Triangle ABC is congruent to triangle DEF based on the SAS congruence theorem.
What is the SAS Theorem?The SAS theorem is a triangle congruence theorem that states that two triangles are congruent if they have two pairs of congruent sides that are corresponding to each other, and a pair of congruent included angles.
Triangles ABC and DEF have:
A pair of congruent included angles - ∠DEF ≅ ∠ABCTwo pairs of congruent sides - AB ≅ DE and CB ≅ FETherefore, they are congruent by SAS.
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A canister if pet is in the shape of a cylinder with a radius of 6 inches and a height of 20 inches. What is the volume of the canister? Round your answer to the nearest cubic inch
Determine all missing angles below.
Answer:
a = 60, b = 19, c = 101, d = 79, e = 50
Step-by-step explanation:
Relations that are helpful here are ...
vertical angles are congruentan exterior angle is equal to the sum of the opposite interior anglesthe sum of angles forming a straight angle is 180°the sum of angles in a triangle is 180°__
Using these relations, we can find the unknown measures.
a° = 60° . . . . . these are vertical angles
51° +b° +110° = 180° ⇒ b° = 180° -161° = 19° . . . . straight angle
a° +b° +c° = 180°
c° = 180° -60° -19° = 101° . . . . sum of angles in a triangle
d° = 180° -101° = 79° . . . . . straight angle
e° = c° -51° = 50° . . . . . c° is exterior to the triangle
+
33 +33
51. Jacob has a lemonade stand. On Monday, he sold x cups of
lemonade. On Tuesday, he sold 14 more cups than he sold on Monday.
Choose the expression below that shows how many cups of lemonade
Jacob sold on Tuesday.
a) 14 - x
b) x + 14
c)X - 14
d) x2 + 14
What expression would I use
Answer:
b) x + 14
Step-by-step explanation:
If I sold 14 more cups that what I sold Monday, then my answer should be (what I sold Monday) + (14).
Its like saying suppose I drank x gallons of water today. And next day, I drank 14 more gallons than yesterday. That means, I drank the initial amount of gallons (x) & 14 more gallons today (x+14)
what is the minimum value of the function 3x^2 -4x +8
Step-by-step explanation:
f(x)=3x²-4x+8
f(1)=(3*1)²-4(1)+8
f(1)=3²-4+8
f(1)=9-4+8 or using BODMAS
f(1)=5+8 or f(1)=9-12
f(1)=13 or f(1)=-3
I need help asap please
Answer:
17.5
Step-by-step explanation:
Two points which lie on the line are : (0, 0) and (4, 70)
Constant of proportionality :
y₂ - y₁ / x₂ - x₁70 - 0 / 4 - 070/417.5let f(x) = 3x² what is f(-2x)
answer : 12x²
steps
means put -2x where x is
let f(x) = 3x² what i f(-2x)
3(-2x)²
pemdas
-2x times -2x
4x²
3 times 4x²
12x²
From the top of a building, 30.15m high, the angle of depression of a point on the ground level 25.88'm from the base is B° find B
Answer:
49.36 degrees to the nearest hundredth.
Step-by-step explanation:
In the right angled triangle formed the adjacent side is 25.88 m and the opposite = 30.15 m.
So tan B = 30.15 / 25.88 = 1.16499
So m < B = 49.36 degrees.
PLS HELP ME ANSWER THIS! 25 POINTS! How much does Janet make in 16 hours?
Answer: 120
Step-by-step explanation:
Janet makes 60 in 8 hours
60 x 2
8 x 2
so the answer is 120
Find the measure of each angle in the diagram.
The measure of each angle in the diagram are 4y° = -82°, (6y - 41)° = 164°, (3x + 2)° = 98°, 2(x + 17)°= 98
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.
Two lines are intersecting each other at a point making two pairs of vertical angles.
The pair of vertical angles are equal in measure.
4y° = (6y + 41)° [Vertical angles]
4y - 6y = 41
2y = -41-----(1)
(3x + 2)° = 2(x + 17)° [Vertical angles]
(3x + 2)° = 2x + 34°
x = 32 ------(2)
Therefore, 4y° = -82°
(6y - 41)° = 164°
(3x + 2)° = 98°
2(x + 17)°= 98
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You conduct a survey that asks 350 students in your class about whether they prefer pizza or chicken for school lunch. One hundred eighty-nine males respond, 95 of which prefer pizza. Fifty-two females prefer the chicken. Part A: Organize the results in the two-way table provided. Male Female Total Pizza Chicken Total 189 161 350 Part B: What percent of females like the pizza?
