The above equation becomes

g(-8b) = 6(-8b) - 9

Open the brackets in the above expression

g(-8b) = -48b - 9

The above equation cannot be firther simplified

Hence, the solution is g(-8b) = -48b - 9

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on5x - 1 < 19

To solve this inequality add 1 to both sides

[tex]\begin{gathered} 5x-1+1<19+1 \\ 5x<20 \end{gathered}[/tex]

Now divide both sides by 5

[tex]\begin{gathered} \frac{5x}{5}<\frac{20}{5} \\ x<4 \end{gathered}[/tex]

The solutions lie in the area left to the number 4

For the second inequality

[tex]-3-x+1\leq1[/tex]

Add first we will add the like terms in the left side

[tex]\begin{gathered} (-3+1)-x\leq1 \\ -2-x\leq1 \end{gathered}[/tex]

Now add 2 for both sides

[tex]\begin{gathered} -2+2-x\leq1+2 \\ -x\leq3 \end{gathered}[/tex]

We need to divide both sides by -1, but we should reverse the sign of inequality

[tex]\begin{gathered} \frac{-x}{-1}\ge\frac{3}{-1} \\ x\ge-3 \end{gathered}[/tex]

We reversed the sign of inequality when divides it by -ve number

Since 2 < 3

Then if we divide both sides by -1, then it will be

-2 < -3 which is wrong -2 greater than -3, then we should reverse the sign of inequality if we multiply or divide it by a negative number

Then the solutions of the 2nd inequality lie right to -3

Let us draw them

The red part is the solution to the 1st inequality

The blue par is the solution to the 2nd inequality

The area with the 2 colors is the area of the common solution of both inequalities

When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.

Notice that the triangle get's inverted on each reflection around the lines.

Probability is expressed as

number of favorable outcomes/number of total outcomes

In a standard deck of cards, the total number of cards is 52.

There are 13 spades in a standard deck. Thus,

probability of selecting a spade = 13/52 = 1/4

There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.

probability of selecting a red card = 26/52 = 1/2

There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,

Probability of selecting a queen = 4/52 = 1/13

Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is

1/4 x 1/2 x 1/13

= 1/104

[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.

The width of the smaller rectangle is 4 inches.

What is the width of a rectangle?

A rectangle has four sides, but because the sides are paired, it only has two distinct dimensions. The width is traditionally the shortest of these two dimensions, but when the rectangle is shown lying on its side, the horizontal side is commonly referred to as the width.

Given:

The dimensions of the smaller rectangle are:

Length = 8 inches

Width = x inches

The dimensions of the larger rectangle are:

Length = 10 inches

Width = 5 inches

Using proportion we determine the value of x,

[tex]\frac{8}{x} = \frac{10}{5}[/tex]

Cross-multiply the terms,

8 × 5 = 10x

x = 40/10 = 4

Therefore, the width of the smaller rectangle is 4 inches.

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The correct answer is Tim

She drives at a variable speed for 2minutes

Verify

REmember that the best deal is the deal with the less unit rate

so the order is

89 0z bottle is the best deal

64 oz cartoon

59 oz bottle

case of 24 10 oz bottles

10 oz bottle

therefore

Jason is not correct

Answer:

See below

Step-by-step explanation:

48 + 3y = 90 degrees so y = 14 degrees

3x + 2x + 12 = 90 so x = 78/5 = 15.6 degrees

Given the question, we need to know that a standard deck contains 52 cards out of which there are 4 cards showing nine.

[tex]\text{Probability = number of possible outcomes/number of total outcomes}[/tex]

To get the probability of randomly drawing a nine will be:

[tex]\begin{gathered} \frac{n\text{ (nine)}}{n\text{ (total cards)}} \\ pr(nine)=\frac{4}{52}=\frac{1}{13} \end{gathered}[/tex]

Hence, the probability of drawing nine is 1/13

The expression used to depict area will be 9 / (3x - 1).

A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.

The given expression for area = 27x - 9

Factorize 27x - 9

Taking 9 as greatest common factor outside, we get

27x - 9 = 9(3x - 1)

We know that the area of rectangle with dimensions length by breadth is given by:-

Area = Length x Breadth

Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).

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Complete Question:

What are possible dimensions of the rectangular area at the right? if area is 27x-9.