Write an equation: The sides of a rectangle are x and ( x - 4 ). The perimeter is 87

Answer:

A, e, F

Step-by-step explanation:

[tex]\tt x^3+4x^2+8x+32\\\\=x^2(x+4)+8(x+4)\\\\=\boxed{\tt(x+4)(x^2+8)}[/tex]

Answer:

(x+4)(x^2+8)

Step-by-step explanation:

x^3 + 4x^2 + 8x + 32

We will factor by grouping

Factor out an x^2 from the first two terms and an 8 from the last two terms

x^2 (x+4) + 8(x+4)

Now we can factor out an (x+4)

(x+4)(x^2+8)

The complete table of values for the equation y = x/4 is

x   4   2  9

y  1   1/2  9/4

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

y = x/4

The missing y values are at x = 4, 2 and x = 9

Substitute the known values in the above equation, so, we have the following representation

y = 1/4 * 4 = 1

y = 1/4 * 2 = 1/2

y = 1/4 * 9 = 9/4

So, the missing values are 1, 1/2 and 9/4

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Final answer:

The rule 'y = X/4' describes division of X by 4 to find Y. The student completes the table by dividing each X value by 4 to find the corresponding Y values, providing an organized data set.

Explanation:

The student is asking about the operation indicated by the rule y = X/4, which involves division. The fraction bar signifies division. Given this rule, we can complete the table for y when x-values are provided.

For x = 4: y = 4/4 = 1

For x = 2: y = 2/4 = 0.5

For x = 9: y = 9/4 = 2.25

To organize the data in the table, you simply divide the x-value by 4 to find the corresponding y-value.

Answer:

[tex]y = \sqrt{x - 16} [/tex]

Step-by-step explanation:

[tex]y = {x}^{2} + 16[/tex]

[tex]x = {y}^{2} + 16[/tex]

[tex]x - 16 = {y}^{2} [/tex]

[tex] \sqrt{x - 16} = y[/tex]

Answer:

f^-1 (x) = ±sqrt(x-16)

Step-by-step explanation:

To find the inverse of a function, exchange x and y and solve for y

y=x^2+16

Exchange x and y

x = y^2 +16

Then solve for y

Subtract 16 from each side

x-16 = y^2 +16-16

x-16 = y^2

Take the square root of each side

±sqrt(x-16) = sqrt(y^2)

±sqrt(x-16) = y

The inverse

f^-1 (x) = ±sqrt(x-16)

Answer:

9 < n < 21

Step-by-step explanation:

15-6 < n < 15+6

9 < n<21

We are limited by the other two sides of the triangle

It can be no smaller than the other two sides subtracted and no larger than the other two sides added

Answer:

see explanation

Step-by-step explanation:

Given

8x + 5y = 10 ← solve for x by subtracting 5y from both sides

8x = 10 - 5y ( divide both sides by 8 )

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

------------------------------------------------------------

Solve for y by subtracting 8x from both sides

5y = 10 - 8x ( divide both sides by 5 )

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

Answer:

18/20 or 9/10

Step-by-step explanation:

The list shows the amount of hours each student USED the computer.

Wherever we see a "0", that means he/she DID NOT USE computer.

There are 2 "zeroes", so 2 didnt use out of 20, so number of student who DID USE is 20 - 2 = 18

To find ratio of total number of students who used to the total number surveyed, it is going to be:

18/20 or 9/10

Answer:

Ratio would be 9 : 10

Step-by-step explanation:

Liliana surveyed 20 students that how many hours they spend on their computers each week.

The results are as follows

8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21

In the above results 2 students did not use computers out of 20 students.

Therefore, The total number of students who used their computers = 20 - 2 = 18

So the ratio would be 18 : 20 or 9 : 10

Answer:

Step-by-step explanation:

x-intercepts are for y = 0.

Put y = 0 to the equation y = 2x² + 5x + 9:

2x² + 5x + 9 = 0

Calculate the discriminant of quadratic equation ax² + bx + c = 0:

Δ = b² - 4ac

if Δ < 0, then an equation has no solution

if Δ = 0, then an equation has one solution

if Δ > 0, then an equation has two solution.

2x² + 5x + 9 = 0

a = 2, b = 5, c = 9

Δ = 5² - 4(2)(9) = 25 - 72 = -47 < 0 - no solution

There are zero x- intercepts of given function.

To find x- intercepts, substitute [tex]y=0[/tex] in the function.

Given function is,  [tex]y=2x^{2} +5x+9[/tex]

Substitute [tex]y=0[/tex] in above equation.

              [tex]2x^{2} +5x+9=0\\\\[/tex]

The graph of function where crosses the x- axis that point is known as x- intercepts of function.

Graph of given function attached below, It is observed that graph will not crosses the x axis at any point.

Thus, There are zero x- intercepts of given function.

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Answer:

Step-by-step explanation:

Setting the denominator = to 0, we get x = -4.  This is the location of the discontinuity.

Setting the numerator = to 0 and solving for x yields the zeros:  They are {-2, -4}.

Answer:

3.75.

