Q1 Write a quadratic polynomial
, sum of whose zeroes is 3 and product is -40​

The solution of  | x | +5 ≤ 1 is  option C, All values are solutions

We need to find the solution of  | x | +5 ≤ 1

Upon removing the modulus function, the term presnet within it can be either negative or positive

considering it as postive

| x | +5 ≤ 1

x + 5 ≤ 1

x ≤ 1 - 5

x ≤ -4

considering it as negative

| x | +5 ≤ 1

-x + 5 ≤ 1

-x ≤ 1 - 5

-x ≤ -4

x ≥ -4

Therefore, the solution of  | x | +5 ≤ 1 is  All values are solutions

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The value of y is 11.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given that Parallelogram ABCD is a rectangle.

Consider that AC and BD are opposite sides. In a parallelogram, we know that opposite sides are congruent which means:

AC = BD

2y + 7 = 3y - 4

Solving;

2y - 3y = -4 - 7

-y = -11

y = 11

Hence, the value of y is 11.

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Answer:

Step-by-step explanation:

Find an equation to represent x or y

2x + 2y = -22

     -2y

2x = -22 - 2y

Divide by 2

x = -11 -y

Plug in the found equation

5 (-11 - y) +6y = - 63

- 55 -5y + 6y = - 63

-55 + y = - 63

+55

y = - 8

Plug in the y to find x

2x + 2(- 8) = - 22

2x - 16 = - 22

    + 16

2x = - 6

Divide by 2

x = - 3

D

Step-by-step explanation:

The domain is the X-values in your function

as you can see, the X values continue to increase as the lines continue, infinitely

Answer:

10t + 20

Step-by-step explanation:

Answer:

Option B is perpendicular to y=-3x+4 and goes through point (-1,5)

Step-by-step explanation:

We will look for an equation of the form y=mx+b, where m is the slope and b the y-intercept.  The reference line, y=-3x+4, has a slope of -3.  A line perpendicular to this line will have a slope that is the "negative inverse" of the refence lines slope.  In this case, it's slope would be +(1/3).

We could graph each of the equation options and look for one that is perpendicular, but it might be faster to simply rearrnaged the options into standard format of y=mx+b. which we'll do here:

Option   Rearranged Equation   Slope

A) 3y=-x+16

                  y = -(1/3)x+(16/3)           -(1/3)

B) 3y=x+16

                   y = (1/3)x + (16/3)         (1/3)

C) y=-3x+8                                           -3

D) y=-3x+2                                            -3

There is only one option that has the required slope to be parallel to the reference equation (y=-3x+4), option B:  y = (1/3)x + (16/3)

Does it go through point (-1,5)?

y = (1/3)x + (16/3)

Enter x = -1 and find 5:

y = (1/3)(-1) + (16/3)

y = (16/3)-(1/3)

y = (15/3) or 5

 Yes, it goes through point (-1,5)

Option B is perpendicular to y=-3x+4 and goes through point (-1,5).

Answer: 1080 [tex]cm^{2}[/tex]

Determine the values of b1, b2, and b3, the sides of the triangular base. Also determine the value of h, the height of the triangular base and l, the length of the prism (the length between the bases).

The sides of the triangular base are:

b1 = 13 in.

b2 = 14 in.

b3 = 15 in.

The triangular base is a right triangle, and so the height is one of our sides. We will use

h = 12 in.

The length of the prism is

l = 20 in.

total surface area = bh + (b1+b2+b3)*l

bh = 12*20 = 240 [tex]cm^{2}[/tex]

l * (b1+b2+b3) = 20*(13 + 14+ 15) = 840 [tex]cm^{2}[/tex]

TSA = bh + l * (b1 + b2 + b3) = 240 + 840 = 1080 [tex]cm^{2}[/tex]

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Answer:

See below

Step-by-step explanation:

11x^2 = - 8

x^2  = - 8/11

x = + - i sqrt (8/11)      or  - .727 i   or   .727 i  

The mason should order 250 cubic yards of grit to use all the cement.

It is given that the mixture has 20 cubic yards of grit for 4 cubic yards of cement.

So the unit rate for the number of cubic yards of grit for per unit of cement is given by : 20 ÷ 4 = 5 cubic yards.

Now amount of grit required for 50 cubic yards of cement

= 50 × 5 = 250 cubic yards.

By utilising 1 as the denominator, a unit rate compares two quantities while using the second quantity as the unit of measurement. If someone runs three kilometers in 30 minutes, they have ran one mile.

