Design An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 12 more than three times the length of the
bottom of the triangle. The last side is 4 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.

Answer:  t₁=1.5-0.5√3 c ≈0.634 c       t₂=1.5+0.5√3 c ≈2.366 c

Step-by-step explanation:

h=-8t²+24t+4      h=16 feet     t₂=?

[tex]16=-8t^2+24t+4\\\\16-16=-8t^2+24t+4-16\\\\0=-8t^2+24t-12\\[/tex]

Divide both parts of the equation by -4:

[tex]0=2t^2-6t+3[/tex]

Thus,

[tex]2t^2-6t+3=0[/tex]

a=2     b=-6    c=3

D=b²-4ac

D=(-6)²-4(2)(3)

D=36-24

D=12

√D=√12

√D=√(4*3)

√D=2√3

[tex]t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-(-6)б2\sqrt{3} }{2(2)} \\\\t=\frac{6б2\sqrt{3} }{4} \\\\t_1=1.5-0.5\sqrt{3}\ c \\\\t_2=1.5+0.5\sqrt{3}\ c[/tex]

The pairs of triangles that are congruent are;

A. Δ1 and Δ5

B. Δ1 and  Δ2

C. Δ2 and Δ3

D. Δ3 and Δ5

E. Δ1 and Δ3

F. Δ3 and Δ4

G. Δ1 and Δ4

H. Δ4 and Δ5

Congruent triangles are triangles that have all three sides  and all three angles on each triangle having the same length and the same measure.

The congruent angles are indicated by the number of markings

The angles in the figures are;

Angle with  one arc

Angles with two arcs marks

Angles with three arc marks

The congruent sides are indicated by one dash, and two dashes

Therefore;

Δ2 s congruent to Δ1 is congruent to Δ3 by  Angle-Side-Angle rule of congruency

Similarly, we have;

Δ3 is congruent to Δ4 by Angle-Side-Angle congruency postulate

Therefore;

Triangle Δ2 is congruent to Δ3  by Angle-Side-Angle congruency postulate

From the diagram, the one arc, two arcs, and three arc angles form a linear pair, therefore;

Therefore, Δ4 is congruent to Δ5

Δ1 is congruent to Δ4

Δ2 is congruent to Δ5, therefore; Δ3 is congruent to Δ5

Similarly;

Δ1 is congruent to Δ3

Δ1 is congruent to Δ2, therefore , therefore, Δ1 is congruent to Δ5

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A circle is a two-dimensional figure with a radius and circumference of

2πr.

The arc length of AB is 10.05.

A circle is a two-dimensional figure with a radius and circumference of

2πr.

We have,

The radius of the circle = 12

The circumference of the given circle.

= 2πr

This means,

The whole circle is 360°.

= 360/360 x 2πr

= 2πr

Now,

We need to find 48°

So,

The arc length of AB.

= 48/360 x 2πr

= 48/360 x 2 x 3.14 x 12

= 48/30 x 2 x 3.14

= 10.048

Rounding to the nearest hundredths.

= 10.05

Thus,

The arc length of AB is 10.05.

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Answer: 10.05

Step-by-step explanation:

The arc length of AB.

= 48/360 x 2πr

= 48/360 x 2 x 3.14 x 12

= 48/30 x 2 x 3.14

= 10.048

Rounding to the nearest hundredths.

= 10.05

The arc length of AB is 10.05.

Ty's visibility if out the upper window of a building with an altitude of 1,602 feet is 49.

What is altitude?

The height of an object in relation to a planet's or a natural satellite's surface, like sea level or land. the degree to which a celestial body is elevated above the horizon.

Here, we have

Given

The formula V = 1.225 √a is used to estimate how far a person can see on a clear day, where V is the visibility in miles and A is the altitude in feet.

We have to find Ty's visibility out the upper window of a building with an altitude of 1,602 feet.

We know that

V = 1.225 √a

a = 1,602 feet.

V = 1.225 √1602

V = 49

Hence, Ty's visibility out the upper window of a building with an altitude of 1,602 feet is 49.

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If log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴.Logarithm identity is used to find the value of the log₂10.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

It is given that, log₁₀2=0.3010

We have to find the log₂10

The following logarithm identity is used as,

logₐn=logₙa

log₂10 =1/ log₁₀2

log₂10 =1/ 0.3010

log₂10 =3.3×10⁻⁴

Thus, if log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴. Logarithm identity is used to find the value of the log₂10.

