problem 4: Solve for x ​

Answer:

10,25, and 145

Step-by-step explanation:

to see if it can make a triangle you have to add 2 of the angles together and it has to be more than the other angle

(ex:40+70>65)

a triangle

(ex:10+25<145)

not a triangle

Given AC=BD.It is also said AB and CD bisect each other.

Since AB and CD bisect each other at O, we can write

AO=OB

CO=OD

Since the three sides of triangle AOC is equal to the corresponding sides of triangle BOD, both the traingles are congruent.

The angles opposite to equal sides of triangles are also equal.

Since AO and

Answer:

63.04728546 miles an hour

Step-by-step explanation:

By evaluating h(x) in x = ^-3 and then squaring it, we will see that:

h(-3) = 1,600

Here we have the function:

h(x) = 2x^2 - 5x + 7

First let's evaluate it in x = -3, to do so we just need to replace the variable x by the number 3, we will get:

h(-3) =2*(-3)^2 - 5*-3 + 7

h(-3) = 2*9  + 15 + 7 = 18 + 15 + 7

h(-3) = 40

Now we square it:

h(-3)^2 = 40^2

h(-3)^2 = 1,600

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The probability that a cookie is randomly picked and it does not contain chocolate or nuts will be 0.52

As per the question statement, a box of assorted cookies has 36% of them containing chocolate and 12% containing nuts, and of those, again 8% contain both chocolate and nuts, and we are assuming that the rest of the cookies neither contain chocolate, nor nuts.

Based on the conditions and our assumptions provided in the above mentioned statement, we are required to calculate the probability that a cookie is randomly picked and it does not contain chocolate or nuts.

Considering the total number of cookies in the box to be 100%, since 36% of them containing chocolate and 12% containing nuts and the rest of the cookies are assumed to contain neither chocolate, nor nuts,

The probability that a cookie is randomly picked and it does not contain chocolate or nuts will be [{100 - (36 + 12)}/100]

                                      = [(100 - 48)/100]

                                      = (52/100)

                                      = 0.52

Probability: It is a branch of Mathematics, that deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.

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f(x) = -x² - 4x - 1 is the equation of the parabola in the graph.

From the graph, the parabola passes through point (-1,2) and has a vertex at point (-2,3).

For a parabola with a vertex (h,k), the general equation is expressed as;

y = a( x - h)² + k

First we find 'a', plug in the given coordinates into the equation.

y = a( x - h)² + k

2 = a( -1 - (-2))² + 3

Solve for a

2 = a( -1 + 2 )² + 3

2 = a( 1 )² + 3

2 = a + 3

a = 2 - 3

a = -1

Now substitute the vertex (-2,3 and a ( -1 ) into the general equation.

y = a( x - h)² + k

y = -1( x - (-2))² + 3

Simplify

y = -1( x + 2 )² + 3

Expand using FOIL method

y = -1( (x + 2)(x+2) ) + 3

y = -1( x² + 2x + 2x + 4 ) + 3

y = -1( x² + 4x + 4 ) + 3

Apply distributive property

y = -x² - 4x - 4 + 3

Add like terms

y = -x² - 4x - 1

f(x) = -x² - 4x - 1

Therefore, the equation of the graph is f(x) = -x² - 4x - 1.

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An item is regularly priced at $78. Martina bought it at a discount of 80% off the regular price. Martina paid $15.6

Sales price:  The price that is paid by the buyer at the time when something is sold: People who sold their homes through real estate agents typically did not get a higher sale price than people who sold their homes themselves

The formula for calculating sales price of an item is:

s=p-(p x d)

where,

s is the sales price (which we are going to calculate in this problem)

p is the regular price of the item which is $78

d is the discount rate which is 80%

which means out of 100 = 80/100

substitute the above values in the formula then we get

s=$78-($78 x 80/100)

s=$78-($6240/100)

s=$78-$62.4

s=$15.6

Martina paid $15.6

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Answer:

5.87 x [tex]10^{-17}[/tex]

Step-by-step explanation:

You need to write the number as 1 or larger than 1, but less than 10.  That means that I need to put the decimal between the 5 and the 8.  Now I have to count how many places I moved the decimal.  I think that I counted right.  It was moved 17 places.  Since the number in standard form is much smaller than 5.87, the exponent will be negative.

