Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh.


What is the volume of the pyramid after dilating by a scale factor of 1/4? Describe the effects.

A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.

B.) 64 m³. The volume of the new pyramid is the volume of the original pyramid times 1/16.

C.) 256 m³. The volume of the new pyramid is the volume of the original pyramid times 1/4.

D.) 1,024 m³. The volume of the new pyramid is equal to the volume of the original pyramid.

Answer:

Both of those are functions.

Step-by-step explanation:

[tex]y=x^2[/tex] is a parabola that opens up.

Any upward or downward parabola is a function because they pass the vertical line test.

[tex]x=\pm \sqrt{1-y}{/tex]

Square both sides:

[tex]x^2=1-y[/tex]

Subtract 1 on both sides:

[tex]x^2-1=-y[/tex]

Multiply both sides by -1:

[tex]-x^2+1=y[/tex]

So this is a another parabola and it is faced down.  So this is also a function.

[tex]y=ax^2+bx+c[/tex] wit [tex]a \neq 0[/tex] willl always be a parabola.  

If [tex]a>0[/tex] then it is open up.

If [tex]a<0[/tex] then it is open down.

Upwards and downward parabolas will always be functions.

[tex]x=ay^2+by+c[/tex] are also parabolas but these open to the left or right.  These will not be functions because they will not pass the vertical line test.  

well, so we know the ratio of compost to soil is 2 : 10, or namely 2/10 which simplifies to 1/5 or namely the ratio of 1 : 5.

the mix will be 6 kgs total, so we'll simply divide the whole amount by (1 + 5), the sum of the ratios, and then distribute accordingly.

[tex]\bf 2:10\implies 1:5\qquad \qquad \cfrac{compost}{soil}\qquad \cfrac{1\cdot ~~\frac{6}{1+5}~~}{5\cdot \frac{6}{1+5}}\implies \cfrac{1\cdot 1}{5\cdot 1}\implies \cfrac{\stackrel{compost}{\boxed{1~kg}}}{5~kg}[/tex]

Answer:

Gabriel Is making a mixture of compost and soil to use for a special plant. He wants his Final mix to be two parts compost to 10 parts potting soil. he wants to end up with 6 kg of mix. How many kg of compost should Gabriel use?

Step-by-step explanation:

We have a total of 12 parts, where 2 are compost, and on the other hand 6 kg which is the total of the whole mixture, divided by 12; 6/12 = 0.5 would be each of the parts, we multiply it by 2; 0.5 x 2 = 1 kg would be the part of compost, and 0.5 x 10 = 5 kg would be the part of potting soil which added, gives us the total 6 kg.

Answer:

6 oz

Step-by-step explanation:

If he spilled 1/4 of the juice, then he has 3/4 of the original volume left.

(3/4)(8 oz) = 6 oz.

He has 6 oz left to enjoy.

Answer:

Option 2) 20°

Step-by-step explanation:

Step 1: Write relevant properties of triangle.

All 3 sides of a triangle are equal to 180 degrees.

In an isosceles triangle, 2 sides and 2 angles are same.

Step 2: Calculate another angles

Since it is an isosceles triangle, two sides will be same therefore, 2 angles will be same.

Angle 1 = Angle 2 = 20 degrees (because isosceles triangle)

Therefore, 20° is the measure of one of the other angles.

Option 2

!!

Answer: FIRST OPTION.

Step-by-step explanation:

It is important to remember that an Acute Isosceles triangle has two congruent sides and all its angles measure less than 90 degrees. Then, the third option and the the fourth option are not one of the other angles.

You know that the sum of the interior angles of a triangle is 180 degrees.

Then, let be "x" one the other angles, let's check the first option:

[tex]80\°+20\°+x=180\°\\x=80\°[/tex]

Since [tex]80\°<90\°[/tex], the angle provided in the first option is one of the other angles.

 Let's check the second option:

[tex]20\°+20\°+x=180\°\\x=140\°[/tex]

Since [tex]140\°>90\°[/tex], the angle provided in the second option is not one of the other angles.

Answer:

14.3178210633

Step-by-step explanation:

distance formula, d= sq root of ((x2-x1)^2+(y2-y1)^2)

Answer:

ab = [tex]\sqrt{42}[/tex].

Step-by-step explanation:

Given  : A= (4,-5) and b=(7,9).

To find : what is the length of ab.

Solution : We have given that  A= (4,-5) and b=(7,9).

Distance formula : [tex]\sqrt{(x_{2}-x_{1}(y_{2} -y_{1})}[/tex].

