Question 22 of 25
Which of the following are solutions to the quadratic equation below?
Check all that apply.
3x2 - 7x-3 = x
D A. 1
B. 3
] j
C. -3
D. -4
E.
=
1
O F..2

Answer:

HL Postulate

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HL Postulate(Hypotenuse - Leg) or RHS theorem -> If any two right angles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.  

AC ≅ DF , BC ≅ EF and ∠B ≅ ∠E ( both 90 0 )

∴ Δ ABC ≅ Δ DEF by RHS theorem

Theorem : Prove RHS theorem or postulate.

Given : AC = DF , BC = EF and ∠B = ∠E = 90 0

Prove that : ΔABC ≅ ΔDEF

Construction : Extend DE to G so that EG = AB. Join GF.

Statements

Reasons

1) AB = GE 1) Construction

2) ∠B = ∠FEG 2) Each 900

3) BC = EF 3) Given

4) ΔABC ≅ ΔGEF 4) By SAS postulate

5) ∠A = ∠G 5) CPCTC

6) AC = GF 6) If the two angles are congruent then angle opposite to them are equal

7) AC = DF 7) Given

8) DF = GF 8) By transitive property

9) ∠D = ∠G 9) Angles opposite to equal sides in ΔDGF are equal

10) ∠A = ∠D 10) From (5) and (9)

11) ∠B = ∠E 11) Given

12)∠A+∠B=∠D+∠E 12) Adding (10) and (11)

13) ∠C = ∠F 13) ∠A + ∠B + ∠C = 180

and ∠D + ∠E + ∠F = 1800

14) ΔABC ≅ ΔDEF 14) By SAS postulate and from (3) (7) and (13)

Step-by-step explanation:

Answer:

Step-by-step explanation:

HL is the the Hypothenuse Leg Postulate that sais that

If the hypotenuse and leg of one triangle are congruent

to the hypotenuse and leg of another triangle

then the triangles are congruent.

Answer:

one solution

Step-by-step explanation:

4x + 8 = -2 -2 + 5x

4x + 8 = -4 + 5x

4x - 4x + 8 = -4 + 5x - 4x

8 = -4 + 5x - 4x

8 = -4 + x

8 + 4 = -4 + 4 + x

12 = x

Step-by-step explanation:

b =-4 (y-intercept)

x =0

m = 0 (the line doesn't have a slope)

y = mx + c

y = 0(0) + (-4)

y = - 4

The relationship between the median and mean shown by the histogram is; The median is less than the mean.

From the given histogram, we see that it has a lot of its data on the left side.

Now, since the histogram has a lot of its' data to the right side, then we can say that it's skewed to the right. However, when the histogram is skewed to the right, it denotes that the mean will be more than the median.

Thus, we can conclude that the median is less than the mean.

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Answer:

b

Step-by-step explanation:

Answer:

56.25 minutes

Step-by-step explanation:

1 mile is 6.25 minutes

9 miles is _____?

6.25 minutes x 9 miles =

56.25 minutes

Find Unit Rate to help solve

Hope this helps :)

.......................

Answer:

The sales tax is 6.5% of the selling price of the book: 0.065($90.00) = $5.85.

Step-by-step explanation:

Answer:

$1800

Step-by-step explanation:

1. Approanch

An easy way to calculate one's salary after they recive a raise is to, convert the percent that one's salary is increased into a decimal; divide the percent by 100. Then multiply the increase as a decimal by the original salary, to attain the amount the salary is raised by. Finally add the amount the salary is raised by to the original salary to find the new salary. A quicker way to do this is to convert the percent by the salary is increased into a decimal. Then add 1 to that number. Finally one will multiply that number by the original slary and get the new salary.

