Find the values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,​

Answer:

2

Step-by-step explanation:

substitute s for 8

then substitute f for 2

that means 2*2 or 4

8/4 is 2

Answer: the answer would be 2

Step-by-step explanation: since f =  2 you would multiple 2 x2 then you would get 4 then you divid 8 and 4 and you get 2

Answer:

<DKF IS 54° BECAUSE IT IS VERTICALLY OPPOSITE ANGLE OF THE<IKL.

Based on the equation of the line that is parallel to the first line, the equation of the line in slope-intercept form is y = 3/4x - 6³/₄

First, find the slope of 3x + 4y = 7:
( 3x + 4y = 7) x 1/4

3/4x + y = 7/4

The slope is therefore 3/4x.

Lines that are parallel to each other have the same slope. You can therefore use this slope to find the formula of the other line by first solving for the y-intercept:
y = Slope(x) + y-intercept

-9 = 3/4(-3) + y-intercept

y-intercept = -6³/₄

The equation of the line is:

y = 3/4x - 6³/₄

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The figure RSTU can represent Quadrilateral, Parallelogram and Rectangle

The figure KLMN  represents Quadrilateral and Parallelogram

The figure ABCD  represents only Quadrilateral

Given,

The figures;

RSTU, KLMN and ABCD

We have to identify the true facts about the figure.

All figure are drawn like a rectangle.

Quadrilateral;

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Parallelogram;

A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.

Now here,

RSTU; This figure can represent all the options.

That is,

Quadrilateral, Parallelogram and Rectangle

KLMN; This figure represents Quadrilateral and Parallelogram

ABCD; This figure represents only Quadrilateral

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x = 9

x + 3 + x - 1 = 20

2x + 2 = 20

2x = 18

x = 9

Answer:

shifted 5 up and 4 to the left

Step-by-step explanation:

Answer:

x = - 4, y = 2

Step-by-step explanation:

First equation: 4x + 3y = - 10

Second equation: 4x+y= - 14

To solve simultaneously:

Rearrange one of the equations and substitute the equation to another equation, I prefer rearranging the second equation because it is easier.

Rearranging the second equation to get y, and then substitute back to the first equation to find x:

y = - 14 - 4x ------> new second equation

Substitute y (new second equation) into the first equation to find x:

4x +3(-14 -4x) = - 10

4x - 42 - 12 x = - 10

       - 8x - 42 = -10

                -8x = - 10 + 42

               - 8x = 32

                 8x = - 32

                   x = - 4

Now we substitute x = - 4 to the second equation to find y:

4x + y = - 14

y = - 14 - 4(-4)

y = - 14 - (-16)

y = - 14 + 16

y = 2

The value of (x + 5) * (x^3 + 6x^2 + 18x) is x^4 + 11x^3  + 48x^2 + 90x

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the polynomial expression?

The polynomial expression is given as

(x + 5) * (x^3 + 6x^2 + 18x)

Express the polynomial expression as a product of factors

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x * (x^3 + 6x^2 + 18x) + 5 * (x^3 + 6x^2 + 18x)

Open the brackets in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 18x^2 + 5x^3 + 30x^2 + 90x

Collect the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 5x^3  + 18x^2 + 30x^2 + 90x

Evaluate the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 11x^3  + 48x^2 + 90x

Hence, the solution is x^4 + 11x^3  + 48x^2 + 90x

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Answer: NM = 40

Step-by-step explanation:

    First, we will label everything. See attached.

    Next, we will set up a proportion to solve. Let the missing side, ? in the picture, be equal to x.

➜ On the left side will be the "smaller top" triangle

➜ On the right side will be the larger triangle

➜ View the second attachment for a visual explanation of this if you are confused.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

    Next, we will cross-multiply and solve.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

48x = 30(x + 24)

48x = 30x + 720

18x = 720

x = 40

Usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.

As given in the question,

Given that:

Usual selling price of shoes = $68

Discount on shoes =40%

Discounts an amount or percentage from something that they are selling, they take the amount or percentage off the usual price.

so, remove 40% from the price and you have left 60%

reduced price = 60% of $68

                         =60/100 * 68 = $40.8

Sales tax is 6% of reduced price= 6% of $40.8

                                           =$2.448 upto 3 decimal digits

Now , price including tax =$40.8+$2.448 =$43.248

Hence, total price including tax= $43.248

Therefore, usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.

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Answer:

25

sum of the interior angles of triangle =180

101+54=155

155-180=25

£1 = 99.72 rupees -> £450 = 44874 rupees.

As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.

The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.

a) 7 video games;

26 - x = 40 - 3x

x = 7

Answer:

-6x-18

Step-by-step explanation:

in class

Answer:-24

Step-by-step explanation: you do -6(x)+(-6)(3) and u get -6+-18 and get -24 hope it helps .

Answer:

Step-by-step explanation:

18=18+x-x*x/x

Answer:

x<-5.5   or x<-11/2

Step-by-step explanation:

2(4x+1)<3(2x-3)

1. First we need to expand the brackets

8x+2<6x-9

2. get the x on one side so we would -6x and -2 on each side

2x<-11

3. divide by 2 on each side as we want to get the value of x which gives

x<-11/2

the fraction can also be written as a decimal

x<-5.5

4) so, the final answer is

x<-5.5 or <-11/2

Q is the set of the rational numbers

Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.