Answer:

B. Distributive

Step-by-step explanation:

Hello, there!

The number outside of the parentheses are being multiplied within the parentheses separated by a symbol, so distributive. (:

Hope this helped, and best of luck with the rest of your assignment.

area = 78.5 ft squared

diameter = ?

Given the exponential model:

Where A is the initial condition, b is the growth factor and x is a time-like variable.

We know that the growth factor is 1.9 and that 1500 people died of AIDS in 1983. If we make x to be the years passed since 1983, then 1500 is our initial condition (because 0 years passed). In our model:

For 2005, x = 22:

The volume of the spherical rubber ball to the nearest cubic inch is 87.11 cubic inches.

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements for sphere volume include m^3, cm^3, and in^3.

The formula of volume of the sphere is

V = 4/3πr3

given that the radius of spherical rubber ball is 2 3/4

here the radius is given in improper fraction

now convert it into the decimal by following procedure.

first multiply the 2 with 4

2 X 4 = 8

now add 8 to 3. 8 + 3 = 11

The proper fraction of 2 3/4 is 11/4.

so, the decimal number is 2.75

now put r = 2.75 in formula to get the volume.

V = 4/3 X 3.14 X 2.75 X 2.75 X 2.75

V = 1.33333 X 3.15 X 20.7968

V = 87.11 cubic inches

Hence,the volume of the spherical rubber ball to the nearest cubic inch is 87.11 cubic inches.

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10 different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it

Permutations and combinations are the many methods for picking objects from a set to form subsets, usually without replacing them. When the order of selection is a factor, this selection of subsets is known as a permutation; when the order of selection is not a factor, this selection of subsets is known as a combination.

I think it is only 10 ways.

Put the teal bead on first. It is the marker bead. This takes care of the rotation aspect.

Then you have 2 lots of 3 identical beads. so that is 6!/(3!3!) ways to place them. Which is 20 ways.

But the bracelet can be flipped so I think this will halve the number of possibilities

For instance  TOOOBBB is the same as TBBBOOO

So I think the answer is 10 ways.

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Answer:

Step-by-step explanation:

We are given the volume formula:

Find the height:

Substitute all into formula:

You may keep it as is or simplify:

To solve this problem we must take into account that the y-axis has intervals of 2 units length, and the x-axis has intervals of 1 unit length. We want to know the value of the function when x = 2, so we look for that value of x in the x-axis, we trace a vertical line from x = 2 to the curve that represents the function, and then a horizontal line to the y-axis, and we read the value of y:

Answer: D. 9

Slope m is positive when

x₁≥ -2

y₁ ≥ -5

Slope, usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine slope. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope, if you view the line from left to right.

Given,

Point (-2. -5)

Slope = [tex]\frac{y_{1}-(-5) }{x_{1}-(-2) }[/tex]

Slope = [tex]\frac{y_{1}+5 }{x_{1}+2 }[/tex]

Slope m is positive when

x₁≥ -2

y₁ ≥ -5

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The total earnings of the bus driver in a year is $28500.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The bus driver works 2000 hours each year and makes $14 per hour.

If the bus driver gets $50 for each new recruit he hired.

Let y be his total earnings and x be the number of new drivers he recruits.

Then his total earnings can be represented by the function:

y = 14 × 2000 + 50 × x

If the bus driver recruits x = 7 new drivers.

y = 28000 + 50 × 7

y = 28000 + 350

y = $28350

The total earnings of the bus driver are $2850.

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1) The equation of line is; y = (1/3)x + 1

2) The x - intercept is -3 and the y-intercept is 2

3) Area of CAT is; 6 sq.units

4) Perimeter is; 14.325 units

1) The coordinates of the line AC on the graph are;

A(-3, 0) and C(3, 2)

Thus, equation of line is gotten from the formula;

(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)

(2 - 0)/(3 + 3) = (y - 0)/(x + 3)

2/6 = y/(x + 3)

3y = x + 3

y = (1/3)x + 1

2) The x - intercept is -3 and the y-intercept is 2

3) Area of CAT is;

Area = 1/2 * base * height

Area = 1/2 * 6 * 2

Area = 6 sq.units

4) Perimeter of ACT is gotten by;

AT + CT + AC

AC = √((2 - 0)² + (3 + 3)²)

AC = √40

Thus;

Perimeter = 2 + 6 + √40

Perimeter = 14.325

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Answer: y = x +8

Step-by-step explanation:

The equation of the line is y = 1/3x - 7

Linear equations are equations that have constant average rates of change.

