The area of a square quilt is 35 ft 2. How will it look stretched across a queen sized bed measuring 60 inches wide and 80 inches long?

Answer:

it matches with equation a

Answer:

[tex]y=-2.5x+8[/tex]

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts. So, first, transform the given equation into the slope-intercept form, [tex]y=mx+b[/tex].

[tex]5x+2y=6[/tex]

[tex]2y=-5x+6[/tex]

[tex]y=-\frac{5}{2} x+3[/tex]

Then, determine the equation of a line that has a slope of [tex]-\frac{5}{2}[/tex] and passes through (1, 5.5). Substitute all the known values and solve for b.

[tex]y=mx+b[/tex]

[tex]5.5 = -\frac{5}{2} *1+b[/tex]

[tex]5.5=-2.5+b[/tex]

[tex]b=8[/tex]

Therefore, the answer is [tex]y=-2.5x+8[/tex].

Answer:

Step-by-step explanation:

x = speed of the boat

y = speed of the current

x + y = 162/3 = 54 mph

x - y = 132/3 = 44 mph

Add the two equations to get

2x = 98

x = 49 mph

y = 54 - x = 54 - 49 = 5 mph or something

The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

From the information given;

The bricklayer needs = 100 pieces of angle

The number of cuts = 54

Length of cuts = 3/ 16'' Inches

a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts

= 20/ 100 × 3/ 16 × 54

= 0. 2 × 0. 1875 × 54

= 2. 0

The number of cuts would be 2

b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle

= 100/ 20

= 5 pieces

The number of pieces of 20' angle is 5

Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

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The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).

It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.

It follows from observation that one of the zeros of the polynomial expression is at; x = -2.

Consequently, one of the factors of the polynomial in discuss is; (x+2).

x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)

= (x+2)(x+2i)(x-2i)

Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).

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The best predicted weight of a person that is 156 cm is 285.4kg

y= 106+1.15

When the adult male is 156 cm tall the weight of this person would be calculated as:

y= 106+1.15*156

y = 106 + 179.4

y = 285.4

Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg

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Answer:

Step-by-step explanation:

143

or

121

We are accepting

does any of this help

If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.

Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.

We have to find the price of one umbrella and one cap.

We have to form equations first to find the price of umbrella and cap.

Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.

let the price of umbrella be x and price of cap is y.

We know that total cost is equal to price of one unit multiplied by the units.

According to question.

2x+y=20----------1

x+2y=16-----------2

Multiply equation 2 by 2 and then subtract resulted equation from equation 1.

2x+y-2x-4y=20-32

-3y=-12

y=-12/-3

y=4

put the value of y in equation 2 to get the value of x.

x+2y=16

x+2*4=16

x+8=16

x=16-8

x=8

Hence the price of one umbrella is $8 and the price of one cap is $4.

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Answer:

3(r + 5)(r - 5)

Step-by-step explanation:

Both 3 and 75 are divisible by 3, so we take out a 3.

3(r^2 - 25)

Next, we can factor r^2 - 25. It's a difference of squares.

3(r + 5)(r - 5)

Brainliest, please :)

There are 180 numbers which are three-digit multiples of 5.

According to the statement

we have to find the three digit numbers which are multiples of 5.

we know that three digit numbers are start from 100 to 999 and in 1 line of counting means 100 to 110 there are 2 numbers are multiples of 5.

Here we use Multiplication method to find the number of digit which are a multiple of 5.

It means there are two numbers which are multiples of 5 in the one line of counting and there are 90 lines of  counting from 100 to 999.

So, it means the answer will become

2*90 = 180.

So, There are 180 numbers which are three-digit multiples of 5.

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The support pole must be approximately 7.8 meters long.

Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:

l/sin 84° = 6 m /sin 50°

l = 6 m × (sin 84°/sin 50°)

l ≈ 7.790 m

The support pole must be approximately 7.8 meters long.

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The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;

x + y = 10

x + y = 105x + 7y = 66

Let

Number of small cars rented = x

Number of large cars rented = y

x + y = 10

x + y = 105x + 7y = 66

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The value of y  / 3 in the equation is x / 4.

Therefore,

x + 4 / 4 = y + 3 / 3

then y / 3 can be found as follows,

x + 4 / 4  = x / 4 + 4 / 4 = x  / 4 + 1

y + 3 / 3  = y / 3 + 3 / 3  = y / 3 + 1

x  / 4 + 1 = y / 3 + 1

subtract 1 from both sides of the equation

x  / 4 + 1 - 1 = y / 3 + 1 - 1

x / 4 = y / 3

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By definition of the zeros of ta quadratic function,  for 5.5 seconds the ball is in the air before it hits the ground.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In summary, the roots or zeros of the quadratic function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.

When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:

0= -16t² + 88t

It can be solved by extracting the term "t" as a common factor:

0= t×(-16t + 88)

The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:

t= 0

or

0= -16t + 88

Solving: -88= -16t

(-88)÷ (-16)=t

5.5= t

Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.

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Answer:

Step-by-step explanation:

In the quadratic form ...

  (x -h)² = 4p(y -k)

The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).

