Please help me do question 21, 22 and 23. I am in 6th grade.

Answer:

False

Step-by-step explanation:

A counterexample goes against what you said in the conjecture. An example of a counterexample in this case would be that your dog ate a burger, which is not dog food, last night.

Answer:

x = 6 and x = -5

Step-by-step explanation:

The zeros are what 2 x-values makes this function equal to zero.

So we need to find  [tex]x^2-x-30=0[/tex]

Now we need 2 numbers multiplied that gives us -30 (constant) and added gives us -1 (coefficient in front of x).

The two numbers are : -6, and 5

Now we can write:

[tex]x^2-x-30=0\\(x-6)(x+5)=0\\x=6, -5[/tex]

Hence the zeroes are x = 6 and x = -5

Final answer:

The zeros of the function f(x) = x^2 - x - 30 are found by factoring the quadratic equation. They are x = 6 and x = -5.

Explanation:

To find the zeros of the function f(x) = x2 - x - 30, we need to solve the equation for when f(x) equals zero. This means we have to solve x2 - x - 30 = 0. This is a quadratic equation, and we can attempt to factor it to find the solutions.

The factors of -30 that add up to -1 (the coefficient of x) are -6 and +5. Thus, we can rewrite the quadratic as (x - 6)(x + 5) = 0. Now, we can set each factor equal to zero to find the zeros of the function:

x - 6 = 0, which gives x = 6

x + 5 = 0, which gives x = -5

Therefore, the zeros of the function are x = 6 and x = -5.

Answer:

96 mm

Step-by-step explanation:

A square has 4 equal lengths. If you cut through with a diagonal, then you have form a right isosceles triangle.

So we have the diagonal, the hypotenuse, is [tex]24\sqrt{2}[/tex] mm.

We need to find the side measurement of the square, one of the leg measurements of the right isosceles triangle.

Let's assume it's leg measurement is x.

So by Pythagorean Theorem we have:

[tex]x^2+x^2=(24\sqrt{2})^2[/tex]

Combine like terms and simplify:

[tex]2x^2=24^2(\sqrt{2})^2[/tex]

The square and square root cancel there.

[tex]2x^2=24^2(2)[/tex]

I'm going to stick 24^2 * 2 in my calculator:

[tex]2x^2=1152[/tex]

Divide both sides by 2:

[tex]x^2=576[/tex]

Take the square root of both sides:

[tex]x=24[/tex]

So each side of the square is 24 mm long.

To find the perimeter I add up add all the side measurements of the square or multiply 24 by 4 since all sides of square are congruent.

24(4)=96

Answer is 96 mm

Given the diagonal of a square is 24 Square root two millimeters, the perimeter is calculated by first finding the side length using the diagonal, which is 24mm, and then multiplying it by 4 to get the perimeter, resulting in 96 millimeters.

The question asks to find the perimeter of a square given that the length of a diagonal is 24 Square root two millimeters. To solve this, we use the property that the diagonal of a square is √2 times longer than its side (a). This stems from the Pythagorean theorem applied in a square, where the diagonal acts as the hypotenuse, leading to the equation a² + a² = d² (where a is the side length and d is the diagonal).

Therefore, a = d / √2. Substituting the given diagonal length, we get a = 24mm. Since the perimeter (P) of a square is 4 times the side length, P = 4a. Thus, the perimeter is 96 millimeters.

Answer:

A:(1,-3/4)

Step-by-step explanation:

Use substitution to solve the system

y= 1/4x-1

y= -1/2x-1/4

1/4x-1 = -1/2x-1/4, Solve for x

3/4x= 3/4, x = 1, Next solve for y by plugging the x-value into either equation.

y=1/4(1)-1

y=-3/4

Answer:

1,-3/4

Step-by-step explanation:

For this case we have that by definition, the volume of a rectangular solid is given by the product of its length (l), its width (w) and its height (h).

Then, according to the data, it is not specified to which side each measurement corresponds. So, we multiply:

[tex]V = 10.5 * 6.5 * 8.5\\V = 580.125[/tex]

Rounding:

[tex]V = 580.1cm ^ 3[/tex]

Answer:[tex]V = 580.1cm ^ 3[/tex]

as you may already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=x^3-9\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^3-9}\implies x+9=y^3\implies \sqrt[3]{x+9}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer: 398

Step-by-step explanation:

200^2 - 199^2 = 399

Answer:

397

Step-by-step explanation:

200^2 - 1 = 40000 - 1 =   39999

199^2 + 1 = 39601+ 1 =    39602

Difference =                         397

A couple of things you should keep in mind.

a = hours worked by the first mechanic

b = hours worked by the second mechanic.

since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.

we know all hours combined are 15, so then a + b = 15.

we also know that all charges combined are $950, so 55a + 80b = 950.

