Four pencils held together with a band

Answer:

t = b+ c

total = bags + cartons

The leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

A sheet of paper measuring 8.5 inches by 14 inches is currently in our possession. The box's volume V, measured in cubic inches, depends on the side length x, where V (x) = (14-2x)(8.5-2x)(x).

So, we have :

V (x) = (14-2x)(8.5-2x)(x)

[tex]V(x) = (14-2x)(8.5-2x)(x).\\V (x) = (14-2x)(8.5x-2x^{2} )\\V(x) = 4x^{3} -45x^{2} + 119x[/tex]

Thus, the leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

Now, we have :
[tex]V(x) = 4x^{3} -45x^{2} + 119x\\V(x) = x ( 4x^{2} -45x +119)\\V(x) = x (x-7)(4x-17)[/tex]

Now, For intercepts, V(x) = 0

[tex]V(x) = x (x-7)(4x-17) = 0\\x (x-7)(4x-17) = 0\\\\x = 0, 7, 4.25[/tex]

Now when x = 0, V(x) =0

when x = 7, f(x) = 135

when x = 4.25, f(x) = 252.89

So, the points are (7, 135) and ( 4.25, 252.89)

These points represent the value of x and their corresponding value of V.

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Answer:

[a] 15

[b] 13

Step-by-step explanation:

       We can use the visual diagram given to solve. We can see that when you input -8 (on the left side) the arrow leads to the output 15, our answer.

       We use the same method for part b. When you input 3 (on the left side) the arrow points to 13 (on the right side) giving us an answer of 13.

Work Shown:

f(x) = -2x+5

f(-9) = -2(-9)+5

f(-9) = 18+5

f(-9) = 23

Answer: Y = -2x + 1

Step-by-step explanation:

The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.

Answer:

x = √213

I would appreciate this being marked as brainliest...

Step-by-step explanation:

This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.

That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.

We can use radicals to represent the common side.

Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.

a² + b² = c²;

Substitute the first triangle.

10² + 7² = c²;

100 + 49 = c²;

149 = c²;

c = √149;

Substitute the second triangle.

(√149)² + 8² = x²;

149 + 64 = x²;

213 = x²;

x = √213;

Answer:

3 cm

Step-by-step explanation:

Given dimensions of the cuboid:

If the total surface area of the cuboid is 112 cm²:

[tex]\begin{aligned}\textsf{Total SA of cuboid}&= 2 (\sf lh +wh + lw)\\\implies 112&=2(10x+2x+10 \cdot 2)\\112&=2(12x+20)\\112&=24x+40\\24x&=72\\x&=3\end{aligned}[/tex]

Therefore, the height of the cuboid is 3 cm.

The solution to the system of linear equations 6 · x + 2 · y - 9 = 0 and y = 2 · x - 3 is (x, y) = (1.5, 0).

In this question we find a system of two linear equations and two variables, this can be done by using a Cartesian plane and drawing each line equation. The solution to the system is represented by the point of intersection of the two lines.

Therefore, the solution to the system of linear equations is (x, y) = (1.5, 0).

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The solution to the system of linear equations will be; 6x + 2y - 9 = 0 and y = 2x - 3 is; (1.5, 0).

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

To solve a system of linear equations by graphic methods: we need a system of two linear equations and two variables, using a Cartesian plane and each line equation.

The solution to the system is shown by the point of intersection of the given lines.

6x + 2y - 9 = 0

y = 2x - 3

6x + 2 (2x - 3 ) - 9 = 0

x = 1.5

(x, y) = (1.5, 0).

Hence, the solution to the system of linear equations would be; (x, y) = (1.5, 0).

