Theo started to solve the quadratic equation (x + 2)2 - 9 = -5. He added 9 to both sides and the resulting equation was
(x + 2)2 = 4. Next, he took the square root of each side.
Which was the resulting equation of that step?

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 3x + 4y = 5 into this form

Add 3x to both sides

4y = 3x + 5 ( divide all terms by 4 )

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes, thus

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (2. 1) into the partial equation

1 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{1}{2}[/tex]

y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of parallel line

Answer:

Step-by-step explanation:

If point (3.4, 1.2) lies on a circle, the distance between this point and the center (1, -2) is equal to the radius r = 4.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]d=\sqrt{(1-3.4)^2+(-2-1.2)^2}=\sqrt{(-2.4)^2+(-3.2)^2}\\\\=\sqrt{5.76+10.24}=\sqrt{16}=4=r[/tex]

The point (3.4, 1.2) lies on the circle, and distance between the two is 4 units.

To determine whether the point (3.4, 1.2) lies on the circle with a center at (1, -2) and a radius of 4, we can use the distance formula to calculate the distance between the center of the circle and the given point. If this distance is equal to the radius of the circle, then the point lies on the circle; otherwise, it does not.

The distance formula between two points[tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Let's calculate the distance between the center of the circle (1, -2) and the given point (3.4, 1.2):

[tex]\[ d = \sqrt{(3.4 - 1)^2 + (1.2 - (-2))^2} \]\[ d = \sqrt{(3.4 - 1)^2 + (1.2 + 2)^2} \]\[ d = \sqrt{(2.4)^2 + (3.2)^2} \]\[ d = \sqrt{5.76 + 10.24} \]\[ d = \sqrt{16} \]\[ d = 4 \][/tex]

The calculated distance between the center of the circle and the given point is equal to the radius of the circle, which is 4 units.

Answer:

It’s 3

Step-by-step explanation:

multiply 3 time 2 and add 4

Since the length of the side labeled 10 and the other side labeled 2y +4 are the same. Set them equal to each other and subtract 4 to the other side and then divide 2 to other side to get y=3. Your welcome.

Answer:

b = √c²-a²

Step-by-step explanation:

b² = c² - a²

b = √c²-a²

The Pythagorean theorem, denoted as a² + b² = c², can be rearranged as b = √(c² - a²) to solve for one of the sides of a right triangle. Once the lengths for a and c are known, they can be substituted into the formula to find the length of b.

The Pythagorean theorem, a key geometric principle, can be used to solve for one of the sides in a right triangle given the lengths of the other two. Usually, it's denoted as a² + b² = c², where a and b are the lengths of the triangle's legs, and c is the length of the hypotenuse. In the question, you want to solve for b.

First, let's isolate b in the formula. Rewrite the formula as b² = c² - a². To find the length of b, take the square root of both sides, resulting in b = √(c² - a²).

Now, once you have the values for a and c, you can substitute them into the formula to find b. This application of the Pythagorean theorem can be very useful in various situations where you have a right triangle, and you know the lengths of two of its sides but need to find the length of the third side.

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Answer:

A. What figures?: Hexagonal prism topped by a hexagonal cone

B. 246 sq cm

Step-by-step explanation:

A. What figures?

Imagine you're rolling up all 6 vertical pointy pieces around the base hexagon.  Then you'll have like a crown top with all the triangles.  You can fold these triangles to have their tips meet and form a hexagonal cone...

So, you'll have a hexagonal prism, topped with a hexagonal cone.

B. Surface area.

That's just a matter of calculating the areas of all triangles, rectangles and hexagon of the assembly.

Triangles: base: 4 cm, height: 5 cm, quantity: 6

A = (b * h) / 2 = (4 * 5) / 2 = 10 sq cm

AT = 6 * V = 6 * 10 = 60 sq cm

Rectangles: base: 4 cm, height: 6 cm, quantity: 6

A = b * h = 4 * 6 = 24 sq cm

AR = 6 * V = 6 * 24 = 144 sq cm

Hexagon: side: 4 cm, quantity: 1

Since it's a regular hexagon and we know its side length...

