On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). These coordinates will be the vertices of a triangle. How would you use the distance formula to determine what kind of triangle this is? Is the triangle equilateral, right, or scalene? Now use the midpoint formula to determine the midpoints of the triangle's sides: segments AB, BC, and CA. Connect the midpoints to make four triangles within the first triangle. Are these four triangles similar?

The value of x to the nearest hundredth is 4.14

The given diagram is a right triangle with the following parameters

Opposite side to 16 degrees = x

Hypotenuse = 15

Using the expression below

sin theta = x/15

sin16 = x/15

x = 15sin16

x = 4.135

Hence the value of x to the nearest hundredth is 4.14

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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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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]

Answer:

45 meters

Step-by-step explanation:

[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]

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Answer:

A=45 m²

Step-by-step explanation:

The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].

where :

[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]

Substitute the values,

[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]

Done !! Hope this made sense to you :)

[tex]\small\boldsymbol{Calligraphy}[/tex]

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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]

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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Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°

Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).

Measure of one of the intercepted arcs = 250°

The second intercepted arc = 360 - 250 = 110°

Positive difference of the intercepted arcs = 250 - 110 = 140°

Measure of angle A = 1/2(140)

Measure of angle A = 70°

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Answer:

the answer is 70. hope this helps <3

Step-by-step explanation:

The area of the equilateral triangle is 110.9 cm

area of a triangle = 1 / 2 bh

where

Therefore,

tan 60 = opposite / adjacent

tan 60 = 8√3 / x

x =  8√3 / √3

x = 8

hence,

b = 8 + 8 = 16

Therefore,

area of a triangle =  1 / 2 × 16 × 8√3

area of a triangle = 64√3

area of a triangle = 110.851251684

area of a triangle = 110.9 cm

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The correlation coefficient is -0.87; strong correlation

The given parameters are:

x = Time spent working out

y = lbs Overweight

Next, we enter the table of values in a graphing tool.

From the graphing tool, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -114.19 / √((22.569)(778.9))

r = -0.8613

Approximate

r = -0.87

This means that the correlation coefficient is -0.87

Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0

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Answer:

31 3/4 %

Step-by-step explanation:

There are 100 squares so each square is a percent.  There at 31 full squares colored and it looks like 3/4 of 1 square.

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).

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:

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 :)

The error is that

[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]

Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.

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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Step-by-step explanation:

T = 2×pi × sqrt(L/9.8)

now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.

the only unknown variable is now L (the length of the rope) :

3.4 = 2×pi × sqrt(L/9.8)

3.4/(2pi) = sqrt(L/9.8)

(3.4/(2pi))² = L/9.8

3.4²/(4pi²) = L/9.8

11.56/(4pi²) = L/9.8

2.89/pi² = L/9.8

9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m

Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.

On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.

Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.

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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:

it matches with equation a

Answer: THE ANSWER IS A) $860

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

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

No hay ninguno de los nimbers que no pertenezca a la secuencia.

Sabemos que una secuencia tiene que ver con un arreglo de números en un orden definido. Todos los números en una secuencia deben tener la misma razón común o diferencia común.

Si miramos todos los números que están escritos en la secuencia, la diferencia común aquí es seis. Se sigue entonces que todos los números son parte de la sucesión y no hay ninguno de los números que no pertenezca a la sucesión.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]

The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.

This can be achieved using the future value and present value formulas or factors.

We can also use an online finance calculator, as follows:

Future value = $5,000

Investment period = 3 years

Annual compound interest = 5%

N (# of periods) = 3 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $5,000 ($4,531.56 + $468.44)

Results:

PMT = $1,510.52

Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)

Total Interest = $468.44

Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

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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:

[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:

0.4

Step-by-step explanation:

4+3+2+1 =10

5m÷10 =0.5

(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)

2 : 1.5 : 1 : 0.5

longest piece= 2 (2m)

4+1= 5

2÷5= 0.4

(0.4×4=1.6, 0.4×1=0.4)

1.6 : 0.4

so the shortest piece is 0.4!

Using the probability concept, the number of blue balls you need to add is:

D) 5.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A probability of 0.5 is reached if the number of red balls is the same as the number of blue balls. Current the difference is of 7 - 2 = 5, hence 5 blue balls must be added.

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You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.