2. Solving

Original salary; 1500

Raise; 20%

a. convert the raise as a percent into a decimal, then add 1

20% = 0.2

0.2 + 1 = 1.2

b. multiply the number by the original salary

1.2 * 1500

1800

Answer:

$ 1800

Step-by-step explanation:

Rise in payment = 20% of 1500

                          [tex]= \frac{20}{100}*1500\\\\=20 *15\\\\= $300[/tex]

New weekly wage = 1500 + 300

                                = $ 1800

Answer:

b=1

Step-by-step explanation:

1) Distribute

6+7b-7=5+b

2) Combine like ter,s

7b-1=5+b

3) Isolate variable

6b=6

4) Solve

b=1

Answer:

b = 1

Step-by-step explanation:

6 + 7b - 7 = 5 + b

7b - b = 5 - 6 + 7

6b = 6

b = 1

Answer: 3x + 1

Step-by-step explanation:

A p e x

Answer:

A would make sense

Step-by-step explanation:

Answer:

The maximum volume the cube could have is 729 cubic inches

Step-by-step explanation:

The total surface area of the cube equals the total area of material used.

Let A = total surface area of cube = 6L² where L = length of side of cube

Since A = total area of material used, A = 486 in²

So 486 in² = 6L²

L = √(486 in²/6)

= √81 in²

= 9 in

The volume of the cube V = L³ where L = length of side of cube

So, V = (9 in)³

= 729 in³

So the maximum volume the cube could have is 729 cubic inches.

The maximum volume that the box could have will be 729inches³.

Based on the information given, the first thing to do is to find the length of the shape. This will be:

Length = ✓(486/6)

Length = ✓81

Length = 9

Therefore, the volume of the cube will be:

= 9³

= 9 × 9 × 9

= 729 in³.

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Answer: a = 45°

Step-by-step explanation:

The measure of∠PSR is given: 90°

Given PS = RS, this is an isosceles triangle. so measure of ∠SPR, labeled "a" is equal to the measure of ∠SPR.  

The total of all angles in a triangle is 180. So subtract 90, then divide by 2.

180-90 = 90

90/2 = 45

a = 45°

If "b" is supposed to be the measure of ∠SRQ, that is 15°  The larger triangle is equilateral; all the angles are 60°. 60 - 45 = 15

Answer:

Area = 7.5

Step-by-step explanation:

The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

Given the triangle with  vertices P(1,1), Q(-2,1), R(-1,-4)

Length between two coordinates (x₁,y₁) and (x₂,y₂) is given by

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

By using this formula

PQ = 3 , QR = 5.099 and PR = 5.385

Now,

The area of a triangle with  all three sides is given by

A = [tex]\sqrt{S(S - A)(S - B)(S - C)}[/tex] where A,B and c are sides and s = (A + B + C)/2

So,

S = (3 + 5.099 + 5.385)/2 = 6.742

Now,

A = [tex]\sqrt{6.742(6.742- 3)(6.742 - 5.099)(6.742 - 5.385)}[/tex]

A = 7.499 ≈ 7.5

Hence "The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square".

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Answer:

20 ; 40 ; 80 ; 10(2^n)

Step-by-step explanation:

Given that:

Initial amount of goo (p) = 10 gram

Total amount of goo increased by 100% every hour ;

How much goo will she have sfter 1 hour?After 2 hours? After 3 hours? After n hours?

Using the relation :

Final amount = initial * (1 + rate)^t

Rate = 100% = 100/100 = 1

t = number of hours

Hence, after 1 hour :

Final amount = 10(1 + 1)^1

Final amount = 10(2)^1 = 20 grams

After 2 hours : t = 2

Final amount = 10(1 + 1)^2

Final amount = 10(2)^2 = 10 * 4 = 40 grams

After 3 hours ; t = 3

Final amount = 10(1 + 1)^3

Final amount = 10(2)^3 = 10 * 8 = 80 grams

After n hours ; t = n

Final amount = 10(1 + 1)^n

Final amount = 10(2)^n grams

Answer:

I haven't learned this but I think it's D.

Step-by-step explanation:

Answer:

m = -1

Step-by-step explanation:

The line is going down from left to right, meaning the slope is negative. The line is going down at the same rate at which it's going to the right, meaning the numerator and denominator are the same (a fraction with the same numerator and denominator is 1)

Answer:

[tex]m = \frac{11}{12} [/tex]

Step-by-step explanation:

m= (y2-y1) / (x2-x1)

m = 19 - (-3) / 19 - (-5)

m = 22 / 24

m = 11/12

Answer:

x = 1425

Step-by-step explanation:

Given that,

A student found out that 8% of the students in his school are left-handed.

Total no of lefties = 114

We need to find the total number of students in the school. Let they are be x.

ATQ,

8% of x = 114

[tex]\dfrac{8x}{100}=114\\\\x=\dfrac{114\times 100}{8}\\\\=1425[/tex]

Hence, there are 1425 students in the school.

Answer:

The correct options are;

1) How many grams of fat are in 1/2 cup of cheese = [tex]6 \div\dfrac{1}{4} \cdot \dfrac{1}{2}[/tex]

2) How many cups of cheese will the chef need to make 13 small pizzas = [tex]\dfrac{1}{2} \cdot 13[/tex]

3) How many small pizzas could the chef make if he has 3/4 cup of cheese is given as follows;

[tex]\dfrac{3}{4} \div \dfrac{1}{2}[/tex]

Step-by-step explanation:

1) How many grams of fat are in 1/2 cup of cheese

The number of grams of fat per 1/4 cup of cheese = 6 grams

Therefore;

The number of grams of fat per kilogram of cheese = 6/(1/4)

The number of grams of fat per 1/2 kilogram of cheese = 6/(1/4) × 1/2, which can be written as follows;

[tex]6 \div\dfrac{1}{4} \cdot \dfrac{1}{2}[/tex]

2) How many cups of cheese will the chef need to make 13 small pizzas

The number of cups of cheese per small pizza = 1/2 cup of cheese

Therefore, the number of cups of cheese in 1 small pizza = 1/2 × 13, which can be written as follows;

[tex]\dfrac{1}{2} \cdot 13[/tex]

3) How many small pizzas could the chef make if he has 3/4 cup of cheese is given as follows;

Given that 1/2 cup of cheese can make one small pizza

(1/2)/(1/2) = 1 cup of cheese can make 1/(1/2) small pizza

3/4 cup of cheese can make 3/4 × 1/(1/2)  = (3/4)/(1/2) small pizza, which can be written as follows;

[tex]\dfrac{3}{4} \div \dfrac{1}{2}[/tex]

Answer:

10,000

Step-by-step explanation:

Answer:

-1,882384 x 10^6 or -1372^2

Step-by-step explanation:

Both forms equal -1882384.

Answer:

15.7

Step-by-step explanation:

circumference = pi x diameter

3.14 x 5 = 15.7

Answer: less,less greater

Step-by-step explanation:

Answer: #1 : less than 930

Answer: #2 : less than 930

Answer: #3 : greater than 930

Hope this helps older sis!

Answer:

The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal" ⇒ A

Step-by-step explanation:

In the given figure

∵ The blue line passes through points A and B

∵ A = (-4, -2) and B = (4, 4)

∴ x1 = -4 and y1 = -2

∴ x2 = 4 and y2 = 4

→ Substitute them in the rule of the slope

∵ m(AB) = [tex]\frac{4--2}{4--4}[/tex] = [tex]\frac{4+2}{4+4}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

∴ The slope of line AB is  [tex]\frac{3}{4}[/tex]

∵ The green line passes through points C and D

∵ C = (0, -3) and D = (4, 0)

∴ x1 = 0 and y1 = -3

∴ x2 = 4 and y2 = 0

→ Substitute them in the rule of the slope

∵ m(CD) = [tex]\frac{0--3}{4-0}[/tex] = [tex]\frac{0+3}{4}[/tex] = [tex]\frac{3}{4}[/tex]

∴ The slope of line CD is  [tex]\frac{3}{4}[/tex]

∵ The slope of line AB = the slope of line CD

∵ Parallel lines have the same slope

∴ AB // CD

∴ AB and CD are parallel lines

The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal"

Answer:

a. they are parallel because their slopes are equal

Step-by-step explanation:

did the review on edge

Answer:

truwwwwwwweeeeeeeeeeeeeeee

Answer: A

they all divide eachother so