Given g(x) = -5x + 1, find g(1).

The length of the side  BC Iis equal to 28 units which we get by using congruency.

In other words, if the lengths of the sides and angles are the same for two shapes, they are congruent (the same in shape and size). When two triangles are congruent, it is frequently useful to know.

* In triangle ABC

∵ Angles B and C comes to be congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect same terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both the sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of side BC

∵ The length of side BC = 4x ⇒ substituting the value of x

∴ The length of side BC = 4 × 7 = 28 units

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What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.

xy + xz is an even integer & x is even and y + xz is an odd integer &  either (x-1) is even or (y-z) is even .

1. xy + xz is an even integer - SUFFICIENT

Given:

xy + z is odd ...(i)

xy + xz is even ...(ii)

subtracting (ii) from (i)

we get xz - z, which should be odd (* since odd - even = odd)

=> z(x-1) is odd

=> both z and (x-1) is odd

=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT

Given:

xy + z is odd ...(i)

y + xz is odd ...(ii)

subtracting (ii) from (i)

we get xy + z - y - xz

= (x-1)(y-z) , which should be even

=> either (x-1) is even or (y-z) is even ....insufficient to determine

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The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)

A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.

A formula would just be 3x - 5 = 16, for instance.

When this equation is solved, we observe that the value of the variable x is 7.

So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.

If the f (x) equation contains (x, y).

Therefore, the f^-1(x) equation is as follows: (y, x).

Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).

So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x)  goes through.

Therefore, the positions through which the equation of f^-1(x) travels are:

(4, 1), (6, 4)

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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?

26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

We have given that standard deck of 52 cards.

And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.

So four hearts + four diamonds + five clubs = 13 cards

The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.

So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26

Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

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Answer:

The change in temperature is -6.64

The average hourly rate of change is

6 hours or -3.32

Answer:

Step-by-step explanation:

1593/13

122.538

answer: 122.5

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Z is the incenter of WXY.

m∠WYX = 86

This means,

m∠WYZ = m∠XYZ = x

m∠WYZ + m∠XYZ = m∠WYX

2x = 86

x = 43

m∠WXZ = 33.

m∠WXZ = m∠WXY

Now,

The triangle WXY.

m∠YWX + m∠WXY + m∠WYX = 180

m∠YWX + 33 + 86 = 180

m∠YWX = 180 - 119

m∠YWX = 61

m∠ZWX = 61/2 = 30.5

Thus,

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

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The best way is to pick the one you think has a higher chance

The probability that the married couple will have adjacent desks is 0.22.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.

= 8 x 7! x 2

= 80640

Ans the total number of possible arrangements is 362880.

= 9!

= 362880

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 80640/362880

probability = 0.22

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The correct answer is this inequality {x | x > -6}

What does a math inequality look like?

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Given that:

-6x < 36

we multiply -1 on both the sides

6x > -36

divide 6 on both the side

x > -6

Hence the correct answer is this inequality {x | x > -6}.

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Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.

The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.

Joni calculated and she'll have a final balance of $230 after three years.

The steps are as following,

Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.

The yearly compound interest rate if 5% is stated above.

As a result, she ought to have used the compound interest calculation when calculating.

A = P(1 + r/n)∧(nt)

Amount then becomes:

A = 200(1 + 0.05)³

A = $231.53.

Thus, final amount will be obtained as  $231.53.

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The complete question is-

Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.

answer:

20-5y+2x=52

step-by-step explanation:

plug in the values of x & y into the expression and calculate using the order of operations to get the answer. hope that helps!

Answer: 52

Step-by-step explanation:

1. plug in x and y into the expression : 20 - 5(-4) +2(6)

2. multiply the numbers in the parenthesis:  20 + 20 + 12
3. add all the numbers together (simplify): 52

Answer: 24 26 37 60

Step-by-step explanation: im sure

The value x of the trapezoid is 3 units.

A trapezoid is a quadrilateral with at least one pair of parallel sides .

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.

The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.

Therefore,

29 = 1 / 2 × (23 + 11x + 2)

29 = 1 / 2 × (25 + 11x)

cross multiply

29 × 2 = 25 + 11x

58 = 25 + 11x

58 - 25 = 11x

33 = 11x

divide both sides by 11

x = 33 / 11

x = 3

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Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

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The number of days that the second voyage last's is 480 days.

Given,

The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.

We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.

We are aware that the first journey lasted 43 days longer than the second.

