No triangles are possible for Options B and D. One triangle is possible for options A, C, and E. Many triangles are possible for option F.
How to interpret Triangles?For it to be a triangle, then it must have 3 vertices and 3 sides with the sum of 2 sides greater than the third side. Also, the sum of interior angles must be 180°.
A) Side lengths of the triangle are; 4 inches, 8 inches and 10 inches.
4 + 8 > 10. Thus, it is a triangle.
B) 60° + 40° + 90° = 190 ≠ 180°
Thus, no triangle is possible because the sum of the angles in triangle is 180°.
C) There are two sides are given and one angle. Thus, from SAS congruency theorem, one triangle is possible.
D) 7 + 5 = 12
There is no triangle possible because the sum of the two sides must be greater than the third side.
E) We are given two angles and one side. Thus, from the ASA Congruency Postulate, one triangle is possible.
F) 60° + 80° + 40° = 180°
There are three angles given, but no sides and so we can say that many triangles are possible.
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Explain how to solve 5^(x-2)=8 using log base b of y equals log y over log b. include the solution for x in your answer. round your answer to the nearest thousandth.
The value of x will be equal to 2.477.
What is a logarithm?The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.
The given expression will be solved as follows;-
[tex]5^{x-2}= 8[/tex]
Taking Log on both sides.
[tex]Log_e 5^{x-2}=Log_e8[/tex]
(x-2) Log5 = Log 8
( x-2) = Log8 / Log 5
(x - 2) = Log 8 - Log 5
(x - 2 ) = Log 3
x-2 = 0.477
x = 2.477
Therefore the value of x will be equal to 2.477.
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Given y=3x-3, find y if x=4
Answer: Given y=3x-3, find y if x=4
y=3x-3
x=4
y=3(4)-3
y=12-3
y=9
Step-by-step explanation: hopes this helps
please mark me as a brainliest
Use Pemdas to evaluate: 5c - 19, c=10
Which of the following statements are true?
Choose all answers that apply:
B
The equation represents a proportional relationship.
The unit rate of change of y with respect to a is
The slope of the line is 2.5.
A change of 5 units in a results in a change of 2 units in y.
A change of 2 units in a results in a change of 5 units in y.
2|5
Based on the function given of y = 2.5x, the true statements are:
The equation represents a proportional relationship.The slope of the line is 2.5.A change of 2 units in x results in a change of 5 units in y.What does the function represent?The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.
For instance, if there is a change of 2 in x, the change in y would be:
= 2.5 × x
= 2.5 x 2
= 5
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The board of directors of streamlined airlines has declared a dividend of $4,300,000. the company has 400,000 shares of preferred stock that pay $0.70 per share and 2,750,000 shares of common stock. after finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock. (round your answer to the nearest cent if necessary)
The dividend per share of common stock is $1.46.
What is the dividend per share of common stock?The first step is to determine the total value of the dividends that was paid to the preferred stock holders.
Total value = 400,000 x $0.70 = $280,000
The total value of the common stock dividends = $4,300,000 - $280,000 = $4,020,000
Dividend per share = 4,020,000 / 2,750,000 = $1.46
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8 Lizzie started a new business that had a profit of $31,124 at the end of the first year. Her
financial advisor estimates her profit will increase by 6% a year. Assuming her advisor is
correct, determine her total profit, to the nearest cent, for the first ten years.
Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that the initial value and the growth rate are given as follows:
A(0) = 31124, r = 0.06.
Hence the profit function is given by:
[tex]P(t) = 31124(1.06)^t[/tex]
Then, the total profit over the first 10 years is given by:
[tex]\int_{0}^{10} P(t) dt[/tex]
[tex]\int_{0}^{10} 31124(1.06)^t dt[/tex]
[tex]\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72[/tex]
Thus, her total profit for the first ten years is of $422,426.72.
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If AC = 41, find the value of x? (Giving 35 points)
[tex]\huge \boxed{\sf x=2}\\\\\\\displaystyle \sf AC=AB+BC\\\\41=3x-1+14x+8\\\\41=17x+7\\\\Subtracting\ 7\ from\ each\ side \\\\ 41-7=17x+7-7 \\\\ 34=17x\\\\Dividing\ each\ side\ by\ 17 \\\\ \frac{34}{17}=\frac{17x}{17} \\\\ 2=x[/tex]
27 Solve for x to the nearest tenth: x² + x - 5 = 0.
Answer:
Step-by-step explanation:
We can use the quadratic formula to get the answer to this
Quadratic Formula: -b +- √b² - 4ac/2a
Once we input A, B, and C into this, and solve any multiplication, we get
x = -1 +- √1 + 20/2
We divide by 2a, which 2a = 2.
-0.5 +- 10.5.
these are the following values of x:
x = 10
x = 11
Pretty sure this is it, hope it helps!
A car travels 294 miles per hour on a full tank of gas . the cars gas tank holds 14 gallons. how many yards per gallon can this car travel?
