An Isosceles triangle has single measures 55,55,and 70. The side across from the 70 angle is 10 inches long. How long are the other sides?

Final answer:

The angle between the longest side and the diagonal of a 577mm by 1000mm rectangle can be found by first calculating the diagonal using the Pythagorean theorem and then using the arccosine function to find the angle with the longest side.

Explanation:

To calculate the angle between the longest side of a 577mm by 1000mm rectangle and the diagonal, we first need to determine the length of the diagonal using the Pythagorean theorem. The diagonal (d) can be found using the formula d = [tex]\sqrt{(width^2 + height^2)}[/tex]. After calculating the diagonal, we can find the angle using trigonometric ratios, specifically the arccosine function or cos-1.

Step 1: Calculate the diagonal
d = [tex]\sqrt{(577mm^2 + 1000mm^2) }[/tex]=  [tex]\sqrt{(333929 + 1000000) }[/tex] = [tex]\sqrt{1333929}[/tex] ≈ 1155mm

Step 2: Calculate the angle
The angle (θ) between the longest side (adjacent side) and the diagonal (hypotenuse) is given by:
θ = cos-1(adjacent side / hypotenuse) = cos-1(1000mm / 1155mm)

To find the angle, use a calculator to compute the arccosine of 1000/1155.

Answer:

? = 5

Step-by-step explanation:

Replacing "?" with x and doing parenthesis first, we have:

[tex](4 * 3) + (4 * 7) = 4 * (? + ?)\\=(4 * 3) + (4 * 7) = 4 * (x + x)\\=12+28=4*2x[/tex]

Now simply doing algebra and solving for "x", we will get the value of "?":

[tex]12+28=4*2x\\40=8x\\x=\frac{40}{8}=5[/tex]

Answer:

The graph of function f of x equals log base 3 of x.

Step-by-step explanation:

We have the following equation:

3^y = 8

Taking logarithm(Logarithm with base equal 3) in both sides, we have:

lg_3 (3^y) = lg_3 (8)

ylg_3 (3) = lg_3 (8)

y = lg_3 (8)

So, you can approximate the value of y using the function f(x) = base 3 log (x). Just look for the value of that function for x = 8.

Answer:

A≈78.56cm²

Hope this helps you out!

c = 2(pi)r = 31.42cm

2(3.14)r = 31.42cm

6.28r = 31.42cm

r = 31.42cm / 6.28

r = 5cm

A = (pi)r^2

= (3.14) (5)^2

5x5 = 25cm

25x3.14= 78.5cm

the area equals 78.5cm

Answer:

-3.2171798824

Step-by-step explanation:

Answer:

∠A = 58°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ACD is an exterior angle

∠A and ∠B are the opposite interior angles, thus

∠A + 80 = 138 ( subtract 80 from both sides )

∠A = 58°

Answer:

2x-1 x -3x1=-9?

Step-by-step explanation:

This might be the right answer unless it is multiple choice

Answer: 44%

Step-by-step explanation:

From the given picture , it can be seen that the rectangle is divided into 25 equal sections.

The number of shaded sections= 11

Now, the percent is represented by the shaded area is given by :_

[tex]\dfrac{\text{Number of shaded sections}}{\text{Total sections}}\times100\\\=\dfrac{11}{25}\times100=44\%[/tex]

Hence, the  percent is represented by the shaded area =44%

Answer:

44%

Step-by-step explanation:

The ratio of shaded pieces to total pieces is 11 : 25.

Percent means per hundred.

So, we need an equivalent ratio that will tell us how many pieces would be shaded out of 100 total pieces.

44:100= 44 per hundred = 44%

44% is represented by the shaded area.

Hope this helped!! :D

Answer:

1/3, 1/2, and 4/5.

Step-by-step explanation:

This is the correct answer to this question.

Hope this helps!!!

Kyle.

Answer:

image 1

Step-by-step explanation:

Given data:

f(x) = (x+3)(x-2)

     = x^2 + x-6

As the given expression is a quadratic expression so the graph will be parabola.

