Four times Joe’s age plus 2 times Tim’s ageequals 50. Tim’s age is also 2 less than Joe’s age.How old is Joe?

Answer:

The perimeter of the new pentagon is [tex]27\ cm[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

To find the perimeter of the new pentagon, multiply the perimeter of the original pentagon by the scale factor

Let

z ----> the scale factor

[tex]z=3/2=1.5[/tex]

The perimeter of the new pentagon is equal to

[tex](18)*1.5=27\ cm[/tex]

Answer:

Step-by-step explanation:Let us find points of intersection of line  

3

x

+

4

y

−

k

=

0

and circle  

x

2

+

y

2

=

16

. We can do this by putting value of  

y

from first equation i.e.  

y

=

k

−

3

x

4

and we get

x

2

+

(

k

−

3

x

)

2

16

=

16

or  

16

x

2

+

k

2

+

9

x

2

−

6

k

x

=

256

i.e.  

25

x

2

−

6

k

x

+

k

2

−

256

=

0

This would give two values of  

x

and corresponding two values of  

y

i.e. two points. But tangent cuts the circle in only at one point. This will be so when discriminant is zero i.e.

(

−

6

k

)

2

−

4

⋅

25

⋅

(

k

2

−

256

)

=

0

or  

−

64

k

2

+

25600

=

0

or  

k

=

±

20

graph{(x^2+y^2-16)(3x+4y-20)(3x+4y+20)=0 [-10, 10, -5, 5]}

Answer:

-1, 7

Step-by-step explanation:

Equation of the circle:

x² + (y − k)² = 16

When the circle intersects y = 3:

x² + (3 − k)² = 16

x² + 9 − 6k + k² = 16

x² = 7 + 6k − k²

x = ±√(7 + 6k − k²)

For the circle to be tangent to the line, it can only intersect at one point.  If x has only one value, then:

√(7 + 6k − k²) = -√(7 + 6k − k²)

2√(7 + 6k − k²) = 0

7 + 6k − k² = 0

k² − 6k − 7 = 0

(k − 7) (k + 1) = 0

k = -1, 7

The two values of k are -1 and 7.

Answer:

914

I think it's the only answer

Hello There!

The answers are 916 and 914

HAVE A GREAT REST OF YOUR DAY!

Answer:

68%

Step-by-step explanation:

The mean is 25 and the standard deviation is 5.  So 20 is one standard deviation below the mean and 30 is one standard deviation above the mean.

According to the Empirical Rule, 68% of the normal curve is between ±1 standard deviations.  So the answer is 68%.

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: The population mean is μ=25 and standard deviation is σ=5.

[tex]Z=\frac{X-\mu}{\sigma}=\frac{X-25}{5}[/tex]

We need to find the percent of the trees that are between 20 and 30 years old.

[tex]P(20<X<30)[/tex]

Subtract 25 from each side.

[tex]P(20-25<X-25<30-25)[/tex]

[tex]P(-5<X-25<5)[/tex]

Divide each side by 5.

[tex]P(-1<\frac{X-25}{5}<1)[/tex]

[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]

Using standard normal table we get

[tex]P(-1<Z<1)=0.84134-0.15866=0.68268\approx 0.68=68\%[/tex]

68% of the trees are between 20 and 30 years old.

Therefore the correct option is 2.

Answer:

The given statement is true.

Step-by-step explanation:

In order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle.

This statement is true.

The INCENTER is the center of the circle that is inscribed in the triangle. Like the centroid, the incenter is always inside the triangle.

Answer:

true

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

(c)A bowler’s scorecard shows he threw a strike on one-fifth of his throws that night. Descriptive statistics describe an event that happens over time, for example, a batting average would be a descriptive statistic or a win/loss ratio.

Answer:

Third choice is the one you want

Step-by-step explanation:

First off, we need to remember that for a line to be perpendicular to another line, its slope is the opposite reciprocal to the other line. The slope of our line is -1/4, so the opposite reciprocal slope is +4/1 or just 4. Now we know that m = 4.