[tex]\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft[/tex]

Answer:

The length of the wire is 22.42 feet

The distance from the base of the pole to the spot where the wire touches the ground is 16.66 feet

Step-by-step explanation:

* Lets explain the situation in the problem

- The telephone pole , the wire and the ground formed a right triangle

- The wire is the hypotenuse of the triangle

- The height of the telephone pole and the distance from the base of

 the pole to the spot where the wire touches the ground are the legs

 of the triangle

- The angle between the wire and the ground is 42°

- The angle 42° is opposite to the height of the telephone pole

- The height of the telephone pole is 15 feet

* Lets use the trigonometry functions to find the length of the wire

 (hypotenuse) and the distance from the base of the pole to the spot

 where the wire touches the ground

∵ sin Ф = opposite/hypotenuse

∵ Ф = 42° and its opposite side = 15 feet

∴ sin 42 = 15/hypotenuse ⇒ by using cross multiplication

∴ sin 42° (hypotenuse) = 15 ⇒ divide both sides by sin 42

∴ hypotenuse = 15/sin 42° = 22.42 feet

∵ The length of the wire is the hypotenuse

∴ The length of the wire is 22.42 feet

∵ The distance from the base of the pole to the spot where the wire

   touches the ground is the adjacent side to the angle 42°

∵ tan Ф = opposite/adjacent

∴ tan 42° = 15/adjacent ⇒ by using cross multiplication

∴ tan 42° (adjacent) = 15 ⇒ divide both sides by sin 42

∴ adjacent = 15/tan 42° = 16.66 feet

∵ The adjacent side is the distance from the base of the pole to the

  spot where the wire touches the ground

∴ The distance from the base of the pole to the spot where the wire

   touches the ground is 16.66 feet

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A=500\left(1+\frac{0.03}{1}\right)^{1\cdot 5}\implies A=500(1.03)^t[/tex]

Answer:

b

Step-by-step explanation:

B. You walk down 10 flights of stairs

The situation that can be represented by the opposite of 10 is B. You walk down 10 flights of stairs. The concept of 'opposite' here refers to the negative version of a number, which, in this case, would be -10. When you climb up 10 flights of stairs, that's a positive movement upward, analogous to a positive 10. However, walking down 10 flights is the opposite direction, corresponding to -10. Similarly, a temperature rise or a plant growing represents an increase, not the opposite of 10.

Answer:

Step-by-step explanation:

i believe it is 4.

assuming feburary it snowed about 8.5 inches and in november it is at about the 3 in line you would subtract to get about 5.5 inches

Answer:

4) 5.4 inches

Step-by-step explanation:

5.4 inches of snow fell in February 1889 than November 1888.

According to the graph:

Feb '89: 8.5 inches

Nov '88: 3 inches

8.5 - 3 = 5.5 or 5.4.

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- To prove that all circles are similar, a translation and a scale factor

  from a dilation will be found to map one circle onto another

- So we can translate the circles to share the same center and dilated

 one of them by the scale factor of the dilation and the center of

 dilation is the common center of the circles

* Lets solve the problem

∵ Circle X has a radius 6 units

∵ Circle Y has a radius 2 units

- At first we translate the circles to share the same center

∴ Use translation to put the centers of the circles at the same point

- Find the scale factor of the dilation from the radii of the two circles

∵ The radius of circle X is 6 units

∵ The radius of circle Y is 2 units

∴ The scale factor = 6/2 = 3

∴ Dilate circle y by scale factor 3

* The steps would prove the circles are similar are;

  Translate the circles so they share a common center point, and

  dilate circle Y by a scale factor of 3.

Answer:

y is 90

Step-by-step explanation:

The y/x is proportional per point (x,y) since this is a direct variation.

That is ,

[tex]\frac{30}{-3}=\frac{y}{-9}[/tex].

Cross multiply:

[tex]30(-9)=y(-3)[/tex]

Simplify:

[tex]-270=-3y[/tex]

Divide both sides by -3

[tex]\frac{-270}{-3}=y[/tex]

[tex]90=y[/tex]

Answer:

  250

Step-by-step explanation:

If we let p represent the 1975 population, we have ...

  p + 140%×p = 600

  p(1 +1.40) = 600

  p = 600/2.4 = 250

There were 250 grizzly bears living in the wild in 1975.

Answer:

$176

Step-by-step explanation:

The function[tex]p(x) = 5x^4-3x^3 + 2x^2 + 24[/tex] represents how much money each girl spent based on the number of hours they were shopping.

Janelle goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Janelle spent $88.

Carmen goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Carmen spent $88 too.