AH =  (3√3 * s²)/2 = (3√3 * 16)/2 = 24√3 = 41.57 sq cm

Then we add everything together:

A = AT + AR + AH

A = 60 + 144 + 41.57 = 245.57 sq cm

Rounded answer: 246 sq cm

Answer:

246 cm²

Step-by-step explanation:

The composite space figure consists of:

The surface area is the sum of all the areas of each figure.

Area of a hexagon = ½√(27) s²

Area of a rectangle = wl

Area of a triangle = ½ bh

So the total area is:

A = ½ √(27) (4)² + 6(4×6) + 6(½×4×5)

A = 8√(27) + 204

A ≈ 246 cm²

Answer:

10/12x100%= 83.3%

Step-by-step explanation:

Answer:

83.3%

Step-by-step explanation:

Charlie worked 10 of the 12 months so

[tex]\frac{10}{12}[/tex] × 100 = 83.3333

Answer:

see explanation

Step-by-step explanation:

The meaning of n factorial → n !

n ! = n(n - 1)(n - 2)........ × 3 × 2 × 1

For example

7 !

= 7 × 6 × 5 × 4 × 3 × 2 × 1

The histogram would look something like this:

Hope I helped and please give me brainliest!

Answer:remove the radical and try not to simplify

Step-by-step explanation:

Answer: 2200 cookies for the week

24 total for the chocolate chip / peanut butter

Step-by-step explanation:

500 + 300 = 800 + 400 = 1200 + 800 = 2000 + 200 + 2200

9 + 15 = 24

To find the total number of cookies sold for the week, add up the number of cookies sold each day. The total is 2200. When considering both types of cookies, the website will have sold 24 cookies in total.

To find the total number of cookies sold for the whole week, we will add up the number of cookies sold on each day. Using the given numbers, the total number of cookies sold is

= 500 + 300 + 400 + 800 + 200 = 2200.

For the second part, we need to find the total number of cookies sold when considering both gooey chocolate chip cookies and peanut butter blossoms. We add up the number of each type of cookie: 9 + 15 = 24.

Therefore, the website will have sold 2200 cookies in total for the week, and when including both gooey chocolate chip cookies and peanut butter blossoms, they will have sold 24 cookies in total.

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Answer: First option

v-3u = 11 j

Step-by-step explanation:

To find the components of the vector v, you must locate the initial and final points of the vector on the graph.

Final point

(7, 2)

Initial point

(-5, 0)

Then the vector v will have the following components:

[tex]v = (7 - (- 5)) i + (2-0) j\\\\v = (7 + 5) i + 2j\\\\v = 12i + 2j[/tex]

Now multiply the vector u by -3

[tex]u = (4, -3)\\\\u =4i -3j\\\\-3u = -12i + 9j[/tex]

Now add both vectors.

[tex]v-3u = (12-12) i + (2 + 9) j\\\\v-3u = 0i + 11j\\\\v-3u = 11j[/tex]

Answer:

3 points, I believe.  

Step-by-step explanation:

ANSWER

[tex] \sqrt{5} [/tex]

EXPLANATION

The given points are (1,0) and (0,2).

We use the distance formula:

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

We substitute the given points into the formula to get:

[tex]d = \sqrt{(0-1)^2 +(2-0)^2} [/tex]

We simplify to get:

[tex]d = \sqrt{1+4} [/tex]

[tex]d = \sqrt{5} [/tex]

Therefore the distance between the two points is √5 units.

Answer:

140

Step-by-step explanation:

The sum of angles is 360.

9x+14x+4x+90 = 360 => 27x+90 = 360 => 27x = 270 => x = 10 => 14x = 140 => the angle is 140

The measure of angle F is 140

Two consecutive right angles make up a right trapezoid, also known as a right-angled trapezoid. The trapezoidal rule employs right trapezoids to calculate the areas under a curve. An obtuse trapezoid has one acute and one obtuse angle on each base, whereas an acute trapezoid has two consecutive acute angles on its longer base edge.