Miles per minute is a unit of measurement for how far something is moving in a certain amount of time. For unit rate, the quantity value 1 is always used.

Hence he should order about 250 cubic yards in order to use all the cement.

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The selling price of the first washing machine is $300

The selling price of the second washing machine is $336

The first washing machine appear to have more savings in cost

The question is a percentage problem

The first is marked down by ​50%

= 50 percent

= 50 / 100

= 0.5

marked down factor = 1 - 0.5 = 0.5

selling price of the first machine = 600 * 0.5 = 300

Similarly the second selling washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 600 * 0.7 = 420

second mark down

20% = 0.2

marked down factor = 1 - 0.2 = 0.8

selling price of the second washing machine at second mark down

= 420 * 0.8 = 336

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a) The length of segment CD is; CD = 10 cm

b) The length of segment AB is; AB = 5 cm

c) Another segment with same length as segment AB is;

Segment AC

From the attached image, we see that Segment AE is a radius of the circle with center of A.

Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.

a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.

Diameter = 2 × radius.

Diameter; CD = 2 × AE

CD = 2 × 5

CD = 10 cm

b) AB is a radius as defined earlier and as such; AB = AE

Thus; AB = 5 cm

c) The other segments that are also radius of the circle and have the same length as segment AB are;

Segment AC

Segment AD

Segment AG

Segment FA

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By using properties of triangle, it can be inferred that

The value of c lies between 5 and 21 and also 5 and 21 are not included

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°

Let a = 8, b = 13 and let the third side be c

We know sum of two sides of a triangle is always greater than the third side

a < b + c

8 < 13 + c

c > 8 - 13
c > -5, which is obvious

b < c + a

13 < c  + 8

c > 13 - 8

c > 5

c < a + b

c < 8 + 13

c < 21

5 < c < 21

The value of c lies between 5 and 21 and also 5 and 21 are not included

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Step-by-step explanation:

X-intercept is where the line crosses the x-axis or where y = 0

So, put y = 0 in the given equation

4x + 2(0) = 12

4x = 12

x = 12/4

x = 3

Using a 98% confidence interval, the total number of customers that should be sampled is 87.

The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.

Given,

Standard deviation σ=300

Confidence level: 0.98

Maximum allowable error: ε=75

The critical value is calculated using the standard normal table at the level of significance (0.02)

The critical value in this case is 2.326.

Sample size is calculated by,

n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²

n=((2.326)²×(300)²)/(75)²

n=86.564≈87

Therefore, the required sample size is 87.

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For the given values of the arithmetic sequence d = -2 , a₂₁ = 18,then the value of a₁ = 58.

As given in the question,

Given values of the arithmetic sequence :

Common difference 'd' = -2

Twenty first term a₂₁ = 18

Formula for the nth term of arithmetic sequence with common difference 'd' and first term a₁ is given by:

aₙ = a₁ + (n -1) d

Substitute the value n =21 , a₂₁ =18 and d = -2 in the above equation we get,

⇒a₂₁ = a₁ + (21 -1)(-2)

⇒18 = a₁ + 20(-2)

⇒ a₁ = 18 +40

⇒a₁ = 58

Therefore, for the given values of the arithmetic sequence d = -2 ,

a₂₁ = 18,then the value of a₁ = 58.

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Answer:

The correct answer is D because Option A won't work neither will option B because a long credit history will help ur credit score, C isn't right either

The value of x and y in the triangle given are 15 and 4 respectively

An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.

In the triangle given, we can equate equal sides and find the missing sides on the triangle.

12/18 = y + 12 / 18 + 6

12/18 = y + 12 / 24

2/3 = y + 12 / 24

solve for y

y = 4

Taking another side and solve for x

12 / x = 12 + y / x + 5

but y = 4

12 /x = 12 + 4 / x + 5

12/x = 16 / x + 5

x = 15

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Answer:

See below

Step-by-step explanation:

It is NOT a right triangle or the diagonal would measure 52 feet (instead of 54 feet) ....it is an OBTUSE triangle

The require angle, angle ABD = 40 degrees

A bisector has two primary characteristics:

Any point along an angle's bisector is equally - spaced from the angle's sides.

The angle bisector divides the other side of a triangle in proportion to the other two sides.