Also coefficient of x^2 is 1, 1>0 hence we'll the parabola opens upwards

that reduces our options to image 1 and 2 only

now to find the x-axis points of parabola

let (x+3)(x-2)=0

    (x+3)=0 and (x-2)=0

     x= -3 and x= 2

when at y=0, x= -3 and x=2

hence the image 1 !

Answer:

[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]

Step-by-step explanation:

To compare fractions is useful to express the fractions as decimals and compare the values of the decimals first.

Using a calculator we can find that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex].

Now, remember that wen comparing negative numbers the smallest number is the greater one; this is because the closest a negative number is to zero the greatest is value.

-0.66666... and -0.25 are both negative. Since -0.25 is smaller (closer to zero), -0.25 is bigger than -0.66666... In other words, -0.25 > -0.66666...

We know that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex], so we can get back to our original fractions:

[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]

We can conclude that [tex]-\frac{2}{8}[/tex] is greater than [tex]-\frac{2}{3}[/tex]

Hi there,

9. Which of the following is the value of x in the solution to the

system of equations given below?

8 + 2x = 5y  (1)

4x - y = 2  (2)

▪ (1)

y = ( 8 + 2x ) ÷ 5

▪ (2)

4x - [( 8 + 2x ) ÷ 5] = 2

( 20x - 8 - 2x ) ÷ 5 = 2

20x - 8 - 2x = 2 × 5

20x - 2x = ( 2 × 5 ) + 8

18x = 10 + 8

18x = 18

x = 18 ÷ 18

x = 1

The answer is : A. 1

•It was nice to help you, SkullNoggin!

Answer: A set of dots that arent in a line-esc shape.

(Think of  a scatter plot)

I'm bad at explaining, sorry.

The best way to define this is *any highest degree term greater than 1⃣*.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

P(tail ) = [tex]\frac{1}{2}[/tex]

numbers less than 3 are 1 and 2, hence

P(number < 3 ) =[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

P(tail ) and P(number < 3 )

= [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{6}[/tex]

the scale factor is .25

6×.25=1.5

Answer: The expression that represents the employee’s take-home pay after all deductions is (0.85x-297.5) dollar.

Source:

https://brainly.in/question/5606640

Answer:

slope = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

Select any 2 ordered pairs from the given table, the use the slope formula to calculate the slope m

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 5) and (x₂, y₂ ) = (4, 10) ← 2 ordered pairs from table

m = [tex]\frac{10-5}{4-2}[/tex] = [tex]\frac{5}{2}[/tex]

Answer:

3x(x^2-4x+9)

Step-by-step explanation:

The polynomial 3x^3 - 12x^2 + 27x is factored by first taking out the greatest common factor of 3x, resulting in the final form of 3x(x^2 - 4x + 9), which cannot be factored further over the real numbers due to a negative discriminant.

To factor the polynomial 3x^3 - 12x^2 + 27x, we look for common factors in each term.

We can see that each term of the polynomial has a factor of 3x. So, we factor out 3x from the polynomial:

3x(x^2 - 4x + 9)

Now, we try to factor the quadratic expression x^2 - 4x + 9. However, this quadratic does not have real roots since the discriminant (b^2 - 4ac) is negative (-4^2 - 4 ×1 ×9 = -20). Therefore, it cannot be factored over the real numbers. Our final factored form of the polynomial is 3x(x^2 - 4x + 9), as we factored out the greatest common factor (GCF).

Answer:

Power: (1/5)^3, 2^6

Expanded: 5x5, 6x6x6, 3x3x3/4, 2x2x2x2x2x2

How to say it: 5 raised to the 2nd power, 6 raised to the 3rd power, 3 raised to the 3rd power over 4

Value: 25, 216, 1/125, 9/4, 64

Step-by-step explanation:

Answer:

the answer is C: 1932 sq. cm

Step-by-step explanation:

