Harriett designed an artistic table top for her dining room
table. Her sketch is shown below at a scale of 1 cm 6
in.
How much area will her dining room table top fill when it is
built?
5 cm
3 cm
A
B
C
D
3 cm
14 cm
9 cm
432 sq. in.
648 sq. in.
864 sq. in.
4 cm
972 sq. in.
5 cm
-
3 cm
there is also
C. 864 sq in
and
D 972 sq in
but it doesnt show

The values of x in the equation given is,  x = -1 and  x = -4/7.

Given equation: 7(x+1)-9=-9=2x+5(-1+x)

Equate both the equations with the given constant to determine the value of x,

⇒ 7(x+1)-9=-9

⇒ 7x + 7 - 9 = -9

⇒ 7x - 2 = -9

Bringing all the variables on one side and constants on another side of the equation,

⇒ 7x = -9 + 2

⇒ 7x = -7

⇒ x = -1

Now we solve the second equation,

⇒ 2x+5(-1+x) = -9

⇒ 2x - 5 + 5x = -9

⇒ 7x = -9 + 5

⇒ 7x = -4

⇒ x = -4/7

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Answer:

11. 6

12. The last option, A=1/4, B=7/16, C=5/8, D=3/4

Step-by-step explanation:

11. look at the denominators, and what do you see? I see that 11 is 88 divided by 8. So, let's divide the numerator by 8 as well! 48/8=6

12. 1/4 is half of 1/2, so it would be between 0 and 1/2, or A

     Same thing with 3/4 but this time in the middle of 1/2 and 1, or D

     5/8 is a little over 4/8, or 1/2, so C

     The last one left is 7/16, B

Answer:

x = 10 , y = 2

Step-by-step explanation:

The solution of the system of equations will be x= 10 and y = 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the system of equations is 2x + 3y = 26 and 3x + 5y = 40. the two equations by elimination method can be solved as;-

2x + 3y = 26

3x + 5y = 40

Cross-multiply with the variable of x,

6x + 9y = 78

-6x - 10y = -80

___________

     -y = -2

      y =  2

The value of x will be:-

2x + 3y = 26

2x + 3 ( 2 ) = 26

2x = 20

x = 10

Hence, the solution of the system of equations will be x= 10 and y = 2.

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Answer:you have 2 lines that cross.

the left angle formed is equal to 3x + 8

the right angle formed is equal to 5x - 20.

the bottom angle formed is equal to 5x + 4y

since the lines are crossed, the opposite angles to each other are equal.

this means that:

3x + 8 = 5x - 20

solve for x to get x = 14 degrees.

the angle on the left side will be equal to 3(14) + 8 = 50 degrees.

the angle on the right side will be equal to 5(14) - 20 = 50 degrees.

this is at it should be since the angles are equal to each other.

since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.

since those 2 angles are equal, then each one must be equal to 130 degrees.

one of those angles is equal to 5x + 4y.

you get 5x + 4y = 130

since x was already found to be 14, replace x with 14 to get:

5(14) + 4y = 130

solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.

when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.

your answers are:

x = 14 degrees

y = 15 degrees

2 of the angles measure 50 degrees each.

2 of the angles measure 130 degrees each.

The total amount in her account after t years will be 1500 + 30t.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The total amount A in an account earning simple interest is given by the equation A = P + Prt, where P is the principal, r is the rate as a decimal, and t is time in years.​

Faith deposited $1500 in an account earning 2% simple interest.

The total amount in her account after t years will be

A = 1500 + 1500 × 0.02 × t

A = 1500 + 30 × t

The total amount in her account after t years will be 1500 + 30t.

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The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

From the question, we have the following parameters that can be used in our computation:

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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Answer:

B. 5

Step-by-step explanation:

The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator.

example, 2,10,21,23,23,38,38

38 - 2 = 36

Answer:

B. 5

Step-by-step explanation:

All you have to do is subtract the highest number by the smallest number so i just had to do:

8-3=5

The total budget last year andersons spend is $42000 which is option (3) .

It is given that andersons spend 12% of their budget on travel and the they plan to spend $5220 on travel.

Let "x" be the total budget of this year , then

       \(12\% \ of \ x =5220\\\\\frac{12}{100} \times x=5220\\\\x=\frac{5220\times100}{12} \\\\x=43500\)

so the total amount anderson spend this year is $43500 .

It is given that their total budget this year is $1500 more than last year which can be represented as

Total budget this year = 1500 + Total budget last year

  Total budget last year = \(43500-1500=\$42000\)

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answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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1)

You tutor for 9 hours.

2)

You tutor for 4 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the tap diagram,

1)

You have three parts.

A friend has one part.

This means,

4 parts = 12 hours

1 part = 3 hours

Now,

You = 3 parts = 3 x 3 = 9 hours.

2)

You have two parts.

A friend has four parts.

This means,

6 parts = 12 hours

1 part = 2 hours

Now,

You = 2 parts = 2 x 2 = 4 hours.

Thus,

You tutor for 9 hours.

You tutor for 4 hours.

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u forgot to add the pic lma.o.

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

4 is the answer

Answer:

4 is the answer I believe

Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

Answer:

3 and 6.

Step-by-step explanation:

Write and evaluate the expression. Then, check all that apply.

Felix divided his shirts into three equal groups. Evaluate when s = 18.

The expression is

The expression is

The expression is s/3

The expression is

The answer is

The answer is 6.

Answer: 20,085

Step-by-step explanation: 2,000x10=20,000. 8.5x10=85. 20,000+85=20,085.

                               I hope I got this right and if I did it right.

We have to a for its value 6, then multiply by its coefficient to then subtract.

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

Answer:

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.

Have a nice day and I hope this helps!

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

A. a translation right 2 units

Step-by-step explanation:

JUST DID IT.

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

The correct answer is: O How to produce? How much to produce?

The statement "A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts" answers the economic questions of "How to produce?" and "How much to produce?"

How to produce: The statement indicates that the manufacturing firm has chosen to employ workers to monitor and maintain specialized machines. This suggests that they have made a decision regarding the production process and how they will go about manufacturing the small metal parts.

How much to produce: The fact that the manufacturing firm has employed workers to monitor and maintain the machines implies that they have determined a level of production that is deemed appropriate or necessary. The number of workers and the capacity of the machines can influence the quantity of small metal parts produced.

Therefore, the correct answer is: O How to produce? How much to produce?

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Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.