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Solution of Square root,  x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30

Given,

Square root x² = 30

Then, the value of:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

x = ∛30 = ∛30² = 3.107

x = -∛30 = -∛30² = -3.107

Now,

Cube root, x³ = 30

x = √30 = √30³ = 164.317

x = -√30 = -√30³ = -164.317

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

Therefore,

Solution of Square root,  x² = 30:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30:

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

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The proportion of baby boys in the United States that are born with low birth weight is 0.0495

In a set with mean  u and standard deviation σ , the z score of a measure X is given by:

Z= X - u / σ

Z = 2.5- 3.41/ 0.55

Z= -1.6545

Z= -1.65 has a p value of 0.0495

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.

the complete question is

In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight

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The equation of parabola in vertex form is y=-3(x+2)^2+6

What is parabola and equation of parabola in vertex form?

Parabola is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The equation of parabola in vertex form is

y=a(x-h)^2+k

Given the vertex (-2,6) and (-1,3)

h=-2 and k=6

y=a〖(x+2)〗^2+6

To find the value of a at vertex (-1,3)

Put y = 3 and x = -1

3=a(-1+2)^2+6

3=a+6

a=-3

The equation of parabola is given by y=-3(x+2)^2+6

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Answer- 3,315.53007332

Step-by-step explanation:

In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .

At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have

displaymath228

The values of x and XZ, calculated by the given equations are  3 and 30 respectively.

What is a equation?

The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.

Given information (and equations) in the question:

Y is between X and Z,

XY = 19,

YZ = 2x+5,

XZ = 6x+12

Since the question say Y is between X and Z, it means:

XY + YZ = XZ

Substituting the values in this equation by the values given in the question:

19 + 2x + 5 = 6x + 12

24 - 12 = 4x

x = 3

putting the value of x in the given equation:

XZ = 6x + 12

XZ = 6(3) + 12

XZ = 18 + 12

XZ = 30

Hence, the values of x and XZ are 3 and 30 respectively.

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The length of the radius of the circle is 44cm.

This problem bothers on the mensuration of flat shapes, a circular shape.

Given data

Circumference of circle C= 88πcm

Radius of circle r=?

To find the length of the radius of the circle.

To solve for the radius let us apply the formula for the circumference of a circle

C=2πr

Substituting our given data

88π=2πr

Making r subject of formula we have

r= 88π/2π

r= 44cm

Hence, The length of the radius of the circle is 44cm.

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Answer:

6. a because a rectangle with sides 8 and 2 has a perimeter of 20 but its area is 16.

7. d because 4 is an even number and it is a perfect square.

8. b because a pen can be used to write but is not a utensil.

Step-by-step explanation:

The required value of x is 34° in figure 4, x is 57° in figure 5, x is 81° in figure 6, x is 122° in figure 7, x is 65° in figure 8, x is 54° in figure 9, x is 90° in figure 10, x is 60° in figure 11, and x is 62° in figure 12.

In any equilateral triangle, the three angles are of equal measure and they equal 60 degrees.

As per figure 4,

x° + 56° + 90° = 180

x = 180 - 146

x = 34°

As per figure 5,

x = 57°

As per figure 6,

36 + 90/2 + 180-x = 180

36 + 45 - x = 180 - 180

x = 36 + 45

x = 81°

As per figure 7,

By the property of Equilateral Triangles

⇒  x = 180 - 58

⇒  x = 122°

As per figure 8,

By the property of Isosceles Triangles

x + 115 = 180

x = 180 - 115

x = 65°

As per figure 9,

6 + x + 60 + 60 = 180

x = 180 - 60 - 60 - 6

x = 54°

As per figure 10,

By the property of Equilateral Triangles

60/2 + 60 + x = 180

x = 180 - 60 - 30

x = 90°

As per figure 11,

By the property of Equilateral Triangles

2(30) + 60 + x = 180

x = 180 - 60 - 60

x = 60°

As per figure 12,

28 + 90 + x = 180

x = 180 - 118

x = 62°

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Answer:18

Step-by-step explanation:

59 - 30 - 11 = 18

In probability , 5148 possible flushes in poker.

What is probability in math?

there are C(13,5) 5-card hands… i.e.

the number of combinations of taking 5 cards from 13 distinct cards.

But, since there are 4 suits, there are then 4*C(13,5) possible “flushes.”

Thus, there are 4*1287=5148 possible flushes in poker.

