The top of a ladder rests at a height of 15 feet against the side of a house. If the base of the ladder is 6 feet from the house, what is the length of the ladder? Round to the nearest foot.

Answer:

x=−7+√130 or x=−7−√130

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²+14x+17=-98

add 98 to each side

x²+14x+115=0

Solve with quadratic formula

a=1

b=14

c=115

\frac{-14 ±\sqrt{14^2-4*1*115} }{2*1}

Answer:

B is not necessarily true

Step-by-step explanation:

A) This is always true

B) This is not necessarily true

When two lines intersect, they form angles at the intersection as D says, but that does not mean that the angle will always be 90 degrees as is required for the two intersecting lines to be perpendicular

C) This is always true

D) This is always true

Option B) The lines are not perpendicular is not necessarily true.

When two lines intersect and following are the three different possibilities:

1) They are parallel, if lines are parallel they can never intersect.

2)They cross each at an angle and the point of intersection is unique that is they intersect at only one point.

3) Two lines coincide, that is every point on line 1 is a point on line 2.

Now

In option B it is given that lines are perpendicular that is the specific case of (2) When angle is 90°.

Therefore, it is not necessarily true.

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For this case we must simplify the following expression:

[tex]\sqrt {\frac {16} {25}}[/tex]

We can rewrite 16 as:[tex]2 ^ 4 = 2 * 2 * 2 * 2[/tex]

We can rewrite 25 as:[tex]5 ^ 2 = 5 * 5[/tex]

[tex]\sqrt {\frac {2 ^ 4} {5 ^ 2}} =\\\frac {\sqrt {2 ^ 4}} {\sqrt {5 ^ 2}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]\frac {2 ^ 2} {5} =\\\frac {4} {5}[/tex]

Answer:

[tex]\frac {4} {5}[/tex]

ANSWER

[tex]y = 3 \pm \sqrt{21} [/tex]

EXPLANATION

The quadratic equation is:

[tex] {y}^{2} - 6y - 12 = 0[/tex]

Group variable terms:

[tex] {y}^{2} - 6y = 12[/tex]

Add the square of half, the coefficient of y to both sides.

[tex] {y}^{2} - 6y + ( - 3) ^{2} = 12 + ( - 3) ^{2} [/tex]

[tex] {y}^{2} - 6y + 9= 12 + 9[/tex]

The LHS us now a perfect square trinomial:

[tex]{(y - 3)}^{2}= 21[/tex]

Take square root:

[tex]y - 3 = \pm \sqrt{21} [/tex]

[tex]y = 3 \pm \sqrt{21} [/tex]

The first choice is correct.

3±√21. The equation [tex]y^{2}-6y-12=0[/tex] has two possible solutions 3+√21 y 3-√21.

If we have a general quadratic equation [tex]ay^{2} +by+c=0[/tex] we can solves the equation by completing the square. First, we divide the quadratic equation by a, we obtain [tex]y^{2} +\frac{b}{a} y+\frac{c}{a} =0[/tex].

For this problem, we have [tex]y^{2}-6y-12=0[/tex]

We can skipped division in this example since the coefficient of [tex]x^{2}[/tex] is 1.

Move the term c to the right side of the equation

[tex]y^{2}-6y=12[/tex]

Completing the square on the left side of the equation and balance this by adding the same number to the right side of the equation, with b = -6.

[tex](\frac{b}{2})^{2} =(\frac{-6}{2})^{2}=(-3)^{2} =9[/tex]

[tex]y^{2}-6y+9=12+9[/tex]

[tex](y-3)^{2}=21[/tex]

Take the square root on both sides of the equation:

y - 3 = ±√21

Add 3 from both sides:

y = 3 ± √21

Answer: D. 0.53

Step-by-step explanation:

From the given picture, the number of persons from California and prefers brand A = 90

The total numbers of persons prefer brand A = 170

The probability that the person is from California, given that the person prefers brand A will be :-

[tex]\dfrac{\text{Persons from California and prefers brand A}}{\text{Persons prefer brand A}}\\\\=\dfrac{90}{170}=0.529411764\approx 0.53[/tex]

Hence, The probability that the person is from California, given that the person prefers brand A = 0.53

Answer:

D 0.53

Step-by-step explanation:

Answer:

m∠4 = 111°

Step-by-step explanation:

∠4 and ∠5 are same side (interior) angles, and since lines A and B are parallel, they will be congruent.

