Select the answer with the correct number of significant figures for each calculation. 31.580 + 4.26 = 35.8 35.84 35.840

The dimensions of the rectangle are 40 and 18 units respectively

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The length of a rectangle is 4 feet more than twice the width.

Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116

                       3x+4      = 58

                             3x    = 54

                               x     = 18

Hence, the dimensions of the rectangle are 40 and 18 units respectively.

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After completing the square, the solution of equation are,

⇒ x = (2 + √2i)

And, x = 2 - √2i

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ x² - 4x + 6 = 0

Completing the square as;

⇒ x² - 4x + 6 = 0

⇒ x² - 4x + 4 + 2 = 0

⇒ (x - 2)² + 2 = 0

⇒ (x - 2)² - (√2i)² = 0

⇒ (x - 2 - √2i) (x - 2 + √2i) = 0

This gives two complex solution as;

⇒ x = (2 + √2i)

And, x = 2 - √2i

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Answer:

8

Step-by-step explanation:

Since it's an equilateral triangle, as you can tell from the red lines, m∠2 = 60. You can substitute to get:

⇒ 60 = 6x + 12

Subtract 12 from both sides

⇒ 48 = 6x

Divide by 6

⇒ x = 8

Therefore, the answer is 8.

The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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Answer:  -7/5

Step-by-step explanation:

The model lies between 0 and 1 on the number line.We can find by dividing number and then add both of number.

The real number line is a horizontal line with arrows on both sides. It consists of the origin “0”. All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.

A number line model is a representation of numbers plotted on an infinite line that extends at both ends.It is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now we find

-2/4 =-0.5

3/4= 0.75

0.75- 0.5=0.25

which is lies between 0 and 1 on the number line.

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Answers to ratios are first one is option B, second one is option A and third one is option C.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

1. Ratio of smoothie size to mangos used for Kim = 8 : 1

Ratio of smoothie size to mangos used for Bri = 24 : 3

                                                                             = 8 × 3 : 1 × 3

                                                                             = 8 : 1

Ratio of smoothie size to mangos used for Angela = 32 : 4

                                                                                    = 8 × 4 : 1 × 4

                                                                                    = 8 : 1

So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

So the answer is option B.

2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3

Ratio of width to length of smaller canvas = 2 : 3

So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

So the answer is option A.

3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19

Total students = 12 + 19 = 31

Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.

So the answer is option C.

Hence the answers on ratios are done.

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The value of x = -7 and y = 9 from the system of equations .

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

The equations are :

-x - y = -2          (i)

and

5x + 7y = 28        (ii)

multipling eqation (i) with 5 and then adding both equations we get,

-5x - 5y +5x + 7y = -10 + 28

⇒ 2y = 18

⇒ y = 9

Again, -x -9 = -2

or, x = -7

The value of x = -7 and y = 9 from the system of equations

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Answer:

no solutions

Step-by-step explanation:

you have to divide the whole first equation by 2 and you would get

2x+y=5

2x+y=-3

That is not true the same thing can’t have different outcomes.
it is no solution

Let C be the number of children who used the public swimming pool and A be the number of adults.

The total number of people at the pool is given by the equation: C + A = 660

The total cost of admission for all the people at the pool is given by the equation: 1.5C + 2.5A = 1279

Solving the system of equations using substitution, we get:

A = 289 and C = 371

There were 371 children and 289 adults at the public pool on the hot summer's day.

According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.

To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.

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The value of x is equal to 3.

The length of diagonal LN is equal to 18 units.

The length of diagonal MP is equal to 15 units.

In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

This ultimately implies that, the length of each diagonal of a rectangle is always equal to each other. Therefore, the diagonals of any rectangle is always equal to one other.

We would determine the value of x by equating the length of each diagonal as follows;

LN = MP

7x - 3 = 4x + 3.

7x - 4x = 3 + 3

3x = 6

x = 6/2

x = 3.

Next, we would calculate length of each diagonal as follows;

LN = 7x - 3

LN = 7(3) - 3

LN = 21 - 3

LN = 18 units.

MP = 4x + 3.

MP = 4(3) + 3.

MP = 12 + 3

MP = 15 units.

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Complete Question:

LMNP is a rectangle. Find the value of x and the length of each diagonal.

LN = 7x - 3 and MP = 4x + 3.

