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What is the value of x?


30°

60°

90°

180°

Answer:

f(x) = x³ + x² - 5x + 3

Step-by-step explanation:

The cubic polynomial has zeros at 1, 1, - 3.

Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.

Hence, we can write the polynomial as a function of x as

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

⇒ f(x) = (x² - 2x + 1)(x + 3)

⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3

⇒ f(x) = x³ + x² - 5x + 3

So, this is the cubic polynomial function in standard form. (Answer)

Answer:

[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]

Step-by-step explanation:

Given equation of line:

[tex]9x+5y=3[/tex]

To find the equation of line perpendicular to the line of the given equation and passes through point (4,-7).

Writing the given equation of line in standard form.

Subtracting both sides by [tex]9x[/tex]

[tex]9x-9x+5y=3-9x[/tex]

[tex]5y=3-9x[/tex]  

Dividing both sides by 5.

[tex]\frac{5y}{5}=\frac{3}{5}-\frac{9x}{5}[/tex]  

[tex]y=\frac{3}{5}-\frac{9x}{5}[/tex]  

Rearranging the equation in standard form [tex]y=mx+b[/tex]

[tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex]  

Applying slope relationship between perpendicular lines.

[tex]m_1=-\frac{1}{m_2}[/tex]

where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of perpendicular lines.

For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex]can be found by comparing [tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex] with standard form.

∴ [tex]m_2=-\frac{9}{5}[/tex]

Thus slope of line perpendicular to this line [tex]m_1[/tex] would be given as:

[tex]m_1=-\frac{1}{-\frac{9}{5}}[/tex]

∴ [tex]m_1=\frac{5}{9}[/tex]

The line passes through point (4,-7)

Using point slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex](x_1,y_1)\rightarrow (4,-7)[/tex] and [tex]m=m_1=\frac{5}{9}[/tex]

So,

[tex]y-(-7)=\frac{5}{9}(x-4)[/tex]

Using distribution.

[tex]y+7=(\frac{5}{9}x)-(\frac{5}{9}\times 4)[/tex]

[tex]y+7=\frac{5}{9}x-\frac{20}{9}[/tex]

Subtracting 7 to both sides.

[tex]y+7-7=\frac{5}{9}x-\frac{20}{9}-7[/tex]

Taking LCD to subtract fractions

[tex]y=\frac{5}{9}x-\frac{20}{9}-\frac{63}{9}[/tex]

[tex]y=\frac{5}{9}x+\frac{(-20-63)}{9}[/tex]

[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]

[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]

Thus, the equation of line in standard form is given by:

[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]

Jimmy can get -18 marks in the Mathematics competition based on his correct, incorrect, and unanswered answers.

To calculate the marks Jimmy can get, we need to consider the number of questions he answered correctly, incorrectly, and left unanswered. Since each question carries 10 marks for a correct answer and deducts 8 marks for a wrong answer, we can calculate his marks as follows:

To get the total marks, we add up his scores from each category:

Total marks = 30 - 48 + 0 = -18 marks.

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The answer is implicit

Answer:

Implicit Differentiation is necessary in order to find derivatives of curves that do not represent a function because the functions cannot be simplified to a simple function. Using dy/dx and implicit differentiation can be used to find the derivative with respect to one variable and determine the affect each variable has on one another and calculate the rate of change of the variables over time. Differentiating both x and y in Implicit Differentiation makes it so that complex functions are much easier and instead of solving for one variable, differentiating one variable to the other is an easier method. My implicit function is 2y^2-x^2+x^3y=2. First Derivative= -3yx^2+2x/4y+x^3 Second Derivative= 3yx^4-4y^3-24y^2x+8y/(4y+x^3)^2 Third Derivative = 6y(-x^6+28yx^3+4y^2x^2-8x^2-16y)/(4y+x^3)^3

Answer:

see explanation

Step-by-step explanation:

Since the lines are parallel then

∠x  = 70° ( alternate angles are congruent )

Since the triangle is isosceles then the base angles are congruent, thus

∠y = ∠x = 70°

The sum of the angles in a triangle = 180°

Subtract the sum of x and y from 180 for z

∠z = 180° - (70 + 70)° = 180° - 140° = 40°

Hence ∠x = ∠y = 70° and ∠z = 40°

Answer:

5 more of the sum would be + 5 to the final answer you are adding

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

'At least 35 years old'  can be written as ≥ 35 ( greater than or equal to 35)  so its graph B.