So, m∠4 = m∠5

Substitute: m∠4 = 111°

I know B is on possible choice for this and maybe d almost certain

c) and d)

c) 4a-6b+2c+c

d) 4a-6b+3c

Answer:

400cm

Step-by-step explanation:

Answer:

it is 400cm2

Step-by-step explanation:

i know things

Hey there!

If we have two white marbles and seven purple marbles, our first probability is out of nine.

First of all, we have the probability of selecting a purple marble, 7/9.

Now, if we do not replace it, there are only eight marbles left. Therefore, getting a white marble is 2/8, or 1/4.

We multiply these probabilities together to get our answer to a.

7/9(1/4)= 7/36

a. 7/36

Now, let's do b. We have 2/9, and then 1/8, giving us 1/36.

b. 1/36

Now, let's calculate selecting two purple to help us with C.

We have 7/9, and then 6/8, or 3/4.

7/9(3/4)= 7/12

Since there is a majority of purple marbles, there is a C) greater probability of selecting two purple marbles in a row.

I hope this helps!

Answer:

A. 7:9 B. 1:4 C. Purple

Step-by-step explanation:

A. Because there are 7:9 B. Because 1:4 C. Because Purple has more

Answer:

Step-by-step explanation:

[tex]k - \text{scale of similar}[/tex]

[tex]\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ \dfrac{length_{AB}}{length_{CD}}=k[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{area_A}{area_B}=k^2[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{volume_A}{volume_B}=k^3[/tex]

[tex]\text{We have}\ B\sim A\ \text{in scale}\ k=5.\ V_A=12\ m^3,\ \text{therefore}\\\\\dfrac{V_B}{V_A}=k^3\to\dfrac{V_B}{12}=5^3[/tex]

[tex]\dfrac{V_B}{12}=125[/tex]            multiply both sides by 12

[tex]V_B=1500\ m^3[/tex]

Answer:

8800

Step-by-step explanation:

a yard is equals 3 feet a mile is 5 280

Answer: 8800 yards

Step-by-step explanation:

1 mile = 1760 yards

1760 yards x 5 miles = 8800 yards

Answer:

4x + y = 32

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, 4) and (x₂, y₂ ) = (5, 12)

m = [tex]\frac{12-4}{5-7}[/tex] = [tex]\frac{8}{-2}[/tex] = - 4, thus

y = - 4x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation.

Using (7, 4), then

4 = - 28 + c ⇒ c = 4 + 28 = 32

y = - 4x + 32 ← in slope- intercept form

Add 4x to both sides

4x + y = 32 ← in standard form

Answer:

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Power: 3

5

^ 3 = 33

53

= 27

125

Answer:

x=-1/2

Step-by-step explanation:

Given:

8x^3+12x^2+6x+1=0

Making factors of the given polynomial by using cube formula, given as

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Re-writting the given polynomial:

(2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3)=0

Hence (2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3) can be written as (2x+1)^3

(2x+1)^3= 0

2x+1= 0

2x= -1

x= -1/2 !

Answer:

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=l\times w[/tex]

l - length

w - width

We have l = x + 12 and w = x - 5. Substitute:

[tex]A=(x+12)(x-5)[/tex]       use FOIL (a + b)(c + d) = ac + ad + bc + bd

[tex]A=(x)(x)+(x)(-5)+(12)(x)+(12)(-5)[/tex]

[tex]A=x^2-5x+12x-60[/tex]         combine like terms

[tex]A=x^2+7x-60[/tex]

[tex](2x-5)(3x^2-4x+2)[/tex]      use the distributive property a(b + c) = ab + ac

[tex]=(2x-5)(3x^2)+(2x-5)(-4x)+(2x-5)(2)\\\\=(2x)(3x^2)+(-5)(3x^2)+(2x)(-4x)+(-5)(-4x)+(2x)(2)+(-5)(2)[/tex]

[tex]=6x^3-15x^2-8x^2+20x+4x-10[/tex]       combine like terms

[tex]=6x^3+(-15x^2-8x^2)+(20x+4x)-10\\\\=6x^3-23x^2+24x-10[/tex]

Answer:

12 gallons

Step-by-step explanation:

let x be the amount tank can hold, then

[tex]\frac{1}{3}[/tex] x + 2 = [tex]\frac{1}{2}[/tex] x

Multiply through by 6

2x + 12 = 3x ( subtract 2x from both sides )

12 = x

The tank can hold 12 gallons

Greg's gas tank can hold 12 gallons of gas. We know this because when Greg's tank is 1/3 full and he buys 2 gallons of gas it becomes 1/2 full. The difference between 1/2 and 1/3 of a tank, or 1/6 of the tank, is equal to 2 gallons.