Given

Sum of all angles of trapezoid = 360

9x + 14x + 4x+ 90 = 360

27x + 90 = 360

27x  = 270

x = 10

F = 14x = 14* 10 = 140

Therefore, The measure of angle F is 140.

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Answer:

It is easy to divide decimals

Step-by-step explanation

To do it

First: Take an example 5/0.2

Second: Make the division more easier by multiplying the denominator and numerator by 10 ( the number of zeros vary according to the number of places in the decimal part, for example if there where three places in the decimal side the use 1000 to multiply, look at the numer of the decimal places and the numer of zeros in the number to multiply). 5*10/0.2*10 = 50/2

Third: Now divide it normaaly in the example we get 25 as the answer.

I hope you liked the answer.

Answer:

C

Step-by-step explanation:

Correct option is C.

Let x be the number of rows in a meeting room. If there are 4 fewer chairs laid out in each row than the number of rows, then in each row there are x-4 chairs.

The total number of chairs is

[tex]x(x-4)[/tex]

The total number of chairs in the room is 60. Hence,

[tex]x(x-4)=60[/tex]

D 27,35,46

You can use the Pythagorean theorem a squared plus b squared equals c squared

the set of numbers that does NOT form a right triangle is option D: 27, 35, 46.

To determine whether a set of numbers forms a right triangle, we need to check if the Pythagorean theorem holds true for them. The Pythagorean theorem states that in a right 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.

Let's calculate the squares of the sides for each option:

A. 14, 48, 50

14² + 48² = 196 + 2304 = 2500

50² = 2500

B. 15, 20, 25

15² + 20² = 225 + 400 = 625

25² = 625

C. 21, 28, 35

21² + 28² = 441 + 784 = 1225

35² = 1225

D. 27, 35, 46

27² + 35² = 729 + 1225 = 1954

46² = 2116

Now, let's compare the squares of the two smaller sides with the square of the largest side for each option:

A. 2500 = 2500 (Forms a right triangle)

B. 625 = 625 (Forms a right triangle)

C. 1225 = 1225 (Forms a right triangle)

D. 1954 ≠ 2116 (Does NOT form a right triangle)

So, the set of numbers that does NOT form a right triangle is option D: 27, 35, 46.

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Answer:

9/20

Step-by-step explanation:

You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 [tex]\frac{45}{100} /5[/tex]

45/5=9

100/5=20

You get 9/20, and this is in simplest form.

Answer:Y9/20

Step-by-step explanation:

Answer:

x= 35 gallons consumed by 1st car

and y= 40  gallons consumed by 2nd car

Step-by-step explanation:

Fuel efficiency of 1st car = 15 miles per gallon

Fuel efficiency of 2nd car = 35 miles per gallon

Let x= gallons consumed by 1st car

and y= gallons consumed by 2nd car

Total gallons consumed by both cars = 75

so, we can write

x + y = 75

Miles covered by both cars = 1925 miles

and we know, Fuel efficiency of 1st car = 15 miles per gallon

Fuel efficiency of 2nd car = 35 miles per gallon

we can write the equation as

15 x + 35 y = 1925

where x and y are gallons consumed by 1st and 2nd car.

We have two equation now,

x + y = 75                   (1)

15 x + 35 y = 1925     (2)

Multiplying eq(1) with 15 and subtracting eq (1) and 2

15 x + 15 y = 1125

15 x + 35 y = 1925

-       -            -

_______________

0 - 20 y = -800

y= -800 / -20

y = 40

Putting value of y in equation 1

x + y = 75

x + 40 = 75

x= 75 - 40

x = 35

x= 35 gallons consumed by 1st car

and y= 40  gallons consumed by 2nd car

The first car consumed 50 gallons of gas and the second car consumed 25 gallons of gas that week.

Let's denote the number of gallons consumed by the first car as x and the number of gallons consumed by the second car as y. Then, we have the following two equations based on the mileage and the total gas consumption:

To solve these two equations, you can first solve the second equation for x, x = 75 - y, and then substitute it into the first equation: 15(75 - y) + 35y = 1925. This gives you y = 25. So, the second car consumed 25 gallons of gas. As the total gas consumption is 75 gallons, the first car must have consumed 75 - 25 = 50 gallons of gas.