Examples:

The given equation is

Insert log on both sides

Use the rule of power with a log

Divide both sides by log(1/5)

Since we can not put the value of x in the form of a/b, then

The equation has NO solution in Q (or empty set { } or Nul)

The original dimensions are 12 m and 20 m.

What is area of rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.

Let x be the width of the rectangle.

Length of the rectangle = x+8

Area of the rectangle = x(x+8)

According to question, new width= x+2

New length = x+2+8 = x+10

New area = (x+2)(x+10)

Area increased = (x+2)(x+10) – x(x+8)

x^2+12x+20-x^2-8x=68

4x-20=68

4x=48

x=12

Hence, the width = 12m and length = 12+8 = 20 m

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Answer:

2(3x+2)

Step-by-step explanation:

i think that's what it is

Answer:

What do you need done here?

Step-by-step explanation:

6x + 4 means nothing unless you want to factor the binomial.

I assume you want to factor.

Factor out 2.

2(3x + 2)

Is this what you are looking for?

Answer:

Step-by-step explanation:

Fuel cost = (Distance / Consumption) × Cost per gallon.

107 X  4.83 = 516.81

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Answer: I got 18

Step-by-step explanation:

Substitute all the variables

18 = 2*3^2

X = 4 * 9^2

X = 4 * 81

X = 324

324/18 = 18

so the is answer is 18.

Also are you going to A+ by any chance?

The values of the expression h(1), h(-7) and h(9) are 6, 50 and 62

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.

Given the following modulus function shown below;

h(x)= |1 - 7x|, we are to find the following.

h(1)

h(-7)

h(9)

If x = 1, then;

h(x)= |1 - 7(1)|

h(1) = |1-7|

h(1) = |-6|

h(1) = 6

If x = -7, then;

h(-7)= |1 - 7(-7)|

h(-7) = |1--49)|

h(-7) = |1+49|

h(-7) = |50|

h(-7) = 50

If x = 9, then;

h(x)= |1 - 7(7)|

h(1) = |1-63|

h(1) = |-62|

h(1) = 62

This gives the equivalent values of the expression

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The value of x that makes the equation shown in the model true is x = -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The model shown can be represented by the equation:

4(-x) + 9(1) = 8(-x) + 3(-1)

-4x + 9 = -8x - 3

-4x + 8x = -3 - 9

4x = -12

x = -3

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Answer:

y=-2/5x +13/5

Step-by-step explanation:

y= -0.4x+b

3=0.4+b

b=2.6

y=-2/5x +13/5

Answer:  [tex]\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}[/tex]

===============================================

Work Shown:

I'll be using point slope form to get these steps

[tex]\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-3 = -\frac{2}{5}(\text{x}-(-1))\\\\\text{y}-3 = -\frac{2}{5}(\text{x}+1)\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}*1\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}\\\\[/tex]

[tex]\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+3\\\\\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+\frac{15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{-2+15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}\\\\[/tex]

This answer has a slope of -2/5 and y intercept of 13/5.

Parallel lines have equal slopes but different y intercepts.

To verify this equation, plugging in x = -1 leads to y = 3.

Answer:

8.0/0.8

=10times

Answer:

9

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]

Answer:

y = 9

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, equate the expressions and solve for y:

[tex]\begin{aligned}(18y-18)^{\circ}&=16y^{\circ}\\18y-18&=16y\\18y-18+18&=16y+18\\18y&=16y+18\\18y-16y&=16y+18-16y\\2y&=18\\2y \div 2 &=18 \div 2 \\y&=9\end{aligned}[/tex]

Therefore, the value of y is 9.

The volume of the remaining solid correct to 2 decimal places is 3634.60 m³

From the question, we are to determine the volume of the remaining solid

Volume of the remaining solid = Volume of the larger prism - Volume of the rectangular prisms carved out

First, we will determine the volume of the larger prism

Volume of the larger prism = 17 × 17 × 17

Volume of the larger prism = 4913 m³

Now, we will determine the volume of one of the rectangular prism that was carved out

Volume = 4 × 9.4 × 17

Volume = 639.2 m³

∴ Volume of the two identical holes carved out = 2 × 639.2 m³

= 1278.4 m³

Thus,

Volume of the remaining solid = 4913 m³ - 1278.4 m³

Volume of the remaining solid = 3634.60 m³

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It will take the bottle of maple syrup 3 hours 45 minutes to reach  20° C from  –16° C.

given data

the bottle temperature will go up a steady 9.6° C every hour

freezer temperature  = –16° C

final temperature = 20° C

The temperature rise from –16° C to 20° C

from –16° C to 0° C = 16° C

from 0° C to 20° C = 20° C

adding both increments gives = 20 + 16 = 36° C

if every hour we have 9.6° C then how many hours will give 36° C

1 hour = 9.6° C

? hour = 36° C

we cross multiply to have

= 36 * 1 / 9.6

= 3.75

This is 3 hours then a fraction of some minutes, the fraction is gotten by

0.75 * 60 = 45

Therefore the time to reach 20° C is 3 hours 45 minutes

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Answer: m= -1/2

Step-by-step explanation: Equation of line in slope intercept form is represented by,. y= mx+c —-(1). Given that the line p passes through A (- 2, 4) and has a slope m= -1/2.