Step-by-step explanation:

Substitute x = 1/2 into x^2 + 3.5:

(1/2)^2 + 3.5

= 1/4 + 3.5

= 3.75.

Answer:

Step-by-step explanation:

[tex]\text{Put the value of}\ x=\dfrac{1}{2}=0.5\ \text{to the expression}\ x^2+3.5:\\\\0.5^2+3.5=0.25+3.5=3.75[/tex]

Answer:

∠A, ∠B, ∠C

Step-by-step explanation:

In a triangle the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side, therefore:

∠A < ∠B < ∠C

Answer:

a,b,c

Step-by-step explanation:

The angle opposite the longest side has the largest angle measure, the angle opposite the shortest side has the most small angle measure etc.

Since BC is the shortest line, the angle opposite will have the smallest measure, this is ∠a.

CA is in the middle with length this means that the angle opposite of it will have an angle measure in between that of the other angle measures.  This is ∠b

AB has the longest length, therefore, the angle opposite it will have the largest measure, this is ∠c

The solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.

The statement that the graph of [tex]\( 2x^2 + 8 = 0 \)[/tex] does not cross the x-axis is correct, as the graph of this equation represents a parabola that opens upwards and is centered above the x-axis, meaning it has no real roots.

To find the solutions for the equation [tex]\( 2x^2 + 8 = 0 \)[/tex], we can start by isolating [tex]\( x^2 \):[/tex]

[tex]\[ 2x^2 = -8 \][/tex]

Dividing both sides by 2:

[tex]\[ x^2 = -4 \][/tex]

Now, to solve for ( x ), we take the square root of both sides:

[tex]\[ x = \pm \sqrt{-4} \][/tex]

[tex]\[ x = \pm 2i \][/tex]

So, the solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.

These are the roots of the equation, even though they do not lie on the real number line.

Hence, while there are no real solutions, there are indeed complex solutions for the given function.

Answer:

35

Step-by-step explanation:

92-5+4-3=35

For this case we must factor the following equation:

[tex]x ^ 2 + x-6 = 0[/tex]

We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2

So, we have to:

[tex](x + 3) (x-2) = 0[/tex]

The roots are:

[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]

ANswer:

[tex](x + 3) (x-2) = 0[/tex]

Answer:

[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]

Step-by-step explanation:

[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]

[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]

Answer:

68%

Step-by-step explanation:

Probability of occurrence of Event v = P(v) = 28% = 0.28

Probability of occurrence of both Events v and Event w together = P(v and w) = 19% = 0.19

We have to find what is the probability  that event w occurs with event v given that event v  occurs on a Tuesday. This is a conditional probability. In other words we have to find what is the probability of event w given that event v occurs of Tuesday. i.e we have to find P(w|v)

The formula to calculate this conditional probability is:

[tex]P(w|v) = \frac{P(v \cap w)}{P(v)}[/tex]

Using the given values, we get:

[tex]P(w|v) = \frac{0.19}{0.28}\\\\ P(w|v) = 0.68\\\\ P(w|v) = 68\%[/tex]

Therefore, the probability that even w will occur with event v given that event v occurs on Tuesday is 68%

Answer:

195

Step-by-step explanation:

9 times 10 is 90 and 7 times 15 is 105  

so 105+90=195

Answer:

195 cm

Step-by-step explanation:

The area of ABCD is 195 cm.

Multiply the sides together:

9 ⋅ 10 = 90

7 ⋅ 15 = 105

Add them together:

105 + 90 = 195

Therefore, the area of ABCD is 195 cm.

Answer:

5x. 5x. 5x. 5x. 5x. 4x. 4x. 4x

Step-by-step explanation:

Just seperate all of the numbers out. Because 5x is raised to the fifth it is being multiplied by itself 5 times, the same goes for 4.

Answer:

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Actually 1 and x both are polynomials. Therefore 1/x is already a quotient of polynomials.

Two polynomial expressions whose quotient, when simplified, is 1/x

x+1/x^2+x

Take the common of the denominator

x+1/x(x+1)

x+1 will be cancelled out by x+1

1/x

1/x is not a polynomial, so polynomials are not closed under division.

Polynomials are closed under addition, subtraction and multiplication. Addition and multiplication are associative and commutative.

There is an additive identity which is 0.

There is a multiplicative identity which is 1....

Polynomial expressions involve variables, coefficients, and exponents, combined by addition, subtraction, and multiplication. They are not closed under division, as shown by the quotient 1/x, which is not a polynomial. However, polynomials are closed under addition, subtraction, and multiplication.

A polynomial expression is a mathematical expression that can involve variables, coefficients, and exponents, that are combined using addition, subtraction, and multiplication operations. For your question, we can consider two polynomial expressions: x and 1. The quotient of these two expressions is 1/x.

However, 1/x is not a polynomial expression, because it involves division by a variable. This shows that polynomial expressions are not closed under division.

In contrast, polynomials are closed under the operations of addition, subtraction, and multiplication. For example, if we add, subtract or multiply any two polynomials we will always get another polynomial.