Given : ∠ ABC is bisected by a ray BD

∠ ABC = 80°

Since the angle ABC is being bisected this means that the angles are equal

Let the bisected angle be x

thus we can write it mathematically as

x + x = 80

2x = 80

dividing both the sides as 2 we would get

x = 40 degrees

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Answer:

4.5 ounces of rice per container

Step-by-step explanation:

27 / 6 = 4.5

Hope this helps :)

The function's y = 3(x + 5)² +11 width will be narrower.

In mathematics, a function from a set x to a set y assigns each element of x precisely one element of y. The subsets x and y are referenced to as the function's domain and codomain, correspondingly. A relationship between a number of inputs and one output per input is referred to as a function. Simply described, a function is an association between inputs in which each piece of data is connected to exactly one output. There is a domain and a codomain, or range, for every function. A function is a type of rule that produces one output from one input. y = x² is a good illustration of this. Any information for x yields a single output for y.

A parabola is made narrow by a large positive value of a and wide by a large positive value of a that is close to 0.

Compare the given equation y = 3(x + 5)² + 11 with y = x² + c

So, a = 3

Therefore, the function will be narrower.

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Jodie has left 13.79 seconds to match the record.

What is a linear equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Here, we have

Jodie aimed to beat Mandy's 74.6-second mark on the obstacle course. She had already spent 10.56 seconds on the ropes and fifty-and-a-fourth seconds ascending the wall. To match the record, we must determine how much time she had remaining.

Jodie's total time for climbing the wall is fifty and one fourth seconds=50.25 seconds

The total time on ropes is 10.56 seconds

The total time she spent is 50.25+10.56=60.81

Left time = Record Time-Spent time

= 74.6-60.81 = 13.79

Hence, Jodie has left 13.79 seconds to match the record.

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The probability of selecting at least one defective item at random is 0.3017.

The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.

Defect rate = P(defect) = 0.05

Probability is defined as the required outcome divided by the total number of possible outcomes.

P( at least 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95

P(none is defective) = P(non defective)^7

P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983

P(at least one is defective) = 1 - 0.6983 = 0.3017

Therefore, probability of at least one defective item is 0.3017.

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From the figure

A. alternate interior angles:  1

B. same side exterior: 4

C. vertical: 4 and 3

D. same side interior: 3

E. obtuse angle: 1

F. adjacent angle pairs: 1 and 2

G. alternate exterior: 2

H. corresponding: 4

I. complimentary:

parallel lines refer too lines that would never meet. When there is a pair of parallel lines with a transversal line like in the figure some angle theorems come into play  

some of the are used in the in the problem and definition of some them include

adjacent angles refer to angles that are next to each other, such angles are being demarcated by a line to the other angle. in the figure angle 1 and 2 alternate angles

Obtuse angles refers to angles that are more than 90 degrees but less than 90 degrees

vertical angles are angles opposite to each other, formed when two lines meet

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Answer:

5√3

Step-by-step explanation:

There are two triangles shown in the image.

First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.

The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.

In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.

This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.

x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.

0.01 is the results of the two-sided significance test  in confidence interval,

What is alpha in statistics?

confidence level = 1 - alpha

so alpha = 1 - confidence level = 1 - 0.99 = 0.01

In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.

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The domain of the given function y = 2√(x - 6)

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.

In order to determine the domain of this function, we would equate the x-value to zero and then evaluate as follows:

x - 6 ≥ 0

x ≥ 6

Therefore, the domain of this function in interval notation is [6, ∞] as shown in the graph attached below.

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Complete Question:

What is the domain of the function y = 2√(x - 6)?

0 ≤ x < ∞

6 ≤ x < ∞

Answer:

12% of men are left handed.

Step-by-step explanation:

Percent of men who are left handed =

325×100=3×4=12 3 25 × 100 = 3 × 4 = .

                  12%

I hope this helps!

Answer:

5

Step-by-step explanation:

The only way I know how to go about this is to multiply 2 until it becomes 32

2x2=4

4x2=8

8x2=16

16x2=32

Now just count how many 2 I used and I used 5 so the missing exponent is 5

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The number of 20 button bags are 2.

Given that, Gassama buys some bags of buttons there are 20 buttons or 21 buttons or 22 buttons or 23 buttons in each bag.

Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.

Here,

Number of 20 buttons = 20×x=20x

Number of 21 buttons = 21×5=105

Number of 22 buttons = 22×3=66

Number of 23 buttons = 23×3=69

Total = 20x+105+66+69

20x+105+66+69=280

⇒ 20x+240=280

⇒ 20x=40

⇒ x=2

Therefore, the number of 20 button bags are 2.

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