Here, [tex]x_{1} =4[/tex]

[tex]x_{2} =7[/tex]

[tex]y_{1} =-5[/tex]

[tex]y_{2} =9[/tex].

Then   [tex]\sqrt{(7-4)(9-(-5))}[/tex].

ab = [tex]\sqrt{(3)(14)}[/tex].

ab = [tex]\sqrt{42}[/tex].

Therefore, ab = [tex]\sqrt{42}[/tex].

Answer:

The price decreased by 16 1/3%, or approximately 16.3%

Step-by-step explanation:

Use the formula for percent change. If the answer is negative, it is a percent decrease. if the answer is positive, it is a percent increase.

percent change = (new price - old price)/(old price) * 100%

In this case, use:

new price = 50

old price = 60

percent change = (new price - old price)/(old price) * 100%

percent change = (50 - 60)/60 * 100%

percent change = -10/60 * 100%

percent change = -1/6 * 100%

percent change = -100/6% = -50/3% = -16 1/3%

The price decreased by 16 1/3%, or approximately 16.3%

Answer:

The x intercept = -3

Step-by-step explanation:

The x intercept is where it crosses the x axis.

Looking at the graph, it crosses at x =-3

Using the equation, we set y=0 and solve for x

2x-y =-6

2x -0 =-6

2x = -6

Divide by 2

2x/2 =-6/2

x=-3

Answer: A

Step-by-step explanation:

Edgen 2023

Step-by-step explanation:

We arrange numbers in ascending order

Range - numbers appearing (without repetition)

Median - middle value

Mean - the sum of the numbers divided by the number of items

Mode - the value that appears most often.

[tex]\bold{Q4.}\\\\22,\ 36,\ 39,\ 39,\ 40,\ 40,\ 41,\ 42,\ 45,\ 46,\ 46,\ 49\\\\\bold{Range:}\ 22,\ 36,\ 39,\ 40,\ 41,\ 42,\ 45,\ 46,\ 49\\\\\bold{Median:}\ 40,\ 41\to\dfrac{40+41}{2}=40.5\\\\\bold{Mean:}\ \dfrac{22+36+39+39+40+40+41+42+45+46+46+49}{12}=40\dfrac{5}{12}\\\\\bold{Mode:}\ 39,\ 40\ and\ 46[/tex]

[tex]\bold{Q5.}\\\\79,\ 83,\ 84,\ 86,\ 86,\ 90,\ 94\\\\\bold{Range:}\ 79,\ 83,\ 84,\ 86,\ 90,\ 94\\\\\bold{Median}:\ 86\\\\\bold{Mean:}\ \dfrac{79+83+84+86+86+90+94}{7}=86\\\\\bold{Mode:}\ 86[/tex]

Answer:

true.

Step-by-step explanation:

(x - y)z = xz - yz

Apply the distributive property of multiplication over addition to the left side:

(x - y)z =

= z(x - y)

= xz - yz

This is the same as the right side, so the statement is true.

[tex]0.0\overline{3}=\dfrac{1}{30}\\0.\overline{03}=\dfrac{1}{33}\\\\\dfrac{0.0\overline{3}}{0.\overline{03}}=\dfrac{\dfrac{1}{30}}{\dfrac{1}{33}}=\dfrac{1}{30}\cdot33=\dfrac{11}{10}=1\dfrac{1}{10}[/tex]

Answer:

N'

Step-by-step explanation:

L corresponds to L'

M corresponds to M'

N corresponds to N'

O corresponds to O'

P corresponds to P'

After the transformation if you copy and paste your picture over the new picture, the corresponding angles should lay on top of each other.

Polygon LMNOP was transformed to create polygon L'M'N'O'P'.  The angle N corresponds to N'.

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

Here,

L corresponds to L'

M corresponds to M'

N corresponds to N'

O corresponds to O'

P corresponds to P'

Hence, The N corresponds to N'.

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Answer:

6 and up

Step-by-step explanation:

this is beacuse when you add all the angels up you you would have to have a minimum of 6 to pass the negative 5

Answer:

x = 80°

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720 degrees. So,

x + (x - 5) + (x - 5) + (2x - 5) + (2x - 5) + (2x + 20) = 720

Eliminating parenthesis

x + x - 5 + x - 5 + 2x - 5 + 2x - 5 + 2x + 20 = 720

Adding and subtracting

9x + 0 = 720

Isolating x

x = 720/9

x = 80

The answer is:

Center: (-4,-4)

Radius: 2 units.

To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Where:

"h" and "k" are the coordinates of the center of the circle and "r" is its radius.

