Y=7/2x-2 need help solving

Answer:

Step-by-step explanation:

We know from the property of 30°x60°x90° right triangle:

We see AC = 2*BC, therefore:

Correct choice is B

The ratio of angles is directly proportional to the ratio of sides

The ratio of sides here is 1:1/2:1

Now

\(\\ \sf\longmapsto 2x+x=90°\)

\(\\ \sf\longmapsto 3x=90\)

\(\\ \sf\longmapsto x=30\)

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

Answer:

h(-2) = -1

Step-by-step explanation:

h(x)=-2x-5

Let x= -2

h(-2)=-2*-2-5

      = 4 -5

h(-2) = -1

Answer:

$3.90

Step-by-step explanation:

78 cents/lb * 5 lb = (78*5) cents = 390 cents (the pound labels divide out)

But 390 cents = $3.90

Answer:

I think it's 256

Step-by-step explanation

Answer:

256

Step-by-step explanation:

why well

it goes like this

write the 2 number as shown

16 gallons            cups

what is more gallons or cups

its gallons so

large to small

lagre to small is mutipling and small to large is dividing so u need to mutiply the amout of cups are in a gallon wichis 16 so 16 times 16 is 256 so there u go

The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer:

The answer is no

Step-by-step explanation:

If you ran a ruler across your screen, then the ruler would be going through three points of the one line. This is called the straight line test. If the line continues intersecting through one point at a time, then it is a function, but this is not.

Answer: \(300\) \(times\)

Step-by-step explanation:

The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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Answer:

b

Step-by-step explanation:

Answer:

The renaissance took place in the 14th all the way to the 17th century.

Step-by-step explanation:

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

22h - 9

Step-by-step explanation:

14h + 12 - 8h - 3

14h + 8h + 12 - 3

22h + 12 - 3

22h + 9

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

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

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

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

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j -21k and the area of the triangle is 11.6 square units.

(a)Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)

PQ = Q - P

= (0 - (-1))i + (7 - 3)j + (2 -1)k

=i + 4j + k

PR = R - P

= (4 - (-1))i + (2 - 3)j + (-1 - 1)k

5i -j - 2k

The orthogonal vector is PQ x QR

\(\left[\begin{array}{ccc}i&j&k\\1&4&1\\5&-1&-2\end{array}\right]\)

(-8 + 1)i - (-2 - 5)j + (-1 -  20))k

-7i + 7j - 21k

Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j - 21k

(b) The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of PQ and QR.

Area = 1/2| PQ x QR|

= 1/2 √(7² + (-7)² + (-21)²)

= 1/2 √(49 + 49 + 441)

= 1/2 (23.21)

= 11.60

= 11.60 square units.

Therefore The non zero vector is  -7i + 7j - 21k and the area of the triangle is 11 .6 square units.

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Answer:

25

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

11 buses

Step-by-step explanation:

Answer:

h = 2.12 , c = 6.93

Step-by-step explanation:

To calculate h:

Apply the cosine identity

\(cos\ x =\frac{base}{hypotenuse}\\\\cos\ 45=\frac{h}{3}\\\\0.707=\frac{h}{3}\\\\h=3(0.707)\\h=2.12\\\)

To calculate c:

Apply the tangent identity

\(tan\ x=\frac{perpendicular}{base}\\\\tan\ 60=\frac{c}{4}\\\\1.732=\frac{c}{4}\\\\c=1.732(4)\\c=6.93\\\)

FG = 16

Step-by-step explanation:

Two pairs of consecutive are congruent so, its a kite,

Opposite sides are equal in kite so,

x + 11 = 3x + 1

or, 11 - 1 = 3x - x

or, 2x = 10

so, x = 5

FG = x + 11 = 5 + 11 = 16

Answer:

17x^2-9x-9 -->B

Step-by-step explanation:

7x^2 -12x +3 +10x^2+3x-12

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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The statement that is true about integrals is; A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

Left-Hand Sums and Right-Hand Riemann sums usually give us different approximations of the specific area under a curve.

Now, If one sum gives us an overestimated value and then the other gives us an underestimated value, then we can try to find out what exactly the actual area under the curve might possibly be. It should be noted that left-hand sum will be an under-estimate of the specific area of R. Thus, as  f is increasing, a left-hand sum will definitely use the smallest value of f on each sub-interval. This therefore tells us that any left-hand sum will not cover all of R and also any right-hand sum will be an over-estimated value of the area of R.

Thus, Since f is increasing, a right-hand sum will utilize the largest value of f on each specific sub-interval. Thus, right-hand sum will definitely cover R and others.

From the above, option A is true because if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.

Meanwhile, option B is false because if the graph is concave upwards, then the trapezoid approximation is an overestimated value, and as such the midpoint will be underestimated.

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Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

Answer:

It began after the stock market crash of October 1929, which sent Wall Street into a panic and wiped out millions of investors. Over the next several years, consumer spending and investment dropped, causing steep declines in industrial output and employment as failing companies laid off workers.

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

The equation of a line:

Use the coordinates of the point and find the value of b:

The line is:

Answer:

y = ½x - 3

Step-by-step explanation:

x = 2

y = - 2

a = ½

y = ax + b

- 2 = ½(2) + b

- 2 = 1 + b

b = - 2 - 1

b = - 3

y = ax + b

y = ½x + (-3)

y = ½x - 3

Answer: t= 2

Step-by-step explanation:

Set them equal each other because they are the same angles.

t + 8 = 5t    now solve for t.

-t         -t

8 = 4t

t = 2