A right-triangle has the hypotenuse length of 5 units long. One of the other sides of the triangle is 3 units. What is the length of the remaining side

The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).

The transformation rules are:

Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)

Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)

It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]

This parabola has vertex at (h, k).

Since this equation is obtained by shifting h units horizontally and k units vertically.

So, the original vertex is at (h - h, k - k) = (0, 0)

Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]

Therefore, the given transformed equation of parabola has vertex (h, k).

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Answer:

B] (h,k)
The next answer is Vertex (-5, -4)

☆
EDGE2022; Good luck :3!!!!

Answer:

150g for 6 servings

x grams for 15 servings

150/6 = 25

15 x 25 = 375

375g of sugar will be required to make 15 servings.

Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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Answer:

f[g(x)] = 6x + 47

Step-by-step explanation:

The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.

f(x) = 6x + 11               g(x) = x + 6

f[g(x)]                                                    <----- Composition expression

f[g(x)] = 6(x + 6) + 11                             <----- Plug g(x) into x

f[g(x)] = 6x + 36 + 11                             <----- Multiply terms in parentheses by 6

f[g(x)] = 6x + 47                                  <----- Add 36 and 11

Answer:A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts

Step-by-step explanation:

Answer:

uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Step-by-step explanation:

looks like circles that meet and overlap and

the middle part explains the relationship of both circles

example

if the left circle says water & right circle says freezing the middle part would say ice

mathworldwolfram

Answer:

width is 8, length is 32

Step-by-step explanation:

* = multiply or times

Let the width be x, then the length would be 4x

Perimeter = 2*length+2*width

80 = 2*4x+2*x

80 = 8x+2x

80 = 10x

8 = x (width)

32 = 4x (length)

Answer:

Step-by-step explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

[tex]x = -y+6[/tex]

By putting this equation in place of x in the first equation, we can solve for y:

[tex]4(-y+6)-2y=6[/tex]

[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]

[tex]-6y+24=6[/tex] [Combining like terms]

[tex]-6y = -18[/tex] [Subtracting 24 from both sides]

[tex]y=3[/tex] [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

[tex]x+3=6[/tex]

[tex]x=3[/tex] [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

[tex]2x+2y=12[/tex]

Now, let's add both equations to cancel out y.

[tex]4x-2y=6[/tex]

[tex]2x+2y=12[/tex]

[tex]6x=18[/tex]

Now, we can divide 6 from both sides to get the value of x.

[tex]\frac{6x}{6} = \frac{18}{6}[/tex]

[tex]x=3[/tex]

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

[tex]3+y=6[/tex]

[tex]y=3[/tex]

The solution to our system of equations is (3,3).

The probability that the student will pass the test is 0.057

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability [tex]p[/tex] and the value 0 with probability [tex]{\displaystyle q=1-p}[/tex]. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.

The student will pass if he at least answers 14 questions correctly .

This can be written as a Bernoulli distribution function [tex]P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)[/tex]

P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) +   P(Q=20)

 P(Q=14) = 20[tex]C_{14}[/tex][tex](1/2)^{20}[/tex]

 P(Q=15) = 20[tex]C_{15}[/tex][tex](1/2)^{20}[/tex]

 P(Q=16) = 20[tex]C_{16}[/tex][tex](1/2)^{20}[/tex]

 P(Q=17) = 20[tex]C_{17}[/tex][tex](1/2)^{20}[/tex]

 P(Q=18) = 20[tex]C_{18}[/tex][tex](1/2)^{20}[/tex]

 P(Q=19) = 20[tex]C_{19}[/tex][tex](1/2)^{20}[/tex]

 P(Q=20) = [tex]20C_{20}(1/2)^{20}[/tex]

On summing up all we get,

P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)

= 15115/262144=0.057

Thus the probability that the student will pass the test is 0.057

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Answer:

( 3 , 4 )

Step-by-step explanation:

Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )

Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]

Gradient (Slope) Formula: (y2-y1) / (x2-x1)

Midpoint Formula:

( (x1+x2)/2 , (y1+y2)/2 )

(2,3) and (4,5)

( (2+4)/2 , (3+5)/2 )

( (6)/2 , (8)/2 )

( 3 , 4 )

wyzant sean w

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

[tex]z\cdot \bar z = 2^{2} + 3^{2}[/tex]

[tex]z\cdot \bar z = 13[/tex]

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The approximate measure of angle G is 41.4°. The correct option is C. 41.4°

From the question, we are to determine the measure of angle G

From the law of cosines, we can write that

[tex]cos\ G =\frac{e^{2}+f^{2}-g^{2} }{2ef}[/tex]

In the diagram,

e = 12

f = 10

g = 8

Putting the values into the equation

[tex]cos\ G =\frac{12^{2}+10^{2}-8^{2} }{2\times 12 \times 10}[/tex]

[tex]cos\ G =\frac{144+100-64 }{240}[/tex]

[tex]cos\ G =\frac{180}{240}[/tex]

cosG = 0.75

G = cos⁻¹(0.75)

G = 41.4°

Hence, the approximate measure of angle G is 41.4°. The correct option is C. 41.4°

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Answer:

60%

Step-by-step explanation:

324/540 x100=60%

Np!

If they sell all the pancakes, they will win $7

We know that they can make a batch of 14 pancakes, such that each one can be sold for $0.50

Then the total amount that they get if they sell all the pancakes is given by the product:

P = 14*$0.50 = $7

If they sell all the pancakes, they will win $7

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Data definition involves describing the properties of the data that go into each database table, specifically the fields or columns that make up the database.

What is a field record table and query?