These operations do not generate any new type of expressions outside the realm of polynomials, unlike division, which can produce non-polynomial results, such as rational expressions.

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In order to find all the types of sweatshirts, we simply have to multiply all the numbers by all the factors.

3 colors * 2 different styles * 3 different sizes = 18 different types of sweatshirts

The total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

The student council is selling sweatshirts with the school name and shirts come in three different colours, two different styles and three different sizes.

Total number of different sweatshirts = 3×2×3

= 18

Thus, the total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.

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Answer:

Option C is correct.

Step-by-step explanation:

If we look at the table,

The amount of Principal of Month 13 is $325.82

The amount of Principal of Month 14 is $328.19

The amount of Principal of Month 15 is $330.57

So, the amount of principal is increasing every month.

Rest of the options seems incorrect.

So, Option C The amount applied to the principal is increasing each month.

is correct.

Answer:

The answer is C

Step-by-step explanation:

I got the right answer on the test in e2020

Answer:

26.6 degrees

Step-by-step explanation:

Use the converting formula:

(-3°C × 9/5) + 32 = 26.6°F

-3 degrees to Fahrenheit would be 26.6

The formula is attached in the image below

-3 × 1.8 = -5.4

-5.4 + 32 = 26.6

Answer:

Segment, line and Ray

Step-by-step explanation:

Lets discuss all the options one by one.

Point:

A point has no length, no width and no depth. It is 0 dimensional.

Line:

A line extends in both directions. It is straight and has no thickness. It is 1 dimensional

Segment:

It is a part of a line bounded by two distinct end points. As it is a part of a line than it is also 1 dimensional.

Triangle:

A triangle has three sides and three corners. It is two dimensional figure. Its interior or oval is also two dimensional.

Plane:

A plane is a two dimensional flat surface with no thickness.

Ray:

A ray is a part of a line with single end point. It goes off in a particular direction infinitely. As it is a part of a line hence it is also 1 dimensional:

Thus according to the above description Segment, Line and Ray are one dimensional

Answer:

C. Line.  F.  Ray   B. Segment ( but see below.)

Step-by-step explanation:

A line is one dimensional, so is a Ray.

As for a segment it depends on what you mean . A line segment is one dimensional, but a segment of a circle has 2 dimensions.

Final answer:

Three equivalent fractions for 60.1% with different denominators are found by converting the percent to a decimal and then to the requested fractions. The fractions are 601/1,000 (simplest form), 60.1/100 simplifies to 601/1,000, and 6.01/10 simplifies to 601/1,000.

Explanation:

To write three equivalent fractions for 60.1% with denominators of 1,000, 100, and 10, we first convert the percent to a decimal by dividing by 100. So, 60.1% becomes 0.601. This decimal can then be written as a fraction with the various denominators.

With a denominator of 1,000: 0.601 × 1,000/1,000 = 601/1,000

With a denominator of 100: 0.601 × 100/100 = 60.1/100 which simplifies to 601/1,000

With a denominator of 10: 0.601 × 10/10 = 6.01/10 which simplifies to 601/1,000

Note that 601/1,000 is the simplest form for the fraction equivalent of 60.1%. When we adjust for the different denominators, we always arrive back at the equivalent fraction of 601/1,000 because it is the simplest form.

Step-by-step explanation:

range is all the y values

{y|y=-9, -3, 0, 5, 7}

The range of a function are all the ys included in the graph. In this case that would be:

(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)

Remember to order it from least to greatest:

{yly = -9, -3, 0,5,7}

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

1 = 2

3 = 14

10 = 56

Step-by-step explanation:

y = 6x - 4

y = 6 - 4

y = 18 - 4

y = 60 - 4

Step-by-step explanation:

In first there is 2

ln second there is 14

ln third there is 56

I hope this is right answer!

Answer:

A''(1,-1) B''(3,2) C''(3,2)

Step-by-step explanation:

A(−5,0) B(−3,3) C(−3,0)

reflection over x=-2

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1

after reflections, the perpendicular distance will be 6,2,2, and the points will be at

A'(1,0) B'(−1,3) C'(−1,0)

again  reflection over x=1

Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2

after reflections, the perpendicular distance will be 0,4,4 and the points will be at

A''(1,-1) B''(3,2) C''(3,2)!

Answer:-12

Step-by-step explanation:

Z-3x=

=3-3(5)

=3-15

=-12

Answer:

-12

Step-by-step explanation:

3 - 3(5)

3 -15 = -12

the answer to the question

For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]

So, we have:

[tex]x + 2 <5\\x <5-2\\x <3[/tex]

The solutions are given by all strict minor numbers to 3.

[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]

The solutions are given by all the major strict numbers to 1.

If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].

The intersection is given by [tex]1 <x <3[/tex]

Answer:

 The solution interval is (1,3)

Answer:

5 boxes

Step-by-step explanation:

Given:

Total crayons : 98

Capacity of each box : 24

Number of boxes of 24 crayons needed to hold 98 crayons,

= 98 ÷ 24

= 4.08 boxes.

However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.

4.08 rounded up to next whole number = 5

Hence he will need 5 boxes to hold all 98 crayons