Solve for z in -3 < z-1 < 3.Give the result in the interval notation and graph on a number line

On solving the equation [tex]v=u+at[/tex] for t the result will be [tex]t=\frac{v-u}{a}[/tex].

How to solve any mathematical equation?

1. Open all brackets by applying the distibutive property.

2. Add the same number on the both sides.

3. Subtract the same number on the both sides.

4. Multiply with the same number on the both sides.

5. Divide with the same number on the both sides.

Consider the equqtion.

[tex]v=u+at[/tex]

Subtact [tex]u[/tex] from both the sides.

[tex]v-u=u+at-u\\v-u=at[/tex]

Now, divide both the sides by [tex]a[/tex].

[tex](v-u)/a=at/a\\(v-u)/a=t\\t=(v-u)/a[/tex]

Hence, on solving the equation [tex]v=u+at[/tex] for t the result will be [tex]t=\frac{v-u}{a}[/tex].

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Solve for y

Subtract 4x both sides

Divide by 3 into both sides

Answer:

If ED is the midsegment of triangle ABC, then that means that the points E and D are the midpoints of segments AC and AB since the midsegment is found by joining the midpoints of a triangle. Since E and D are midpoints then:

Also, by the midsegments theorem we have:

Also, since segments ED and BC are parallel, that means that:

Answer:

x = 3

y = -1

Step-by-step explanation:

x-y=4 [1]

2x+y=5 [2]

rearrange [1] and label it [3]

x = 4 + y [3]

substitute [3] into [2]

2(4 + y) + y = 5

8 + 3y = 5

3y = -3

y = -1

substitute y = -1 into [1]

x - (-1) = 4

x = 3

Answer: $1.33

This can be worked out as a simple algebra problem: 15x=20, x being 1 pizza dough. In order to find the value of one pizza dough (x) you need to isolate it. To do that, divide 15 from both sides and you'll be left with x=1.33

15x=20

/15   /15

x=1.33

Given

A = (3.5, 2.2)

B = (1.5, -4.8)

Procedure

A midpoint is a point on a line segment that divides the segment into two equal segments.

Answer:

X = 9
Landyn is 9 and his brother is 14

Step-by-step explanation:

X + Y = 23
Y = X + 5
X + X + 5 = 23
2x + 5 + 23

     - 5   - 5  

2x / 2 = 18 / 2

Simplified = 9 / 1
Y = 9 + 5
Y = 14

Age and you can also use weight too

you can easily group people by their age and weight but not by eye color

example

age people

5 - 10 14

10 - 15 5

the table above shows that we have 14 people within the range of 5 to 10 years

and likewise the weight of the people can serve the same purpose

Given the function:

To graph the given function, first, we will graph the parent function [ cot x]

the function [cot x] has a period of π and has an x-intercept at x = π/2

then we will make a shift to the left side by (π/6)

the graph of the function will be as shown in the following picture:

As shown, the red dot graph is the function [cot x]

and the blue graph is the given function f(x)

The equation of the line that passes through the point (-4, -5) and is parallel to y = 1/2x -4 is y = 1/2x - 3

From the question, we are to determine the equation of the line that passes through the given point and is parallel to the given equation.

The given point is (-4, -5)

The given equation is y = 1/2x - 4

NOTE: If two lines are parallel, then their slopes are equal

Now, we will determine the slope of the given line '

y = 1/2x - 4

Compare to the general form of an equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

Therefore, m = 1/2

That is, the slope of the line is 1/2

Now, we will determine the equation of the line that has a slope of 1/2 and that passes through the point (-4, -5)

Using the point-slope form of the equation of a straight line

y - y₁ = m(x - x₁)