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Answer:

S = 2((12(8) + 8(2) + 12(2))

= 2(96 + 16 + 24)

= 2(136)

= 272 square feet

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}10&-30\\-10&-2\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]X-3\left[\begin{array}{ccc}2&-8\\-4&2\end{array}\right] =\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]\\\\X-\left[\begin{array}{ccc}(3)(2)&(3)(-8)\\(3)(-4)&(3)(2)\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]\\\\X-\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right][/tex]

[tex]X-\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]+\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]+\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]\\\\X=\left[\begin{array}{ccc}4+6&(-6)+(-24)\\2+(-12)&-8+6\end{array}\right]\\\\X=\left[\begin{array}{ccc}10&-30\\-10&-2\end{array}\right][/tex]

Answer:

10.49

Step-by-step explanation:

(picture shows)

That would be:

10.49

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Distributive Property

Step-by-step explanation:

6(2 + x) = 12 + 6x illustrates the distributive property.

An algebraic property called the distributive property is utilized to multiply a single value by two or more values contained between parenthesis.

The distributive property of binary operations generalizes the distributive law, which declares that equality exists always accurate in elementary algebra.

Given

6(2+x )

[tex]= 6*2 + 6*x[/tex]

= 12+6x

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Answer:

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

Step-by-step explanation:

These two lines do intersect and do not have the same y intercept so it cannot be the first two options

And since the problem is in term of x only, the third option is true

ANSWER

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

EXPLANATION

The given functions are:

f(x)=5x-1

g(x)=4x-8

To solve the equation 5x−1=4x−8 graphically, we need to graph f(x)=5x-1 and g(x)=4x-8 on the same graph sheet.

The x-coordinates of the point of intersection of the graphs of the two functions is the solution to the equation:

5x−1=4x−8

The third choice is correct.

Answer:

The scale factor is [tex]0.25[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional , and this ratio is called the scale factor

Let

z----> the scale factor

x ----> the corresponding side of the resulting image

y-----> the corresponding side of the first rectangle

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

we have

[tex]x=1.5\ units[/tex]

[tex]x=6\ units[/tex]

substitute

[tex]z=\frac{1.5}{6}=0.25[/tex]

Answer:

0.25

Step-by-step explanation:

z=\frac{1.5}{6}=0.25

Answer: No Solution

Step-by-step explanation:

When you subtract p on both sides, you get -4=-9 and that is not a true statement.

Hope this helps!

Area shaded = Area big circle- Area of small circle;

200 pi= pi•(2x)^2 -pi•6^2;

200pi= pi•4x^2 -pi•36;

200pi=pi•4(x^2 -9) divide both sides by 4pi;

50=x^2 -9; So x=sqrt(59)~7.68cm

Answer:

Yes.

Step-by-step explanation:

The vertex is 1,3. The vertex is in quad 1. The graph is shifted 1 to the right and up 3.

Answer:

C: because one pair of congruent corresponding angles is sufficient to determine similar triangles

Step-by-step explanation:

on edge! hope this helps!!~ （‐＾▽＾‐）

The information in the diagram is enough to determine that △LMN ~ △PON using a rotation and dilation because one pair of congruent corresponding angles is sufficient to determine similar triangles. Therefore, option c is the correct answer.

The information in the diagram is enough to determine that △LMN ~ △PON using a rotation about point N and a dilation because one pair of congruent corresponding angles is sufficient to determine similar triangles.

In order to determine that two triangles are similar, you need to establish that their corresponding angles are congruent, and their corresponding sides are in proportion.

In the given scenario, you have △LMN and △PON. The key information is that ∠MNL and ∠ONP are congruent angles. This means that one pair of corresponding angles is equal.

According to the Angle-Angle (AA) similarity theorem, if you have two pairs of corresponding angles that are congruent, the triangles are similar. In this case, you have one pair of congruent corresponding angles, ∠MNL ≅ ∠ONP, which is sufficient to determine that △LMN ~ △PON.