El oh Elllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
Rewrite in simplest radical form sqrt x * sqrt[4] x each step of your process
I assume the given expression is
[tex]\sqrt x \sqrt[4]{x}[/tex]
We can write each root as a rational power of x, then add the exponents:
[tex]\sqrt x \sqrt[4]{x} = x^{\frac12} x^{\frac14} = x^{\frac12 + \frac14} = x^{\frac34}[/tex]
Then putting it back into radical form, we have
[tex]\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}[/tex]
help me plssssssssssssssssssssss
A cylinder has a surface area of 1,890 m^2 and a radius of 9 cm what is the volume of the cylinder to the whole number
Answer:
The answer is ≈ 6214.78
(could put the sign because it wouldnt let me)
Step-by-step explanation:
Formulas:
[tex]A= {2} \pi r h + 2\pi r^{2}[/tex]
[tex]V=\pi r^{2}h[/tex]
[tex]V= A \frac{r}{2} -\pi r^{2} =1890 *\frac{9}{2} -\pi *9^{3} = 6214.77896[/tex]
rounded= 6214.78
~rere
Two similar polygons have a scale factor of three. The smaller polygon has an area of 42 cm² and perimeter of 50 cm. what is the area of the larger polygon? and what is the perimeter of the larger polygon?
Step-by-step explanation:
a scale factor applies to every line, that means also to every side of the polygon.
the area of a polygon is always created out of the product (multiplication) of 2 dimensions (or sides).
while a perimeter is a pure sum of sides.
so the perimeter grows by the same factor as the sides : scale factor 3.
the perimeter of the larger polygon is therefore :
50 × 3 = 150 cm
and the area of the larger polygon ?
remember, that the area is always the product of 2 sides (or the sum of products of 2 sides).
and so, the scale factor enters these multiplications twice, and it gets therefore squared : 3×3 = 9.
so, the area of the larger polygon is then
42 × 9 = 378 cm²
what is the product of 2.31 and 0.21
Assume you are going to buy a new Nissan Rouge priced at $38250.00 and after the deal you have found out that the sales tax is 9%. Estimate the answer
The points P(6,-3), Q(-2,3), R(-5, -1), and S(3,-7) form quadrilateral PQRS. what type of quadrilateral is it?
HELP IMMEDIATELY, ASAP, INSTANTLY, `NOW!!! THANKS
Which type of graph is often the LEAST accurate? A) a pie chart B) a pictograph C) a bar graph D) a line graph
Answer:
Pictograph is the least accurate!
Step-by-step explanation:
Because pictographs have specific pictures and you need to divide it specifically whereas other graphs, you can just graph your information and it'll be accurate.
If Jessica has money into savings accounts worry is 5% in the other is 10% if she has $950 more in the 10% account and the total interest is 281 how much invested is in each savings account
Answer:
5% account = $1,240
10% account = $2,190
Step-by-step explanation:
Let's assume the amount of savings in the 5% account is x.
Thus the amount of savings in the 10% account is (x + $950).
We can write the following equation from the interest amount:
[5% x ] + [10% (x + $950)] = $281
5%x + 10%x + $95 = S281
15%x = $186
x = $1,240
There is $1,240 in the 5% account
Therefore, on the 10% account there is $1,240 + $950 = $2,190
What is the solution set to this equation? log₂ (x - 2) + log₂x = 3
Let's see
[tex]\\ \rm\Rrightarrow log_2(x-2)+log_2x=3[/tex]
[tex]\\ \rm\Rrightarrow log_2(x(x-2))=3[/tex]
[tex]\\ \rm\Rrightarrow x²-2x=8[/tex]
[tex]\\ \rm\Rrightarrow x(x-2)=8[/tex]
Either x=8
Or
x-2=8x=10Solution set
x[8,10]
please help will mark Brainliest!!
Answer:
number 2
Step-by-step explanation:
im not that sure but i think it's that one
Help me please
Simplify (5x3 + 7x - 8) + (2x3 – 5x2 – X + 3). Choose the standard form of the answer.
A. 7x3 + 6x - 5x2 - 5
B. 7x3 - 5x2 + 6x - 5
C. 7x3 – 5x2 + 6x + 5
D 7x3 – 5x2 + 8x - 5
Answer:
==7x3−5x2+6x−5
Step-by-step explanation:
=5x3+7x+(-8)+2x3+−5x2+−x+3
Combine Like Terms:
=5x3+7x+−8+2x3+−5x2+−x+3
=(5x3+2x3)+(−5x2)+(7x+−x)+(−8+3)
=7x3−5x2+6x−5
Evaluate 0.2x for x = 5.
A. 0.1
B. 1
C. 10
D. 0
help with this??? i beg of you☹️☹️
Answer:
The answer is 3 cm.
Step-by-step explanation:
To find the width of the cereal box, we must first take the volume and divide it by the length and then divide that by the height.
For this equation, we would do the following:
3456 ÷ 36 = 96 cm²
Now that we have divided volume by length, let's divide by height next:
96 ÷ 32 = 3 cm
Now we know the height of the box. To check if this is correct, lets multiply the length, height, and width and see if we get the volume that we started with.