Note there is a filled circle on the 35 meaning the 35 years is included in the range.

The ratio of time taken by Henry to time taken by Gavin is 3:5

Step-by-step explanation:

Time taken by Henry for each set = 36 minutes

Time taken by Gavin for each set = 1 hour

We will convert Gavin's time into minutes.

Time taken by Gavin for each set = 60 minutes

Ratio;

Time taken by Henry : Time taken by Gavin

[tex]36:60[/tex]

Dividing by 6

[tex]\frac{36}{6}:\frac{60}{6}\\6:10[/tex]

Dividing by 2

[tex]\frac{6}{2}:\frac{10}{2}\\3:5[/tex]

The ratio of time taken by Henry to time taken by Gavin is 3:5

Keywords: ratio, division

Learn more about ratios at:

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Answer:

y = -2/3 x + 1/3

Step-by-step explanation:

Use the slope-intercept linear formula: y = mx + b

x and y represent point on the line

m is the slope

b is the y-intercept

The equation of the line requires "m" and "b". We already have "m".

Substitute point (-4, 3) and slope -2/3 into the formula. x=-4; y=3; m=-2/3. Find b by isolating the variable.

y = mx + b

3 = (-2/3)(-4) + b   Simplify

3 = 8/3 + b     Subtract 8/3 from both sides

b = 1/3

Put b = 1/3 into the formula.

y = -2/3 x + 1/3

The amount at end of 1 year is $ 109.2025

Solution:

Given that,

Principal = $ 100

Rate of interest = 9 % compounded semiannually

Number of years = 1

The formula for total amount using compounded semiannually is:

[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here, [tex]r = 9 \% = \frac{9}{100} = 0.09[/tex]

Here, n = 2 since interest is compounded semiannually

Substituting the values in formula,

[tex]A=100\left(1+\frac{0.09}{2}\right)^{2 \times 1}[/tex]

[tex]\begin{aligned}&A=100(1+0.045)^{2}\\\\&A=100(1.045)^{2}\\\\&A=100 \times 1.092025=109.2025\end{aligned}[/tex]

Thus the amount at end of 1 year is $ 109.2025

Answer:

The volume of the box is [tex]V=(4x^3+16x^2+15x)\ in^3[/tex]

Step-by-step explanation:

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

where

L is the length of the box in inches

W is the width of the box in inches

H is the height of the box in inches

we have

[tex]L=(2x+5)\ in\\W=(2x+3)\ in\\H=x\ in[/tex]

substitute in the formula

[tex]V=(2x+5)(2x+3)x[/tex]

[tex]V=(4x^2+6x+10x+15)(x)[/tex]

[tex]V=(4x^2+16x+15)(x)[/tex]

[tex]V=(4x^3+16x^2+15x)\ in^3[/tex]

Answer:

Step-by-step explanation: the answer is A beacause the sentence is in the past tense and answer A is the only one that would be gramatically correct

Final answer:

The correct phrase to complete the sentence is 'A. Will have gone' since it requires the future perfect tense to indicate that nine years will have passed after the upcoming summer.

Explanation:

The correct phrase to complete the sentence "After this summer we __ for nine years straight." is A. Will have gone. This is because the sentence is referring to a future event where the duration of nine years will have been completed after this coming summer, which requires the future perfect tense. The future perfect tense is formed with 'will have' followed by the past participle of the verb, which in the case of 'go' is 'gone'.

