Solve the equation using square roots
3x^2+22=49

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

Any equation of the form [tex]ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Given work of Penelope is

[tex]$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$$[/tex]

Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following

[tex]$$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$$[/tex]

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

To learn more about quadratic equations visit : https://brainly.com/question/1214333

Answer:

C) Penelope should have added 4 to both sides instead of adding 1.

Step-by-step explanation:
Got it right on edge! Good Luck <3

Answer:

1.75/n

Step-by-step explanation:

1.75 divided by n is equal to 0.35

Answer:

2

Step-by-step explanation:

Use z score formula.

55 is x

plug in u and sd.

Answer:

11.4

Step-by-step explanation:

Subtract 14-7 to get the height of the triangle. 9 is the width.

Now we need to find the hypotenuse which is c^2=a^2+b^2

x^2=7^2+9^2=11.4

Let me know if this helped <3

Answer:

wait i will comment

can you wait

Answer:

48 feet.

step-by-step explanation:

using Pythagoras theorem:

a² + b² = c²

h² + 55² = 73²

h² = 73² - 55²

h² = 5329-3025

h² = 2304

h = √2304

h = 48

Answer:

x = 48 ft

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for x:

⇒ x² + 55² = 73²

⇒ x² + 3025 = 5329

⇒ x² = 5329 - 3025

⇒ x² = 2304

⇒ x = ±√2304

⇒ x = ±48

Since distance is positive, x = 48 ft

Abby's January finance charge is $7.22, the correct option is C.

Adjusted balance method: Based on finance charges on the amount(s) owed at the end of the current billing cycle after posted credits and payments.

The total amount on which interest will be applied using the adjusted balance method is;

[tex]=722.10 + 18.12-65.00 +18.00 + 44.79+ 34.25 - 40.00\\\\= 732.26[/tex]

Abby’s January finance charge will be;

[tex]= 732.26 \times 11.83 \times \dfrac{30}{360}\times \dfrac{1}{100}\\\\= 7.22[/tex]

Hence, Abby's January finance charge is $7.22.

To get more about the adjusted balance method please refer to the link,

brainly.com/question/14351468

Abby has a credit card which uses the adjusted balance method to compute finance charges. her card has an apr of 11.83%, and she is on a 30-day billing cycle. the table below shows her transactions in the month of January. date amount ($) transaction 1/1 722.10 beginning balance 1/6 18.12 purchase 1/7 65.00 payment 1/14 18.00 purchase 1/20 44.79 purchase 1/23 34.25 purchase 1/27 40.00 payment what will Abby’s January finance charge be? a. $6.08 b. $7.12 c. $7.22 d. $8.25

The answer is C.

Answer:

tax is 37,750 $

Step-by-step explanation:

Hope It Helps

Answer:

Solving steps:

Question:5 boys and 4 girls are randomly arranged to sit in a row. find the probability that all girls sit together.

Find:the probability that all girls sit together.

Solution: 5 boys and 4 girls, 9 kids in all, can be seated in a row in 9! ways. In order to find the number of ways, where the 4 girls are seated together, we place them in an imaginary group Z, so that they are not separated in the seating arrangements. Now we have 6 entities, namely 5 boys and one group of girls, and the number of ways of their seating is 6!. For each of these 6! ways, the 4 girls can be seated within the group Z in 4! ways. So the number of ways in which the 4 girls are seated together, is 6!/4!.

So the probability, as requested, is (6!4!)/9! = 24/(7x8x9) = 1/21

Answer:

[tex]y^{10}-\dfrac{25}{64}x^2[/tex]

Step-by-step explanation:

Given expression:

[tex](\frac58x+y^5)(y^5-\frac58 x)[/tex]

Change the order of the terms in the first parentheses:

[tex]\implies (y^5+\frac58x)(y^5-\frac58 x)[/tex]

Apply the Difference of Two Squares: [tex](a+b)(a-b)=a^2-b^2[/tex]

[tex]\implies (y^5)^2-(\frac58x)^2[/tex]

Apply exponent rule [tex](a^b)^c=a^{b\cdot c}[/tex]

[tex]\implies y^{10}-(\frac58x)^2[/tex]

Apply exponent rule [tex]\left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}[/tex]

[tex]\implies y^{10}-\left(\dfrac{5^2}{8^2}x^2\right)[/tex]

[tex]\implies y^{10}-\dfrac{25}{64}x^2[/tex]

Answer:

I have no idea and I'm not that smart

Answer:

ok ez

Step-by-step explanation:

a) 119/1009=11.79%

b) 264/1009=26.17%

c) 75/1009= 7.43%

d) 9/1009= 0.89%

u are welcome :)

Answer:

448

Step-by-step explanation:

This is  a proportion question. Keep the heights on one side of the proportion and the shadow length on the other.

height ratio  shadow ratio

40 cm / x = 25 / 280             Cross multiply

25x = 40 * 280                      Combine

25x = 11200                            Divide by 25

x = 11200/25

x = 448 cm

The height of the corn plant is 448 cm

Answer:

9,508.8 dollars spent

Step-by-step explanation:

subtraction.