You want to break down the sections (which is double for each)

there are 6 rectangles but you will only need to calculate for 3

1st rectangle

a = (25) (12)

a = 300 sq. cm

**then multiply by 2 = 600 sq. cm**

2nd rectangle

a = (12) (18)

a = 216 sq. cm

then 216 * 2 = 432 sq. cm

3rd rectangle

a = (25) (18)

a = 450 sq. cm

then 450 * 2 = 900 sq. cm

Total Surface Area

SA = 600 sq. cm + 432 sq. cm + 900 sq. cm

SA = 1932 sq. cm

Subtract 1/3 from both sides

x/12 = 5/6 - 1/3

Simplify 5/6 - 1/3 to 1/2

x/12 = 1/2

Multiply both sides by 12

x = 12 × 12

Simplify 1/2 × 12 to 12/2

x = 12/2

Simplify 12/2 to 6

x = 6

13 classmates because 55/4 = 13.75 and the .75 is the extra three pieces

I did 55-3=52 and then divided 52 by 4 to get 13 !!

Answer:

  [tex]2a^{\frac{5}{2}}-4a^{-\frac{1}{2}}[/tex]

Step-by-step explanation:

It looks like you want to expand the expression ...

  [tex]\sqrt{a}\left(2a^2 -\dfrac{4}{a}\right)[/tex]

Use the distributive property and rules of exponents.

  [tex]=2a^{(\frac{1}{2}+2)}-4a^{(\frac{1}{2}-1)}\\\\=\boxed{2a^{\frac{5}{2}}-4a^{-\frac{1}{2}}}[/tex]

_____

The relevant rules of exponents are ...

  √a = a^(1/2)

  1/a = a^-1

  (a^b)(a^c) = a^(b+c)

To simplify the expression {x⁵}/{x²}, you subtract the exponents (5 - 2), resulting in x³, which is x cubed.

The given expression is {x⁵}/{x²}. To simplify this, we use the Division of Exponentials rule, which states that when dividing two expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator.

In this case, we subtract 2 from 5 (because the base is x and we have x to the power of 5 divided by x to the power of 2), giving us:

(x⁵⁻² which simplifies to (x³).

The simplified expression is therefore x cubed, or (x³).

Answer:

r = 5.9984789350480924657633167413961‬ yards

Step-by-step explanation:

h = 4 yards

V = 452.16 yards Cubed (cubic yards)

V = π[tex]r^{2}[/tex]h

452.16 = π[tex]r^{2}[/tex]*4

divide by pi and 4 and you get approx 35.98

35.981 = [tex]r^{2}[/tex]

the square root of 35.98 is approx 5.9984789350480924657633167413961‬

which is equal to r, or the radius

r = 5.9984789350480924657633167413961‬ yards

The right answer is Function F.

Explanation:

f(x)=10(2)+2=22

g(x)= 2^(2)=4

h (x)=(2)^2+2 (2)+1=9

Answer:

A, Function f

Step-by-step explanation:

to see which function has the greatest output when x = 2, we simply plug in 2 into each function

f(2) = 10(2) + 2 ---> 20 + 2 = 22

f(2) = 22

g(2) = [tex]2^(2)[/tex] = 4

g(2) = 4

h(2) = (2)² + 2(2) + 1 ----> 4 + 4 + 1 = 9

h(2) = 9

comparing the functions, we see that the function with the largest output is f(x)

our answer is A, Function F

Answer:

The perimeter = 26 unites

Step-by-step explanation:

* Lets revise some facts of parallelogram

- Every two opposite sides are parallel and equal

- Every two opposite angles are equal

- Every two adjacent angles are supplementary

- Th two diagonals bisects each other

- The perimeter = 2(S1 + S2)

* Now lets solve the problem

- ABCD is a parallelogram, where

 A = (-2 , 6) , B = (1 , 2) , C = (-2 , -2) , D = (1 , -6)

- To find the perimeter we need the length of AB and BD

- The rule of the distance between two point is

  d = √[(x2 - x1)² + (y2 - y1)²]

* Lets find AB

∵ AB = √[1 - -2)² + (2 - 6)²] = √[(3²) + (-4)²]

∴ AB = √25 = 5

* Lets find BD

∵ BD = √[(1 - 1)² + (-6 - 2)² = √[(0)² + (-8)²]

∴ BD = √64 = 8

* Lets find the perimeter

∵ The perimeter = 2 (5 + 8) = 26 unites

Answer:

26 units

Step-by-step explanation:

The attached image shows the coordinates drawn as a parallelogram.

The perimeter is sum of all the sides, AB + BD + DC + CA

Both BD and CA are straight lines with 8 units

AB and DC are not straight lines. So we need to find it using the pythagorean theorem, which is , one leg squared of a triangle + another leg squared will give us hypotenuse squared.

Looking at the triangle AYB, we can write and solve for AB:

[tex]AY^2+YB^2=AB^2\\4^2 + 3^2 = AB^2\\16+9=AB^2\\25=AB^2\\AB=5[/tex]

we can use the same argument and lengths for the triangle CXD. We will have DC = 5 units

Perimeter = AB + BD + DC + CA = 5 + 8 + 5 + 8 = 26 units

Answer:

6

Step-by-step explanation:

Answer:

[tex]f^{-1}(x) = log_2(x-6)[/tex]

Step-by-step explanation:

To find the inverse [tex]f^{-1}(x)[/tex] of a function follow the following steps.

1) Do y = f (x)

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

[tex]y= 2 ^ x + 6[/tex]

2) Solve the equation for the variable x.

[tex]y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)[/tex]

3) exchange the variable y with the variable x

[tex]x=log_2(y-6)\\\\y=log_2(x-6)[/tex]

Finally the inverse is:

[tex]f^{-1}(x) = log_2(x-6)[/tex]

ANSWER

[tex]Volume = 480.0{cm}^{3} [/tex]

EXPLANATION

The volume of the square pyramid is given by;

[tex]Volume = \frac{1}{3} {l}^{2} \times h[/tex]

Where l=12cm is the length of the square base and h=10cm is the height of the pyramid.

We substitute the values into the formula to get;

[tex]Volume = \frac{1}{3} \times {12}^{2} \times 10 {cm}^{3} [/tex]

This simplifies to,

[tex]Volume = \frac{1}{3} \times {12} \times 12\times 10 {cm}^{3} [/tex]

[tex]Volume = 4 \times 12\times 10 {cm}^{3} [/tex]

[tex]Volume = 480.0{cm}^{3} [/tex]

Third option is correct.

Answer:

The correct option is 3.

Step-by-step explanation:

The volume of a square pyramid is

[tex]V=\frac{1}{3}(\text{Base area})h[/tex]

[tex]V=\frac{1}{3}a^2h[/tex]                  .... (1)

Where, a is th side of base and h is the height of pyramid.

From the given figure it is clear that the height of the pyramid is 10 cm and the  length of base is 12 cm.

Substitute a=12 and h=10 in equation (1), to find the volume of the square pyramid.

[tex]V=\frac{1}{3}\times (12)^2\times (10)[/tex]

[tex]V=\frac{1}{3}\times (144)\times (10)[/tex]

[tex]V=(48)\times (10)[/tex]

[tex]V=480[/tex]

The volume of pyramid is 480 cm³. Therefore the correct option is 3.

Answer:

AB=14 cm

Step-by-step explanation:

step 1

Find the measure of major arc AC

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠B=(1/2)[major arc AC]

we have

m∠B=120°

substitute

120°=(1/2)[major arc AC]

240°=major arc AC

so

major arc AC=240°

step 2

Find the measure of arc ABC

we know that

arc AC+arc ABC=360°

substitute

240°+arc ABC=360°

arc ABC=120°

step 3

Find the measure of angle AOC  

m∠AOC=arc ABC=120° ------> by central angle

so

The triangle AOC is an isosceles triangle

OA=OC=14 cm ------> is the radius

The internal angles of triangle AOC are

m∠CAO=m∠OCA=30°

The triangle ABC is an isosceles triangle

AB=BC

The internal angles of triangle ABC are

m∠BAC=m∠ACB=30°

so

Triangles AOC and ABC are congruent by ASA similarity postulate ( two angles and included side)

therefore

AO=AB=14 cm