Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

x2 + 14x - 2 = 0


2x2 + 10x - 7 = 0


3x2 + 12x - 7 = 0


4x2 + 10x - 1 = 0

The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Dr. Grumman earned $141,340 in 2020.

The social security he paid is:

(141340)(6.2/100) = 8763.08

Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

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The missing side length is x = 30

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side

from the given figure,

tan 37° = x/40

0.75 = x/40

x = 30

Therefore, The missing side is 30.

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Answer:

∴Sum of interior angles in ΔABC = 180°

∠A + ∠B + ∠C = 180°

2x° + 4x° + 6x° = 180°

              12x° = 180°

                = x =

                ∴x = 15

∴∠C = (6)×(15)

      = 90°

This means AC makes a 90° angle (i.e. ∠C) with BC.

∴AC is perpendicular to BC (Proved)

Also ΔABC is a right-angled triangle

Answer:

22% = 163.63636364 litres.

50% = 409.090909 litres

Step-by-step explanation:

when 22% acid solutions = 180 litres

then 20% acid solutions = ?

therefore =

[tex] = \frac{20}{22} \times 180 \\ = \frac{3600}{22} \\ = 163.63636364.litres[/tex]

Also when 22% acid solutions = 180 litres

then 50% acid solutions = ?

therefore

[tex] = \frac{50}{22} \times 180 \\ = \frac{9000}{22} \\ = 409.090909.litres[/tex]

therefore 22% = 163.63636364 litres.

50% = 409.090909 litres.

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

An inequality response is defined?

An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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The solution set to the inequality is w > 3

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

w+ 4<4 (w - 2)

Open the bracket

So, we have the following representation

w+ 4 < 4w - 8

Evaluate the like terms

So, we have the following representation

12 < 3w

Divide by 3

4 < w

So, we have

w > 4

See attachment for number line

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Answer:

$115

Step-by-step explanation:

12 + 11 = 23

There are 23 students in the class.

Cost of supplies: $5 per student.

total cost = 23 × $5 = $115

The total cost to purchase the supplies is,

⇒ $115

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

There are 12 girls and 11 boys registered for the class.

And, You need to purchase supplies that will cost $5 per student.

Here, Total students = 12 + 11 = 23

Hence, The total cost to purchase the supplies is,

⇒ 23 x $5

⇒ $115

Thus, The total cost to purchase the supplies is,

⇒ $115

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By applying standard deviation concept, it can be concluded that all the students had the same score.

The mean is the average of all the scores. It is calculated by adding up all the scores and dividing them by the number of scores.

The standard deviation is a measure of how spread out the scores are. It is calculated by finding the difference between each score and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.

If all the scores are the same, then the difference between each score and the mean will be 0. This means that the standard deviation will also be 0. Therefore, the correct answer is "all the students had the same score."

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Answer:

D. 2x^3−6x^2−x

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Hope this helps.

Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

Recall that the function for the trapezoid area is:

A(x)=(B+b)*h/2

where

B and b are the bases and

h is the height.

Thus, given a height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x) * 14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

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Answer:

(-1, 2)

Step-by-step explanation:

The solution to a system of equation will always intersect on a graph, which means that at a certain point, they will have the same x and y coordinate.

As we can see from the table, for both f(x) and g(x) when x = -1, y = 2, which is the intersection point.

Answer: 12

she has 15 cups of sugar and needs 1.25 cup for a batch so we say 15/1.25 to get 12

Answer:

12

Step-by-step explanation:

15 / 1.25 = 12 she can make 12 batches

Answer:

5 < x <  15

Step-by-step explanation:

The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side

In the given triangle we are provided measures of two of the sides as 10 and 5

Let the measure of the third side be x

So the three sides are 10, 5 and x

Then by the inequality theorem
10 + 5 > x

==>  15 > x or

x < 15    This is an upper bound for x

when we switch sides in an inequality > changes to < and < changes to >

We also have
x  + 5 > 10  ==> x > 10 - 5 ==> x > 5

and

x + 10 > 5 ==> x > -5

Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x

Combining all inequalities we get

5 < x <  15

Note

We could also state the lower and upper bound limits as

difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5

or

5 < x < 15

While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students

The system of equations has infinite solutions.

Given:

y = -6x +2

-12x - 2y= -4

To solve for Equation 2,

The value of y is already given in equation 1,

Thus,

substituting the value of y in equation 2,

-12x -2(-6x +2) = -4

-12x - 12x = -4 +4

0=0

The solution of the two equations is 0. Also, we can see that both equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

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How many solutions does this linear system have?

y = -6x +2

-12x - 2y= -4

one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.

In geometry, two triangles are said to be congruent if they are the same size and shape. This means that all corresponding angles and sides are equal.

To prove that two triangles are congruent, we must use one of the five congruency tests: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).The SSS test states that if all three sides of two triangles are equal, then the triangles are congruent. The SAS test states that if two sides and the included angle of two triangles are equal, then the triangles are congruent. The ASA test states that if two angles and the included side of two triangles are equal, then the triangles are congruent. The AAS test states that if two angles and a non-included side of two triangles are equal, then the triangles are congruent. Lastly, the HL test states that if the hypotenuse and a leg of a right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.In order to prove that two triangles are congruent, we must show that one of the five congruency tests is true. To do this, we can use techniques such as the Reflexive Property, the Symmetric Property, and the Transitive Property. We can also use logical reasoning, such as if two angles are equal and their corresponding sides are proportional, then the triangles must be congruent.

