A ladder is leaning against the side of a 10cm house. If the base of the ladder is a 3cm away from the house, how tall is the Ladder

Answer:

m∠J = 32°

m∠G = 78°

Step-by-step explanation:

ΔHJI ≈ ΔGEF respectively means;

∠H ≅ ∠G

∠I ≅ ∠E

∠J ≅ ∠F

Therefore;

Since  ∠F = 32°, then ∠J = 32°

Since ∠H = 78°, then ∠G = 78°

Hope this helps!

Answer:

the answer is 8,000.

Step-by-step explanation:

Answer:

Quesiton is not clear. here is the asnswer basing on our understand

Step-by-step explanation:

(8-32)3 = (-24*3) = =72

Answer:

w=-1+[tex]\sqrt{2}[/tex], w=-1-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

45544554554554445455544

Step-by-step explanation:

Answer:

y = mx + b

m =(-2--4)/(-6--7)

m = 2

-2 = 2(-6) +b

b = 10

y= 2x + 10

Answer:

i need more informatiion

Step-by-step explanation:

The best i could find out is 450p

Answer:

$1,260

Step-by-step explanation:

30% off  

pay 70%

70% = 0.7

1,800 * 0.7 = 1,260

$1,260

We know that ,

[tex]\pi rad = 180^o[/tex]

Using Unitary Method ,

[tex]\implies 1 \ rad = \dfrac{180^o}{\pi } [/tex]

Therefore ,

[tex]\implies \dfrac{10\pi}{6} rad = \dfrac{10\pi}{6} * \dfrac{180^o}{\pi } [/tex]

[tex]= \boxed{\red{ 300^o }}[/tex]

Required answer !

Answer:

Step-by-step explanation:

11 no

46+4x=90 degree(being perpendicular)

4x=90-46

x=44/4

x=11

12 no

They are complementary angles

6 no

angle B+27=180 degree(being straight line)

angle B=180-27

angle B=153

10 no

angle 38 +angle DFE=180 degree(being supplementary)

angle DFE=180-38

angle DFE=142 degree

5 no

They are vertically opposite angles.

7 no

angle AGF and angle CGD (because they have common arm and vertex)

Answer:

Solution given:

11.4x+46=90[being right angle]

4x=90-46

x=44/4

x=11

12.

Complementary angles

5.

vertical

6.

<ABD+27=180°[linear pair]

<ABD=180-27

<ABD=153° degree

10.

<DFE+38=180[being supplementary]

<DFE=180-38

<DFE=142 degrees.

7.

angle DGE and angle DGC

8.

<AGB and <AGE

Answer:

answer is optioc c

Step-by-step explanation:

area of circular pizza=pie*diameter

=1/4*pie*d^2

=3.14/4*100

=314/4

=78.5

area of square pizza=l^2

=9^2

=81

therefore square pizza is bigger in area than circular pizza.

Answer:

[tex]A + B + E = 32[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

Required

Find [tex]A +B + E[/tex]

We have:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

Using integration by parts

[tex]\int {u} \, dv = uv - \int vdu[/tex]

Where

[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]

Solve for du (differentiate u)

[tex]du = 2x\ dx[/tex]

Solve for v (integrate dv)

[tex]v = -\frac{1}{4}e^{-4x}[/tex]

So, we have:

[tex]\int {u} \, dv = uv - \int vdu[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]

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

Solving

[tex]\int xe^{-4x} dx[/tex]

Integration by parts

[tex]u = x[/tex] ---- [tex]du = dx[/tex]

[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]

So:

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]

[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]

So, we have:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]

Open bracket

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]

Factor out [tex]e^{-4x}[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]

Rewrite as:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]

Recall that:

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]

[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]

By comparison:

[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]

[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]

[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]

Solve A, B and C

[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]

Divide by [tex]-x^2[/tex]

[tex]\frac{1}{4} = \frac{1}{64}A[/tex]

Multiply by 64

[tex]64 * \frac{1}{4} = A[/tex]

[tex]A =16[/tex]

[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]

Divide by [tex]-x[/tex]

[tex]\frac{1}{8} = \frac{1}{64}B[/tex]

Multiply by 64

[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]

[tex]B = 8[/tex]

[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]

Multiply by -64

[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]

[tex]E = 8[/tex]

So:

[tex]A + B + E = 16 +8+8[/tex]

[tex]A + B + E = 32[/tex]

Answer: C 22.5 ft2!

Step-by-step explanation:

i took the test, have a great day:) <3

Answer:

right

Step-by-step explanation:

Answer:

hope it helps uh

Answer:

11 inches

Step-by-step explanation:

Given :

15 in of wire = 90 cents

At the same rate :

x inch of wire = 66 cents

Cross multiply :

90x = 15 * 66

90x = 990

x = 990 / 90

x = 11

11 inches of wire

Answer:

Length of Line AC = 26 units

Step-by-step explanation:

Given:

Line AC = [3x + 1] + 8

Line BC = [x - 2] + 2

Find:

Length of Line AC

Computation:

Line AB ║ Line L

So,

Using Mid-Point theorem;

[3x + 1] / 8 = [x - 2] / 2

2[3x + 1] = 8[x - 2]

6x + 2 = 8x - 16

8x - 6x = 16 + 2

2x = 18

x = 9

So,

Line AC = [3x + 1] + 8

Line AC = [3(9) + 1] + 8

Line AC = [27 + 1] + 8

Line AC = 28 + 8

Length of Line AC = 26 units

9514 1404 393

Answer:

  a = 6, b = 12, c = 6, d = 6√3

Step-by-step explanation:

The two triangles are the "special" triangles.