So, we need to complete the square for both variable "x" and "y".

The given equation is:

[tex]x^{2}+y^{2}+8x+8y+28=0[/tex]

So, solving we have:

[tex]x^{2}+y^{2}+8x+8y=-28[/tex]

[tex](x^2+8x+(\frac{8}{2})^{2})+(y^2+8y+(\frac{8}{2})^{2})=-28+((\frac{8}{2})^{2})++(\frac{8}{2})^{2})\\\\(x^2+8x+16 )+(y^2+8y+16)=-28+16+16\\\\(x^2+4)+(y^2+4)=4[/tex]

[tex](x^2-(-4))+(y^2-(-4))=4[/tex]

Now, we have that:

[tex]h=-4\\k=-4\\r=\sqrt{4}=2[/tex]

So,

Center: (-4,-4)

Radius: 2 units.

Have a nice day!

Note: I have attached a picture for better understanding.

The radius of the circle is 2 units.

To find the radius of the circle with equation x²+y²+8x+8y+28=0, we need to rearrange the equation into the standard form (x-h)²+(y-k)²=r², where (h,k) is the center of the circle and r is the radius. By completing the square, we can rewrite the equation as (x+4)²+(y+4)²=4.

Comparing this with the standard form, we can see that the center of the circle is (-4,-4) and the radius is √4 = 2. Therefore, the radius of the circle is 2 units.

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Answer:

42

Step-by-step explanation:

all I did was multiply 6 by 7 and i got 42

Answer:

a) 3

b) 364

Step-by-step explanation:

A geometric sequence in explicit form is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We are given:

[tex]a_5=9 \cdot a_3[/tex]

[tex]a_6+a_7=972[/tex].

What is a) r?

What is b) the sum of the first 6 terms?

So I'm going to use my first equation and use my explicit form to find those terms in terms of r:

[tex]a_1 \cdot r^4=9 \cdot a_1 \cdot r^{2}[/tex]

Divide both sides by [tex]a_1r^2[/tex]:

[tex]r^2=9[/tex]

[tex]r=\sqrt{9}[/tex]

[tex]r=3[/tex].

So part a is 3.

Now for part b).

We want to find [tex]a_1+a_2+a_3+a_4+a_5+a_6[/tex].

So far we have:

[tex]a_1=a_1[/tex]

[tex]a_2=3a_1[/tex]

[tex]a_3=3^2a_1[/tex]

[tex]a_4=3^3a_1[/tex]

[tex]a_5=3^4a_1[/tex]

[tex]a_6=3^5a_1[/tex].

We also haven't used:

[tex]a_6+a_7=972[/tex].

I'm going to find these terms in terms of r (r=3).

[tex]3^5a_1+3^6a_1=972[/tex]

[tex]243a_1+729a_1=972[/tex]

You have like terms to add:

[tex]972a_1=972[/tex]

Divide both sides by 972:

[tex]a_1=1[/tex]

The first term is 1 and the common ratio is 3.

The terms we wrote can be simplify using a substitution for the first term as 1:

[tex]a_1=a_1=1[/tex]

[tex]a_2=3a_1=3(1)=3[/tex]

[tex]a_3=3^2a_1=9(1)=9[/tex]

[tex]a_4=3^3a_1=27(1)=27[/tex]

[tex]a_5=3^4a_1=81(1)=81[/tex]

[tex]a_6=3^5a_1=243(1)=243[/tex].

Now we just need to find the sum of those six terms:

1+3+9+27+81+243=364.

Answer:

8/100.   Eight hundredths  or we can write it as 8 * 10^-2.

Step-by-step explanation:

The first digits after the decimal point is  tenths ( 7 tenths) and the second is hundredths, the third is thousandths.

Answer:

(3x-2)(2x+5)

or

(2x+5)(3x-2) by commutative property

Step-by-step explanation:

Let's try factoring by grouping.

[tex]6x^2-4x+15x-10[/tex]

I'm going to group the first two terms together and the second two terms together.

[tex](6x^2-4x)+(15x-10)[/tex]

Now I'm going to factor what I can from each pair:

[tex]2x(3x-2)+5(3x-2)[/tex]

Now if you look at the terms 2x(3x-2) and 5(3x-2) you should see they have a common factor of (3x-2) so we can factor that out now.

(3x-2)(2x+5)

Factoring by grouping was a successful here.