Answer:
36960 yards
Step-by-step explanation:
294/14=21
1 gallon is 21 miles
1 mile is 1760 yard
21 miles is 36960 yards
36960 yard is the answer assuming 14 gallons is a full tank of gas
What is the median of the following distribution?
26, 26, 28, 29, 31, 33, 35, 36, 37, 38, 40, 42, 43, 46, 48
OA. 33
OB. 37
O C. 56
OD. 43
OE. 36
Sandra wants to wrap a gift box 6 inches in length, 4 inches in height, and 13 inches in width. How much wrapping paper does Sandra need to buy
Answer:312
Step-by-step explanation: multiply 6*4*13
A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.
Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.
If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?
Trenton will need
square feet of plywood.
The amount of plywood needed by Trenton = total surface area of the triangular prism-shaped ramp = 21 ft².
What is the Surface Area of a Triangular Prism?Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).
The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.
We are given the parameters:
s1 = 2 fts2 = 1.5 fts3 = 2.5L = 3 ftb = 2 fth = 1.5 ftTotal surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)
= (18) + (3)
Total surface area = 21 ft²
Trenton will need 21 square feet of plywood.
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Rachael took her dogs, Rico, Mocha, and Biscuit, to the vet. Rico weighed 45.7 kilograms, Mocha weighed 15.5 kilograms, and Biscuit weighed 22.1 kilograms. How much more did Rico weigh than Biscuit?
Subtraction is a mathematical operation that reflects the removal of things from a collection. The amount by which Rico weighs more than Biscuit is 23.6 kilograms.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Rico weighed 45.7 kilograms, Mocha weighed 15.5 kilograms, and Biscuit weighed 22.1 kilograms. Therefore, the amount by which Rico weighs more than Biscuit is,
Difference = 45.7 kgs - 22.1 kgs = 23.6 kgs
Hence, the amount by which Rico weighs more than Biscuit is 23.6 kilograms.
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PLEASE HELP ME! I NEED HELP, THIS IS REALLY IMPORTANT!!!
80 POINT QUESTION
Answer: A translation left 3 units and up 6 units
In order to find the translation of a shape in the graph.
Take particular one point from the original shape: (0, 2)
Take particular one point from the translated shape: (-3, 8)
Let the translation be (x, y)
Original + Translation = Translated Image
(0, 2) + (x, y) = (-3, 8)(x, y) = (-3, 8) - (0, 2)(x, y) = (-3, 6)This implies the shape has been translated 3 units left and 6 units up.
A ball is thrown upward in the air. The height h, in feet, of the ball t seconds
after being thrown can be determined by the equation
h=-16t² + 40t + 4
How long does it take for the ball to hit the ground? Round to one decimal
place.
By solving a quadratic equation, we will see that the ball hits the ground after 2.6 seconds.
How long does it take for the ball to hit the ground?
Here we need to solve the equation:
h(t) = 0 = -16t² + 40t + 4
This represents that the ball hits the ground.
So we just need to solve that quadratic equation, using the general formula we get:
[tex]t = \frac{-40 \pm \sqrt{(40)^2 - 4*4*(-16)} }{2*-16} \\\\t = \frac{-40 \pm 43.1 }{-32}[/tex]
We only care for the positive solution, which is:
t = (-40 - 43.1)/-32 = 2.6s
So the ball hits the ground after 2.6 seconds.
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Please help! Giving brainlist!
Answer:
2
Step-by-step explanation:
The rise is two using the slope formula
rise/run
2/3
2 is the rise
Give brainliest please.
Hope this helps
Answer:
2
Step-by-step explanation:
Remember the rise-run formula
rise ÷ run
The rise is 2, and the run is 3, making this two-over-three.
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 36t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
The ball's maximum height is 30.25 feet.
What is quadratic equation?A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.
Given:
h= -16t²+36t+10
Differentiate w.r.t. 't',
h' = -32t+36
When h=0, that will be the maximum height
32t= 36
t= 9/8
t= 1.125 sec.
So, The maximum height is
h(1.123)= -16(1.125)² + 36*1.125+10
h(1.125) = 30.25 feet.
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r,s and t are the vectors given by 4i+j,3i+2j and 4i +j respectively.find [r+s+t]
Answer:
11i+4j
Step-by-step explanation:
add the i's together and the j's together.
For a science project, billy observed a chipmunk and a squirrel stashing acorns in trees. the chipmunk hid 3 acorns in each tree. the squirrel hid 4 acorns in each tree. they each hid the same number of acorns, although the squirrel needed 2 fewer trees. you are going to investigate the number of acorns that each animal hid.
The number of acorns that each animal hid is 48
What is an Equation ?An equation is formed when two algebraic expressions are equated by an equal sign.
It is asked to calculate the number of acorns that each animal hid.
Total number of acorns hid = number of acorns hid per tree * number of trees
Let T be the number of trees chipmunk used
For chipmunk: = 3*T
For squirrel: = 4*(T-4)
As both the animals hid same number of acorns.