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• Using distributive property

[tex]6x + 6 = 3x - 15[/tex]

• Solving the like terms

[tex]6x - 3x = - 15 - 6[/tex]

[tex]3x = - 2 1[/tex]

[tex]x = - \dfrac{21}{3} [/tex]

[tex]x = - 7[/tex]

Hope it helps you any confusions you may ask!

The distance travelled is 10 m

The velocity gained at the end of the time is 2 m/s

From the question, we are to determine distance travelled and the velocity gained

From one of the equations of motion for linear motion, we have that

S = ut + 1/2at²

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

First, we will calculate the acceleration

Using the formula,

F = ma

Where F is the force

m is the mass

and a is the acceleration

∴ a = F/m

Where F is the force

and a is the acceleration

From the given information,

F = 50 N

m = 250 kg

Putting the parameters into the equation,

a =  50/250

a = 0.2 m/s²

Thus,

From the information,

u = 0 m/s (Since the object was initially at rest)

t = 10 s

S = 0(t) + 1/2(0.2)(10)²

S = 10 m

Hence, the distance travelled is 10 m

For the velocity

Using the formula,

v = u + at

Where v is the velocity

v = 0 + 0.2×10

v = 2 m/s

Hence, the velocity gained at the end of the time is 2 m/s

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Answer:

she rides her bike at a rate of 8mph during the second part of the trip.

Step-by-step explanation:

for the first part of the trip, she rides 18 miles in 2 hours which means that she bikes at a rate of 9 miles per hour.

subtracting 18 from 58 gives us the distance she biked during the second part of her trip (which is 40 miles). subtracting 2 from 7 gives us that she biked for 5 more hours. Putting this together means she biked 40 miles in 5 hours.

Now divide miles by hours [tex]\frac{40mi}{5hrs} =8mph[/tex] to get your average rate of change for the second part of the trip.

Barack be able to bring 1029 dirham with him.

The amount of one currency needed to buy items in another is shown by conversion rates.

Currency rates and spot prices on the foreign exchange market are comparable to conversion rates.

In relation to supply and demand, conversion rates are impacted.

Governments and central banks implement policies in response to supply and demand dynamics that affect the conversion rate.

According to the question,

The conversion rate from cad to uae dirham is 2.94

Money, in dirham,  Barack would be able to bring with him,

=(350*2.94) dirham

=1029 dirham

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Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

The average rate of change will be 5 miles per hour from 0.75 to 1 hour.

The average rate of change is the ratio of change in the y-value or the function value by the change in the x-value.

So according to the question,

the interval between 0.75 to 1 hour is =1-0.75=0.25 hour.

At 0.75 hours elapsed, the distance traveled is 3.5 miles

at 1 hour elapsed, the distance traveled is 4.75miles.

during the interval, 0.75 hours to 1-hour distance travelled=4.75-3.5=1.25 miles.

the average rate of change will be = change in distance traveled during the interval/interval time.

=(4.75-3.5)/(1-0.75)=1.25/0.25=5 miles per hour

Therefore the average rate of change will be 5 miles per hour from 0.75 to 1 hour.

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Answer:

B

Step-by-step explanation:

If you don’t want to read

Answer:

the correct answer is c (x+8)

Step-by-step explanation:

x+8=0

=x= -8

put x= -8 in the given polynomial

(-8)²+5(-8)-24

= 64-40-24

=24-24= 0

When sampling is finished without replacement, each member of a population could also be chosen just once. during this case, the chances for the second pick are full of the results of the primary pick. The events are considered to be dependent or not independent.

lets understand with the help of an Example

You have a good, well-shuffled deck of 52 cards. It consists of 4 suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.

Sampling without replacement:

Suppose you decide three cards without replacement. the primary card you choose out of the 52 cards is that the K of hearts. you place this card aside and pick the second card from the 51 cards remaining within the deck. it's the three of diamonds. you place this card aside and pick the third card from the remaining 50 cards within the deck. The third card is that the J of spades. Your picks are . Because you have got picked the cards without replacement, you can not pick the identical card twice.

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Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.

Area of a triangle = 1/2(base)(height).

Find the height of the triangle using the Pythagorean theorem:

Height = √(5² - 1²) ≈ 4.9 cm.

Base = 2 cm

Area of the two triangles = 2[1/2(base)(height)]

Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².

Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.

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Answer: 129.82

Step-by-step explanation: its on edge I got it right :)

Answer:

Horizontal reflection

Step-by-step explanation:

a math chart that was labeled had these pattern examples with the the translation and transformation.

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

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

The base of the pyramid is x cm while the height is x + 2, hence:

Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

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The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

In this problem we have the following relationship bewteen the two quadratic equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):

[tex]k = \frac{x_{g}}{x_{f}}[/tex]

Let suppose that y = 3, then [tex]x_{f} = - 5.5[/tex] and [tex]x_{g} = - 1.8[/tex], then the value k is:

k = (- 5.5)/(- 1.8)

k = 3.056

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

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Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line

It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.

Coherence is known to be a key quality for kind of good academic write up.

Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.

Therefore  without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.

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The y-intercept which is the point at which x = 0 is; A: -10

The general form of an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the slope;

m = -4

Now, the line passes through the point 0, -10. Thus;

(y - y1)/(x - x1) = -4

(y + 10)/(x - 0) = -4

y + 10 = -4x

y = -4x - 10

Thus, the y-intercept which is the point at which x = 0 is; y = -10

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Answer: 115.5 cubic m

Step-by-step explanation:

[tex]V=\frac{1}{2}(7)(11)(3)=115.5[/tex]