Which congruence postulate or theorem is stated below?

we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

According to the given question.

We have a function.

f(x) = x^2 + 7x  + 1

As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".

Now, we will apply the theorem for the given function f(x).

So,

f(0) = 0^2 +7(0) + 1 = 1

And,

f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145

Here,  f(0) = 1< 19< 145 = f(9).

So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.

To find, c,

We have to solve the quadratic equation f(c) =19.

This equation is

c² + 7c + 1 = 19.

Rearranging, c²+ 7c - 18=0.

Factor the expression to get

c² + 9c - 2c -18 = 0

⇒ c(c + 9) - 2( c + 9) = 0

⇒ (c - 2)(c + 9) = 0

⇒ c = 2 or -9

c = -9 is not possible beacuse it is not in the interval [0, 9].

So, the value of c is 2.

⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19

Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

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Answer:

Let Ji and Bi represent the initial amounts that Joe and Bill have at the start.  Number after J and B will be used to indicate subsequent steps in the problem.

We are told that "Joe has five times as much money as Bill," which we can write as:

   1)  Ji = 5Bi

We learn that "Joe pays Bill $5," which we can represent as:

   2)  J1 = Ji - 5

This would mean that Bill has added $5:

   3)  B1 = Bi + 5

We are then told that "Joe has just twice the amount Bill now has," which we can write as:

   4)  J1 = 2B1

===

We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)

J1 = Ji - 5                [from 2]

2B1 = Ji - 5              [Substitute 4 to eliminate J1]

Ji = 5Bi                    [from 1]

2B1 = 5Bi - 5           [Substitute 1 to eliminate Ji]

B1 = Bi + 5               [Rearrange]

2(Bi + 5) = 5Bi - 5    [Use the above expression in the previous equation to eliminate B1]

2Bi + 10 = 5Bi - 5    [Simplify]

-3Bi = -15                  [Simplify]

Bi = $5                       [Solve]

Ji = 5Bi                    [from 1]

Ji = 5*(5)                  [Since Bi = $5]

Ji = $25                    [Solve]  

===

CHECK:

Does Joe has five times as much money as Bill?

Ji = $25 and Bi = $5  YES

When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?

J1 = $25 - $5 = $20

B1 = $5 + $5  = $10    YES

Answer:

Option 3

Step-by-step explanation:

Since the denominators are the same, you can just subtract the numerators.

The length of the altitude AD is 12 units.

The height of the triangle can be found as follows:

We have to find an angle using cosine law before  we can find the height.

Therefore,

20² = 13² + 21² - 2 × 21 × 13 cos B

400 = 169 + 441  - 546 cos B

400 - 610 = - 546 cos B

-210 = - 546 cos B

cos B = -210 / -546

cos B = 0.38461538461

B = cos⁻¹ 0.38461538461

B = 67.3810899783

B = 67.38°

Hence,

sin 67.38° = opposite / hypotenuse

sin 67.38° = AD / 13

cross multiply

AD = 13 sin 67.38°

AD = 11.9999882145

AD = 12 units

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The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.

Simultaneous equation is an equation which involves the solving for two unknown values at the same time.

x + y = 3,500

x – y = 2,342

Add both be equation

x + x = 3,500 + 2,342

2x = 5,842

x = 5,842 ÷ 2

x = 2,921

Substitute x = 2,921 into

x – y = 2,342

2,921 - y = 2, 342

-y = 2,342 - 2,921

-y = -579

y = 579

Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.

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Answer:

[tex]a = 1, \ - 3[/tex]

Explanation:

[tex](a-6)(a+8) = -45[/tex]

distribute

[tex]a^2 + 8a - 6a - 48 = -45[/tex]

collect terms

[tex]a^2 + 8a - 6a - 48 + 45=0[/tex]

simplify

[tex]a^2 + 2a - 3=0[/tex]

factor

[tex](a - 1)(a + 3)= 0[/tex]

set to zero

[tex]a = 1, \ - 3[/tex]

Answer:

a = 1,  -3

Step-by-step explanation:

Given equation:

[tex](a-6)(a+8)=-45[/tex]

Expand the brackets:

[tex]\implies a^2+8a-6a-48=-45[/tex]

[tex]\implies a^2+2a-48=-45[/tex]

Add 45 to both sides:

[tex]\implies a^2+2a-48+45=-45+45[/tex]

[tex]\implies a^2+2a-3=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].  