The value of 4p is given as 8. This means p = 8/4 = 2.

The length of the latus rectum is 8.

The end points of the latus rectum have the same y-value as the focus:

  y = k +p = -1 +2 = 1

The end points of the latus rectum have x-values that are h±2p.

  x = h ± 2p = -4 ± 2·2 = {-8, 0}

The end points of the latus rectum are (-8, 1) and (0, 1).

Answer:

Step-by-step explanation:

Let  [tex]x_{n}[/tex] represent the nth term in the sequence. Then  [tex]x_{n-1}[/tex] represents the previous term

The first term, [tex]x_{1}[/tex] = -7

Each consecutive term is obtained by adding 4 to the previous term.

So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]

Answer:

74

Step-by-step explanation:

(73 + 85 + 70 + 63 + x)/5 = 73.

You find the average by adding all of the test scores and dividing that number by the number of tests.  We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4.  We already know what we want the average to be, we want the average to be 73.  We now have:

(291 + x)/5 = 73  Multiply both sides by 5

291 + x =365  Subtract 291 from both sides to get

x = 74

Answer: 74

Step-by-step explanation:

The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.

With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:

[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]

that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix

There are 80 students studying at least one language

The given parameters are:

Using the above parameters, we have:

German and French only = 5 - 3 = 2

Italian and French only = 10 - 3 = 7

Italian and German only = 8 - 3 = 5

French only = 42 - 7 - 2 - 3 = 30

German only = 30 - 2 - 5 - 3 = 20

Italian only = 28 - 7 - 5 - 3 = 13

See attachment for the Venn diagram

This is calculated as:

None + At least one = Total

Using the Venn diagram, we have:

None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

This gives

None + 80 = 100

Subtract 80 from both sides

None = 20

Hence, there are 20 students studying none of the languages

This is calculated as

French only = French - French and Italian - French and German + All three

So, we have:

French only = 42 - 10 - 5 + 3

Evaluate

French only = 30

Hence, there are 30 students studying French only

In (b), we have:

None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

By comparing both equations, we have

At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30

This gives

At least one = 80

Hence, there are 80 students studying at least one language

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Answer: [tex]160^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem,

[tex]4x-14+5x-182=5x-100\\\\9x-196=5x-100\\\\4x=96\\\\x=24\\\\\implies m\angle BCD=20^{\circ}\\\\\implies m\angle BCA=160^{\circ}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

By Exterior angle property :

[tex]\qquad❖ \: \sf \:4x - 114 + 5x - 182 = 5x - 100[/tex]

[tex]\qquad❖ \: \sf \:9x -29 6 = 5x - 100[/tex]

[tex]\qquad❖ \: \sf \:9x - 5x = - 100 + 296[/tex]

[tex]\qquad❖ \: \sf \:4x = 96[/tex]

[tex]\qquad❖ \: \sf \:x = 24 \degree[/tex]

Next, Angle BCA = 180° - Angle BCD

( linear pair )

[ let angle BCA = y ]

[tex]\qquad❖ \: \sf \:y = 180 - (5x- 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - (5(24) - 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - (120 - 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - 20[/tex]

[tex]\qquad❖ \: \sf \:y = 160 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Using proportions, it is found that they must win 19 of their next 30 games.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:

Hence:

[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]

3(5 + x) = 72

15 + 3x = 72

3x = 57

x = 19.

The Rangers must win 19 of their next 30 games.

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Answer:

Step-by-step explanation:

2x+3y=15

multiply by 2

4x+6y=30   ...(1)

6y=-4x+12

4x+6y=12    ...(2)

(1) and (2) represent parallel lines.

Hence no solution.

The inequality of the graph is y < -1/2(x - 16)^2 + 32

A quadratic function is represented as:

y = a(x - h)^2 + k

The vertex of the graph is

(h, k) = (16, 32)

So, we have:

y = a(x - 16)^2 + 32

The graph pass through the point

(x, y) = (12, 24)

So, we have:

24 = a(12 - 16)^2 + 32

Evaluate the like terms

-8 = a(-4)^2

This gives

16a = -8

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x - 16)^2 + 32

y = -1/2(x - 16)^2 + 32

The graph is a less than graph.

So, we have

y < -1/2(x - 16)^2 + 32

Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32

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Answer: THE ANSWER IS A) $860

Step-by-step explanation: I GOT A 100 ON THE TEST

The point-slope equation of the line is: y - 2 = 8(x - 2).

The point-slope equation is: y - b = m(x - a), where:

Using the coordinates of the point shown in the graph, substitute (a, b) = (2, 2) and m = 8 into y - b = m(x - a):

y - 2 = 8(x - 2)

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The point of intersection of both graphs will have the coordinate (5, 9).

We are given the functions;

f(x) = x + 4

g(x) = -2x + 19

Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;

x + 4 = -2x + 19

x + 2x = 19 - 4

3x = 15

x = 15/3

x = 5

Thus;

f(x) = 5 + 4 = 9

g(x) = -2(5) + 19 = 9

Thus, the point of intersection of both graphs will have the coordinate (5, 9)

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