A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground.

To the nearest tenth of a foot, how far from the building is the base of the ladder?


9.1 ft


30.5 ft


32.3 ft


39.5 ft

Answer:

Acute angle : 30*      Obtuse angle : 120*

Step-by-step explanation:

Hope this helps :)

Answer:

acute angle- less than 90 degrees

obtuse angle- 120 degrees

Step-by-step explanation:

Answer:

[tex]38.47 {m}^{2} [/tex]

Step-by-step explanation:

The formula to find the area of a circle is

[tex] a= \pi {r}^{2} [/tex]

We know that

[tex]\pi = 3.14 \: \: \: \: \: \: r = 3.5[/tex]

Therefore the area is

[tex] a= \pi {r}^{2} \\ \\ a = (3.14) {(3.5)}^{2} \\ \\ a = 3.14 \times 12.25 \\ \\ a = 38.47 {m}^{2}[/tex]

Answer:

we are given A collector’s item is purchased for $150so, its value increases by 3% each yearso, t is time in yearsLet's assume cost of item after t years is C(t)so, we can use formula now, we can plug values so, equation is After doubling C(t)=2*150=300so, we can set C(t)=300and then we can solve for twe get so, doubling time is 23.44977 years

Answer:

B works ; it starts at 150, is positive, and slowly reaches 300

Step-by-step explanation:

Edge

1. A reasonable price for my friend to sell the car is $13,480.

2. This price is determined as an average of the prices of similar cars.

An average is a typical value in a dataset.

An average is the mean of a set of numbers.

The average value can be computed by summing the set of numbers and dividing the result by the number of items.

Prices of similar cars:

A. 13,500

B. 12,900

C. 15,300

D. 13,700

E. 12,000

Sum = $67,400

Average = $ 13,480 ($67,400/5)

Thus, a reasonable price for my friend to sell the car is $13,480, which is the average price of similar cars.

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Hence, [tex]x=13cm[/tex].

What is the triangle?

A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.

Here given that,

Perpendicular is [tex]12cm[/tex]

Base is [tex]5cm[/tex]

Hypotenuse is [tex]x[/tex]

As we know,

[tex]H^2=B^2+P^2[/tex]      ........[tex](1)[/tex]

Now substitue these values in equation [tex](1)[/tex], we get

[tex]H^2=(5)^2+(12)^2\\\\x^2=25+144\\\\x^2=169\\\\x=\sqrt{169}\\\\x=13cm[/tex]

Hence, [tex]x=13cm[/tex].

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Answer:

The slope is 0

Step-by-step explanation:

Solve the equation for y

y+3=0

y = -3

The slope intercept form is

y = mx+b

where m is the slope and b is the y intercept

y = 0x-3

The slope is 0 and the y intercept is -3

Answer: The Slope Is 3

Step-by-step explanation:

You are missing the x after the 3.

considering the linear equation y=mx+b, the coefficient of x is ALWAYS the slope (rate of change)

Solid is a substance that can be measured. The required volume of a solid is 90 cubic cm

The formula for calculating the volume of a solid ie expressed as:

V = lwh

l is the length

w is the width

h is the height

For the given figure;

Volume =  (11 * 2 * 3) + (2 * 3 * 4)
Volume = 66 + 24
Volume = 90 square cm

The required volume of a solid is 90 cubic cm

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Answer:

Length = 12 ft.

Width = 8 ft.

Step-by-step explanation:

Given :

Let :

Solving :

The dimensions are :

Length = 12 ft.

Width = 8 ft.

Answer:

- 8.14 = m = slope

Step-by-step explanation:

We know from the diagram that  8x-7  + 5x+18  = 180    so x = 13

  so 8x -7  =  97

slope = tan 97 = -8.14

Answer:

x = 10.5

Step-by-step explanation:

Intersecting chord theorem : If two chords intersect within a circle then the product of the measures of the segemnts made up of the chords are equal to each other.
For more reference to this, kindly view the attatched image.