Two numbers that multiply to -3 and sum to 2 are: 3 and -1.  

Rewrite the middle term as the sum of these two numbers:

[tex]\implies a^2+3a-a-3=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies a(a+3)-1(a+3)=0[/tex]

Factor out the common term (a + 3):

[tex]\implies (a-1)(a+3)=0[/tex]

Apply the zero product property:

[tex]\implies (a-1)=0 \implies a=1[/tex]

[tex]\implies (a+3)=0 \implies a=-3[/tex]

Verify the solutions by inputting the found values of a into the original equation:

[tex]a=1 \implies (1-6)(1+8) & =-5 \cdot 9 = -45[/tex]

[tex]a=-3 \implies (-3-6)(-3+8) & =-9 \cdot 5 = -45[/tex]

Hence both found values of a are solutions of the given equation.

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the expression is simplified to give - 39

Given the expression;

= 24- 4 to the power of 2 x 3+15

= 24 - (4^2 × 3 ) + 15

First, expand the bracket

= 24 - ( 16 × 3) + 15

Find the product of the bracket

= 24 - 48 + 15

From our knowledge of BODMAS, we add before we subtract

Now, let's add first

= 24 - 63

The, subtract

= - 39

The expression is simplified to - 39

Thus, the expression is simplified to give - 39

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Answer:

23

Step-by-step explanation:

The question gives the first equation:

0.05N + 0.10D = 2.20

It can be rewritten as:

0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.

Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.

The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.

Therefore...

N+D = 23

Answer:

C) 98

Step-by-step explanation:

Hope this helps! sry  if I'm wrong

The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.

An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.

The given equation is

15x + 120 = 5x + 1100

Take the like terms together,

15x - 5x = 1100 - 120

10x = 980

x = [tex]\frac{980}{10}[/tex]

x = 98.

Thus, the option C is correct stating that the value of x in the given equation is 98.

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The complete question is as follows:

Find the value of x in the equation:

15x + 120 = 5x + 1100.

A. 66

B. 122

C. 98

D. 76

SUBMIT.

The value of x in the system of equation is 6

The system of equations is given as:

y = 1/2 * 2^x

y = 5x + 2

Substitute y = 1/2 * 2^x in y = 5x + 2

1/2 * 2^x = 5x + 2

Multiply through by 2

2^x = 10x + 4

Next, we use the trial by error.

Set x = 6

This gives

2^6 = 10 * 6 + 4

Evaluate the product and the exponent

64 = 60 + 4

Evaluate the sum

64 = 64

Hence, the value of x in the system of equation is 6

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The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

To find the total surface area of the 27 blocks:

A cube's surface area

Given that the box's side length is 15 inches:

Surface Area of 3-inch side length blocks:

Surface Area of 4-inch side length blocks:

Surface Area of 5-inch side length blocks:

Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.

To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:

So,

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

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3/12, or 1/4 is the probability that it is blue.

What is probability?

Probability = number of successes / total number of outcomes

Total marbels in bag = 4+ 3 + 5 = 12  

A total of 12 marbles are in the bag.

3 blue marbles are in the bag.

Therefore, the probability of picking a blue is 3/12, or 1/4.

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The greatest common factor of the two expressions given as in the task content is; 3v².

It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².

15v³ and 12v²

= 3v²(5v) and 3v²(4)

= 3v²(5v) and (4)

Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².

The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's calculate its discriminant ~

[tex]\qquad \sf  \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]

[ Multiply both sides by 2 ]

[tex]\qquad \sf  \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 289 - ( - 80)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 369[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]

So, by quadratic formula :

[tex]\qquad \sf  \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]

[tex]\qquad \sf  \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]

The term that is not possible in the domain of a sequence is:

-5.

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

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Answer:

  67 square units

Step-by-step explanation:

The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.

The attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.

The approximate area is 67 square units.

Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition

[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]

where the left endpoint of the [tex]i[/tex]-th interval is

[tex]\ell_i = i - 1[/tex]

with [tex]i\in\{1,2,3,4,5,6\}[/tex].