Now, let's solve some practice questions:

For each blank, you would choose the correct verb tense depending on the context of the sentence provided.

Answer:

801-792

Step-by-step explanation:

I got my answer by picking out a big number first (801) and subtracting it by another big number (701) to get an answer less than 100.

To form a subtraction equation with two three-digit numbers having different hundreds digits and a difference of less than 100, choose numbers where the hundreds digits are one number apart and the tens and ones digits are close, such as 756 - 657 = 99.

To write a subtraction equation that involves two three-digit numbers with different hundreds digits and a difference of less than 100, we need to select numbers where the hundreds digit is only 1 apart and the tens and ones digits are close. For example, the numbers 654 and 756. Subtracting these gives us:

756 - 654 = 102

We notice the result is slightly over 100. Therefore, we can adjust the tens or ones digits to reduce the difference. If we change 654 to 657, then:

756 - 657 = 99

In this case, we achieved a result that is less than 100. It's important to note that, in subtraction, we change the sign of the subtracted number before operating the addition as per standard arithmetic rules.

Answer:

7/10

Step-by-step explanation:

3/10+2/5=3/10+4/10=7/10

Step-by-step explanation:

You first find the LCM and multiply both fractions by it. Over here the LCM is 10.

(10 (3/10) + 10 (2/5))/10

(3+4)/10

7/10

Answer:

3

Step-by-step explanation:

You want a number that if it is multiplied by 3 1/3 the result will be 10. Let the number be x

3 1/3 * x = 10                         Change to a mixed number

10/3 * x = 10                          Multiply by 3/10

(10/3)*x * 3/10 = 10 * 3/10     Combine

x = 10*3 / 10                          Simplify

x = 30/10 = 3

Answer:

3

Step-by-step explanation:

Answer:

the answer would be 85

Step-by-step explanation:

because they are added by an increasing value of 5 so 60 plus 25 would be 85

Answer: -5 1/2

Step-by-step explanation:

Answer:

[tex]\sqrt{-5}=i\sqrt{5}[/tex]

[tex]\sqrt{-25}=5i[/tex]

Step-by-step explanation:

i is an imaginary unit, this means

[tex]i^2=-1[/tex]

Rewrite -5 as [tex]5\cdot (-1)=5\cdot i^2,[/tex]

then

[tex]\sqrt{-5}=\sqrt{5i^2}=\sqrt{5}\cdot \sqrt{i^2}=\sqrt{5}\cdot i=i\sqrt{5}[/tex]

Rewrite -25 as [tex]-25=25\cdot (-1)=25\cdot i^2,[/tex]

then

[tex]\sqrt{-25}=\sqrt{25\cdot i^2}=\sqrt{25}\cdot \sqrt{i^2}=5\cdot i=5i[/tex]

50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Step-by-step explanation:

Given,

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let,

x represent the number of small boxes of papers.

y represent the number of large boxes of papers.

According to given statement;

50x+80y=1750

y = x+4  

50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Keywords: linear equation, addition

Learn more about linear equations at:

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The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:

50x+80y=1750

y = x+4 ,

where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

We have:

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let us consider that  the number of small boxes of papers be x.

The number of large boxes of papers be y.

 Then, according to question

50x+80y=1750

y = x+4  

Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.

where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.

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Answer:

6.39

Step-by-step explanation:

6.39

Answer:

6.39

Step-by-step explanation:

When dividing by 10 you can always just move the decimal place once to the left.

Glad I was able to help!!

Answer:

[tex]x=\frac{d+c}{b-a}[/tex]

Step-by-step explanation:

The question is

Solve for x

we have

[tex]bx-c=ax+d[/tex]

Solve for x

That means ----> isolate the variable x

Group terms

[tex]bx-ax=d+c[/tex]

Factor x left side

[tex]x(b-a)=d+c[/tex]

Divide by (b-a) both sides

[tex]x=\frac{d+c}{b-a}[/tex]

Answer:

2

Step-by-step explanation:

Answer:

A. 0

Step-by-step explanation:

Because there is no correlation between any of the points.

