The descriptions that can define more than one triangle is
a) angle measurements of 35°, 35°, and 110°
b) angle measurements of 40°, 60°, and 80°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now the measurements of the triangle are
a)
angle measurements of 35°, 35°, and 110°
A triangle must have length sides that fulfil the Triangle Inequality Theorem and interior angles that add up to 180 degrees.
When two triangles are comparable, their corresponding sides have a proportionate ratio and their corresponding angles have a congruent relationship.
So , several triangles with the same internal angles are possible
b)
angle measurements of 40°, 60°, and 80°
Now , several triangles with the same internal angles are possible
Hence , the triangle is solved
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The descriptions that can describe more than one triangle are:
Angle measurements of 35°, 35°, and 110°
Side lengths of 6 ft, 8 ft, and 10 ft
The descriptions that can describe more than one triangle are:
Angle measurements of 35°, 35°, and 110°: This set of angles can form more than one triangle because the sum of angles in a triangle is always 180°. So, even though two angles are equal (35° each), their combination with a larger angle (110°) allows for multiple triangle constructions.
Side lengths of 6 ft, 8 ft, and 10 ft: This set of side lengths satisfies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Thus, there are multiple triangles possible with these side lengths.
Question
Which descriptions can describe more than one triangle? Select two options.
side lengths of 6 ft, 8 ft, and 10 ft
angle measurements of 35, 35, and 110°
angle measurements of 30°, 40, and 50°
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
If you invest $100,000 in an account earning 8% interest compounded annually, how long will it take until the account holds $300,000?
(Round to the nearest 0.1 of a year.)
( answergoes here ) ______________________
Compound interest formulas:
A=P(1+rn)ntA=P(1+r/n)^nt and A=Pe^rt
We have been given that you invest $100,000 in an account earning 8% interest compounded annually. We are asked to find the time it will take the amount to reach $300,000.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]8\%=\frac{8}{100}=0.08[/tex]
[tex]300,000=100,000(1+\frac{0.08}{1})^{1\cdot t}[/tex]
[tex]300,000=100,000(1.08)^{t}[/tex]
[tex]\frac{300,000}{100,000}=\frac{100,000(1.08)^{t}}{100,000}[/tex]
[tex]3=(1.08)^{t}[/tex]
[tex](1.08)^{t}=3[/tex]
Let us take natural log on both sides of equation.
[tex]\text{ln}((1.08)^{t})=\text{ln}(3)[/tex]
Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]t\cdot \text{ln}(1.08)=\text{ln}(3)[/tex]
[tex]\frac{t\cdot \text{ln}(1.08)}{\text{ln}(1.08)}=\frac{\text{ln}(3)}{\text{ln}(1.08)}[/tex]
[tex]t=\frac{1.0986122886681097}{0.0769610411361283}[/tex]
[tex]t=14.274914586[/tex]
Upon rounding to nearest tenth of year, we will get:
[tex]t\approx 14.3[/tex]
Therefore, it will take approximately 14.3 years until the account holds $300,000.
a scale drawing if a living room is shown below. the scale used to create the drawing is 1in. = 2ft ANSWER NEEDED QUICK PIC ABOVE
Answer:
144 ft^2
Step-by-step explanation:
6 inches to feet (comparison based on scale) would make each side 12 feet long (6x2). 12 times 12 is 144.
Answer:
144
Step-by-step explanation:
(5x-2)+(3x+4)+90=180 find x
Answer:
92 i believe .
Step-by-step explanation:
ASAP!!!!10 Points!!!!!
Which describes the correlation show in the scatter plot?
There is a positive linear correlation
There is a negative linear correlation,
There is no positive or negative correlation
There is a nonlinear correlation
The correlation show in the scatter plot There is no positive or negative correlation
What is Correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
Given:
The positive linear correlation shows a line which is Diagonally rising.
and, The negative linear correlation shows a line which is Diagonally falling.
So, the graph we have no Correlation because it does not any falling and rising line.
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Select all the correct locations on the table.
Classify each situation as exponential growth, exponential decay, or linear
Answer:
Situation 1 is exponential decay. Situation 2 is linear. Situation 3 is exponential growth.
Step-by-step explanation:
Situation 1 is exponential decay because it declined in a non linear way.
600-480=120 480-364=116
Situation 2 is linear because when it declined it has a dependent to another.
400-340=60 340-280=60
Situation 3 is exponential growth because is increases.
If a randomly selected person can ride a bike to school, what is the probability the person is a boy?
Biking to School
Can Bike Can't Bike Total
Boys
7
4
Girls
9
10
19
Total
16
14
30
the answer would be 11 out of 30 because there is 11 boys in total and the total of boys and girls is 30 so the answer is 11 out of 30
The probability that a randomly selected person who can bike to school is a boy is 7/16 or 0.4375, which means there is a 43.75% chance that the person is a boy.