3 × 32 × 36 = 3456 cm³
Since we got the original volume that we started with, we know that the width is 3 cm which is your answer.
Ok Saturday a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer:
78 HAMBURGERS!!!
Step-by-step explanation:
LET H BE THE NUMBER OF HAMBURGERS HOLD!!!
2H IS THE NUMBER OF CHEESEBURGERS BECAUSE THERE WERE 2 TIMES AS MANY CHEESEBURGERS SOLD AS HAMBURGERS!!!
H+2H=234 | THE TOTAL NUMBER OF CHEESEBURGER AND HAMBURGER SOLD!!!
3H=234 | ADD LIKE TERMS!!
DIVIDE BOTH SIDES BY 3 | ISOLATE THE VARIABLE!!!
H=78
THAT IS YOUR ANSWER!!!
- Khan Academy Advance!!!
Answer: 78 hamburgers
Step-by-step explanation:
Let x be the number of hamburgers sold. We will write an equation for the problem and solve.
2x + x = 234
3x = 234
x = 78
78 hamburgers were sold on Saturday.
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The points A(4, 3) and B(4, –5) are plotted on the coordinate plane. Rectangle ABCD has a perimeter of 30 units. If points C and D were plotted on the grid shown, what would their coordinates be if point C is below point D? Alt_text C: ( , ) D: ( , )
The possible coordinates of C and D are: C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
How to determine the coordinates of C and D?The given parameters are:
A = (4,3)
B = (4,-5)
Perimeter, P = 30 units
Since points A and B are on the same x-coordinate, then the distance between them is:
AB = 3 - - 5
AB = 8
The perimeter of the rectangle is calculated using:
P = 2 *(AB + CD)
This gives
2 * (8 + CD) = 30
Divide by 2
8 + CD = 15
Subtract 8 from both sides
CD = 7
This means that points C and D are 7 units from points A and B, respectively.
If A = (4,3) and B = (4,-5), then the possible coordinates of C and D are:
C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
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D. 40
E. 44
8. A CD and a DVD cost $31. If a CD
a
and two DVD's cost $50, then how
much does a CD cost?
F. $ 9
G. $11
H. $12
J. $15
Answer:
The correct answer is $12
Step-by-step explanation:
To check, subtract 12 from 31
31 - 12 =19
Multiply 19 by 2
19 x 2 =38
Add 12
38 + 12 =50
Solve for the variable: 3(x+2) - 9 = 15 - 4(5x - 2)
[tex]\tt 3(x+2)-9=15-4(5x-2)[/tex]
To solve this equation, let's apply the distributive property:-
Multiple 3 by ( x+2)/ Subtract 9 from 6 = -3/ and then use the distributive property to multiply −4 by (5x-2) :-
[tex]\tt 3x - 3=15 - 20x+8[/tex]
Add 15 and 8 = 23
[tex]\tt 3x - 3=23 - 20x[/tex]
Now, add 20x to both sides:-
[tex]\tt 3x - 3=23 - 20x[/tex]
Combine like terms:-
[tex]\tt 23x-3=23[/tex]
Add 3 to both sides:-
[tex]\tt 23x=23+3[/tex]
[tex] \tt 23x=26[/tex]
Divide both sides by 23:-
[tex]\tt \: x = \dfrac{26}{23} [/tex]
- :)
The table below shows the number of marbles of different colors in a bag:
Marble Experiment
Color of
Marbles Number of
Marbles
Red
5
White
8
Black
2
Deja draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing red marbles in both the trials?
5 over 15 multiplied by 4 over 14
5 over 15 multiplied by 4 over 15
5 over 15 added to 4 over 14
5 over 15 added to 4 over 15
Answer:
[tex]\huge\boxed{\sf \frac{5}{15} + \frac{4}{14} }[/tex]
Step-by-step explanation:
Formula for probability: [tex]\boxed{\displaystyle Probability = \frac{number\ of\ possible\ outcomes}{total\ number\ of \ outcomes} }[/tex]Solution:Total number of marbles = 5 + 8 + 2 = 15
Number of red marbles = 5
Probability to draw a red marble at the first trial = 5/15
Number of marbles left = 15 - 1 = 14
Number of Red marbles left = 5 - 1 = 4
Probability to draw a red marble at the second trial = 4/14
Total probability:[tex]\displaystyle =Probability \ of \ drawing \ a \ red \ marble \ at \ the \ (second \ attempt +first \ attempt)\\\\= \frac{5}{15} + \frac{4}{14} \\\\\rule[225]{225}{2}[/tex]
The length of a rectangle is 2 yd longer than its width.
If the perimeter of the rectangle is 48 yd, find its length and width.