3.
The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.

Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

7/8 <> 0.875

0.875 * 6 = 5.25

5.25 <> 42/8

(<> is used to show decimal to fraction and vice versa [the other way around])

Answer:

The points present in the first quadrant are of the form (a, b) where a, b>0.

Step-by-step explanation:

The points present in the first quadrant are of the form (a, b) where a, b>0.

In the first quadrant both the abscissa and ordinate are positive.

In the second quadrant the abscissa is negative and ordinate is positive.

In the third quadrant both the abscissa and ordinate are negative.

In the forth quadrant both the abscissa is positive and ordinate are negative.

The examples of points in the first quadrant are (1,0), (2,3), (11,4) and many other.

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Answer: The y-coordinates in the first quadrant are positive. because y represents the profit made, positive y values signify profit. The points in quadrant I represent the baseball team making a profit.

Step-by-step explanation: Source - I took the test.

For the graphed function we can see:

For a function y = f(x), the domain is the set of the possible inputs "x" and the range is the set of the possible outputs "y".

In this case, we can see that in the right side we have a parabola, and on the left side a linear equation which increases up to the left (so it has a negative slope).

Then the domain will be the set of all real numbers.

Similar for the range, as we can see that on the left side, the line goes upwards, while on the right side, the parabola goes downwards. So this function has a range of all real numbers.

Then:

domain = set of all real numbers

range = set of all real numbers.

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By using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is:

Solve for X given that sin(5X - 28)° = cos(3X - 50)°.​

We have given:

sin(5X - 28)° = cos(3X - 50)°.

[tex]\rm \sin \left(5x-28\right)=\sin \left(\dfrac{\pi }{2}-\left(3x-50\right)\right)[/tex]

[tex]\rm \left5x-28\right= \left\dfrac{\pi }{2}-\left(3x-50\right)\right[/tex]

[tex]\rm x=\dfrac{4\pi n+156+\pi }{16}[/tex]     (n = 0, 1, 2, ...)

[tex]\rm x=\dfrac{\pi +4\pi n-44}{4}[/tex]

Thus, by using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

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Answer:

<

Step-by-step explanation:

0.4<0.7

4 is smaller than 7 so the sighn points to 0.7

Answer:

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Step-by-step explanation:

First find the area of the triangle.

The formula of the area of triangle is: [tex]\frac{1}{2} * h*b[/tex]

h=height

b=base or width.

[tex]\frac{1}{2}*16*12[/tex]

But, since we have two triangles we can skip the [tex]\frac{1}{2}[/tex] because [tex]2*\frac{1}{2} =1[/tex].

[tex]16*12=192[/tex], that is the area of the two triangles combined.

Now let's find the area of the rectangles. I'll start with the diagonal one.

The formula of the area of the rectangle is: [tex]h*b[/tex].

[tex]20*9=180[/tex].

The next rectangle.

[tex]9*16=144[/tex]

The final rectangle.

[tex]12*9=108[/tex]

Now combine all the areas to find the surface area of the triangular prism.

[tex]192+180+144+108=624[/tex]

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Hope this helps!

If not, I am sorry.

If 30 is half price, then what is full price?

You can set up this problem like this:

30 = x/2

OR

30 = (1/2)x

where x is the full price.

To solve, simply multiply each half by 2:

2(30) = 2((1/2)x)

x = $60

Answer:

or D

The probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be 1/4 or 0.25.

The complete question is given below.

I rolled a number cube and spun a spinner. The number cube is numbered 1 to 6. The spinner has 4 equal parts: red, blue, yellow, and green. What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner?

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be

The probability of getting even number on dice will be

Total event = 6 {1, 2, 3, 4, 5, 6}

Favorable events = 3 {2, 4, 6}

P₁ = 3/6

P₁ = 1/2

The probability of getting red or yellow will be

Total event = 4 {red, blue, yellow, green}

Favorable events = 2 {red, yellow}

P₂ = 2/4

P₂ = 1/2

Then the both event occur simultaneously, then we have

P = P₁ × P₂

P = 1/2 × 1/2

P = 1/4

P = 0.25

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Answer:

A)  3%

B)  Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

[tex]f(x) = 0.69(1.03)^x[/tex]

The base (b) is 1.03.  As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

[tex]\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

[tex]\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%[/tex]

Check using different two consecutive values of f(t):

[tex]\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%[/tex]

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

[tex]\implies f(t) = 10100(1.01)^{t-1}[/tex]

To check this, substitute the values of t for 1 through 4 into the found function:

[tex]\implies f(1) = 10100(1.01)^{1-1}=10100[/tex]

[tex]\implies f(2) = 10100(1.01)^{2-1}=10201[/tex]

[tex]\implies f(3) = 10100(1.01)^{3-1}=10303.01[/tex]

[tex]\implies f(4) = 10100(1.01)^{4-1}=10406.04[/tex]

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

The results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

From the question, we are to determine the results that could be displayed on the calculator screen

The given expression is

(2.6 × 10⁻²)(1.5 × 10⁻⁴)

= 2.6 × 1.5 × 10⁻²× 10⁻⁴

= 3.9 ×10⁻²⁺⁻⁴

= 3.9 ×10⁻²⁻⁴

= 3.9 ×10⁻⁶

= 3.9 E-6 OR 0.0000039

Hence, the results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

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Answer:

-2090

Step-by-step explanation:

1)  Remove parentheses.

-2 -8 -32 -2048

2) Simplify - 2 - 8 to -10.

-10 - 32 - 2048

3) Simplify -10-32 to -42.

-42 - 2048

4) Simplify.