Answer:

$9,508.8

Step-by-step explanation:

10,000-491.2=ans

Answer:

Reduce the expression, if possible, by canceling the common factors.

Exact Form:

15/32

Decimal Form:

0.46875

Step-by-step explanation:

Good Luck!

Answer:

hope this helps

Step-by-step explanation:

Answer:

vertex: (0,-1)

axis of symmetry: x=0

Answer:

There were 5 students in the back of the room.

Step-by-step explanation:

8x3=24

Which means that there were 24 students on the stage

Then...

29-24=5

Which means that there were 5 students in the back of the room.

Thanks!

Answer:

38 degrees

Step-by-step explanation:

To get the answer, we need to subtract the first angle from the second angle:

84-46=38

The minute hand turned 38 degrees from its first to second position.

How to check the answer? Use inverse operations.

46+38=84

Answer:

x = 5

Step-by-step explanation:

Given:

To Find:

What is the value of x?

Note:

Two angles that add up to give you 90° is a complementary angle.

Thus, Since angle A and angle B sum up to give 90°, they are complementary angles.

Solve:

The following equation can be created to solve for the value of x:

m ∠A + m∠ B

Substitute

40 + 4x + 30 = 90

Add like terms

4x +70 = 90

Subtract 70 from both sides

4x = 90-70

4x = 20

Divide both sides by 4

x = 5

Therefore, the value of x is 5

~Learn with Lenvy~

Answer:

ok........

Step-by-step explanation:

Answer:

2533 1/3

Step-by-step explanation:

becuase if you take the denominator you get it[tex]\sqrt{x} x_{123} \\ x^{2} x^{2} \alpha \beta \lim_{n \to \infty} a_n \leq \alpha \\[/tex]

Answer:

D: 5253 3/25 mm²

Answer:

883.57

Step-by-step explanation:

closet answer I can find

Answer:

(10 + q) ÷ 5

Explanation:

the sum of  10 and a number q is 10 + q

one fifth is dividing by 5

so (10+q) ÷ 5

Answer:

Given expression ,

[tex]\bold\purple{5y + \frac{x}{z}} \\ [/tex]

Also ,

value of x = 12

value of y = 8

value of z = 3

Substituting the values of x , y and z in the expression given , we get

[tex]\bold{⇢5(8) + \cancel{\frac{12}{3} }} \\ \\ \bold{ ⇢40 + 4} \\ \\ \bold\red{ ⇢44}[/tex]

hope helpful~

Hello.

First, let's plug in the values of the variables.

x=12

y=8

z=3

[tex]\mathrm{5(8)+\displaystyle\frac{12}{3}}[/tex]

5 times 8 equals 40:

[tex]\mathrm{40+\frac{12}{3}}[/tex]

12 divided by 3 equals 4:

[tex]\Large\boxed{44}[/tex]

I hope it helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

The claim supported by the confidence interval is as follows:

The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.

The 95% confidence interval for the difference(southern - northern) is given by:

(7.1, 8.1)

Since the entire confidence interval is above 0, the claim supported by it is as follows:

The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.

More can be learned about confidence intervals at https://brainly.com/question/25890103

Answer:

x = 6 cm

Step-by-step explanation:

We can write equations for length and width using the information given:

length = 2 + x

width = 2x - 5

Area = (length)(width) = 56

Area = (2 + x)(2x - 5) = 4x - 10 + 2x² - 5x

Simplifying:

Area = 2x² - x - 10 = 56

2x² - x - 66 = 0

Factoring:

(2x + 11)(x - 6) = 0

x = 6, -11/2

We choose the positive number: x = 6 cm

To check, plug in 6 for x:

Area = (2 + x)(2x - 5) = 56

(2 + 6)(12 - 5) = 56

(8 × 7) = 56

56 = 56

Answer:

2√34

Step-by-step explanation:

→ Find the difference between the x coordinates

-4 - 6 = -10

→ Find the difference between the y coordinates

2 - 8 = -6

→ Use Pythagoras

√ -10² + 6²= 2√34