Together they spent

$88+$88=$176

Answer:

176

Step-by-step explanation:

Answer:

60 inches squared

Step-by-step explanation:

The formula for the area of a triangle is as follows:

[tex]A=\frac{1}{2} bh[/tex]

Where A=area, b=base, and h=height.

Plug in 15 for your base and 8 for your height and solve.

[tex]A=\frac{1}{2} (15)(8)\\A=7.5(8)\\A=60[/tex]

Answer:

B) 60 squared inches

Step-by-step explanation:

To find the area of a triangle you have to use this equation:

A = 1/2 b*h

Now plug in the numbers,

A = 1/2 15*8

15*8 = 120

1/2 of 120 = 60

A = 60

The area of this triangle is 60 squared inches.

Answer:

The surface area of the structure is [tex]SA=2,500\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

In this problem we have

[tex]r=50/2=25\ m[/tex] -----The radius is half the diameter

substitute

[tex]SA=4\pi (25)^{2}[/tex]

[tex]SA=2,500\pi\ m^{2}[/tex]

Answer:

The answer is D.

Step-by-step explanation:

AQRT is a 30-60-90 triangle.

Answer:

The answer id D. AQRT is a 30-60-90 triangle.

Hope this Helps!

Answer:

y = 2x + 14

Step-by-step explanation:

As we move from  (-8, - 2) to (-4, 6)​, x increases by 4 and y increases by 8.

Thus, the slope, m, equal to rise / run, is m = 8/4, or m = 2.

Use the slope-intercept form of the equatino of a straight line:

y = mx + b.  This becomes 6 = 2(-4) + b, or 6 = -8 + b.  Thus, b = 14, and the desired equation is y = 2x + 14.

Step-by-step explanation:

Definition:

A pyramid is a polyhedron formed by connecting a one polygonal base and a point, called the apex. Each base edge and apex form a triangle.

A) A pyramid has only one base.   TRUE   (definition)

(look at any photo with the pyramid)

B) The base of a pyramid is a polygon.   TRUE    (definition)

(look at any photo with the pyramid)

C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.   TRUE

(look at the picture)

D) The slant height is always the same length as the base of the pyramid.

FALSE

E) The lateral faces of a pyramid are rectangles.   FALSE   (definition)

(the lateral faces of a pyramid always are triangles)

F) The slant height is used to calculate the lateral area.   TRUE

(the lateral faces of a pyramid are triangles. The formula of an area of a triangle is A = (bh)/2. Where b - base of triangle, h - height of triangle)

Answer:

A: pyramid has only one base.

B: The base of a pyramid is a polygon.

C: If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.

F: The slant height is used to calculate the lateral area.

[tex]\bf \begin{array}{ccll} \stackrel{teaspoons}{pepper}&potatoes\\ \cline{1-2} \frac{1}{4}&3\\ x&9 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{3}{9}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{1}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{1}{3}\implies 3=4x\implies \cfrac{3}{4}=x[/tex]

Answer:

Since 9 is 3 times the denominator of the first ratio, multiply the numerator of the first ratio by 3 to get the numerator of the second ratio. The amount of pepper is 3/4 teaspoon.

Step-by-step explanation:

For this case we have that by definition of multiplication of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

So, we can rewrite the given expression as:

[tex]8 ^ {3-5 + y} = \frac {1} {8 ^ 2}\\8 ^ {- 2 + y} = \frac {1} {8 ^ 2}[/tex]

So, if [tex]y = 0[/tex]:

[tex]8 ^ {- 2} = \frac {1} {8 ^ 2}\\\frac {1} {8 ^ 2} = \frac {1} {8 ^ 2}[/tex]

Equality is met!

Answer:

[tex]y = 0[/tex]

Answer:

Value of y=0

Step-by-step explanation:

We need to solve

[tex]8^3*8^{-5}*8^y=1/8^2[/tex]

We know that 1/a^2 = a^-2

[tex]8^3*8^{-5}*8^y=8^{-2}[/tex]

[tex]8^y=\frac{8^{-2}}{8^3*8^{-5}}\\8^y=\frac{8^{-2}}{8^{3-5}}\\8^y=\frac{8^{-2}}{8^{-2}}\\8^y=1[/tex]

Taking ln on both sides

[tex]ln(8^y)=ln(1)\\yln(8)=ln(1)\\y= ln(1)/ln(8)\\We\,\,know\,that\,\,ln(1) =0\\y=0[/tex]

So, value of y=0

Answer:

Step-by-step explanation:

[tex](g-f)(x)=g(x)-f(x)\\\\f(x)=4-x,\ g(x)=6x\\\\(g-f)(x)=6x-(4-x)=6x-4-(-x)=6x-4+x=7x-4\\\\(g-f)(3)-\text{put}\ x=3\ \text{to the expression}\\\\(g-f)(3)=7(3)-4=21-4=17[/tex]