Answer:

(3x - 2)(2x + 5)

Step-by-step explanation:

Given

6x² - 4x + 15x - 10 ( factor the first/second and third/fourth terms )

=2x(3x - 2) + 5(3x - 2) ← factor out (3x - 2) from each term

= (3x - 2)(2x + 5) ← in factored form

Answer:

See below.

Step-by-step explanation:

To multiply a monomil by a polynomial, multiply the monomial by each term of the polynomial.

Example: Multiply 3x^2 by 4x^2 + 5x - 2

3x^2(4x^2 + 5x - 2) =

= 3x^2 * 4x^2 + 3x^2 * 5x + 3x^2 * (-2)

= 12x^4 + 15x^3 - 6x^2

To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.

To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.

For example, let's multiply the monomial 3x^2 by the polynomial 4x^3 + 2x - 1:

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Answer:

Absolute value means the distance between a number and 0.

Examples:

The absolute value of -7 is 7.

The absolute value of 5 is 5.

Key Concepts:

The absolute value sign is |x|, where x is any real number.

The absolute value removes any negative sign in front of a number.

Absolute value is an important math concept to understand. To represent the absolute value of a number, we use a vertical bar on either side of the number. Absolute value means "distance from zero" on a number line. Let's try an example to understand how absolute value works.

What is the absolute value of 4 and -4?

To find the absolute value of 4, we know that 4 is 4 units from zero on a number line. Therefore, the absolute value of 4 is 4.

For the absolute value of -4, we know that -4 is also 4 units from zero on the number line. Therefore, the absolute value of -4 is also 4.

Another way that I like to think about absolute value is no matter what number you have inside the absolute value, the result will always be positive. In other words, the absolute value of any number is the positive version of that number.

A scalene triangle has all different side lengths and different sized angles. This means that a scalene can NOT have two congruent angles.

This means that the answer is:

True

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

it is actually false

cause you can change the angles or sides to turn it scalene

Step-by-step explanation:

Answer:

obtuse, because 6^2+10^2 is greather than 12^2

Step-by-step explanation:

The triangle with side lengths 6 cm, 10 cm, and 12 cm is a right triangle. This is determined by applying the Pythagorean theorem (a^2 + b^2 = c^2) to the side lengths of the triangle.

The classification of a triangle can be determined by its side lengths. In this context, you have a triangle with side lengths 6 cm, 10 cm, and 12 cm. This is not an acute triangle, contrary to the original statement. It is, in fact, a right triangle.

To determine this, one can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2.

If we apply the Pythagorean theorem to our triangle, we find that 6^2 + 10^2 equals 36 + 100, which is 136. Similarly, 12^2 equals 144. Since 136 is less than 144, the triangle is indeed a right triangle, not an acute triangle.

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Answer:

=20.0

Step-by-step explanation:

We can first find the angle B using the sine rule as follows:

a/Sin A=b/Sin B

9/Sin 15=12/ Sin B

Sin B= (12 Sin 15)/9

=0.345

B=Sin⁻¹ 0.345

=20.18°

We then find C by using the summation of the interior angles of a triangle.

C=180-(20.18+15)

=144.82

Finding the length of c:

a/Sin A= c/ Sin C

9/Sin 15=c/Sin 144.82

c=(9 Sin 144.82)Sin 15

=20.0

Answer:

20.0 unit ( approx )

Step-by-step explanation:

Here,

ABC is a triangle in which,

m∠A=15°, a=9, and b=12,

By the law of sine,

[tex]\frac{sin A}{a}=\frac{sin B}{b}=\frac{sin C}{c}----(1)[/tex]

[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]

[tex]\implies sin B=\frac{b sin A}{a}[/tex]

By substituting the values,

[tex]\implies sin B=\frac{12\times sin 15^{\circ}}{9}\approx 0.3451[/tex]

[tex]\implies B \approx 20.19^{\circ}[/tex]

Now, by the property of triangle,

m∠A + m∠B+ m∠C = 180°

⇒ m∠C = 180° - 15° - 20.19° = 144.81°,

By the equation (1),

[tex]c=\frac{b sin C}{sin B}=\frac{12\times sin 144.81^{\circ}}{sin 20.19^{\circ}}=20.0370532419\approx 20.0[/tex]

[tex]\huge{\boxed{32\%}}[/tex]

We can find this information using the table. The number of female students that like peas is 64, and the total number of students is 200. That gives us the following fraction. [tex]\frac{64}{200}[/tex]

Now, turn this into a percentage by making the denominator 100. This is done by dividing the numerator and denominator each by 2, since the denominator is 100. [tex]\frac{64 \div 2}{200 \div 2}= \frac{32}{100}=32%[/tex]

Required probability that one of these students is female and

likes peas is 32/100 or 32%

According to the problem,

∴ Required probability = 64/200 = 32/100 = 32%

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Answer:

56√10.