Explanation:To determine the probability that a randomly selected person who can ride a bike to school is a boy, we will use the provided data.
Looking at the data table, we can see there are 7 boys who can bike to school, and the total number of students who can bike to school is 16 (this is the sum of boys and girls who can bike). In probability terms, the boys who can bike are the 'favorable outcomes' and the total students who can bike are the 'possible outcomes'.
Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. Thus, the probability a randomly selected person can ride a bike to school is a boy is 7/16, or approximately 0.4375.
This means, if we were to randomly select a person who can bike to school, there is a 43.75% chance that the person is a boy. I hope this explanation helps explain how to determine probability using a data set.
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Select the correct answer from each drop-down menu.
A cross section is the intersection Of a ___ and a ___
Answer:
a cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Which graph represents this sysytem? y=3 x+y=4
Answer:
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
Step-by-step explanation:
a 11%
b 81.7%
c 18.3%
d 22.4%
Answer: c. 18.3
Step-by-step explanation: 100 times .6 equals 60 so if you divide 11 by .6 you get 18.3
Answer:
here you go
Step-by-step explanation:
add them all together = 60
+ 40 = 100
4 boxed
40 divided by 4 = 10
add 10 onto each number
red = 21%
silver = 34%
grey = 26%
black = 19%
all of them added together = 100%
Six friends share 15 fruit bars equally how many fruit bars does each friend get
Answer:
2 1/2 bars each.
Step-by-step explanation:
That would be 15/6.
Jenny is making bracelets using different colored
beads. Jenny has 60 green beads and 105 blue
beads. What is the greatest number of identical
bracelets Jenny can make if she wants to use all of
the beads?
Answer:Jenny can make
18
identical necklaces, each containing 5 green and 6 blue beads.
Explanation:
Assume, each necklace contains
G
green and
B
blue beads and we have
N
such necklaces. All these variables are natural numbers.
Then we can establish the following equations in natural numbers:
N
⋅
G
=
90
N
⋅
B
=
108
Our task is to find a maximum
N
for which these two equations have a solution in natural numbers.
Obviously,
N
is a maximum common denominator of
90
and
108
.
To find the maximum common denominator of
90
and
108
, let's represent these two numbers as a product of prime numbers:
90
=
2
⋅
3
⋅
3
⋅
5
108
=
2
⋅
2
⋅
3
⋅
3
⋅
3
As we see, the maximum common denominator (a product of all prime numbers that are identical for both
90
and
108
) is
P
=
2
⋅
3
⋅
3
=
18
Therefore, assigning
N
=
18
,
G
=
5
and
B
=
6
, we obtain the solution:
Maximum number of identical necklaces is
N
=
18
with each necklace containing
G
=
5
green beads and
B
=
6
blue beads.
Answer
Step-by-step explanation:
The equation h = –0.005x2 + x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.
a. What is the equation of the axis of symmetry?
b. What is the maximum height reached by the baseball?
c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?
Answer:
(a)x=100
(b)Maximum Height, h=53 Units
(c)x=200 Units
Step-by-step explanation:
Given the equation which describes the path of the baseball
[tex]h = -0.005x^2 + x + 3[/tex]
(a)Equation of the axis of symmetry
For a quadratic function of the form [tex]y=ax^2+bx+c[/tex], its equation of the axis of symmetry is determined by the equation:
[tex]x=-\dfrac{b}{2a}[/tex]
In the function given: a=–0.005, b=1
Therefore:
[tex]x=-\dfrac{1}{2*-0.005}=\dfrac{1}{0.01}\\\\x=100[/tex]
Equation of the axis of symmetry, x=100
(b)Maximum height reached by the baseball
The maximum height reached by the baseball occurs at the line of symmetry.
Therefore, when x=100
Maximum Height, [tex]h = -0.005(100)^2 + 100 + 3[/tex]
=53 Units
(c)When the height =3 feet, we want to determine the value of x.
[tex]h = -0.005x^2 + x + 3\\3 = -0.005x^2 + x + 3\\-0.005x^2 + x=0\\x(-0.005x + 1)=0\\-0.005x + 1=0\\-0.005x =-1\\$Divide both sides by -0.005\\x=200 Units[/tex]
Final answer:
The equation of the axis of symmetry is x = -100, the maximum height reached by the baseball is 103 feet, and to find the specific distance traveled when caught at 3 feet would require solving the quadratic equation given.
Explanation:
The equation h = –[tex]0.005x^2[/tex]+ x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.
a. What is the equation of the axis of symmetry?
The equation of the axis of symmetry for a quadratic equation in the form of [tex]ax^2 + bx + c[/tex] is given by x = –b/2a. Hence, for our equation, the axis of symmetry is x = –(1)/(2×–0.005) = –100.
b. What is the maximum height reached by the baseball?
The maximum height can be found by substituting the x-value of the axis of symmetry into the original equation. So, h = –[tex]0.005(100)^2[/tex] + 100 + 3 = 103 feet.
c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?