In mathematics, f = 43 plus s. (I)

The cumulative duration of the two journeys was 1003 days. Mathematically:

f + s = 1003........(ii) (ii)

We transform I into ii

43 + s + s = 1003

43 +2s = 1003

2s = 1003 - 43

2s = 960

s = 960/2 = 480 days

That is,

The second voyage lasted about 480 days

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After solving the equation in terms of y will be y = (2/3)x - 4/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equation is,

6x - 9y = 12

Then, the equation in terms of y will be,

9y = 6x - 12

Divide the above equation by 3,

3y = 2x - 4

y = (2/3)x - 4/3

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The probabilities when choosing a card of the respective color are

1/26, 1/8, 3/169, 1/676

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

Multiply the total number of possible outcomes by the total number of occurrences. Divide the entire number of ways the event can occur by the total number of potential outcomes after determining the probability event and its related consequences.

The probabilities are:-

p= (1/13)*(1/2)=1/26

p=(1/2)*(1/4)=1/8

p=(1/13)*(3/13)=3/169

p=(1/52)*(1/13)=1/676

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Answer:

-2n+4

-2×54+4

-108+4

-104

By evaluating the function we will see that the difference is:

f(1) - f(-7)  = 3

Here we have a piecewise function, this is a function that behaves differently on different intervals of its domain.

On the image you can see the different pieces of the function, and on the right the domain of each of the pieces.

The first part works for all the values smaller than -4 and x = -4.

So if we want to evaluate the function in x = -7, we need to use that piece:

f(-7) = |-7 + 5| - 9 = -7

And the second piece works on the interval (-4, 1], so to evaluate in x = 1 we need to use that piece.

f(1) = -1³ - 3*1 = -4

Then the difference is:

f(1) - f(-7) = -4 + 7 = 3

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Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.

Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.

So, the weight of the person will be:

The scale measures the passenger's normal upward force as it is applied by the floor.

When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).

When there is a downhill acceleration, the normal force is at its lowest.

For any such circumstance:

∑F y​ =ma y  becomes for starting  +591N−mg=+ma and for stopping      +391N−mg=−ma.

Where a stands for the acceleration's magnitude.

To get rid of a and find mg, add these two simultaneous equations:

+591N−mg+391N−mg=0

OR

982N–2mg=0

Fg​ = mg = 982N/2​ = 491N

Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.

Answer:

eighty-four thousand fifty-two

Step-by-step explanation:

the way i think about it is writing it as the sum of the digits together.  

80000+4000+50+2

eighty-four thousand fifty-two

Answer: Welp, here it is.

Step-by-step explanation:

I clicked the keyboard :)

hhhhhhhhhhhhhhhhhhhhhhhhh

The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.

Here, we are given that a fair coin is tossed 130 times.

Thus,

number of trials ⇒ n = 130

p = P(getting tails in a single toss) = 0.5

mean of a binomial distribution = np

= 130*0.5

= 65

variance = np(1-p)

= 65*0.5

= 32.5

standard deviation = sqrt(variance)

= sqrt(32.5)

= 5.7

Now, x = number of tails

X follows a normal distribution with mean 65 and variance 5.7

P(70 < x < 82)

= P( 69.5 < X < 82.5)  [applying continuity correction]

= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]

= P(0.79 < Z < 3.07)

= P(Z < 3.07) - P(Z < 0.79)

= 0.9989- 0.7852

= 0.2137

Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .

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The function representing the points relation is f(x) = 32(3x - 1)

A function is defined as a relation between a set of inputs having one output each.

Given a table, represents some points on the graph of linear function f.

x = -2, 1, 5, 10

f(x) = -224, 64, 448, 928

From option A)

f(x) = 32(3x - 1)

Put x = -2

= 32(-2x3-1)

= 32x(-7) = -224

Hence, The function representing the points relation is f(x) = 32(3x - 1)

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Answer: n >= -18

Step-by-step explanation:

n/-3 >= 6

(-3)      (-3)

n >= -18

The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 5985&4\frac{3}{4}\\[1em] 8505&h \end{array}\implies \cfrac{5985}{8505}~~ = ~~\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{h}[/tex]

[tex]\cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{\frac{h}{1}}\implies \cfrac{19}{27}=\cfrac{19}{4}\cdot \cfrac{1}{h}\implies \cfrac{19}{27}=\cfrac{19}{4h}\implies 76h=513 \\\\\\ h=\cfrac{513}{76}\implies h=\cfrac{27}{4}\implies {\Large \begin{array}{llll} h=6\frac{3}{4} \end{array}}[/tex]