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Answer: -4/5x - 22/5

Step-by-step explanation:

To find an equation of a line that is perpendicular to a given line and passes through a given point, we need to first find the slope of the given line. The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate of any two points on the line. For example, the slope of the line 5/4x + 2 is 5/4.

To find the equation of a line that is perpendicular to a line with slope m, we need to use the equation:

y - y1 = -1/m(x - x1)

where (x1, y1) is the given point that the line passes through. In this case, the given line has slope 5/4 and the given point is (-6,2), so the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is:

y - 2 = -1/((5/4))(x + 6)

y - 2 = -4/5(x + 6)

y - 2 = -4/5x - 24/5

y = -4/5x - 22/5

Therefore, the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is -4/5x - 22/5 (option "-4/5x - 22/5").

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Answer:

  a.  $3155.19

  b.  $1,135,868.40

  c.  $705,868.40

  d.  interest

Step-by-step explanation:

You want to find the monthly payment, total repaid, and finance charge on a 30-year mortgage for $430,000 at the rate of 8%.

You can use a spreadsheet, financial calculator, app, or the amortization formula to find the payment amount.

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the principal amount of the loan, r is the annual interest rate, and t is the number of years.

  A = 430,000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 3155.19

The monthly payment is $3,155.19.

The total of the 12·30 = 360 payments is ...

  360 · $3155.19 = $1,135,868.40

It will take about $1,135,868.40 to pay off the loan.

The finance charge is the difference between the amount repaid and the original loan amount:

  $1135868.40 -430000 = $705,868.40

The finance charge is $705,868.40.

The finance charge at $706k is considerably greater than the original cost of the home, $430k.

The finance charge is greater.

Answer:

Step-by-step explanation:

To find 50% of 950, you can multiply 950 by 0.50. 50% is the same as 0.50.

The calculation is: 50% * 950 = 0.50 * 950 = <<50*.01*950=475>>475

So, 50% of 950 is 475.

B. There is no function rule

For the first graph, slope = 1/5.

For the second graph, slope = -1/2.

For the third graph, slope = 2.

For the fourth graph, slope = 1.42.

What is the slope of the line?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

                  [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the first graph, the coordinates will be (-15, 0) and (0, 3)

          Slope = 3 - 0/0-(-15)

                     = 3/15

            Slope = 1/5

For the second graph, the coordinates will be (0, 5) and (10, 0)

          Slope = 0 - 5/10- 0

                     = -5/10

            Slope = -1/2

For the third graph, the coordinates will be (2.5, 0) and (0, -5)

          Slope = -5-0/0 - 2.5

                     = -5/-2.5

            Slope = 2

For the fourth graph, the coordinates will be (-2.8, 0) and (0, 4)

          Slope = 4 - 0/0 - (-2.8)

                     = 4/2.8

            Slope = 1.42

Hence,

For the first graph, slope = 1/5.

For the second graph, slope = -1/2.

For the third graph, slope = 2.

For the fourth graph, slope = 1.42.

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Answer:

88.75% is the percentage Tami earned.

Evaluation of E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid  z = 4 - x² - y² is [tex]\frac{128}{15} + \frac{8\pi}{3}[/tex]

Cylindrical coordinates are a set of three coordinates used to locate a point in the cylindrical coordinate system.

When the polar coordinates are extended to a three-dimensional plane, an additional z coordinate is added.

These three measurements combine to form cylindrical coordinates. The coordinates describe two distances and one angle.

According to the question,

We have to find the area under paraboloid

Given : E is a region that lies under paraboloid  z = 4 - x² - y² and in the first octant.

The intersection of this paraboloid with the xy plane will give z = 0,

z = 4 - x² - y² , z = 0, that is a circle  x² +y² = 4 with radius 2

Therefore , 0 ≤ z ≤ 4 - r²

Therefore, the region E in cylindrical coordinates is

[tex]E = ( r , \theta , z ) | 0 \leq \theta \geq \frac{\pi}{2} , 0 \leq 4 \geq , 0 \leq z \geq 4 - r^2[/tex]

f(x , y ,z ) = x + y + z

=> f(x , y ,z ) = rcosθ + rsinθ + z

=> f(x , y ,z ) = r(cosθ + sinθ) + z

Integration ,

[tex]{\int \int \int }\limits_E {z} \,dv[/tex]

=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r ( cos \theta + sin \theta) + z] r \, dzdrd\theta[/tex]

simlifying,

[tex]= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r^2 ( cos \theta + sin \theta) + rz] \, dzdrd\theta\\= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [r^2 ( cos \theta + sin \theta)z + r\frac{z^2}{2}] \, drd\theta[/tex]

=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [(4r^{2} - r^{4})( cos \theta + sin \theta) + \frac{r(4 - r^2)^2}{2}] \, drd\theta[/tex]

=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(\frac{4}{3} r^{3} - \frac{r^{5}}{5})( cos \theta + sin \theta) + \frac{(4 - r^2)^3}{12}]^{2}_{0} \, d\theta[/tex]

Putting the limit and solving,

=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(cos \theta + sin\theta )\frac{64}{15} + \frac{16}{3} \theta ]\, d\theta[/tex]

=> [tex][(sin\theta - cos\theta )\frac{64}{15} + \frac{16}{3} \theta ]^\frac{\pi}{2} _0[/tex]

Evaluating the limits,

[tex]\int\int\int\limits_E {x + y +z } \,dV = \frac{128}{15} + \frac{8\pi}{3}[/tex]

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Answer:155m

Step-by-step explanation:GK is congruent to HI

b,d and e option are correct

What is statement?

A statement, like "Pizza is tasty," is a declaration that something is true. In the fields of law, finance, and government, there are more types of statements. Every statement makes a claim or a point.

These statements are true:

The least Marcus would pay for a laptop from electro's is $500

Marcus can accept to pay about $700 for a laptop from electro's and  $1500 for a laptop from bits and bytes.

The middle 50% of laptops from electro's are priced between $500 and $900.

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Answer:

-9

Step-by-step explanation:

-3+-6=-9

Answer:

[tex]\huge\boxed{\sf d = 1.25\ m}[/tex]

Step-by-step explanation:

Work = W = 22 J

Force = F = 17.5 N

Distance = d = ?

W = Fd

Put the given data in the above formula.

22 = 17.5 (d)

Divide 17.5 to both sides

22/17.5 = d

1.25 m = d

[tex]\rule[225]{225}{2}[/tex]

Answer:

Parabola

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, When the plane is parallel to the edge of one cone.

Thus, The intersection is a parabola.

Answer: degenerate hyperbola

Step-by-step explanation:

degenerate hyperbola because its the thickest of the plane so it can be formed.

Bearing is a topic that deals with angles and distance. Thus, the required answers to the given question are:

i. Distance of 1034.2 miles

ii. Bearing of [tex]158^{o}[/tex]

The speed of an object is the rate of movement of the object with time.

speed = [tex]\frac{distance}{time}[/tex]

So that:

distance = speed x time

i. In the given question; let the initial distance covered be represented by d, so that:

d = 250 x 2

  = 500 miles

ii. Let the second distance covered by the pilot be represented by D, so that:

D = 300 x 2

   = 600 miles

iii. Thus let the distance to the starting point be represented by x. From Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

[tex]x^{2}[/tex] = [tex]500^{2}[/tex] + [tex]600^{2}[/tex] - 2(500 x 600)Cos [tex]140^{o}[/tex]

   = 250000 + 360000 - 600000(-0,7660)

   = 610000 + 459600

   = 1069600

x = [tex]\sqrt{1069600}[/tex]

  = 1034.22

x = 1034.2 miles

Using the Sine rule to determine the required internal angle, we have:

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{500}{Sin A}[/tex] = [tex]\frac{1034.22}{Sin 140}[/tex]

Sin A = [tex]\frac{500*0.6428}{1034.22}[/tex]

         = 0.3108

A = [tex]Sin^{-1}[/tex] 0.3108

   = 18.11

A = [tex]18^{o}[/tex]

To determine angle B, we have:

140 + 18 + B = 180 (sum of angles in a triangle)

158 + B = 180

B = 180 - 158

  = 22

B = [tex]22^{o}[/tex]

Thus, the required bearing is 180 - 22 = 158

Therefore the distance and bearing required to fly to starting point are 1034.2 miles and [tex]158^{o}[/tex] respectively.

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The quadratic equation of the function C(t) is; C(t)= (x - 4)²

We are given the coordinates as;

When t = 2, C(t) = 4

When t = 3, C(t) = 1

When t = 4, C(t) = 0

When t = 5, C(t) = 1

When t = 6, C(t) = 4

The general formula formula for quadratic equation is;

y = ax² + bx + c

where c is y-intercept

We are given that x = 4, when y = 0. Thus, x = 4 is a root of the equation.

Put x = 2and y = 4  into the equation to get;

4a + 2b + c = 4    -----(1)

Put x = 3 and y = 1  into the equation to get;

9a + 3b + c = 1    -----(2)

Put x = 4 and y = 0  into the equation to get;

16a + 4b + c = 0    -----(3)

Using simultaneous equation solver gives;

a = 1, b = -8 and c = 16. Thus, our equation is;

y = x² - 8x + 16

By factorization;

y = x² - 4x - 4x + 16

y = x(x - 4) - 4(x - 4)

y = (x - 4)²

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In linear equation, 96 is the quotient.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(x) =  6x^3-+18x^2-18x+12

x - 2 = 0

x = 2

f( x) = 6 * 8 + 18 * 4 - 18 * 2 + 12

     =  48 + 72 - 36 + 12

      = 132 - 36

      = 96

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If the midpoint of AB is at (0,4). and A = (3,0) then B is at point (-3, 8)

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ - x₁)/2

Y = (y₂ - y₁)/2

solving for B (x₂, y₂)

0 = (x₂ + 3)/2

0 = x₂ + 3

x₂ = -3

4 = (y₂ + 0)/2

8 = y₂ + 0

y₂ = 8

point B = (-3, 8)

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Answer:

x + y = 87

1.5x + 0.5y = 78.50

Step-by-step explanation:

Let x be the number of nachos sold and y be the number of sodas sold

x nachos will cost 1.50x dollars
y sodas will cost 0.50y dollars

So total sales = 1.5x + 0.5y and we know he made $78.50

so one equation is
1.5x + 0.5y = 78.50

Total sold = x + y and we know that this number is 87

So the second equation is

x + y = 87

The total ticket sales was $ 2298, and the theater was filled to capacity

Children: 158

Students: 158

Adults: 79

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper. Now picture that your square is composed of smaller unit squares.

According to Study.com, area is a mathematical concept that is defined as the two-dimensional space occupied by an item. Area is used in many real-world contexts, including building, farming, architecture, science, and even determining how much carpet you'll need to cover your home's rooms.

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Answer:

(8, 11)

x=8

y=11

Step-by-step explanation:

I solved using elimination.

I set the equations over one another getting x+2y=30 over -2x-2y=-38.

I chose elimination because the y values were already the opposite so it can easily cancel each other out. After it get's canceled out I get x=30 over  -2x=-38. When using elimination we always add so you'd add x+ -2x and 30+ -38. When you add x + -2x you'd get -1x. When you add 30 + -30 you'd get -8. Now you have 1x=-8 divide both sides by -1 and you get x=8. Now you plug in 8 to one of the equations. I chose to plug it into the 1st equation which is x+ 2y=30. But because I plugged in the 8 the equation is now 8+2y=30. I subtracted 8 on both sides canceling the 8 out. So now I have 2y=22. divide both sides by 2 and x=11. So your order pair is (8, 11)
(Hopefully you were able to understand it..)

The vertex labels of Δ QRT are : ∠2 label is Q, ∠8 label is T and the remaining vertex label is R. The vertex labels for ΔSTR are: ∠5 label is S, ∠9 label is R and the remaining label is T.

The polygon having three sides and three vertices are known as triangle.

If we separate the two triangles as shown in the figure. We can find the vertex labels with the help of the angles marked in the figure.

For Δ QRT, the vertex labels are:

∠2 is Q, ∠1 is R and ∠8 is T

Similarly. for ΔSTR, the vertex labels are:

∠5 is S, ∠6 is T, and ∠9 is R

Hence,  For Δ QRT, we can label as ∠2 is Q, ∠1 is R and ∠8 is T and for ΔSTR we can label as  ∠5 is S, ∠6 is T, and ∠9 is R.

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The rate of change of temp w.r.t time is -1.875°F

What is rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta () is frequently used to represent the ROC.

The term "rate of change" (ROC) describes the rate at which something changes over time.

Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace).

Time             Temperature              Difference

4                          89.5                               -

10                        78.25              78.25 - 89.5 = -11.25

16                        67.00              67 - 78.25 = -11.25      

There is a common difference of -11.25 in each successive term.

Therefore, cooling of a chemical represents a linear function.

Rate of change of temp from 4 min to 10 min

=78.25 - 89.5 = -11.25

= -11.25/6

=-1.875

So, the rate of change of temp w.r.t time is -1.875°F

which means temperature is decreasing continuously when the time is increasing

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Answer:10

Step-by-step explanation:10 times two is twelve and minus 2 is ten.

Answer: A

Step-by-step explanation:

From the statement.

Times = Multiplication

The sum of a number and 18.3 = (r + 18.3)

Equals = 27.9

Therefore,

-6 x (r + 18.3) = 27.9

If a graph G has an Euler path, then it must include precisely two odd vertices. Or, to put it another way, G cannot have an Euler path if the number of odd vertices is less than 2.

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