Cai tried to prove that \triangle FGH\cong \triangle HIJ△FGH≅△HIJtriangle, F, G, H, \cong, triangle, H, I, J. Statement Reason 1 FG=HI=6FG=HI=6F, G, equals, H, I, equals, 6 Given 2 FH=HJ=4FH=HJ=4F, H, equals, H, J, equals, 4 Given 3 \overline{FG} \parallel \overline{HI} FG ∥ HI start overline, F, G, end overline, \parallel, start overline, H, I, end overline Given 4 \angle HFG\cong\angle JHI∠HFG≅∠JHIangle, H, F, G, \cong, angle, J, H, I When a transversal crosses parallel lines, alternate interior angles are congruent. 5 \triangle FGH\cong \triangle HIJ△FGH≅△HIJtriangle, F, G, H, \cong, triangle, H, I, J Side-angle-side congruence What is the first error Cai made in his proof? Choose 1 answer: Choose 1 answer: (Choice A) A Cai used an invalid reason to justify the congruence of a pair of sides or angles. (Choice B) B Cai only established some of the necessary conditions for a congruence criterion. (Choice C) C Cai established all necessary conditions, but then used an inappropriate congruence criterion. (Choice D) D Cai used a criterion that does not guarantee congruence

Answer:

Option 1 and 4

Step-by-step explanation:

Answer:

3x² is "monomial" according to the number of term(s) and "Quadratic" based on degree

Answer:

[tex]A=2000e^{0.085t}[/tex]

Step-by-step explanation:

Make sure you understand the formula for continuous compounding first. The formula is:

[tex]A=Pe^{rt}[/tex] where

A= Total

P= Principal (or the amount invested at beginning)

r= Interest rate (as a decimal)

t= Time (in years)

Note: e is an irrational mathematic number similar to π. Its value is around 2.72, but for these problems, you’ll need to use the version already on your calculator that will be called “[tex]e^{x}[/tex].” On most calculators, it can be accessed by 2nd → ln.

Find the values that you are given:

A= What you are looking for

P= 2000

r= 8.5% as a decimal = 0.085

t= What you change

Plug these into the equation:

[tex]A=2000e^{0.085t}[/tex]

This is the answer!

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

In △ABC,

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]

[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]

[tex]\\[/tex]

In △ABC,

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]

[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

Answer:

☐ [tex]\displaystyle \textcolor{blue}{A.}\:\angle{S}\:and\: \angle{J}[/tex]

☑ [tex]\displaystyle \textcolor{blue}{B.}\:\angle{G}\:and\: \angle{M}[/tex]

☐ [tex]\displaystyle \textcolor{blue}{C.}\:\angle{H}\:and\: \angle{P}[/tex]

☑ [tex]\displaystyle \textcolor{blue}{D.}\:\angle{R}\:and\: \angle{U}[/tex]

Explanation:

Accourding to the Vertical Angles Theorem, vertical angles are considered congruent. So, we need to make sure find all pairs of angles that reflect each other like a mirror [NO LINEAR INTERFERENSES], and those would be the above checked checkboxes.

I am joyous to assist you at any time.

Answer:

4.1 meters each

1000 milileters go into 1 meter

Step-by-step explanation:

Answer:

Step-by-step explanation:

12300/3= 4100    1 meter = 1000 millimeters

4100/1000=4.1 meters

Answer:

Hope this helps

Step-by-step explanation:

Similar Triangles... Yes

QR similar to SR

ang. QRP = ang. SRT

ang. p = ang. t

=> similar

Answer:

∠BAC = 35°

AC = 5 cm

BD = 2.4 cm

Step-by-step explanation:

As ΔABC ~ ΔBDC then ∠CBD ≅ ∠BAC

As ∠CBD = 35° then ∠BAC = 35°

Using Pythagoras' Theorem

CB² + AB² = AC²

⇒ 3² + 4² = AC²

⇒ 25 = AC²

⇒ AC = 5 cm

As ΔABC ~ ΔBDC then

AB : AC = BD : BC

⇒ 4 : 5 = BD : 3

[tex]\sf \implies \dfrac45=\dfrac{BD}{3}[/tex]

[tex]\sf \implies BD=\dfrac{12}{5}=2.4\:cm[/tex]

**A right triangle with legs of 3cm and 4cm, and a perpendicular line from the hypotenuse to the right angle vertex, does not have an internal angle CBD of 35°.  It should be 36.87°.  So if you use SOHCAHTOA to find the length of BD, it will be incorrect. See attached diagram**

Answer:

Step-by-step explanation:

Given

Corresponding angles are congruent

Use Pythagorean to find the length of AC

The ratio of corresponding sides is equal

Step-by-step explanation:

y = 4

2x + 3y = 6

1) 2x + (3 x 4) = 6

2) 2x + 12 = 6

3) 2x = -6

4) x = -3

Answer:

1. 2x + 3(4) = 6, 2. 2x + 12 = 6, 3. 2x = -6, 4. x = -3

Step-by-step explanation:

Step 1: 2x + 3(4) = 6
Step 2: 2x + 12 = 6
Step 3: 2x = -6
Step 4: x = -3

Hope this helps :)

The amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.

A discount refers to an amount deducted from the normal selling price of an object.

Let x be the original price of one game and y be the original price of one security program.

Given pay $35.70 each for two games and $22.96 for a security program.

The total pay with discount

$35.70 + $22.96 = $58.66

Also, 100% - 15% = 85%

100% - 18% = 82%

here, we have

0.85 (2x) = 35.70

1.70x = 35.70

x = $21

0.82 y = 22.96

y = $28

the total pay without discount

2x + y = 2 (21) + 28

          = $70

The amount saved is 70 - 58.66 = 11.34

Therefore, the amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.

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Answer:

d. $11.34

Step-by-step explanation:

Answer:

5/11.

Step-by-step explanation:

The number of ways 2 balls can be selected = 12P2

= 12!/10!

= 12*11

= 132.

There are 6 even numbers and 6 odd numbers in the bag.

If both numbers drawn are even there are 6P2 = 30 ways that sum is even.

If the 2 numbers are odd there are also 30 ways that sum is even.

Any other combination wil be odd.

So the required probabilit = 2(3) / 132

= 60/132

= 5/11.

Answer:

The answer is 12

Step-by-step explanation:

1-8(6)

The multiples of 3 would be 3 and 6.

3 and 6 are found 12 times within those 6 spins

Option 12 is the correct answer.

The permutation refers to the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

For the given situation,

The spinner has 8 identical sectors {1,2,3,4,5,6,7,8}.

The multiples of three from the given sectors are 3 and 6.

Multiples of 3 in the sector = 2

The spinner is expected to have to spin the multiples of 3 to be spun 6 times = [tex]2[/tex] × [tex]6[/tex]

⇒ [tex]12[/tex]

Hence we can conclude that option 12 is the correct answer.

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For using completing the square, first make sure that the coefficient of x² is 1, if it's not 1, then you need to make it 1, by dividing both sides of the equation by the coefficient whatever it is. So, jere the coefficient of x² is 1, so now we need to develop a whole square on both sides, for which,we will add the square of half of coefficient of x on both sides, so adding (-16/2)² = (-8)² = 64 on both sides, we will be having :

[tex]{:\implies \quad \sf x^{2}-16x+64=-21+64}[/tex]

Which suits the B) option

Hence, Option B) is correct

The missing expressions to the empty blanks are 2x, 2x - 1, x - 1 and x + 3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Sum of each row = sum of each column = x + 2 + x + 2 = 2x + 4

Hence:

a + x + 2 + 2 - x = 2x + 4

a = 2x

b + 5 - x + x = 2x + 4

b = 2x - 1

c + 5 - x + 2x = 2x + 4

c = x - 1

d + 2 + x - 1 = 2x + 4

d = x + 3

The missing expressions to the empty blanks are 2x, 2x - 1, x - 1 and x + 3.

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Answer:

5/26

Step-by-step explanation:

There are 26 letters in the english alphabet then out of that 26 there are 5 vowels so the probability is 5/26

Answer: 18.0 feet

Step-by-step explanation:

Answer:

they would get 1 piece each and would probably have to fight for the last one

Step-by-step explanation:

12 divided by 3 = 4

4x2=8

12-8=4

4 divided by 3 = 1 remainder 1

The number of slices would each of them receives will be 2 ²/₃ pieces.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Aiden and his two friends ordered a pizza with 12 slices. Together they ate 2/3 of the pizza.

Then the number of pieces eaten is calculated as,

⇒ 2/3 x 12

⇒ 8

If they are evenly divided. Then we have

⇒ 8 / 3

⇒ 2 ²/₃

The number of slices would each of them receives will be 2 ²/₃ pieces.

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The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

Volume of cylinder is the amount of quantity, which is obtained by the bylinder in the 3 dimensional space.

Volume of cylinder is the can be given as,

[tex]V=\pi r^2h[/tex]

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.

The diameter is 8 cm and the radius of a cylinder is half of its radius. Thus the radius of the cylinder is,

[tex]r=\dfrac{8}{2}\\r=4\rm\; cm[/tex]

Put the values in the above formula a,s

[tex]V=\pi (4)^2(20)\\V=320\pi\\V=1005.31\\V=\approx 1005\rm\;cm^3[/tex]

The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

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Answer:

it will land on "1" exactly 12 times

[tex]\\ \rm\rightarrowtail 11y^2+7y+12[/tex]

Un factorable

let's see why?

There are no factors which gives sum +7 and product 132.

Answer: change to inches:41 inches tall. 31 inches wide. perimeter:144 inches. perimeter insulation: costs $72

Step-by-step explanation:

Answer:

Step-by-step explanation:

Note: 1 foot is made up of 12 inches.

3 feet 7 inches = 3 * 12 + 7 = 36 + 5 = 41

2 feet 7 inches = 2 * 12 + 7 = 24 + 7 = 31

Part A

P = 2L + 2W                   Substitute the above Values into this equation

P = 2*41 + 2*31              Combine

P = 82 + 62                    Add

Answer: P = 144

Part B

1 inch costs 0.5 dollars

144 inches cost x

1/144 = 0.5/x              Cross Multiply

x = 144 * 0.5

Answer: x = 72 dollars

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the Radius ~

[tex]\qquad \sf  \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} } [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:r \approx 11.28 \: ft[/tex]

I hope you understood the whole procedure, let me know if you have doubts ~

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Jennifer’s graph is vertically shifted from Matt’s graph by 2 units. and none of the graphs has their vertex at maximum.

A function assigns the value of each element of one set to the other specific element of another set.

The function of the graph that is drawn by Jennifer is f(x)=2x²+4x, while the function that is drawn by Matt is g(x)=2(x+1)².

If we compare the function of the two graphs,

[tex]g(x)=2(x+1)^2\\g(x)=2(x^2+1+2x)\\g(x) = 2x^2+2+4x\\\\f(x)=2x^2+4\\[/tex]

As we can see that the only difference between the two of the function is +2, therefore, the only difference between Jennifer's graph and Matt's graph is that the graph of Jennifer’s graph is vertically shifted from Matt’s graph. As shown in the below image.

Thus, Jennifer’s graph is vertically shifted from Matt’s graph by 2 units.

If we draw two of the graph on the graph we will notice that the two of the functions will have their maximum at their vertex, as both graphs are opening upwards.

Hence, Jennifer’s graph is vertically shifted from Matt’s graph by 2 units. and none of the graphs has their vertex at maximum.

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Answer:
1. 2 units down
2. 0 units left or right
3. the same shape as
4. Neither Jennifer's nor Matt's

correct on edge 2023 have a good day :)

Answer:

  a. (A, B, C) = (90°, 65°, 25°)

  b. BCD = 155°

Step-by-step explanation:

The interior acute angles of the right triangle can be found by writing an equation representing the relation between them. The exterior angle can be found using the relations between exterior angles and interior angles.

__

Angle A is given as a right angle, so measures 90°. Let C represent the measure of angle C in degrees. Then angle B has measure 3C-10. Those two angles are complementary, so ...

  C +(3C-10) = 90

  4C = 100

  C = 25

  B = 3(25) -10 = 65

The angle measures are ...

__

Angle BCD is the exterior angle adjacent to interior angle C. As such, it is supplementary to angle C:

  BCD = 180° -C = 180° -25° = 155°

An exterior angle is equal to the sum of the remote interior angles. That means ...

  BCD = A +B = 90° +65° = 155°

_____

Additional comment

An exterior angle is equal to the sum of the remote interior angles, because both the exterior angle and the sum of the remote interior angles are supplementary to the adjacent interior angle. Angles supplementary to the same angle have the same measure.

Answer:

part b is 155

Step-by-step explanation:

Answer

Let's get to it!

Step-by-step explanation:

1) There are 15 pounds of chees on that platter. (3+5+3+4=15)

2) The total weight is 32 ounces and 6 pounds.

3) 35 gallons of coffee are brewed per day. (5+5+5+5+5+5+5=35)

4) The cook peeled 50 pounds of potatoes per hour (200 divided by 4)

5) There is a total of 4/8 or 1/2 of an ounce

6) 2/8 ounces of oregano is left.

7) This recipe requires 1 and 1/2 pounds of meat.

(This is all I could do without paper) sorry, hope this helps.

Answer:

10 red
8 white
6 yellow

Step-by-step explanation:

1/3 of 24 is 8 white
1/4 of 24 is 6 yellow
8+6 is 14
24-14 is 10
there are 10 red

The probability that the three they choose will consist of each of their favorite movies is 1/29791.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Finn, Michael, and Chris are going to have a movie night this weekend. Together, they have 31 movies.

Total number of outcomes = 31

They choose three movies out of 31

Let us assume that  Finn, Michael, and Chris have 1 favorite movie out of 31.

The probability that the three they choose will consist of each of their favorite movies:

= (1/31)(1/31)(1/31)

= 1/29791

Thus, the probability that the three they choose will consist of each of their favorite movies is 1/29791.

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Answer:

The measure of angle PRT would be:
B.) 90 degrees

Step-by-step explanation:

Have a great rest of your day
#TheWizzer


The angle letters PRT all will connect at one point which is the angle we will measure.
Angle PRT = 90 degrees