Answer:

Part A: x^2 + 6x + 8 = 0 use the factoring the equation method

Part A: x^2 + 6x + 8 = 0 use the quadratic formula

Step-by-step explanation:

Part A;

The equation is  x^2 + 6x + 8 = 0 , looking at this quadratic expression, you notice it is written in a quadratic equation standard form  of ax^2+bx+c=0. Additionally, you notice that can find what multiplied to get the quadratic equation,factor.You can identify two numbers that multiply to get ac and add to give b.In this question;

a=1,b=6,c=8

ac=8

The numbers are 4 and 2. Factoring the equation method will give;

x²+6x+8=0

x²+4x+2x+8=0

x(x+4)+2(x+4)=0

(x+2)+(x+4)=x²+6x+8

x+2=0, x=-2  and x+4=0, x=-4

Part B

The quadratic equation is ;

x²+6x-11=0

You notice that there are no factors that multiply direct to get the quadratic equation like in part 1. When you observe, a=1, b=6 and c=-11

ac=1×-11=-11 and b=6 .You notice there are no factors that multiply to give -11 and add to get 6, hence the factorizing the equation method can not be used.However, you can apply the quadratic formula that requires coefficients. You have a=1, b=c and c=-11 as the coefficients to use in the quadratic formula.

Answer:

Part A  -  use the factor method

Part B - use the quadratic equation

Step-by-step explanation:

Thinking process:

Let's look at the two parts in the problem:

Part A: x^2 + 6x + 8 = 0

This is a quadratic equation. Now, the product of the first and last term produces 8x². This product is a common multiple of 4 x and 2 x. These numbers can be added to get the middle term: 6x. Hence the equation can be solved by factorization.

Part B: x^2 + 6x - 11 = 0

Part B is also a quadratic equation. This equation can be analysed as follows:

The product of the first and last product gives -22x². Two factors are possibe: -11x and 2x or -2x and 11 x. These factors wjhen added or subtracted do not give the middle term (6x). Hence factorization will not work.

The best way to solve the equation is to use the quadratic formula:

[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Answer:

x = 3, plus or minus, radical 5 all over 2

Step-by-step explanation:

Answer:

The correct option is Option B.   $1293

Step-by-step explanation:

It is given that,the cost function for Judy’s new clothing store where she sells t-shirts is c=$11.50n + 925.  She sells 32 t-shirts this month

To find the total cost for this month

cost for n shirt , c=$11.50n + 925

 Cost for 32 shirts = 11.50 * 32 + 925

 =  368 + 925

 = 1293

Therefore the total cost = $1293

The correct answer is option B.  $1293

Answer:

When you graph all the equations into a graphing calculator, you find the answer is:

C. x-2y=1 and 3x-y=-1

The system of equations has a solution of approximately (0.6, –0.8) are;

x + 2 y = - 1 and 3 x + y = 1

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

From this information, it is clear that the green line and the Purple line intersect each other at an approximate point (0.6, -0.8).

Since, the green line passes through the x-intercept (-1,0) and y-intercept (0,-0.5).

Therefore, the equation of the green line will be;

⇒ x + 2y = - 1

Again, the purple line passes through the point (0,1) and has a negative slope thus, the equation of purple line will be;

3x + y = 1 {Since it has negative slope}

Therefore, the first option will be the answer.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ6

well, the difference is 21330 - 19700 = 1630.

now, if we take 21330 as the 100%, what is 1630 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 21330&100\\ 1630&x \end{array}\implies \cfrac{21330}{1630}=\cfrac{100}{x}\implies \cfrac{2133}{163}=\cfrac{100}{x} \\\\\\ 2133x = 16300\implies x=\cfrac{16300}{2133}\implies x \approx 7.64[/tex]

Answer:

Change in the price of the car was 7.64%

Step-by-step explanation:

Cindy bought a car for $21330.

After few years she sold the car for $19700.

Net loss she suffered = Selling price - Cost price

= 21330 - 19700

= $1630

Now the percent change in the value will be = [tex]\frac{\text{Difference in the price}}{\text{Cost price of the car}}\times 100[/tex]

= [tex]\frac{1630}{21330}\times 100[/tex]

= 7.64%

Therefore, change in the price of the car was 7.64%

Answer:

Option a) dodecahedron

Step-by-step explanation:

we know that

case a) Dodecahedron

it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12). Each face has 5 edges (a pentagon)

case b) Octahedron

it is a polyhedron that has 8 faces (from Greek okto- meaning eight).

case c) Icosahedron

it is a polyhedron that has 20 faces (from Greek icos- meaning twenty).

case d) Terrahedron

it is a polyhedron composed of four triangular faces (from Greek tetra- meaning four).

therefore

The answer is dodecahedron