-2090

1) [tex]\overline{NQ}[/tex] is the bisector of [tex]\angle MNP[/tex] and [tex]\angle NMQ \cong \angle NPQ[/tex] (given)

2) [tex]\angle MNQ \cong \angle QNP[/tex] (a bisector splits an angle into two congruent angles)

3) [tex]\overline{NQ} \cong \overline{NQ}[/tex] (reflexive property)

4) [tex]\triangle MNQ \cong \triangle PNQ[/tex] (AAS)

Answer:

1.1, 1.2, 1.3, 1.4, 1.5     or        11/10, 12/10, 13/10, 14/10, 15/10

Explanation:

Rational numbers can be expressed as fractions (p/q), decimals, whole numbers, natural numbers, integers.

Some rational numbers between 1 and 2 are: -

1.05, 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.95, 1.97

Five rational numbers are

Answer:

y=⅓x+b

Step-by-step explanation:

So basically the formula of slope-intercept is:

y=mx+b

and m=⅓

so

y=⅓x+b and it includes the point (0, 6) so:

6=⅓(0)+b===> b=6===> y=⅓x+6

The matrix elements are nothing more than the matrix entries. The correct option is B.

The matrix elements are nothing more than the matrix entries. They can be integers, variables, mathematical formulas, or any other type of character included within the matrix.

The value of a₁₄ is the value of the element of the given matrix, where 1 represents the row and 4 represents the column. Therefore, the value of a₁₄ is the element of the first row and the fourth column, which means the value of a₁₄ is 5.

Hence, the correct option is B.

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Answer:

69 degrees

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

<1 = 39+ 30

<1 = 69

Answer:

a) Angle X = 108°

as AD is parallel to EH both the angles are equal

Answer:

108 degrees, vertical angles

Step-by-step explanation:

Angle x is 108 degrees because angle x and angle EFB are vertical angles, meaning that they are equal since opposite angles have the same measures.

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The width of the card to the nearest tenth of an inch is 6.15 inches

Area of a rectangle = Length × Width

88 = (2x + 2) × x

88 = 2x² + 2x

2x² + 2x - 88 = 0

x = -b ± √b² - 4ac / 2a

= -2 ± √2² - 4(2)(-88) / 2(2)

= -2 ± √4 - (-704) / 4

= -2 ± √708 / 4

= -1/2 ± √177/2

x = 6.15 or -7.15 inches

The width of the rectangle can not be negative, so, 6.15 inches is the width.

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Assuming [tex]a[/tex] is a non-negative real number...

Raise both sides to the power 2 :

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^2 = 8^2 \implies a^{3/2} = 64[/tex]

which follows from the exponent product property, [tex](x^y)^z=x^{yz}[/tex]. In particular, 3/4 × 2 = 6/4 = 3/2.

Raise both sides to the power 1/3 :

[tex]\left(a^{3/2}\right)^{1/3} = 64^{1/3} \implies a^{1/2} = 4[/tex]

where we use the same property as before, and 4³ = 64. This time, 3/2 × 1/3 = 3/6 = 1/2.

Take the reciprocal of both sides. This negates the exponent, so we end up with

[tex]\dfrac1{a^{1/2}} = \dfrac14 \implies \boxed{a^{-1/2} = \dfrac14}[/tex]

Of course, you could also solve for [tex]a[/tex] immediately by raising both sides of the original equation to the power 4/3. We have 4/3 × 3/4 = 12/12 = 1, so

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^{4/3} = 8^{4/3} \implies a = 8^{4/3}[/tex]

Now 2³ = 8, so [tex]8^{4/3} = \left(8^{1/3}\right)^4 = 2^4 = 16[/tex], and since 4² = 16, it follows that

[tex]a = 16 \implies a^{1/2} = \sqrt{16} = 4 \implies a^{-1/2} = \dfrac14[/tex]

Answer:

John is 19 and his sister is 23.

Step-by-step explanation:

See attached image.

Answer:

80%

Step-by-step explanation:

I'm assuming you meant express 4/5 as a percent and not 4/5%. So simply evaluate 4/5 to get 0.80. Now multiply this value by 100 to get the percentage which gives you 80%

Answer:

7 units to the left.

Step-by-step explanation:

On the number line , the number will always decrease when we move towards the left, and likewise will always increase when we move towards the right. In this case since the number is moving from 0 to -7, it is definitely decreasing therefore we will move 7 units to the left.

The attached graph represents the graph of the equation 3x + y = 10

The given parameters are:

Represent the number of smoothies with x and the number of candy bears with y.

So, the equation is:

3x + 1y = 10

This gives

3x + y = 10

Next, we plot the graph of the above equation

See attachment for the graph of 3x + y = 10

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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.

Let's suppose the number of smoothies is x and the number of candy bars is y:

Then, we can frame a linear equation in one variable:

3x + y = 10

Drawing the above the line on the coordinate plane:

Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.

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The  polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).

The given polynomial to us is p(x) = x³ + 5x² - x - 5.

We are asked to factor the polynomial by grouping.

We can do this by following these steps:

Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).

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Answer:

Step-by-step explanation:

Answer:

angle CAD

Step-by-step explanation:

look at the 3 points that make up the angle

An expression is defined as a set of numbers, variables, and mathematical operations.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are given below,

If the given expression 2.3p – 10.1 = 6.5p – 4 – 0.01 is simplified, then the expression can be written as,

2.3p – 10.1 = 6.5p – 4 – 0.01

2.3p – 10.1 = 6.49p – 4

Thus, Option A is one of the option.

Using the multiplication property of Equality, if we multiply both the sides of the equation by 100, then we will get,

230p – 1010 = 650p – 400 – p

Thus, c is one of the option.

Hence, the correct options are A and C.

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