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The length is 16.6ft and the width is 8.9ft

Area of the rectangular area = Length × width

A = LW … 1

If he wants to have a rectangular area  of turf with length one foot less than 3 times the width, then

L = 3W - 1 … 2

Substitute 2 into 1

A = (2W-1)W

A = 2W^2 - W

Since area = 150sq.ft

150 = 2W^2 - W

2W^2 - W - 150 = 0

Factorize

2W^2 - W - 150 = 0

W = 1±√1+4(300)/2(2)

W =  1±√1201/2(2)

W = 1±34.655/4

W = 35.655/4

W = 8.91375

W = 8.9 (to nearest tenth)

Get the length

L = A/W

L = 150/8.9

L = 16.85

L = 16.6ft

Hence the length is 16.6ft and the width is 8.9ft

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Answer:

v = -16

Step-by-step explanation:

Move the variable to the left-hand side and change its sign, so it would then be -28 - v = -12

Then move the constant to the right-hand side and change its sign, so it would become - v = -12 + 28

Then you would calculate the sum: - v = 16

After doing so, change the sides on both sides of the equation, v = -16

So, your answer should be v = -16

The real world knowledge we use to understand the STEM task are :

A) STEM integrates it's concepts and applications to real life.

B) STEM helps in finding solution to the practical issues.

C) Focuses on building models and replicating scenarios.

What is STEM ?

STEM education refers to the integrated teaching and learning of the subjects such as science, technology, engineering, and mathematics.

We know that STEM teaches critical thinking skills and instills a passion for innovation. Beyond the advantages of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.

The real world knowledge we use to understand the STEM task is as follows :

Therefore , the real world knowledge we use to understand the STEM task are :

A) STEM integrates it's concepts and applications to real life.

B) STEM helps in finding solution to the practical issues.

C) Focuses on building models and replicating scenarios.

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To answer this question, we only need to replace x by 5, and then solve the resulting operations:

Therefore, the value for the expression 4x-13 when x = 5 is equal to 7.

⇒Vertical angles are equal .

This means that ∠1=∠2

⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.

[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]

x=23°

To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:

[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]

∠1=127°

The equation y = 2/3x + 1  has a solution of (6, 5) and not (9, 8)

From the question, the equation is given as

y = 2/3x + 1

Also, we have the ordered pairs to be

(6, 5) and (9, 8)

For (6, 5), we have

x = 6 and y = 5

So, the equation becomes

5 = 2/3 x 6 + 1

Evaluate

5 = 5 --- true

For (9, 8), we have

x = 9 and y = 8

So, the equation becomes

8 = 2/3 x 9 + 1

Evaluate

8 = 7 --- false

Hence, (6, 5) is part of the solution and (9, 8) is not

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In a case whereby Kaylie is 6 years old and  Her sister, Amanda is 2x younger. Kaylie is now 36 the, Amanda age will now be expressed as  33 years.

This implies that when  Kaylie is 6 years old  then her  Her sister, Amanda will be 6/2 = 3 years old.

Then we were told again that Kaylie is now 36, then the age of Amanda will now be (36-3)= 33 years

This is because when Kaylie was 6 years old , she was older by her sisiter by just just 3 years, which is still the same when she grown in age again, the 3 years interval is maintained.

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The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]

                                                = 500 hours

Mean service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]

                                                  = 515 hours

Mean service life of sample 3 =  [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]

                                                  = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]

                                               = 500 hours

Mean service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]

                                                 = 515 hours

Mean service life of sample 3 =  [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]

                                                 = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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Answer:

1 41/100

Step-by-step explanation:

Answer:

141/100 (Already in simplest form). As a mixed number, it is: 1 41/100

Step-by-step explanation:

Answer:

b=2

z=3

again b=2

d=3

Step-by-step explanation:

don't know what to explain

S={7}

1) Let's solve for x, for the given equation :

-x = 6 -3x +8 Add 3x to both sides

3x-x=-3x+3x +6 +8

2x =14 Divide both sides by 2

x= 7

S={7}

And that is the answer