The length of each leg of an isosceles triangle is 4cm less than twice the base. The perimeter of the triangle is 17 cm. Find the measure of each side of the triangle.

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]

Answer:

-3.2171798824

Step-by-step explanation:

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.

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

Answer:

The graph would look like this

Step-by-step explanation:

The equation is less than so it is below the dotted line. The line is dotted becuase the answer is equal to anything on the line.

The graph will be a dashed line and the region below the line is hatched. Then the correct option is A.

The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.

The linear function is given below.

4y + 8 < -3x

The graph will be a dashed line and the region below the line is hatched.

Then the correct option is A.

The missing options are attached below.

More about the graph of the function link is given below.

https://brainly.com/question/9834848

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Answer:

35 cm

Step-by-step explanation:

To find the area of the bottom portion, you would use the formula for finding out a triangle (B*H*1/2) which is:

(4+4)*5.75*1/2=23

Then, for the top portion, one would find the area of the triangles on the sides (with two marks going through). Since along the middle is 8cm, and along the top is 4, we can see that there is 2cm on either side, so that is the length of the base of the triangle. To solve for the top triangles, you would do almost the same thing as the last one:

2*2*1/2=2

But since there's two identical triangles on either side, we can multiply that by two, which would bring it to 4.

That just leaves the rectangle that is left between the two triangles. To solve this, it's just B*H and luckily both of those are labeled for you already:

4*2=8  

Now, to find the total area, all you have to do is add up the areas of the different sections:

23+4+8=35 cm

Hope this helps!

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

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

Source:

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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:

The weight of the three blades together is [tex]134\ g[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

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

we have

[tex]r=4\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(4)^{2}[/tex]

[tex]A=50.24\ in^{2}[/tex]

step 2

Find the area of the 3 blades

we know that

The area of the 3 blades represent a central angle of 60 degrees, so

its a 1/6 of the area of complete circle

[tex]A=50.24/6=8.37\ in^{2}[/tex]

step 3

Find the weight of the three blades together to the nearest gram

[tex](8.37\ in^{2})*(16\ g/in^{2})=134\ g[/tex]

Hi! The answer is c downloads per a day

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:

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:

∠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°

the scale factor is .25

6×.25=1.5

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:

? = 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: 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:

[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]

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

Answer:

She skates at 0.5 miles per hour :) hope it helped

Answer:

[tex]f^{-1}(x) = log_{12}(y)[/tex]

Step-by-step explanation:

We have the following function

y = 12^x, and we need to find the inverse function.

To find the inverse function we should solve the equation for "x". To do so, first, we need to:

1. Take the logarithm in both sides of the equation:

lg_12 (y) = log _12 (12^x)

(Please read lg_12 as: "Logarithm with base 12")

From property of logarithm, we know that lg (a^b) = b*log(a)

Then:

lg_12 (y) = x*log _12 (12)

We also know that log _12 (12) = 1

Then:

x = log_12(y).

Then, the inverse of: y= 12^x is:

[tex]f^{-1}(x) = log_{12}(y)[/tex]

Answer: There are 150 bars in a case, and 2 cases per day are used (or 300 bars), Thus, in 7 days you would use 7 x 2 or 14 cases, or 2100 bars.

Step-by-step explanation:

Answer:

14 cases of soap bars.

Step-by-step explanation:

In one case of soap bars there is = 150 bars

You use amount of soap bars per day = 300

You need to order to have enough for 7 days  = 300 × 7 = 2100 bars

150 bars ⇒ 1 case

2100 bars ⇒ [tex]\frac{2100}{150}[/tex] = 14 case

You need to order 14 case of soap bars for 7 days.

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:

The answer is B

Inequalities help us to compare two unequal expressions. The correct option is A, (6+x)/15>(9/10).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Melinda will take 15 quizzes this semester. She would like to score a B or better on at least 90% of them.  Therefore, the ratio of the number of questions done to the total number of questions should be greater than 90%.

Also, given that Melinda has already gotten a b or better on 6 quizzes. Therefore, we can write the inequality as,

(6+x)/15 > 90%

(6+x)/15 > 90/100

(6+x)/15 > 9/10

Learn more about Inequality:

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Answer:

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

Step-by-step explanation:

This might be the right answer unless it is multiple choice

Answer:

Option d. [tex]f(x)=\$1,000(1+0.0355)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=x\ years\\ P=\$1,000\\ r=0.0355\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$1,000(1+\frac{0.0355}{1})^{1*x}[/tex]  

[tex]A=\$1,000(1+0.0355)^{x}[/tex]  

Convert to function notation

[tex]f(x)=\$1,000(1+0.0355)^{x}[/tex]  

C. 226.87 in 2

Using the area of a circle formula

A=πr2

Answer:

226.87 in^2

Step-by-step explanation:

Formula

Area = pi*r^2

r = d/2

Givens

pi = 3.15

d = 17 inches.

Solution

r = d/2

r = 17/2

r = 8.5

Area = pi*r^2

Area = 3.14 * 8.5^2

227.87 in^2

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