The subject of this question is mathematics, specifically within the scope of fractions and simple algebra. The question tells us that when Greg's gas tank is 1/3 full and he adds 2 gallons, the tank becomes 1/2 full. This tells us that the difference between 1/2 and 1/3 of the tank's capacity is equal to 2 gallons. In mathematical terms, this can be represented as 1/2 - 1/3 = 2/6 - 2/6 = 1/6. Therefore, 1/6 of Greg's gas tank equals 2 gallons. If 1/6 of the tank equals 2 gallons, the entire tank (or 6/6) would hold 12 gallons of gasoline.

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Answer:

the answer is 37.7 so the point closest to 40.

Step-by-step explanation:

Answer: the one between 30 and 40

Step-by-step explanation:

Answer:

-4,4

Step-by-step explanation:

I just answered it on edge and got it right trust me

The coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

Rectangle ABCD is rotated 360 around the origin.

If any object is rotated by 360 degrees about the origin. Then the position of the object does not change.

Then the coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.

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Answer:

The value of x is 4√5 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the rules in the right angle triangle when we draw the

 perpendicular from the right angle to the hypotenuse

- In triangle ABC

# Angle B is a right angle

# The hypotenuse is AC

# BD ⊥ AC

∴ (AB)² = AD × AC

∴ (BC)² = CD × AC

∴ (BD)² = AD × CD

∴ BD × AC = AB × BC

* Lets use one of these rules to solve the problem

- y is the perpendicular from the right angle to the hypotenuse

- x is one leg of the right angle

∵ The length of the hypotenuse = 5 + 11 = 16 units

∵ The part nearest to x = 5

* Lets use the rule (AB)² = AD × AC

∴ x² = 5 × 16 = 80 ⇒ take √ for both sides

∴ x = √80 = 4√5 units

Find the circumference:

Circumference = 2 x PI x radius

Circumference = 2 x 3.14 x 19 = 119.32

Divide by 4: 119.32 / 4 = 29.83 rounded to 29.8

The answer is C.

Answer:

C. 29.8 inches

Step-by-step explanation:

Length of complete hula hoop(L)= circumference of hoop

=>[tex]L=2\pi r[/tex]

where radius, r= 19 inches

Therefore length of arc(l) subtending 1/4 of the hoop is

=>[tex]l=\frac{1}{4}\times L=\frac{1}{4}\times2\pi r=\frac{\pi r}{2}[/tex]

=>[tex]l=\frac{\pi \times 19}{2}inches=29.8 inches[/tex]

Thus the length of the arc subtending 1/4 of the hoop is 29.8 inches

Answer:

Step-by-step explanation:

Without a second equation relating x and y, we can solve 3x - 1/2y = 2 ONLY for x in terms of y or for y in terms of x:

x in terms of y:    Multiply all three terms of 3x - 1/2y = 2 by 2, to eliminate the fraction:  6x - y = 4.  Now add y to both sides to isolate 6x:  6x = 4 + y.

Last, divide both sides by 6 to isolate x:

x = (4 + y)/6

y in terms of x:    

y = 6x - 4

If you want a numerical solution, please provide another equation in x and y and solve the resulting system.

[tex]

\frac{\sqrt{9}}{\sqrt{81}}=\frac{3}{9}=\boxed{\frac{1}{3}}

[/tex]

The answers are A and B.

Hope this helps.

r3t40

Answer:

C

Step-by-step explanation:

proportion can be used to show that the slope of AC is equal to the slope of CG

Slope of AC = (2-0)/(3-0) = 2/3

Slope of CG = (6-2)/(9 -3) = 2/3

So answer is :

C)

      2 − 0        6 − 2

   ------------ =  -----------

      3 − 0         9 − 3

Answer:C

Step-by-step explanation:

Answer:

The missing image from the problem is attached

The answer is (C) Each of the lateral faces has an area of 464 square inches.

Step-by-step explanation:

Base is a square that is 32 in

The height of one of the 4 lateral faces is 29 in

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

Base is L*W --> 32*32 = 1024 square inches

(1) Lateral face is 1/2*b*h = 0.5*32*29 = 464 square inches

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

Since the answers are about the face and/or one lateral face only, those two numbers are important. (C) is the only answer that matches

Each of the lateral faces has an area of 464 square inches , Option C is the correct answer

A square pyramid is a three dimensional figure , having square as the base and four triangular faces which meet at a single point called at a single point.