The point-slope form of a line is

[tex]y-y_{1}=m(x-x_{1})[/tex]

where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point. Filling in:

[tex]y-5=4(x-(-3))[/tex] which simplifies to

[tex]y-5=4(x+3)[/tex] which simplifies further to

[tex]y-5=4x+12[/tex]

Add 5 to both sides to get the equation into slope-intercept form:

y = 4x + 17

choice 3

Answer:

Day 5

Step-by-step explanation:

There are 2 ways to solve this, one using exponents and the other using logs. The equation regardless of how you solve it looks like this:

[tex]y=3^x[/tex]

where y is the number of customers on day x.  Filling in the number of customers we were given:

[tex]243=3^x[/tex]

There's a rule in exponents that says if the bases on both sides of the equals sign are like, then their exponents are equal to each other.  So if we can rewrite 243 in terms of a base of 3, then we're good.  I went to my calculator and started raising 3 to increasing powers of x:  3 to the first is 3; 3 squared is 9; 3 cubed is 27; 3 to the fourth is 81; 3 to the fifth is 243!  That means that

[tex]3^5=3^x[/tex]

Since the bases are like, then x = 5.

Using logs to solve it:

Take the log of both sides:

[tex]log(243)=log(3)^x[/tex]

There's a law of logs that says when you take the log of a number with an exponent, you can bring down the exponent in front like this:

[tex]log(243)=xlog(3)[/tex]

Now to solve for x, divide both sides by log(3):

[tex]\frac{log(243)}{log(3)}=x[/tex]

You can do that on your calculator and get that x = 5.

Whichever way is easier for you to understand OR whichever way your teacher is teaching according to where you are in your log unit, do it that way!  You can see that both give the same answer, the methods to get there vary.

Answer:

Part 27) Option D. 89.12°

Part 28) Option B. 66.42°

Step-by-step explanation:

Part 27)

we have

tan(x)=65

so

using a calculator

x=arctan(65)=89.12°

Part 28)

we have

cos(x)=2/5

so

using a calculator

x=arccos(2/5)=66.42°

Answer:

Option D. 89.12°

Option B. 66.42°

Step-by-step explanation:

tan(x)=65

x=arctan(65)=89.12°

Part 28)

cos(x)=2/5

x=arccos(2/5)=66.42°

Answer:

700 im not sure

Step-by-step explanation:

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

10d² + 8

Step-by-step explanation:

Given

(11 + 4d²) - (3 - 6d²) ← distribute parenthesis, second by - 1

= 11 + 4d² - 3 + 6d² ← collect like terms

= (4d² + 6d²) + (11 - 3)

= 10d² + 8

Answer:

91 degrees.

Step-by-step explanation:

This is a parallelogram (a quadrilateral with 2 pairs of parallel sides).

The 2 interior adjacent angles add up to 180 degrees in a parallelogram so

m < DAB = 180 - 89 = 91 degrees.

Answer: The measure of ∠DAB is 91°.

Step-by-step explanation:

Since we have given that

AB = CD

AD = BC

So, ABCD is a parallelogram.

m∠D=89°

and we know that

∠A and ∠D are adjacent angles.

So, their sum would be supplementary.

Now, it becomes,

[tex]89^\circ+\angle A=180^\circ\\\\\angle DAB=180^\circ-89^\circ\\\\\angle DAB=91^\circ[/tex]

Hence, the measure of ∠DAB is 91°.

Formula for volume of cone:

V = [tex]\pi r^{2}  \frac{h}{3}[/tex]

r = 6 km

h = 12 km

V = [tex]\pi 6^{2} \frac{12}{3}[/tex]

V = [tex]\pi 36*4[/tex]

V = [tex]\pi 144[/tex]

V = 452.389 km^3 <----------------------Using the calculators pi button

V = 452.16 km^3 <-------------------------Using 3.14 for pi

Hope this helped!

~Just a girl in love with Shawn Mendes

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, cross multiply to eliminate the fractions. Then collect the y terms on one side and the constant terms on the other side. Finally, divide both sides by the coefficient of y to find the value of y.

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, we first cross multiply to eliminate the fractions.

This gives us 3(y + 4) = 15(y - 5). Expanding this equation, we have 3y + 12 = 15y - 75.

Next, we collect the y terms on one side and the constant terms on the other side. Simplifying the equation, we get 12 + 75 = 15y - 3y.

Combining like terms, we have 87 = 12y. Finally, we divide both sides of the equation by 12 to solve for y.