Then,

y - (-5) = 1/2(x - (-4))

y + 5 = 1/2(x + 4)

y + 5 = 1/2x + 2

y = 1/2x + 2 - 5

y = 1/2x -3

Hence, the equation of the line is y = 1/2x - 3

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Solution

Total cards in a deck = 52

Total Queens = 4

Total King = 4

Total Ace = 4

P(Queen, King, or Ace). =

The answer is 3/13

The excise tax on 1 gallon of gasoline = 18.2 cents

You will buy 18.5 gallons

We need to find the excise tax you should pay

At first let us change the cent to dollar

1 cent = 1/100 dollars

18.2 cents = 18.2 * 1/100 = 0.182 dollars

Now you will buy 18.5 gallons

You will pay = 18.5 * 0.182 = 3.367 Dollars

The state excise tax = $3.367

Round the number to the nearest cent, then it will be $3.37

Answer:

$2.90

Step-by-step explanation:

87 cents / 3 packs = 29 cents per pack

$0.29 × 10 = $2.90

From the given information, we know that the expression that models the population of amoebas with respect to time is:

Where x is the number of hours. by replacing 9 for x, we can find the population after 9 hours, like this:

Then, the population of amoebas after 9 hours is 5832.

The rules of the transformations using the translation notation are;

11) [tex]T_{(2, \,-1)}[/tex]

12) [tex]T_{(-5, \,2)}[/tex]

13) [tex]T_{(-1, \,3)}[/tex]

14) [tex]T_{(0, \,-1)}[/tex]

15) [tex]T_{(3, \,4)}[/tex]

16) [tex]T_{(-3, \,1)}[/tex]

17)  [tex]T_{(1, \,0)}[/tex]

18) [tex]T_{(6, \,-5)}[/tex]

19) [tex]T_{(4, \,0)}[/tex]

20) [tex]T_{(2, \,4)}[/tex]

21) [tex]T_{(1, \,-5)}[/tex]

22) [tex]T_{(5, \,-1)}[/tex]

23) [tex]T_{(0, \,-1)}[/tex]

24) [tex]T_{(-2, \,-1)}[/tex]

25) [tex]T_{(-3, \,-2)}[/tex]

A translation transformation is a rigid transformation in which the location of the image obtained from the pre-image is different, but the dimensions are the same.

11) The transformation is similar to a rigid transformation

The change in coordinate is from (2, 2), to (4, 1), which is a translation 2 units to the right and -1 unit down

12) The shape is preserved and the length of the sides are also preserved, therefore, the transformation is a rigid transformation, with a change from (5, 3) to (0, 5), which is a translation 5 units to the left  and 2 units up.

13) The change in the coordinates from the pre-image to the image are from V(-3, 2) to V(-4, 5), which is a transformation of 1 unit to the left and 3 units up

14) The coordinates of a point on the pre-image is T(-5, 2), and the coordinates of the corresponding point on the image is T'(-5, 1), which is a translation of one unit downwards, [tex]T_{(0, \,-1)}[/tex]

15) A point on the pre-image is T(-3, -1), the corresponding point on the image is T'(0, 3), which indicates that the rule for the transformation is a translation of 3 units to the right and a vertical translation of 4 units upwards

16) The difference between the x and y values are;

Δx = 0 - 3 = -3

Δy = -3 - (-4) = 1

The transformation is therefore of the form [tex]T_{(-3, \,1)}[/tex], which is a translation of 3 units to the left and 1 unit upwards

17) The change in the x and y values are;

Δx = -2 - (-3) = 1

Δy = -3 - (-3) = 0

The rule of the transformation is therefore of the form [tex]T_{(1, \,0)}[/tex], which is a translation one unit to the right.

18) The change in the x and y values of the transformation are;

Δx = 1 - (-5) = 6

Δy = -4 - 1 = -5

The rule of the transformation is therefore, [tex]T_{(6, \,-5)}[/tex], which is a translation of 6 units to the right and 5 units down

19) The transformation of J(-5, 3), K(-3, 5), L(0, 1) to J'(-1, 3), K'(1, 5), L'($, 1) is a transformation of the form [tex]T_{(4, \,0)}[/tex] which is a horizontal translation 4 units to the right