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What is the definition of congruent triangles?

Note that the lenght of segment LN = 55.14 (Option D)

This is arrived at using the Chord Bisector Theorem and the  lengths of the sides of a right-angled triangle.

According to the theorem, the line that goes through the circle's center and is perpendicular to the chord also bisects it.

This means that LK (as per the attached image) is the same as MK.

The Right Angle Postulate also means that:

LX = √[KX² - LK²]

LX = √[29² - 9²]

LX = √(841  81)

LX = √760

LX = 27.57

Since LN = LX *2
LN = 27.57 * 2

LN = 55.14

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The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.

The average rate of change of a function is the ratio of how much the output of the function changes over a given period to the length of that period. We can calculate this for the function R(t) = 210 + 30t3 by considering the time intervals [t, t+h] at h = 1, 0.1 and 0.01 days.

For h = 1 day, the average rate of change of R(t) is 90 dollars/day. This can be calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+1)3 = 1080, by the length of the period, h = 1 day.

For h = 0.1 day, the average rate of change of R(t) is 900 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.1)3 = 9, by the length of the period, h = 0.1 day.

For h = 0.01 day, the average rate of change of R(t) is 9000 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.01)3 = 0.9, by the length of the period, h = 0.01 day.

The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.

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The surface area of a cylinder with radius 5.9 ft and height 4.4 ft is  381.8 square feet.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the  the surface area of a cylinder with radius 5.9 ft and height 4.4 ft.

The surface area of cylinder=2πr(r+h)

r=5.9

h=4.4

The value of pi is 3.14

The surface area of cylinder=2×3.14×5.9(5.9+4.4)

=37.052(10.3)

=381.8 square feet.

Hence, the surface area of a cylinder with radius 5.9 ft and height 4.4 ft is  381.8 square feet.

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It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true

The set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.

Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.

Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.

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Answer:

3:23

Step-by-step explanation:

The water fight ended at 4:28 and lasted for 32 minutes so

4:28 - 32 minutes = 3:56

3:56 - 33 minutes = 3:23

Answer:

4) 7 SqrRt( 5 )

5) 2 SqrRt( 10 )

6) 8 SqrRt( 6 )

Answer:

[tex]x = \frac{17}{3} = 5\frac23 = 5.\overline6[/tex].

Step-by-step explanation:

No idea what your question is, but [tex]x = \frac{17}{3} = {5\frac23} = 5.\overline{6}[/tex].

Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

Acceleration is the rate of change of the velocity of an object with respect to time.

Jonathan's initial velocity, u = 12 m/s East

His final velocity, v = 5 m/s East

The time taken, t = 23 seconds

We can use the formula for acceleration:

a = (v - u) / t

Substituting the given values, we get:

a = (5 m/s - 12 m/s) / 23 s

a = -7 m/s / 23 s

a = -0.3043 m/s^2 East

Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

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Answer:

Center is (10, 3)

Radius = 6

Step-by-step explanation:

The standard equation of a  circle is

(x - a)² + (y - b)² = r²

where
(a, b) is the center of the circle and

r is the radius

Comparing (x - 10)² + (y - 3)² = 36

it is easy to  see that a = 10, b = 3 and r =√36 = 6
So center is(10, 3) and radius is 6

Answer:

20 boxes

Step-by-step explanation:

Each box ca hold 12 eggs

There are 230 eggs

So you will need 230/12 = 19 1/6 boxes =  19.167 boxes

Since you cannot get less than 1 box, round up to 20 boxes. There will be some empty spaces in one of the boxes

Answer:

y = -17/18x + 5/18

Step-by-step explanation:

isolate the y so add five to the other side
18y = 5 + -17x

divide everything by 18

18y/18 -17x/18 5/18
y= -17/18x + 5/18

As per unitary method, Reeta's salary is 21,000 rupees.

The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.

In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.

Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:

2/7 * x

Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:

2/7 * x = x - 15,000

Simplifying this equation, we get:

2x = 7(x - 15,000)

2x = 7x - 105,000

5x = 105,000

x = 21,000

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Yes!

[tex](2^{2} )^{3}[/tex] = 2^6 = 64

(8-4)^2 = 4^2 = 16

then for the last part

4^-4 is the same as [tex]1/4^{4}[/tex] or 1/256

Then it is order of operations:

do 16 x 1/256 first which is 1/16

and then 64 - 1/16 to get 63 15/16 :)

In the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given ,

AQRS is an isosceles triangle. Complete the statement that explains whether RT is the height of the triangle.

So, from the given triangle we can say that ,

[tex]6^{2}[/tex] + [tex]\sqrt{85 }^2[/tex] = [tex]11^{2}[/tex]

By the pythagorean theorem , we can say that ,

the sum of squares of base and opposite side is always equals to square of hypothenuse.

so it is equal to square of 11 and RT is height.

Therefore, in the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.

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