The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,

[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]

where we use the well-known sums,

[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]

[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]

Answer:

$0.17425/Km

Step-by-step explanation:

8.5L/100Km*$2.05/L

= $0.17425/Km

See below for the combination of the arithmetic operations and exactly five 3's

The conditions are given as:

There are no direct rules to this, except by trial and error.

After several trials, we have the following operations:

(3 * 3 - 3 * 3)/3 = 0

3 - 3/3 - 3/3 = 1

(3 + 3 - 3 / 3)-3 = 2

(3 * 3 - 3 + 3)/3 = 3

3 *3/3 + 3/3 = 4

3 +3/3 + 3/3= 5

3 + 3 + (3 - 3)/3 = 6

(3^3 - 3 - 3)/3 = 7

3 + 3 + (3 + 3)/3 = 8

3 + 3 + 3+ 3 -3 =9

3 + 3 + 3 + 3/3 = 10

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Answer:

100 miles

Cost = $63

Step-by-step explanation:

Let us assume that the distance driven for both plans when they both equal in cost is X miles

Plan 1

Cost = 48  + 0.15X

Plan2

Cost = 53 + 0.1X

If they are both equal then

48 + 0.15X = 53 + 0.10X

Collecting like terms

0.15X - 0.10X = 53 - 48

0.05X = 5

X 5/0.05 = 100 miles

Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63

Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63

The height of the tree and the building are 7.6 m and 28.6 m respectively.

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

Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle BGD, CHD and AFD are similar triangles.

CH = 1.6, DH = 8, GH = 30,  GF = 105

FH = GF + GH = 105 + 30 = 135

FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38

Hence, using similar triangles:

BG/CH = GD / DH

BG / 1.6 = 38/8

BG = 7.6 m

Also:

building/CH = DF / DH

building / 1.6 = 143/8

building = 28.6 m

The height of the tree and the building are 7.6 m and 28.6 m respectively.

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Answer:

9

Step-by-step explanation:

when you divide 576 by 9 you get 64 which is a perfect cube

cbrt(64) = 4

so your answer is 9

Using the binomial distribution, we have that you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 0.2308 = 8

You would expected to draw a face card 8 times.

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Answer:

C. slope

Greetings !

The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).

Answer: slope.

Step-by-step explanation:

The Total surface area of the rectangular prism = 168 in.²

The Volume of the rectangular prism = 108 in.³

The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:

w = width of the rectangular prism

h = height of the rectangular prism

l = length of the rectangular prism

The volume of a rectangular prism = l × w × h

Find the Total surface area of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²

Find the volume of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Volume of the rectangular prism = l × w × h = 9 × 2 × 6

Volume of the rectangular prism = 108 in.³

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Answer:

4

Step-by-step explanation:

the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200

The geometric sequence when the first term is 1/5 and the common ratio is 5 is; f(n) = f(n-1) . 5.

The geometric sequence described in the task content is one whose first term is; f(1) = 1/5.

Additionally, it follows from convention that the recursive function for a geometric sequence is; a product of a previous term and the common ratio.

Hence, we have; f(n) = f(n-1) . 5.

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The price of the board game before the markup is $21.50.

Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.

Price of the item before the mark up = price the retailer sells / ( 1 + percentage)

$26.88 / 1.25 = $21.50

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The diagonals of the qudrilateral will not be perpendicular to each other.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.

The slope of a coordinate pair is given by the change in y divided by the change in x, that is:

For the diagonal AD the slope will be:-

Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )

For the diagonal BC, the slope will be:-

Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1

The multiplication of the two slopes will be,

M  =  ( 1 / 3 ) x -1 = ( - 1 / 3 )

Therefore,  the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.

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Answer:

The product of the slopes of the diagonals is -1.

Step-by-step explanation:

I had the question and got it right.

The true statement is that no number in base 10 can be written in multiple ways in base 4

The base of the numbers are given as:

Base 10 and base 4

Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers

There is only one equivalent of each number in each base.

This means that (for instance)

357 in base 10 is 11211 in base 4

The above number does not have any other representation in base 4 and it can not be written in another way.

This is the same for other numbers in base 10

Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4

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In quadrant I, [tex]\cos(A)[/tex] is positive. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]