Applying this theorem we would create an equation which would be 2 × x = 7 × 3

We then solve for x

2 × x = 7 × 3

==> simplify both sides

2x = 21

==> divide both sides by 2

x = 10.5

Answer:

Original price = t = $24

Expression = t + 0.05t

—-

New price = t + 0.05t = 24 + (0.05*24) = $25.20

—-

Have a nice day!!

Answer:

$25.20

Step-by-step explanation:

Original price = t = $ 24

New price = 1.05*24

                 = 25.20

Just multiply 1.05 by 24

Answer:

Step-by-step explanation:

what is the mean of 10,16,14,12and 16?

Find the sum of the values by adding them all up.

Divide the sum by the number of values in the data set.

10 + 16 + 14 + 12 + 16 = 68

68 : 5 = 13.6

or

(10 + 16 + 14 + 12 + 16) : 5 = 13.6

Answer:

The to 42 x 42 is 1764

Step-by-step explanation:

22 x 22 = 484

Answer:(approx) 6.

Step-by-step explanation:Here μ=51 and σ=15

Z=

σ

X−μ

​

=

15

X−151

​

When X=120, Z=

15

120−151

​

=−2.067

When X=155, Z=

15

155−151

​

=0.2667

When X=185, Z=

15

185−151

​

=

15

35

​

=2.2667

(i) P(120<X<155)=P(−2.07<Z<0.27)

=∫

−2.067

0.2667

​

ϕ(z)dz=∫

0

0.2667

​

ϕ(z)dz+∫

0

2.0667

​

ϕ(z)dz

=0.4803+0.1026=0.5829.

Here N=500

∴ The number of students whose weight is between 120 and 155 pounds is

0.5872×500=291

(ii) P(X<185)=P(Z>2.27)=∫

2.2667

∞

​

ϕ(z)dz

=∫

0

∞

​

ϕ(z)dz−∫

0

2.2667

​

ϕ(z)dz=0.5−0.4881=0.0119

∴ the number of students with weight about 185 pounds.

=0.0119×500= (approx) 6.

Answer:

1 out of 3 people vote for junior

Step-by-step explanation:

Answer:

120h = 5 days

240h = 10 days

144h = 6 days

720m = 1/2 (half a day)

13w = 91 days

please make this brainliest

Answer:

8.2 * 10^-3 is the greatest and 5.2 * 10^-6 is the smallest.

Step-by-step explanation:

Check the picture below.

[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]

Absolute value of a graph formula:

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

 [tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]

Join them to build the equation:   [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]

Answer:

[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

-----------------------------------------------------------------------------------------

Parent function:  [tex]f(x)=|x|[/tex]

[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]  

From inspection of the graph, the vertex of the transformed function is at (6, -7).  Therefore, there has been a translation of:

[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]

[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]

The line goes through point (0, -3)

Substituting this point into the above equation to find [tex]a[/tex]:

[tex]\implies a|0-6|-7=-3[/tex]

[tex]\implies 6a=4[/tex]

[tex]\implies a=\dfrac{2}{3}[/tex]

Therefore,

[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]

The measure of the third angle in the triangle is 104 degrees

Let the three angles in the triangle be x, y and z.

Such that:

x = 51

y = 25

The sum of angles in a triangle is 180 degrees.

So, we have:

x + y  + z = 180

Substitute known values

51 + 25 + z = 180

Evaluate the sum

76 + z = 180

Subtract 76 from both sides

z = 104

Hence, the measure of the third angle is 104 degrees

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Answer:

6/4-3/2(12/8+27/4)9/8x30/12=

Answer:

[tex]-20\sqrt{3}-5\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]4 \sqrt{12}-\sqrt{50}-7\sqrt{48}[/tex]

Rewrite 12 as 4 · 3  and 50 as 25 · 2 and 48 as 16 · 3 :

[tex]=4 \sqrt{4 \cdot 3}-\sqrt{25 \cdot 2}-7\sqrt{16 \cdot 3}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a \cdot b}=\sqrt{a}\sqrt{b} :[/tex]

[tex]=4 \sqrt{4}\sqrt{3}-\sqrt{25}\sqrt{2}-7\sqrt{16}\sqrt{3}[/tex]

As [tex]\sqrt{4}=2[/tex] and [tex]\sqrt{25}=5[/tex] and [tex]\sqrt{16}=4[/tex] then:

[tex]=4 \cdot 2 \sqrt{3}-5\sqrt{2}-7 \cdot 4\sqrt{3}[/tex]

Simplify:

[tex]=8\sqrt{3}-5\sqrt{2}-28\sqrt{3}[/tex]

Collect like terms:

[tex]=8\sqrt{3}-28\sqrt{3}-5\sqrt{2}[/tex]

Combine like terms:

[tex]=-20\sqrt{3}-5\sqrt{2}[/tex]

If ɑ and β are roots of 2x² - 5x + 7, then

2x² - 5x + 7 = 2 (x - ɑ) (x - β)

Expanding the right side and matching up coefficients, it follows that

2ɑβ = 7   ⇒   ɑβ = 7/2

-2 (ɑ + β) = -5   ⇒   ɑ + β = 5/2

Now consider a polynomial whose roots are 3ɑ + 4β and 4ɑ + 3β, which can be written with factorization

(x - (3ɑ + 4β)) (x - (4ɑ + 3β))

and expanded to get

x² - (7ɑ + 7β) x + (3ɑ + 4β) (4ɑ + 3β)

Expand/factor the coefficients to rewrite them in terms of the known relations above.

x² - 7 (ɑ + β) x + (12ɑ² + 25ɑβ + 12β²)

x² - 7 (ɑ + β) x + 12 (ɑ² + β²) + 25ɑβ

Recall the square of a binomial,

(x + y)² = x² + 2xy + y²

so we rewrite the latter quadratic as

x² - 7 (ɑ + β) x + 12 ((ɑ + β)² - 2ɑβ) + 25ɑβ

x² - 7 (ɑ + β) x + 12 (ɑ + β)² + ɑβ

Then substituting the expressions whose values we know, we get

x² - 7 (5/2) x + 12 (5/2)² + 7/2

= x² - 35/2 x + 157/2

which we can multiply by 2 to get integer coefficients like in the given quadratic,

= 2x² - 35x + 157

Answer:

(0, -12)

Step-by-step explanation:

The y-intercept of a line can be found when taking x = 0.

Therefore,

The y-intercept of the line is (0, -12)

                 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

       ◈ What is the y-intercept of the line, [tex]\bold{y=\dfrac{x}{5} -12}\textit{?}[/tex]

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]

    ◈ Here's a shortcut to find the y-intercept.

Here's the equation:-

[tex]\large\textbf{y=x/5-12}[/tex]

         [tex]\square\!\!\!\!\!\!\triangle[/tex] The y-intercept is a negative or positive constant that's added to or subtracted from the slope.

       Constant:- A number with no variables next to it (for example, in the expression d-12, -12 is the constant)

So we conclude that

             [tex]\Huge\textit{The y-intercept is -12}[/tex].

The y-intercept is usually written as (0, -12).

                       - -- - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - - - - -

The model for representing the ratio of the number of orange and green rolls are  [tex]\dfrac{3}{2}[/tex].

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G

The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.

A model that represents the ratio of different colored streamers.

[tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.

D=3O   and  D=2G

3O=2G

Hence the models are  [tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]  and  3O=2G.

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Answer:

    j = 11

    j = 12

Step-by-step explanation:

   The inequality:

8 ≤ j

   We will test all the options given.

-> In short, all options greater or equal to 8 will be solutions.

j = 12

8 ≤ j

8 ≤ 12 ✓

-

j = 5

8 ≤ j

8 ≤ 5 ✗

-

j = 6

8 ≤ j

8 ≤ 6 ✗

-

j =11

8 ≤ j

8 ≤ 11 ✓

Answer:

12.

Step-by-step explanation:

There are 3 * 4 = 12 possible outcomes

for example

Walk / Red

Walk/Green

Walk/Blue

Walk/Orange

- and there are  4 similar outcomes for Run and Stop.

Answer:

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

Step-by-step explanation:

We can see that with every [tex]x[/tex] value that increases, the [tex]y[/tex] value decreases by [tex]-6[/tex]. Thus the slope is [tex]-6[/tex], which would make the equation: [tex]y = -6x[/tex].