Step-by-step explanation:

7√8 * 4√5

= 28 √40

= 28 √4√10

= 28 * 2√10

= 56√10.

Answer:

56[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

7[tex]\sqrt{8}[/tex] × 4[tex]\sqrt{5}[/tex]

= 7 × 4 × [tex]\sqrt{8(5)}[/tex]

= 28 × [tex]\sqrt{40}[/tex]

= 28 × [tex]\sqrt{4(10)}[/tex]

= 28 × [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]

= 28 × 2 × [tex]\sqrt{10}[/tex]

= 56[tex]\sqrt{10}[/tex]

Hey there! :)

1/2(n - 1) - 3 = 3 - (2n + 3)

Simplify.

1/2n - 1/2 - 3 = 3 - 2n - 3

Add like terms.

1/2n - 3 1/2 = -2n

Add 3 1/2 to both sides.

1/2n = -2n + 3 1/2

Then, add 2n to both sides.

1/2n + 2n = 3 1/2

Simplify!

2 1/2n = 3 1/2

Make everything into improper fractions!

5/2n = 7/2

Multiply everything by 2 to get rid of the denominators.

5/2n × 2 = 7/2 × 2

Simplify!

5n = 7

Divide both sides by 5.

n = 7/5

Hope this helped! :)

Answer:

[tex]\frac{7}{5} = n[/tex]

Step-by-step explanation:

[tex] \frac{1}{2} (n - 1) - 3 = 3 - (2n + 3) \\ [/tex]

Solve the brackets.

[tex] \frac{n}{2} - \frac{1}{2} - 3 = 3 - 2n - 3 \\ [/tex]

Make the denominator the same to solve the fractions.

[tex] \frac{n}{2} - \frac{1}{2} - \frac{3 \times 2}{1 \times 2} = 3 - 2n - 3 \\ [/tex]

Combine like terms.

[tex] \frac{n}{2} - \frac{1}{2} - \frac{6}{2} = - 2n \\ \\ \frac{n - 7}{2} = - 2n \: \: \: \: \: \: \: \: [/tex]

Use cross multiplication to solve for n.

[tex]n - 7 = - 4n \\ \\ - 7 = - 4n - n \\ \\ - 7 = - 5n \: \: \: \: \: \: \\ \\ \frac{ - 7}{ - 5} = \frac{ - 5n}{ - 5} \: \: \: \: \\ \\ \frac{7}{5} = n \: \: \: \: \: \: \: [/tex]

Answer:

[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]

C is the correct option.

Step-by-step explanation:

The given function is [tex]f(x)=3x-4[/tex]

Replace f(x) with y

[tex]y=3x-4[/tex]

Interchange x and y as shown below

[tex]x=3y-4[/tex]

Solve the equation for y

[tex]x+4=3y\\\\y=\frac{x+4}{3}[/tex]

Therefore, the inverse of f(x) is given by

[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]

C is the correct option.

Answer:

auditory nerve

Step-by-step explanation:

the auditory nerve carries sound signals to the brain. The cochlea picks up sound waves and makes nerve signals.

Answer:

The auditory nerve

Step-by-step explanation:

Answer:

2 gallons

Step-by-step explanation:

If you use one whole gallon, you will have covered 2/4.

When you simplify this fraction, you get 1/2. This means you have another half to cover.

So, 1 gallon plus another gallon is 2.

Answer:

2 gallons of paint.

Step-by-step explanation:

Since [tex]\frac{1}{2}[/tex] gallon of paint covered = [tex]\frac{1}{4}[/tex] of the wall.

Therefore, 1 gallon of paint covered = 1 × [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] of the wall.

To paint 1 wall we need the paint = [tex]\frac{1}{\frac{1}{2} }[/tex] = [tex]1\times\frac{2}{1}[/tex] gallon of paints

                                                      = 2 gallons of paint.

2 gallons of paint covers the whole wall.

Answer:

[tex]f(n) = \frac{n}{3} [/tex]

Step-by-step explanation:

Recall that:

[tex]3ft = 1 \: yd[/tex]

This implies that:

[tex] 6ft = 2yds[/tex]

[tex] 9ft = 3yds[/tex]

In general:

[tex] n \: ft = \frac{n}{3} \: \: yds[/tex]

We can therefore write the function rule:

[tex]f(n) = \frac{n}{3} [/tex]