The equation is x² + y² = 277 and the value of x and y is 9 and 14 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the two number be x and y

One integer is 5 less than another

So , x = y - 5  

x - y = -5   be equation (1)

And , sum of their squares is 277

So , x² + y² = 277   be equation (2)

On simplifying the equation , we get

( x - y )² = x² + y² - 2xy

Substituting the values in the equation , we get

( -5 )² = 277 - 2xy

2xy = 277 - 25

2xy = 252

And , ( x + y )² = x² + y² + 2xy

Substituting the values in the equation , we get

( x + y )² = 277 + 252

( x + y )² = 529

( x + y ) = 23   be equation (3)

Adding equation (1) and equation (3) , we get

2x = 18

x = 9

So , y = 14

Therefore , the value of x and y is 9 and 14 respectively

Hence , the equations are solved

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Answer:

The graph of the cube root function is a continuous and smooth curve that starts at the point (0,0) and extends indefinitely in both the positive and negative directions on the x-axis. The graph increases as x increases from negative infinity to 0, and then decreases as x increases from 0 to positive infinity.

The graph has a vertical asymptote at x = 0, meaning that as x approaches 0 from either direction, the y-values of the points on the graph become very large. However, since the function is defined as the cube root of x, the function is not actually defined at x = 0, so the asymptote is not part of the graph.

The function is an odd function, which means that it is symmetrical about the y-axis. This means that if we were to reflect the part of the graph that is to the right of the y-axis over the y-axis, the resulting graph would exactly match the part of the graph that is to the left of the y-axis.

Overall, the graph of the cube root function is a smooth curve that starts at (0,0) and extends indefinitely in both directions on the x-axis, with a vertical asymptote at x = 0 and symmetry about the y-axis.

The correct comparison between two function is

Both functions are increasing, but function g increases at a faster average rate.

The Correct option is (B).

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume

f(x) = [tex]ab^x[/tex]+ c

so, at x=0, f(0)=-10

a +c = -10

Similarly, by satisfying the above table in the f(x)

f(x) = -33/5 [tex](1/11)^x[/tex] - 17/5

and, f'(x) > 0

Thus, f(x) is an increasing function.

Now, g(x) = -18 [tex](1/3)^x[/tex] +2

g'(x) = -18 [tex](1/3)^x[/tex] log(1/3)

as log 1/3 <0

So, g'(x) > 0

Thus, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).

Hence, Both functions are increasing, but function g increases at a faster average rate.

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Answer: 28%

Step-by-step explanation: First, we need to find how much she runs in total on Tuesday and Wednesday. So, we add 3 + 4 to get 7. With that, we need to determine how much 7 is from 25. So, it'd look like this:

7 * 100 / 25

700 / 25

=28

Therefore, she's done 28% of her goal (within the 2 days) I hope this helped!

Answer:

I think the other person who answered the question is right

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

50/125×100%

=40%

Mr Smith has covered 40 percent of the journey

Answer:

40%

Step-by-step explanation:

50/125 ×100= 40%

Answer:

[tex]y1 = 4 \\ x1 = 3[/tex]

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 4 = 0(x - 3)[/tex]

[tex]y - 4 = 0[/tex]

[tex]y = 4[/tex]

a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8) is: f(x) = - 2 (x + 3) (x - 1) (x - 4)

A cubic function is a function whose expression contains the cube of the x variable. A function is referred to as a cubic function if its formula is f(x) = ax³ + bx² + cx + d. a, b, c, and d can all be constants in this case, but make sure that a 0. The b, c, or d might all be zeros.

A cubic function has 3 roots.

Let, assume α, β and γ.

So, f(x) = K (x - α). (x - β). (x - γ)

f(x) is defined by values of x where f(x) = 0

0 = K (x - α). (x - β). (x - γ)

x = α, β, γ

The given cubic function graph is cutting x - axis at 3 points: (-3, 1 ,4)

Now, f(x) = K (x - (-3). (x - 1). (x - 4)

f(x) = K (x + 3) (x - 1) (x - 4)

Next, f(x) passes through point (0,8) which means:

f(0) = 8

so, 8 = K (0 + 3) (0 - 1) (0 - 4)

or, k = - 2

Now, f(x) = - 2 (x + 3) (x - 1) (x - 4)

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a) The patient weight in pounds is 234 lbs.

b) The patient weight in kilograms is 106.36 Kg.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

The patient’s weight is 245 lbs.