Answer:

a=0.41

Step-by-step explanation:

7(a-10)=13-202a+3

7a-70=13+3-202a

7a-(-202a)-70=16

7a+202a=16+70

209a=86

a=86/209

a=0.41

To solve the equation 7(a - 10) = 13 - 202a + 3, begin by simplifying both sides of the equation and combining like terms. Then isolate the variable 'a' to one side and the constant terms to the other. Finally, divide both sides by the coefficient of 'a' to solve for 'a'.

To solve the equation 7(a - 10) = 13 - 202a + 3, you can start by simplifying both sides of the equation. Expand the terms on the left side by distributing the 7 to the terms inside the parentheses. Combine like terms on both sides of the equation. Then, isolate the variable by moving all the terms with 'a' to one side of the equation and all the constant terms to the other side. Finally, divide both sides of the equation by the coefficient of 'a' to solve for 'a'.

Step-by-step solution:

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Step-by-step explanation:

4x > 36-4

4x > 32 (divide both sides of the inequality by 4 )

4x ÷ 4 > 32 ÷ 4

x > 8

Final answer:

To determine the solution set of the inequality 4x + 4 > 36, subtract 4 from both sides to get 4x > 32 and then divide by 4 to find x > 8. Any number greater than 8 is part of the solution set.

Explanation:

To find which number is in the solution set of the inequality 4x + 4 > 36, we need to solve for x by performing a series of steps:

Subtract 4 from both sides of the inequality to get 4x > 32.

Divide both sides of the inequality by 4 to solve for x, resulting in x > 8.

Thus, any number greater than 8 is in the solution set of the given inequality.

Answer:

y+2=3/4(x-4)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-(-2))/(12-4)

m=(4+2)/8

m=6/8

m=3/4

----------

y-y1=m(x-x1)

y-(-2)=3/4(x-4)

y+2=3/4(x-4)

Answer:

1 liter × 0.2642 gallons liter × 33.817 fluid ounces gallon.

Step-by-step explanation:

Given:

1 gallon = 3.785 liters

We need to find how many fluid of ounce are there in 1 liter.

First we will find number of gallons in 1 liter.

We know that;

3.785 liters = 1 gallons

1 liters = number of gallons in 1 liter.

By using Unitary method we get;

number of gallons in 1 liter = [tex]\frac{1}{3.785}= 0.2642\ gallons[/tex]

Now we know that:

1 gallons = 128 fluid ounce

So 0.2642 gallons = Number of fluid ounce in 0.2642 gallons

Again by using Unitary method we get;

Number of fluid ounce in 0.2642 gallons = [tex]128 \times 0.2642\approx 33.817\ oz[/tex]

Hence we can say,

1 liter ×0.2642 gallons liter × 33.817 fluid ounces gallon.

Answer:

1/6 of one minute, 10 seconds.

Step-by-step explanation:

8/48=1/6

Answer:

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Step-by-step explanation:

Given:

Shape is of Trapezoid

Height = 14xy² cm

Length 1 = 3x² cm ( one Parallel side)

Length 2 = 7x² cm ( other Parallel side)

To Find:

Area of Trapezoid = ?

Solution:

We know that

[tex]\textrm{Area of Trapezoid }= 0.5(length\ 1+length\ 2)Height[/tex]

substituting the given values we get

[tex]\textrm{Area of Trapezoid }= 0.5\times(3x^{2}+7x^{2})\times 14xy^{2}[/tex]

[tex]\textrm{Area of Trapezoid }= (10x^{2})7xy^{2}[/tex]..((x^{a}x^{b}=x^{(a+b)})

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Answer:

-11

Step-by-step explanation:

Because -2+(-9)=-2-9=-11.