20) H(-4, -3), I(-5, 0), J(-3, 0), K(-2, 1) to H'(-2, 1), 'I(-3, 4), J'(-1, 4), K'(0, 5) The transformation rule is [tex]T_{(2, \,4)}[/tex], which is a translation 2 units to the right and 3 units up

21) E(0, 1), F(-1, 5), G(0, 5), H(3, 2), to E'(1, -4), F'(0, 0), G'(1, 0), H'(4, -3), which is a transformation with the rule, [tex]T_{(1, \,-5)}[/tex], which is a translation one unit to the right and five units down

22) B(-4, -2), C(-3, 3), D(-2, 1) to B'(1, -3), C'(2, 2), D'(3, 0), which is a transformation of the form [tex]T_{(5, \,-1)}[/tex], which is a translation of 5 units to the right and 1 units down

23) I(2, 1), H(4, 4), G(5, 0) to  I'(2, 0), H'(4, 3), G'(5, -1), which is a transformation with the rule [tex]T_{(0, \,-1)}[/tex], which is a translation of one unit down

24) X(1, -4) W(3, 0), V(3, -4) to X(3, -5) W(5, -1), V(5, -5), which is a transformation with the rule, [tex]T_{(-2, \,-1)}[/tex], which is a translation of 2 units to the left and 1 units down

25) G(1, -1), F(2, 3), E(4, 2), D(4, -3) to G'(-2, -3), F'(-1, 1), E'(1, 0), D'(1, -5) which is a transformation with the rule, [tex]T_{(-3, \,-2)}[/tex], which is a translation of 3 units to the left and 2 units down

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Answer:

length = 12 miles

width = 6 miles

Step-by-step explanation:

        length = x miles

       width = (x - 6) miles

  Area of rectangle = 72 square miles

         length * width = 72

           x * (x - 6)        = 72

          x*x - 6*x          = 72

             x² - 6x - 72 = 0

Sum = -6

Product = -72

Factors = 6 , (-12)         { 6 + (-12) = -6 and 6*(-12) =-72 }

Rewrite the middle term using the factors.

x² + 6x - 12x - 72 = 0

x(x + 6) -12(x + 6) =0

(x + 6)(x - 12) = 0

    {x + 6 = 0 is rejected as length will not have negative value}

x - 12 = 0

     [tex]\sf \boxed{\bf x = 12 \ miles}[/tex]

length = 12 miles

Width = 12 - 6 = 6 miles

The function describes the motorboat's distance from the shore

y = -4x+50

Given,

In the question:

A motorboat moves across a lake as a constant speed. when it begins, it is 50 km from the shore

After 9 minutes, it is 14 km from the shore.

So, The rate of change =

                 =   [tex]\frac{Final Distance - initial distance}{time} \\\\\frac{14-50}{9} = -4[/tex]

Negative sign shows that there is decrease in distance per minute

The rate of change of distance is 4 km / minutes

General equation : y = mx+ c

Where m is the slope and c is the constant

Substitute the values in the equation :

y= -4x +50

Where y is the final distance and x is the minutes

So, Option C is true

Hence, The function describes the motorboat's distance from the shore

y = -4x + 50.

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The volume of a sphere is (4/3)(Pi)(r^3)

If the ball has a diameter of 27 cm, the radius would be 27/2 = 13.5 cm

Unsing the formula:

V = (4/3)(3.1416)(13.5)^3 = (4/3)(3.1416)(2460.375) = 10306.0188

Answer: Volume is 10,306.0188 cm^3

Answer: 8.953333333.

Step-by-step explanation: All I know is that a negative divided (or times) a negative is always a positive.

Answer:

x = 10

Step-by-step explanation:

2(2x-14) = x+2

4x - 28 = x + 2

3x = 30

x = 10

Answers:

We see that ∠2 and ∠3 are corresponding angles

And since the lines u and v are parallel, ∠2 and ∠3 are congruent.

So, m∠3 = 150

We see that ∠1 and ∠2 are vertically opposite angles

Thus, ∠1 and ∠2 are congruent

So, m∠1 = 150

The relationship between ∠1 and ∠3 is an example of the following rule

When parallel lines are cut by a transversal, alternate interior angles are congruent.