The given parameters are

Slope, m = 1/3

y-intercept, c = -7

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

Where m =  1/3 and c = -7

So, we have

y = 1/3x - 7

Hence. the linear equation is y = 1/3x - 7

See attachment for the graph

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If I dilate a number by 1 half, then I will have to dilate it again by 2, to get the same to the same number.

As per the question statement, I dilate a number by 1 half.

We are required to calculate that by what should I dilate the result, to reverb back to the same number that I started with.

To solve this question, first we need to understand the concept of Dilation.

Here, since our first dilation of the original number, say "x" reduces it by 1 half, that is, x becomes (x/2),

To get back to x, we will need to multiply (x/2) by 2 again.

[(x/2) * 2] = x.

Therefore, I will need to enlarge our result with a multiplication with 2 to get back to our original number.

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[tex]2x(4x - 3) + 5(4x -3 ) \\ = {8x}^{2} - 6x + 20x - 15 \\ = 8 {x}^{2} + 14x - 15[/tex]

ATTACHED IS THE SOLUTION

Answer:

I think it would be 8x2^ + 14x − 15

We take a look at the reduction in the area of the bacteria.

In the first hour, its arae is 20cm2. Following that, it reduces 1.25x, to 16. Then another 1.25x, from 16 to 12.8. And another 1.25x, from 12.8 to 10.24.

So, every hour, the bacteria's area reduces by 1.25x
Therefore, in the 5th hour (prediction probably if this is all a coincidence), the bacteria's area will be : 10.24 : 1.25 = 8.192 cm2.

Given

You throw the bowling ball at the pins.You have two throws to knock down ten pins.

Procedure

The events are not independent. Before the first throw, there will be 10 pins to knockdown. Let the number of pins knocked down in the first throw is x.

In the second throw, there will not be 10 pins to knockdown. The number of pins to knockdown in the second throw depends on the number of pins being knocked down in the first throw. Hence, the number of pins to knockdown in the second throw is (10 - x). Thus, the events are dependent

Answer: 104.3

Step-by-step explanation: To divide a decimal by another decimal: Move the decimal point in the divisor to the right until it is a whole number.

The best approach to provide an answer to the question would be: Calculate a confidence interval using t*

The confidence interval is often used to obtain the true population mean. The question asks us to identify evidence that points to the fact that the mean amount of water drank by each teenager is more than 1.5 liters.

We are here searching for the true population mean. We calculate a confidence interval using t when the population variance is not known as is the case here. So, to solve this question, we would calculatethe confidentce interval using t*.

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The answer is C y=x+8

If this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.

In the given question,

A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.

We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.

From the question,

Mean [tex]\mu=22[/tex] minutes

Standard deviation [tex]\sigma=6.9[/tex] minutes.

Since the given percentage is [tex]1\%[/tex] and percentage means division of [tex]100[/tex] so we can write [tex]1\%=1/100=0.01[/tex]

So the one percent of response times take at least how many minutes is

[tex]P(x\geq a)=0.01[/tex]

[tex]P(x\geq \frac{a-\mu}{\sigma})=0.01[/tex]

As we know the all values. SO putting the values in the formula

[tex]P(x\geq \frac{a-22}{6.9})=0.01\dots\dots[/tex]Equation 1

From the z table

[tex]P(z\geq 2.33)=0.01\dots\dots[/tex]Equation 2

Now from Equation 1 and Equation 2

[tex]\frac{a-22}{6.9}=2.33[/tex]

Multiply by [tex]6.9[/tex] on both side

[tex]\frac{a-22}{6.9}\times6.9=2.33\times6.9[/tex]

Simplifying

[tex]a-22=2.33\times6.9[/tex]

[tex]a-22=16.077[/tex]

Add [tex]22[/tex] on both side

[tex]a-22+22=16.077+22[/tex]

[tex]a=38.077[/tex]

Hence, if this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.

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