It is given in the question (figure is attached )

Base of the square pyramid is 32 in

The height of one of the 4 triangle is 29 in

Area of the base = 32* 32

= 1024 sq.in

Area of the lateral face (triangle ) =  1/2*b*h

= (1/2) * 32 * 29

= 464 sq. in

Therefore Option C is the correct answer , Each of the lateral faces has an area of 464 square inches.

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Answer:

No triangle can be constructed with given measures.

Step-by-step explanation:

Refer the following figure.

     AB = c = 7.6 cm

     AC = b = 5.4 cm

     ∠ABC = B = 50°

Sine rule is given by [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting

        [tex]\frac{5.4}{sin50}=\frac{7.6}{sinC}\\\\sinC=1.078[/tex]

Value of sinC is more than 1, which is not possible.

Hence no triangle can be constructed with given measures.

Answer:

y=-1x+5

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-1}{5-4}\implies \cfrac{-1}{1}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-1(x-4) \\\\\\ y-1=-x+4\implies y=-x+5[/tex]

Hey there! :D

f(-3)= 4(2)^x

Just plug in -3 as x and solve.

4(2)^-3

First do the exponent, and then multiply the four on the outside.

4(1/8)

=1/2

I hope this helps!

~kaikers

Final answer:

To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.

Explanation:

To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:

Start with the original function f(x) = 4(2)ˣ.

Replace every x with -3 to get f(-3) = 4(2)⁻³.

Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.

Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.

Therefore, f(3) for the given function equals 1/2.

Answer:

13%

Step-by-step explanation:

Please use the $ sign.

The simple interest formula is i = p*r*t, where p is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years.  Here, t = 1/4 year; r is unknown, p is $5004 and i is $162.63.

Writing this out with the given info, we get:

$162.63 = $5004*r*(1/4).

We can solve this for r by multiplying both sides by 4/$5004:

(4/$5004)($162.63)  = (4/$5004)($5004)*r*(1/4) = r

Evaluating r, we get (4)($162.63)/$5004 = 0.13

The interest rate, r, is 0.13, or 13%.

Answer:

[tex]1.\ m<6\\2.\ g\leq-4\\3.\ y<41\\4.\ b<4\\5.\ h<-30\\6.\ x>-2\\7.\ t>9\\8.\ w<28[/tex]

Step-by-step explanation:

1. Subtract 10 from both sides. Then:

[tex]m+ 10< 16\\ m+ 10-10< 16-10\\m<6[/tex]

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-2g\geq8\\\\\frac{-2g}{-2}\geq\frac{8}{-2}\\\\g\leq-4[/tex]

3. Add 22 to both sides. Then:

[tex]y-22< 19\\ y-22+22<19+22\\y<41[/tex]

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-7b>-28\\\\\frac{-7b}{-7}>\frac{-28}{-7}\\\\b<4[/tex]

5. Subtract 30 from both sides. Then:

[tex]h+30<0\\ h+30-30<0-30\\h<-30[/tex]

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-5x<10\\\\\frac{-5x}{-5}<\frac{10}{-5}\\\\x>-2[/tex]

7. Subtract 13 from both sides. Then:

[tex]t+13>22\\ t+13-13>22-13\\t>9[/tex]

8. Add 12 to both sides. Then:

[tex]w-12< 16\\ w-12+12<16+12\\w<28[/tex]

Answer:

First option: (1, 1)

Second option: (-3, 4)

Step-by-step explanation:

Substitute each point into the inequality:

Point (1,1):

[tex]x + 2y \geq3\\\\(1) + 2(1) \geq3\\\\3\geq3[/tex]

(The inequality is satisfied with this point)

Point (-3, 4):

[tex]x + 2y \geq3\\\\(-3) + 2(4) \geq3\\\\5\geq3[/tex]

 (The inequality is satisfied with this point)

Point (-2, 2):

[tex]x + 2y \geq3\\\\(-2) + 2(2) \geq3\\\\2\geq3[/tex]

(The inequality is not satisfied with this point)

Point (5, -2):

[tex]x + 2y \geq3\\\\(5) + 2(-2) \geq3\\\\1\geq3[/tex]

(The inequality is not satisfied with this point)

Answer:

Your answer would be A and B

Step-by-step explanation: