<HFG ≅ <JHI because they are corresponding angles, therefore: A. Cai used an invalid reason to justify the congruence of a pair of sides or angles.
What are Corresponding Angles?When two parallel lines are crossed by a transversal, the angles that are formed in matching corners along the transversal are regarded as corresponding angles which are congruent to each other.
In the proof, HFG and JHI are corresponding angles that are forrmed. Therefore, they are equal based on the fact that corresponding angles are congruent.
Thus, Cai's first error in the proof was made in his 4th statement. <HFG ≅ <JHI because they are corresponding anglles, therefore: A. Cai used an invalid reason to justify the congruence of a pair of sides or angles.
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Answer:Answer is A
Step-by-step explanation:
just did it on khan academy
If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.
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.
Solution:-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.
A bag contains 12 balls which are numbered from 1 to 12. If two ball are selected at random, what is the probability that the total sum of the balls will be an even number
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.
**PLS HELP ILL GIVE BRAINLIEST** Explore
Fill in each blank with a number or expression such that each row and column has the same sum.
The missing expressions to the empty blanks are 2x, 2x - 1, x - 1 and x + 3.
What is an equation?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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I need help 1 through 13 please and thank you
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.
Compare the graphs that jennifer and matt drew by completing the statements. jennifer’s graph is vertically shifted from matt’s graph. jennifer’s graph is horizontally shifted from matt’s graph. jennifer’s graph is matt’s graph. which graph has a vertex that is a maximum?
Jennifer’s graph is vertically shifted from Matt’s graph by 2 units. and none of the graphs has their vertex at maximum.
What is a Function?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 :)
please help!!!!! i will give brainliest!
Answer:
Option 1 and 4
Step-by-step explanation:
What is the approximate volume of the tube? round to the nearest whole cubic centimeter. 1,005 cm3 1,340 cm3 3,351 cm3 4,021 cm3
The approximate volume of the cylinderical tube is 1005 cm³ round to the nearest whole cubic centimeter.
What is of volume of cylinder?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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Help me with this question!!
50 points + Brainliest
No spammers allowed
Thanks in advance.
No. 7.a
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:
35°, 5 units, 2.4 unitsStep-by-step explanation:
Given
ΔABC ~ ΔBDCCorresponding angles are congruent
∠BAC ≅ ∠DBC m∠BAC = m∠DBC = 35°Use Pythagorean to find the length of AC
[tex]AC = \sqrt{AB^2+BC^2} =\sqrt{3^2+4^2} =\sqrt{25} =5[/tex]The ratio of corresponding sides is equal
BD/AB = BC/ACBD/4 = 3/5BD = 4*3/5BD = 2.4A software store has put some of its inventory on sale. games are marked down by 15%, and security programs are marked down by 18%. if you pay $35.70 each for two games and $22.96 for a security program, how much have you saved? a. $17.64 b. $14.84 c. $12.24 d. $11.34
The amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.
What is the discount?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:
Hello people ~
factorise: 11y ^ 2 + 7y + 12
[tex]\\ \rm\rightarrowtail 11y^2+7y+12[/tex]
Un factorable
let's see why?
11×12=132There are no factors which gives sum +7 and product 132.
Hence it's not factorableCan someone help me with this question
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 :)
Please help! Will mark brainliest <3. (Click on the photo too see the question!)
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.
Finn, Michael, and Chris are going to have a movie night this weekend. Together, they have 31
movies. If they decide to randomly choose three movies, what is the probability that the three they choose will consist of each of their favorite movies? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
The probability that the three they choose will consist of each of their favorite movies is 1/29791.
What is probability?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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Find the measure of angle PRT.
Select one:
A. 45°
B. 90°
C. 120°
D. 180°
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
Please help! will give brainlest! locks in 30 min!
!!40 points and Brainliest if it’s correct!!ANSWER IT ONLY IF YOU KNOW THE ANSWER. IF YOU DONT KNOW DONT ANSWER IT. Make sure you explain please!
Which of the following shows the correct first step to solve x^2 - 16x = -21 by completing the square?
A)x^2 - 16x + 64 = -21
B) x^2 - 16x + 64 = -21 + 64
C) x^2 - 16x + 16 = -21 + 16
D) x^2 - 16x + 8 = -21 + 8
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
Jimmy invests $2000 in a money market account earning 8.5% interest compounded continuously. Which of the following is an equation that can be used to determine the value
of Jimmy's investment account after t years?
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!
Shelly rolls a dice 36 times. How many of those times should she expect it to land on a 1?
Answer:
it will land on "1" exactly 12 times
A window in Lynn and Jorge's house needs to be
replaced. The rectangular window is 3 feet 5 inches
tall and 2 feet 7 inches wide. Change each of the
measurements to inches.
(a) Find the perimeter of the window in inches.
(b) If the perimeter needs to be sealed with insulation
that is $0.50 per inch, how much will it cost to insulate
the perimeter?
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
PERSEVERE The Flatiron Building in New York City is one of America's oldest skyscrapers, completed in 1902. Its floor plan is approximately a
right triangle. As shown in the figure, 5th Avenue is perpendicular to East 22nd Street, and m 2B is 10 less than 3 times mLC.
a. find the angle measures in the floor plan ( measure of A, B, and C )
b. find measure of BCD in two ways. explain each method in simple terms.
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.
__
a.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 ...
A = 90°B = 65°C = 25°__
b.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:
classify these polynomials based on the degree and number terms 3x^2
Answer:
3x² is "monomial" according to the number of term(s) and "Quadratic" based on degree
A spinner is divided into 8 identical sectors and labeled 1 through 8.
How many spins are expected for a multiple of 3 to be spun 6 times?
Select from the drop-down menu to correctly complete the sentence.
The spinner is expected to have to spin approximately
Choose...
times for a multiple of 3 to be spun 6 times.
12
16
24
48
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.
What is permutation?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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Twenty-six cards with the letters from A to Z are face down. What is the probability that a vowel will be chosen?
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
An isosceles triangle has area of 140 ft2. If the base is 18 ft, what is the length of each leg? Round your answer to the nearest tenth
Answer: 18.0 feet
Step-by-step explanation:
Mr. Nathan ordered a total of 24 roses in three different colors. 1/3 white 1/4
yellow, and the rest red. What is the number of red roses Mr. Nathan ordered? Enter your answer in the box.
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
PLSSSSSS HELPPP Assemble the proof by dragging the tiles to the Statements and Reasons columns.
Answer:
Hope this helps
Step-by-step explanation:
Similar Triangles... Yes
QR similar to SR
ang. QRP = ang. SRT
ang. p = ang. t
=> similar
What is 2925 divided by 15
Carlos has a 12300 millimeters long piece of wook. he wants to cut it into 3 equal lengths. how long will each piece be in meters?
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
A sector with arc measure 72º has an
area of 80 square feet. Determine
the radius of the circle.
A 18 ft
C 12 ft
B 20 ft
D 16ft
[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 ~
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Aiden and his two friends ordered a pizza with 12 slices. Together they ate 2/3 of the pizza. If they evenly divided what was left, how many slices would each of them receive
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.
What is Algebra?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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