The 45-45-90 triangle has side lengths in the ratios 1 : 1 : √2.

The 30-60-90 triangle has side lengths in the ratios 1 : √3 : 2.

Then ...

  c : a : 6√2 = 1 : 1 : √2   ⇒   c = a = 6

and ...

  a : d : b = 1 : √3 : 2   ⇒   d = 6√3 and b = 12 . . . (since a=6)

The lengths are ...

  a = 6, b = 12, c = 6, d = 6√3

Answer:

Step-by-step explanation:

There are 20 men and 8 of them prefer movies.

Answer:

Step-by-step explanation:

angle 3 and angle 4 are co interior angles.so,

angle 3+angle 4=180 degree

sum of co interior angle is always 180 degree.

Answer: Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary

Step-by-step explanation:

It should be noted that Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary.

For example, if angle 3 is 60°, the value of angle 5 will be:

= 180° - 60°

= 120°

Answer:

2 is the probability

Step-by-step explanation:

Answer:

[tex]y = \frac{-1}{5}x -4[/tex]

Step-by-step explanation:

[tex]x + 5y = -20\\\\5y = -x - 20\\\\y = \frac{-1}{5}x - 4[/tex]

Step-by-step explanation:

Given in the question,

C(8,2)

Formula to use:

nCr = n! / r! * (n - r)!

here n = 8

r = 2

We have to calculate combinations of 8 object taken 2 at a time, then

C(8,2)

8C2

8! / 2! * (8 - 2)!

56/2

28

So, 8C2 = 28

Answer:

8 days

Step-by-step explanation:

1 ton=2,000 pounds and If you divide 2,000÷250=8 days. It will talk 8 days for the baby whale to weigh his first ton.

Answer:

the equation is 11+1.2d= h      so the height after 9 days would be 21.8cm

Step-by-step explanation:

Answer:

f(h) = 11 + 1.2h

f(9) = 21.8 cm

Step-by-step explanation:

let 'h' = height

f(h) = 11 + 1.2h

height after 9 days:

f(9) = 11 + 1.2(9)

= 11 + 10.8

= 21.8 cm

Answer:

62 degrees since there are supplementary angles

Step-by-step explanation:

∠PQO= 180 degrees - 118 degrees

∠PQO= 62 degrees is the answer.

∠PQO= 180°-∠RQO -------(Supplementary Angles)

∠PQO= 180° - 118°

∠PQO= 62° answer.

Answer:

a) The null hypothesis is [tex]H_0: \mu = 310[/tex] and the alternative hypothesis is [tex]H_1: \mu < 310[/tex].

b) The test statistic is [tex]t = -1.54[/tex]. The critical value is [tex]t_c = -2.473[/tex].

c) The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.

Step-by-step explanation:

Question a:

Costco is interested in finding out whether the mean transaction time is less than 310 seconds.

At the null hypothesis, we test if the mean is of 310 seconds, that is:

[tex]H_0: \mu = 310[/tex]

At the alternative hypothesis, we test if the mean is of less than 310 seconds, that is:

[tex]H_1: \mu < 310[/tex]

b) Find the test statistic and the critical value at 1% significance level.

Test if the mean is less than a value, sample of 28, and standard deviation for the sample. Thus, we have a left-tailed t-test with 28 - 1 = 27 degrees of freedom and a 0.01 significance level, and the critical value is [tex]t_c = -2.473[/tex].

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation pf the sample and n is the size of the sample.

310 is tested at the null hypothesis:

This means that [tex]\mu = 310[/tex].

A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds.

This means that [tex]n = 28, X = 296, s = 48[/tex].

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{296 - 310}{\frac{48}{\sqrt{28}}}[/tex]

[tex]t = -1.54[/tex]

The test statistic is [tex]t = -1.54[/tex].

c) At 1% level of significance, what is your conclusion

The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.

Answer:

Step-by-step explanation:

1). If two right triangles are congruent by HL property of congruence,

   Their corresponding sides will be congruent.

   By this property,

   x - 4 = y + 3

   x - y = 7 -----(1)

   x = 2y ------(2)

   By substituting x = 2y in equation (1),

   2y - y = 7

    y = 7

    From equation (1)

    x - 7 = 7

    x = 15

2). If both the right triangles are congruent by HL property of congruence,

    Their height and and hypotenuse will be congruent.

    y + x = x + 7

    y = 7

    y + 5 = 2y - x

    y - 2y + 5 = -x

    -y + 5 = -x

    x = y - 5

    By substituting y = 7 in the equation,

    x = 7 - 5

    x = 2

Answer: c

Step-by-step explanation: because yes

Answer:

d po answer

yan po sinagot ko

hehe