Therefore, the value of y is 7.25.

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24

Explanation:

8×3=24

12.5 percent is the percent decrease.

Answer:

Step-by-step explanation:

lets do 3/7.

3.0/7 is .4 and .2

.20/7 is .14 and 6/7

.4+.14 is .54

but with 6/7 hundredth you add 1 more

so .55

Answer:

The area of pentagon B is [tex]83\frac{1}{3}\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x----> perimeter pentagon B

y----> perimeter pentagon A

[tex]z=\frac{x}{y}[/tex]

substitute the values

[tex]z=\frac{25}{15}[/tex]

Simplify

[tex]z=\frac{5}{3}[/tex] ----> scale factor

step 2

Find the area of pentagon B

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> area pentagon B

y----> area pentagon A

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{5}{3}[/tex]

[tex]y=30\ in^{2}[/tex]

substitute and solve for x

[tex](\frac{5}{3})^{2}=\frac{x}{30}[/tex]

[tex](\frac{25}{9})=\frac{x}{30}[/tex]

[tex]x=30*(\frac{25}{9})=83.33\ in^{2}[/tex]

convert to mixed number

[tex]83.33=83\frac{1}{3}\ in^{2}[/tex]

To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional.

To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional. If the perimeter of pentagon A is 15 in and the perimeter of pentagon B is 25 in, we can set up the proportion:

perimeter of pentagon B / perimeter of pentagon A = corresponding side lengths of pentagon B / corresponding side lengths of pentagon A

To find the corresponding side lengths of pentagon B, we can multiply the corresponding side lengths of pentagon A by the ratio of the perimeters:

corresponding side lengths of pentagon B = corresponding side lengths of pentagon A * (perimeter of pentagon B / perimeter of pentagon A)

Once we have the corresponding side lengths of pentagon B, we can use the formula for the area of a regular pentagon: Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * s^2, where s is the length of a side. Calculate the area of pentagon B using the corresponding side lengths.

Answer:

Step-by-step explanation:

sec(-x) − sin(-x) tan(-x)

So the first step is often to write everything in terms of sine, cosine, or tangent.  So let's rewrite using sec x = 1 / cos x:

1/cos(-x) − sin(-x) tan(-x)

Now we need to deal with those -x angles.  For that, we use reflection identities:

sin(-x) = -sin x

cos(-x) = cos x

tan(-x) = -tan x

Therefore:

1/cos(x) − sin(x) tan(x)

Now let's rewrite tan(x) as sin(x) / cos(x):

1/cos(x) − sin²(x)/cos(x)

Factoring:

(1 − sin²(x)) / cos(x)

Using Pythagorean identity: sin²(x) + cos²(x) = 1.  So 1 − sin²(x) = cos²(x).

cos²(x) / cos(x)

And finally, we divide.

cos(x)

Answer:

D. 1024 π units²

Step-by-step explanation:

We have sphere, with a radius of 16 units.

The surface area of a sphere is given by the following formula:

Surface Area of a sphere = 4 π r²

We already know r, which is 16.  So,

SA = 4 * π * 16² = 256 * 4 * π  = 1024 π  units²

That's enough for our answer, which matches answer D from the list.

If we want to have an actual number.... we would have to multiply 1024 by π.

SA = 1024 * π = 3217 units²

Answer:

option D

1024π units²

Step-by-step explanation:

Given in the question that radius of a sphere = 16 unit

Formula to use to calculate the surface area of the sphere

here r is the radius of the sphere

4 π (16)²

4 π (256)

1024π units²

Surface area of a sphere with radius 16 units = 1024π units²

I don't really understand the 3 5. Are you talking about 3.5? Same with the 1 4 are you talking about 1.4 or 14 or what? I'll be willing to help if  you could help me with that! :)

Answer: $58.00

Step-by-step explanation:

Answer:

(500π)÷3

Step-by-step explanation:

area=4πr^2 , volume=4(πr^3)÷3

area=100π ,so r=5

Answer:

[tex]\frac{500\pi }{3}[/tex] ft³

Step-by-step explanation:

The surface area of a sphere = 4πr², hence

4πr² = 100π ( divide both sides by 4π )

r² = 25 ( take the square root of both sides )

r = [tex]\sqrt{25}[/tex] = 5, hence

V = [tex]\frac{4}{3}[/tex]πr³

   = [tex]\frac{4}{3}[/tex]π × 5³

   = [tex]\frac{4}{3}[/tex]π × 125 =   [tex]\frac{500\pi }{3}[/tex] ft³

Answer:

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Step-by-step explanation:

we have

[tex]v(t)=1,350(1.017)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem

a=$1,350

b=1.017

Remember that

b=1+r

so

1+r=1.017

r=1.017-1=0.017

therefore

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Answer:

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Step-by-step explanation:

we have

This is a exponential function of the form where

a is the initial value

b is the base

In this problem

a=$1,350

b=1.017

Remember that

b=1+r

so

1+r=1.017

r=1.017-1=0.017

therefore

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Answer:

C

Step-by-step explanation:

The volume of a cone is given by  [tex]V=\frac{1}{3}\pi r^2h[/tex]

The volume of a cylinder is given by  [tex]V=\pi r^2 h[/tex]

Where h is the height and r is the radius

The first figure is a cone with height 6 and radius 5, we can put it into the formula and find the volume:

[tex]\frac{1}{3}\pi r^2 h\\\frac{1}{3}\pi (5)^2 (6)\\=157.08[/tex]

The second figure is a cylinder with height 50 and radius 1, we can put it into the formula and find the volume:

[tex]\pi r^2 h\\\pi (1)^2 (50)\\=157.08[/tex]

We can see that they are equal. So answer choice C is right.

Answer:

Option C.

Step-by-step explanation:

From the graph we can find the points (2,3) for first straight line (blue) and (2,2) for second straight line (red). These points Andre satisfied by option C.

x+2y=8

2+2×3=8

8=8.

Again, 2x+4y=12

2×2+4×2=12

12=12

The correct answer is Option C.

x + 2y = 8

2x + 4y = 12

In its simplest format in algebra, the definition of an equation exists as a mathematical statement that indicates that two mathematical expressions exist equal. For instance, 3x + 5 = 14 exists an equation, in which 3x + 5 and 14 exist two expressions separated by an 'equal' sign.

Equation of line in Two point form

When we know any two points on a line lets say [tex](a_1,b_1)[/tex] and [tex](a_2,b_2)[/tex], we can write its equation as:

[tex]y-b_1=m(x-a_1)[/tex]

where

[tex]m=\dfrac{b_2-a_2}{b_1-a_1}[/tex]

Here we have points of red line:( from graph) (0,3) and (6,0)

Equation of line: y-3=m(x-0)

m=0-3/6-0=-1/2

Equation:2y-6=-1(x)

               2y+x=6

Now from graph, we can see that the blue line is parallel to red line, therefore their slopes are same

The equation of blue line is as follows

y=mx+c

Point on blue line :(0,4)

4=(-1/2)*(0)+c

c=4

The equation is x+2y=8.

Therefore, it matches with option C.

x + 2y = 8

2x + 4y = 12

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The remaining 4600 numbers are neither multiples of 2 nor 5.

There are 10,000 total four-digit numbers (1000 through 9999).

Multiples of 2 end in 0, 2, 4, 6, and 8.

4-digit numbers are those numbers that consist of only 4 digits in which the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0 and 9.

There are 9*10*10*5 = 4500 four-digit multiples of 2.

Multiples of 5 end in 0 or 5.

There are 9*10*10*2 = 1800 four-digit multiples of 5.

There is redundancy between the two sets of numbers, namely those that end in 0, which are both multiples of 2 and 5.

There are 9*10*10*1 = 900 four-digit multiples of both 2 and 5.

Then there are 4500 + 1800 - 900 = 5400

total four-digit numbers that are either multiple of 2 or 5,

which means the remaining 4600 numbers are neither multiples of 2 nor 5.

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Answer:

3600

Step-by-step explanation:

9000 total 4 digit numbers minus 5400 multiples of both 2 and 5=3600 numbers

Answer:

95%

Step-by-step explanation:

Assuming each person can only vote once, just divide the amount of people that voted divided by the number of members. 38/40 gives a decimal of 0.95, and to find the percentage, just simply times it by 100.