3T = 4(T-4)
3T = 4T - 16
16 = T
Therefore the chipmunk hid 16 * 3 = 48 acorns
and the squirrel hid 4(16-4) = 48 acorns.
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20 points!!!What is the equation to plug this into a graph?
t = 0
t = 5
Step-by-step explanation:
(-10t^2+50t)/(t^2+4t+3)
I'm making t into x so its not confusing with the plus sign
(-10x^2+50x)/(x^2+4x+3)
with (x^2+4x+3) :
what 2 numbers when multiplied make 3 and when added make 4 ?
they are 1 and 3
(x+1)(x+3)
(-10x^2+50x)/(x+1)(x+3)
(-10x(x-5))/(x+1)(x+3) =0
(-10t(t-5))/(t+1)(t+3)=0
t = 0
t = 5
which represents the inverse of the function f(x)=4x?
Answer:
h(x) = 1 / 4x
last choice
Step-by-step explanation:
y = 4x becomes x = 4y
we want to solve for y,
divided both sides by 4
x / 4 = 4y / 4
x / 4 = y
Answer:
[tex]h(x) = \dfrac 14 x[/tex]
Step-by-step explanation:
[tex]y = f(x) = 4x\\\\\text{Replace x with y and then solve for y:}\\\\~~~~~x = 4y\\\\\implies y = \dfrac x4\\\\\implies f^{-1}(x) = \dfrac 14x[/tex]
si se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados de pared,cuantos litros de pntura necesitanpara pinatr 1 metro cuadrado de pared
Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:
c = 9.01/1.7 = 8.42 litros.
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What is the quadratic regression equation that fits these data?
the answer is:
y = 2. 13x^2 + 0. 13x + 6. 39
hope it helps
The regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39
How to determine the regression equation?The attached table represents the missing information in the question.
Next, we enter the data values in a graphing technology
Using the graphing technology, we have:
a =2.13; b = 0.13 and c = 6.39
A quadratic regression is represented as:
y = ax^2 + bx + c
So, we have:
y = 2.13x^2 + 0.13x + 6.39
Hence, the regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39
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geometry please answer
Answer: 8
Step-by-step explanation:
[tex]\frac{180(n-2)}{n}=135\\180(n-2)=135n\\180n-360=135n\\-360=-45n\\n=\boxed{8}[/tex]
A helicopter travels 30 kilometers in 3 minute. What is the speed in terms of
33
10
kilometers per minute?
The speed is the distance covered by an object at a particular time. The speed of the helicopter is equal to 10 kilometer/minute.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given the helicopter travels 30 kilometers in 3 minute. Therefore, the speed of the helicopter is equal to,
Speed = 30 kilometer/ 3minutes = 10 kilometer/minute.
Hence, the speed of the helicopter is equal to 10 kilometer/minute.
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Twenty-five students are competing in a Science Fair. In how many ways can 3 students win first, second, and third place?
A) 2.6 · 10^24 B) 3.9 · 10^25 C) 13,800 D) 19,656
Please help
Answer:
C
Step-by-step explanation:
[tex]\frac{25!}{(25-3)!} =13800[/tex]
How was life different for Romans with low incomes and wealthy Romans? Romans living in poverty had few duties and more free time. Wealthy Romans had many responsibilities and few days off. Wealthy Romans relied on servants to run their households. Romans living in poverty were not allowed to work a trade.
Wealthy Romans relied on servants to run their households.
https://brainly.com/question/16395373
Answer:
The correct answer is Wealthy Romans relied on servants to run their households.
Step-by-step explanation:
I got it right on edge 2022
What is the median of the following data set?
{6, 3, 9, 1, 7}
3
6
8
9
Answer:
6
Step-by-step explanation:
First order them from least to greatest:
1, 3, 6, 7, 9
The median is 6 because it is the middle value.
Hope this helps! Brainliest would be really appreciated
HELP I can’t figure it out
Answer:
[tex]\huge\bold\color{pink}{- Magdonal -}[/tex]
[tex]\blue{\rule{50pt}{999999pt}} \purple{\rule{50pt}{999999pt}} \
\green{\rule{27pt}{999999pt}} \blue{\rule{10pt}{999999pt}} \
[/tex]
PLEASE HELP ANSWER ALL!!! WITH DIAGRAM!!!
You toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then use it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."
2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.
3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."
4. How many outcomes are in the event "Toss a tails, spin yellow"?
5. What is the probability of tossing tails and spinning yellow?
Answer:
For Questions 1 , 2 and 3 check the attached diagram
4. How many outcomes are in the event "Toss a tails, spin yellow"?
There is only one outcome ‘TY’ in this event .
5. What is the probability of tossing tails and spinning yellow?
[tex]p\left( TY\right) =\frac{1}{6}[/tex]
Step-by-step explanation:
Diagram