The statement "because one pair of congruent corresponding angles is sufficient to determine similar triangles" is the correct explanation for why △LMN is similar to △PON using a rotation about point N and a dilation.

Therefore, option c is the correct answer.

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Answer:

Part 1) The simple interest earned when you invest $1,000 for 3 years at 10 % is $300

Part 2) The interest compounded when you invest the same sum for 2 years at 5 % is $102.50

Part 3) [tex]f(t)=7(2)^t[/tex]

Part 4) [tex]f(t)=3,000(0.93)^t[/tex]

Part 5) [tex]f(t)=300(1.015)^t[/tex]

Part 6) [tex]f(t)=300(0.985)^t[/tex]

Step-by-step explanation:

Part 1) What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$1,000\\r=0.10[/tex]

substitute in the formula above

[tex]I=\$1,000(0.10*3)=\$300[/tex]

Part 2) What will be the compound interest earned when you invest $1,000 for 2 years at 5 percent ?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

I 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=2\ years\\ P=\$1,000\\ r=0.05\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$1,000(1+\frac{0.05}{1})^{1*2}[/tex]  

[tex]A=\$1,000(1.05)^{2}=\$1,102.50[/tex]  

The interest is equal to

[tex]I=\$1,102.50-\$1,000=\$102.50[/tex]  

Part 3) There are 7 trout fish in a pond,  and the population doubles every year.

Find the population after t years.

we know that

This question is about exponent function of the form

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

where

a is the initial value

b is the base of the exponent.

In this problem we have

There are 7 trout fish in the pound ----> initial value a=7

The population is double every year ------> the base is b=2

substitute

[tex]f(t)= 7(2)^t[/tex]

Part 4) A company buys a machine for $3,000.  The value of the machine depreciates  by 7% every year. Find the value of  the machine after t years.

we know that

This question is about exponent function of the form

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

where

a is the initial value

b is the base of the exponent.

we have

Company buys a machine for $3,000 --> initial value is a=3,000

The value depreciate 7% a year

Since it was decreased by 7% every year, it will become: 100%-7%=93%

the base is 93%, b=0.93

substitute

[tex]f(t)=3,000(0.93)^t[/tex]

Part 5) The initial population of a colony of ants  is 300. The number of ants increases  at a rate of 1.5% every month. Find the  population of ants after t months.

we know that

This question is about exponent function of the form

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

where

a is the initial value

b is the base of the exponent.

we have

Initial population of ants is 300----> initial value is a=300

The number of ants increases 1.5% per month.

Since it will increases by 1.5% every month, it will become: 100%+1.5%=101.5%

the base is 101.5%, b=1.015

substitute

[tex]f(t)=300(1.015)^t[/tex]

Part 6) A research laboratory is testing a new  vaccine on 300 infected cells. The decay  rate is 1.5% per minute. Find the  number of infected cells after t minutes.

we know that

This question is about exponent function of the form

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

where

a is the initial value

b is the base of the exponent.

we have

A research laboratory is testing new vaccine on 300 infected cells

 initial value is a=300

The decay/decrease rate is 1.5% per minute

Since it will decrease by 1.5% every min, it will become: 100%-1.5%=98.5%  

the base is 98.5%, b=0.985

substitute

[tex]f(t)=300(0.985)^t[/tex]

Answer:

C.  [tex]\pi (5^{2} )(13)+\frac{1}{3} \pi (5^{2} )(12)[/tex]

Step-by-step explanation:

Edge 2021

The volume of the composite figure is given by the expression π(5²)(13) + (1/3)π(5²)(12)

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of the composite figure = volume of cylinder + volume of cone.

Hence:

The volume of the composite figure = π(5²)(13) + (1/3)π(5²)(25 - 13)

The volume of the composite figure = π(5²)(13) + (1/3)π(5²)(12)

The volume of the composite figure is given by the expression π(5²)(13) + (1/3)π(5²)(12)

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