Explanation:

The angles formed by two parallel lines and a transversal that are on the same side of the transversal and in the same position from the parallel lines are called corresponding angles. These angles have the same measure so they are also congruent.

So, we can fill the first part as:

We see that ∠2 and ∠3 are corresponding angles

And since the lines u and v are parallel, ∠2 and ∠3 are congruent.

So, m∠3 = 150

On the other hand, two opposite angles formed by two lines that cross are called vertically opposite. So, these angles have the same measure.

So, we can fill the second part as:

We see that ∠1 and ∠2 are vertically opposite angles

Thus, ∠1 and ∠2 are congruent

So, m∠1 = 150

Finally, we can fill the third part as:

The relationship between ∠1 and ∠3 is an example of the following rule

When parallel lines are cut by a transversal, alternate interior angles are congruent.

Because alternate interior angles are the angles that are inside the parallel line and on opposite sides of the transversal.

There is no statistical evidence of a prolonged lifetime of the stents.

Given data,

n (sample size) = 100

X (sample mean) = 9.3

s (sample standard deviation) = 3.8

Next, we need to define the null hypothesis and alternative hypothesis

Null hypothesis

[tex]H_{o}[/tex] : u (mu) = 8.7

Alternative hyptohesis

[tex]H_{o}[/tex] : u (mu) > 8.7

Next, we need to do hypothesis testing to get the claim about a population mean is tested under the null and the alternative hypotheses by using t-test and p-value.

t-test is a sampling test statistic and used when the population standard deviation is unknown.

the t-test can be calculated as follows:

= [tex]\frac{X-u}{s/\sqrt{n} }[/tex]

= [tex]\frac{9.3-8.7}{3.8/\sqrt{100} }[/tex]

= 1.578

Next, we need to calculate the p-value using Microsoft excel function. The p-value helps decide whether to reject the null hypothesis.

Enter the function below in excel to calculate p-value:

=TDIST(1.578,40-1,1)

= 0.061322.

The p-values is greater than the common threshold ( p<0.05), which means We can conclude that there is no statistical evidence of a prolonged lifetime of the stents.

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the given expression is,

16x = 156.8

x = 156.8/16

x = 9.8

thus, the answer is 9.8

Answer:

x = 9.8

Step-by-step explanation:

16x=156.8

x = 156.8/16

x = 9.8

divyaraval92, this is the solution:

False

x could be either 6 or -6

The number of ways the customer can select 4 appetizers , 4 main course and 4 desserts for a banquet is 220500 ways .

In the question,

it is given that ,

number of appetizers that catering service can offer = 6

number of main courses that catering service can offer = 8

number of desserts that catering service can offer = 4 ,

The number of ways 4 appetizers can be selected out of 6 = ⁶C₄

number of ways 4 main courses can be selected out of 8 = ⁸C₄

number of ways 4 desserts can be selected out of 10 = ¹⁰C₄

So , total number of ways = ⁶C₄ × ⁸C₄ × ¹⁰C₄

= 15 × 70 × 210

= 1050 × 210

= 220500 ways

Therefore , The number of ways the customer can select 4 appetizers , 4 main course and 4 desserts for a banquet is 220500 ways .

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Answer:

3.88

Step-by-step explanation:

Find the number in the hundredth place (7) and look one place to the right for the rounding digit 5. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

The expression to represent the change in elevation would be 13 - 150.

The change in elevation would be - 137 feet.

The change in elevation refers to the difference between the elevation that a person ends up in, from the elevation that they started out at.

The change in elevation for the goat would therefore be:

= Ending elevation - Starting elevation

= 13 - 150

= - 137 feet

In conclusion, the change in elevation of the goat in its travels was - 137 feet.

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Solution

We have

square will cancel out the square root

Option A

Answer:

24:14

Step-by-step explanation:

According to the diagram, we can conclude: