From a hot-air balloon, Ian measures a 30^{\circ}
∘
angle of depression to a landmark that’s 1250 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

∠ABC = 39°

Step-by-step explanation:

Since ED bisects ∠CBD :

∠EBD = ∠CBE = 30°

Now, ∠ABD = ∠ABC + ∠CBE + ∠EBD = 99°

Solving :

Answer:

Slope: [tex]\frac{4}{1}[/tex]

Y - intercept: -1

Step-by-step explanation:

We can see from the graph that the slope is [tex]\frac{4}{1}[/tex].

We can also identify the y - intercept as -1.

Therefore, the linear equation would be y = [tex]\frac{4}{1}[/tex]x -1

Hope this helps:) Goodluck!

Answer:

a) Length= (x+2) and breadth=(x-1) b) 4 m^2 c) R1000

Answer:

answers in photo / +explanation

Step-by-step explanation:

a)

length: x+2

width/breadth: x-1

b)

length: 4m

width/breadth: 1m

area: 4m²

c)

R1000

Answer:

The answer is option A

Step-by-step explanation:

The solution is in the image

Answer:

BD = BE

Step-by-step explanation:

If BD = BE , angle BED = angle BDE.

Because they are in a same triangle.

And also they are congruent.

The value of the function g(x) = x^3 + 6x^2 + 12x + 8 when x = -1 is 1

The equation of the function is given as:

g(x) = x^3 + 6x^2 + 12x + 8

When x = -1, we have:

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

Evaluate the expression

g(-1) = 1

Hence, the value of the function g(x) = x^3 + 6x^2 + 12x + 8 when x = -1 is 1

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Answer:

g(-1) = 1

Step-by-step explanation:

Answer:

V = 3053.63 mm^3

Step-by-step explanation:

radius : 9mm

V = 4/3 * pi * r^3

V = 4/3 * (3.1415926535898...) * 9^3

V = 3053.63 mm^3

The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,

8/ Sin(30°) = 11/ Sin(θ)

Sin(θ) = [11 × Sin(30°)]/8

Sin(θ) = 0.6875

θ = Sin⁻¹ (0.6875)

θ = 43.4325° ≈ 43°

Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

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The total cost for a person who purchases a car share and uses it for 72 hours is $1207.

The total cost is a function of the yearly fee and the cost per hour.

Total cost = yearly fee + (total hours the car was used for x cost per hour)

$199 + (72 x $14)

$199 + $1008 = $1207

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Answer:

$164.66

Step-by-step explanation:

Just subtract them from each other

Answer: ~96.83°

Step-by-step explanation:

1) It's obvious that the largest angle is the opposite to the largest side.

▪︎ QR = 18 (the largest side)

=> <QPR is the largest angle

2) Cosine Rule:

▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)

▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)

▪︎ 324 = 169 + 121 - 286*cos(QPR)

▪︎ 34 = -286*cos(QPR)

▪︎ cos(QPR) = -34/286

▪︎ <QPR = arccos(-34/286) = 96.827...°

Answer:

(a) 6ab² - 8a²b + 3ab

Step-by-step explanation:

Given: 5ab² - 12a²b + 3ab + ab² + 4a²b

In this question, we will be combining like terms.

What are like terms?

Like terms are terms with the same variables and power. For example, 2x and 4x, as well as 2a² and 4a².

Combine like terms:

5ab² - 12a²b + 3ab + ab² + 4a²b

(5ab² + ab²) + (-12a²b + 4a²b) + 3ab

6ab² - 8a²b + 3ab

[tex]~~~~~~~~y = (x-4)^2 +6\\\\\implies (x-4)^2 = y-6 \\\\\implies x -4 = \pm\sqrt{y-6}\\\\\implies x = \pm\sqrt{y-6} +4[/tex]

Answer:

Vertex(1,7)

Vertex form: [tex]f(x)=-2\left(x-1\right)^2+7[/tex]

Step-by-step explanation:

Vertex form equations for x is [tex]v=-\frac{b}{2a}[/tex]

which the vertex here is

[tex]-\frac{4}{2\left(-2\right)}[/tex]

->

x = 1, plugin to find y, y = 7

if its diameter is 9, that means its radius is half that, or 4.5.

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]

The surface area of the basketball with diameter of 9 in will be 254.34 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given that, a basketball has a diameter of 9 inches we need to find its surface area,

Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²

Therefore, the surface area of the basketball =

= 4×3.14×(9/2)²

= 4×3.14×4.5×4.5

= 254.34 in²

Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².

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Answer:

A

Step-by-step explanation:

for the relation to be a function then each value of x in the domain must map to exactly one unique value of y in the range

this is the case for A

in B : 3 → 2 and 3 → 8 ← not a function

in C : - 2 → 5 and - 2 → 7 ← not a function

in D : 2 → 2 and 2 → 3 and 3 → 3 and 3 → 2 ← not a function

Answer:

6-2w(w+2)

Step-by-step explanation:

6-2w²+4w

6-2w(w+2)

Answer:

your answer is 9 large binders

Answer:

1.8125 lb(pounds)

Step-by-step explanation:

there are 16  oz in 1 lb

so 29/16 = 1.8125

Answer:

See below

Step-by-step explanation:

y = -3 x^7   is NOT a parabola....   y = -3x^2  IS a parabola that opens downward due to the negative coefficient (-3)

A quadratic equation is in the form of ax²+bx+c. It took 3seconds for the golf ball to reach the green.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

A.) The time that the ball takes to reach the green can be found by equation the equation against zero. As the ball will have 0 height when it will be on the green,

t²+4t-21=0

t²+7t-3t-21=0

t(t+7)-3(t+7)=0

(t+7)(t-3)=0

t = -7, 3

Hence, it took 3seconds for the golf ball to reach the green.

B.) Since the time can not be negative the second value is wrong.

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Answer:

Given function:

[tex]f(x)=6x^2+x-2[/tex]

To find the zeros of the function, set the function to zero and factor:

[tex]\implies 6x^2+x-2=0[/tex]

[tex]\implies 6x^2+4x-3x-2=0[/tex]

[tex]\implies 2x(3x+2)-1(3x+2)=0[/tex]

[tex]\implies (2x-1)(3x+2)=0[/tex]

Therefore, the zeros are:

[tex]\implies (2x-1)=0 \implies x=\dfrac{1}{2}[/tex]

[tex]\implies (3x+2)=0 \implies x=-\dfrac{2}{3}[/tex]

If α and β are the zeros of the function:

Question 1

[tex]\begin{aligned}\implies \alpha^2+\beta^2 & =\left(\dfrac{1}{2}\right)^2+\left(-\dfrac{2}{3}\right)^2\\\\& = \dfrac{1}{4}+\dfrac{4}{9}\\\\& = \dfrac{9}{36}+\dfrac{16}{36}\\\\& = \dfrac{25}{36}\end{aligned}[/tex]

Question 2

[tex]\begin{aligned}\implies \dfrac{1}{\alpha}+\dfrac{1}{\beta} & = \dfrac{1}{\frac{1}{2}}+\dfrac{1}{-\frac{2}{3}}\\\\& = 1 \times \dfrac{2}{1}+1 \times -\dfrac{3}{2}\\\\& = 2 - \dfrac{3}{2}\\\\& = \dfrac{1}{2}\end{aligned}[/tex]

Answer:

[tex]1) ~\alpha^2+\beta^2 = \dfrac{25}{36}\\\\\\2)~\dfrac 1 {\alpha} + \dfrac 1{\beta} = \dfrac 12[/tex]

Step-by-step explanation:

[tex]\text{Given that,}\\\\f(x) = 6x^2 +x -2~ \text{and the roots are}~ \alpha, \beta\\\\\text{Now,}\\\\\alpha + \beta = -\dfrac{b}{a} = -\dfrac{1}{6}~~~~~;[\text{Compare with the standard form}~ ax^2 +b x + c = 0]\\\\\alpha \beta = \dfrac ca = -\dfrac2 6 = - \dfrac 13\\\\\\\textbf{1)}\\\\\alpha^2 +\beta^2\\\\\\=\left(\alpha +\beta \right)^2 - 2 \alpha \beta \\\\\\=\left( -\dfrac 16 \right)^2 -2 \left(- \dfrac 13 \right)\\\\\\=\dfrac{1}{36}+\dfrac 23\\\\\\=\dfrac{25}{36}[/tex]

[tex]\textbf{2)}\\\\\dfrac 1{\alpha} + \dfrac 1{\beta} \\\\\\=\dfrac{\alpha + \beta}{\alpha \beta }\\\\\\=\dfrac{-\tfrac16}{-\tfrac 13}\\\\\\=\dfrac{1}{6} \times 3\\\\\\=\dfrac{1}{2}[/tex]

Answer:

5. m<STP = 134

6. m<PTS = 158

Step-by-step explanation:

5. Since ray TR bisects <PTS, angles PTR and STR are congruent.

m<PTR = m<STR

3x - 8 = 2x + 17

Subtract 2x from both sides.

x - 8 = 17

Add 8 to both sides.

x = 25

m<STP = 2m<PTR

m<STP = 2(3x - 8)

m<STP = 2(3 × 25 - 8)

m<STP = 2(67)

m<STP = 134

6.

2m<PTR = m<PTS

2(x - 23) = x + 56

2x - 46 = x + 56

x = 102

m<PTS = x + 56

m<PTS = 102 + 56

m<PTS = 158

Answer:

86

Step-by-step explanation:

the equation that needs to be made is

(95+ 91+ 88+ x)/4 = 90

this means that the sum of 95, 91, 88, and x is 360.

95 plus 91 is 186. 186 plus 88 is 274

360-274 = 86

give brainliest please!
hope this helps :)

Answer:

255 students

Step-by-step explanation:

we can solve for the number of students who said their favorite color was red by setting up a cross-multiplication equation.

85% is nothing but 85/100

85/100 = ?/300

85 times 300 is 25500

25500/100 = 255

give brainliest, please!

hope this helps :)

Answer: 1

Step-by-step explanation:

.✎let's answer it :3

question ⇩

✎ The area of a newspaper page (opened up) is about 640.98 square inches. Determine the length and width of the page if its length is about 1.25 times its width.

The area of a newspaper page (opened up) is about 640.98 square inches. Determine the length and width of the page if its length is about 1.25 times its width.The width of the page is ___ inches.

hope it helps

correct me if I am wrong

Answer:

P(AUB)=P(A)+P(B)

Step-by-step explanation:

I found it somewhereI don't know?Trust me:)