Each week patient loses = 1 Kg

So, In 5 week patient loses = 5 Kg

As, 1 kg = 2.2 lbs

In 5 week patient loses = 11 lbs

a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.

                                                                      = 234 lbs.

b) The weight of the patient after 5 weeks =  234 lbs.

The weight of the patient after 5 weeks in Kg

= 234 lbs x 1 kg per 2.2 lbs.

= 106.36 kg

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Answer: Set of integers

Integers are positive and negative whole numbers, with 0 included.

Answer: Set of Integers

Step-by-step explanation:

{...,-2,-1,0,1,2...}

since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.

hope that helps...

Using the concept of proportion to find the value of x in the similar triangle, x is equal to 6.67

Similar triangle theorem states that if two triangles have corresponding angles that are equal, then the sides of the triangles are proportional to each other. This theorem can be used to solve problems involving triangles, such as finding the lengths of missing sides.

We can use the concept of ratio to find the value of x.

12 / 5 = 16 / x

Cross multiply both sides and solve for x

12 × x = 16 × 5

12x = 80

x = 80 / 12

x = 6.67

The value of x is 6.67

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Tracy gets $1299.375 interest after 8 years and 3 months for an investment of  $3,500 at a 4.5% annual interest rate.

What is Simple Interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The formula for calculating Simple Interest is -

S.I. = (P×R×T)/100

where, P = initial principal balance, R = annual interest rate and T = time (in years)

So, the principal rate, P = $3,500, the interest value, R = 4.5%, and the Time is T= 8.25 years.

Applying the formula for Simple Interest -

S.I. = (P×R×T)/100

S.I. = (3500×4.5×8.25)/100

S.I. = 1299.375

Therefore, the interest amount obtained is $1299.375.

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The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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the blank space must be 2 or x must be zero, I don't know what you mean by one solution

the blank must equal 2 because on the right side the coefficient of x is 2 so it must be same

Answer:

To find Q1, Q2, Q3, and the interquartile range (IQR) of a data set, we need to first arrange the data in numerical order. For the given data set, the ordered data is:

7, 8, 10, 12, 12, 14, 15, 15, 16, 19, 21, 23, 24

To find Q1, we need to find the median (Q2) of the lower half of the data. The lower half of the data is:

7, 8, 10, 12, 12, 14

There are 6 values in the lower half of the data, so the median (Q2) is the average of the 3rd and 4th values, which is (10 + 12) / 2 = 11. Therefore, Q1 = 11.

To find Q3, we need to find the median (Q2) of the upper half of the data. The upper half of the data is:

15, 15, 16, 19, 21, 23, 24

There are 7 values in the upper half of the data, so the median (Q2) is the fourth value, which is 19. Therefore, Q3 = 19.

To find the IQR, we need to subtract Q1 from Q3. The IQR is equal to Q3 - Q1 = 19 - 11 = 8.

The correct answers are:

1.  Interquartile Range = 8

2.  Q3 = 19

3.  Q2 = 11

4.  Q1 = 8

Therefore, the correct answer choices are:

a. 15 (incorrect)

b. 9 (incorrect)

c. 20 (incorrect)

d. 11 (correct)

On solving the question, 5 topping would pay the same amount for Pizza A and Pizza B,  the value of equation 0.50x=2.50=>   x=5

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x be the number of toppings,the total cost of a pizza is given by:

pizza cost+topping cost

for pizza a =10+1.50x

for pizza b=12.50+1.00x

we solve for when cost are same and for how many toppings

   10+1.50x=12.50+1.00x

   10+0.50x=12.50

   0.50x=2.50

        x=5

would pay the same amount for Pizza A and Pizza B. are 5 toppings,

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Answer:

D. [tex]L > J > K[/tex]

Step-by-step explanation:

Thus, we have to utilize the angle relationships in a triangle.

⭐The largest side is always opposite of the largest angle

⭐The smallest side is always opposite of the smallest angle

1. Identify the side lengths of triangle JKL

2. Determine which vertecies are opposite of each side length (draw the figure)

3. Determine which angles are the greatest, smallest, and in-between

4. Write what you found in #3 in terms of inequalities

∠L > ∠J > ∠K

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