To find the horizontal distance when h is 3, we set the equation equal to 3: –[tex]0.005x^2 + x + 3 = 3.[/tex] Simplifying gives x values where the ball is at 3 feet off the ground. After simplification, one possible solution would be the distance before the ball reaches its peak. However, solving this particular quadratic may require a calculator for precise roots, implying the distances at which the ball is 3 feet high.
Isabell some music playlist has 12 rock songs 15 pop songs 13 hip-hop songs and 10 oldies songs.if she sets the playlist on random shuffle what is the probability that the first song will be a pop song?
Answer:
3/10 or 30%
Step-by-step explanation:
it is the number of pop songs in the list divided by all of the songs combined.
so 15 pop songs
over
12+13+10+15=50
15/50 is you answer
simplify and get
3/10
Please helppp meee the picture is up there to answer the question
Answer:
-6x-5
Step-by-step explanation:
Answer:
6x^2-10
Step-by-step explanation:
(5x^2+2)-(-4x^2+7)+(-3x^2-5)=
5x^2+2+4x^2-7-3x^2-5=
5x^2+4x^2-3x^2+2-7-5=
9x^2-3x^2-5-5=
6x^2-10
two similar trapezoids have areas of 180 cm2 and 45cm2. what is their ratio of similarity
The ratio of similarity between the two trapezoids is 2:1, which means that the linear dimensions of the larger trapezoid are twice those of the smaller one.
To find the ratio of similarity between two similar trapezoids with areas of 180 [tex]cm^2[/tex] and 45 [tex]cm^2[/tex], we use the principle that the ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions. In other words, if the ratio of similarity (scale factor) between the linear dimensions of two similar figures is 'k', then the ratio of their areas is '[tex]k^2[/tex]'.
Let the ratio of similarity be 'k'. Then we have 180/45 = k^2. Simplifying this, we get 4 = [tex]k^2[/tex] and thus, k = 2. This means the linear dimensions of the larger trapezoid are twice those of the smaller one.
Therefore, the ratio of similarity between the two trapezoids is 2:1.
Find the area of the triangle below.
Answer:
73.72
Step-by-step explanation:
Using law of Sines in area:
A(triangle) = S1 * S2 * sin(theta) /2
A(triangle) = 12 * 15 * sin(55) / 2 = about 73.72 when rounded
ANSWER: 73.72
What PERCENT of 250 is 60?
Answer:150.
Step-by-step explanation:
Quadrilateral BCDE is inscribed in circle A, and mBED = 160".
C
А
84
160°
E
m BCD =
[Select]
degrees and mZBCD = [Select]
degrees.
what is the measure of
Answer:
20°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
∠C = 180° -∠E = 180° -160°
m∠BCD = 20°
Consider the figure shown. What solid three dimensional object is
produced by rotating the rectangle about line m?
Answer:a wide cylinder
Step-by-step explanation:
Help ASAP!! Will mark the brainliest
Answer:
a, c, b, a
Step-by-step explanation:
Sam needs to find the circumference of a circle with a diameter of 24 inches. He uses a calculator to find the circumference. Which answer is reasonable?
A. 72.013678 in
B. 75.398223 in
C. 80.332161 in
D. 85.335372 in
Answer: B
Step-by-step explanation:
Using 6 decimals for pi = 3.141592
[tex]Formula: C= \pi d\\[/tex]
[tex]C=(3.141592)(24in)\\C=75.398223in[/tex]
1. Using the floorplan below, calculate the total area of the space.
YOU MUST SHOW ALL WORK FOR CREDIT.
Breakfast)
nook
Kitchen
Formal Dining
1 unit = 5 feet
Answer:
i believe it is 185 feet
Danielle had planned her gift basket to be priced at $50 with a 40% gross margin. She forgot packaging costs which will be $3 per unit. If she still keeps the price at $50, how much will her gross margin percentage be after packaging costs?
a) 30%
b) 34%
c) 43%
d) 47%
The gross margin percentage after packaging costs would be a) 30%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Danielle had planned her gift basket to be priced at $50 with a 40% gross margin.
let, The original price be 'x'.
Therefore, $50 is 140% of 'x' which is,
(140/100)×x = 50.
1.4x = 50.
x = 50/1.4.
x = 35.71.
Now, The packaging cost is $3 which makes the cost of the product 38.71.
So, (50/38.71)×100.
= 29% gross margin.
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The rule at Anna's house is that if she eats all
of her vegetables and does all of her chores
each day, she earns 2 hours of internet time
which she can save. Anna started her week
with 3 hours saved. If she eats all of her
vegetables and does all of her chores each
day for 4 days straight, how many hours does
she have after the 4 days if she uses 6 hours
of her internet time?
Which of the following sets of equations
correctly represents this situation?
On a certain hot summer's day, 744 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.00 for adults. The receipts for admission totaled $ 1392.25 .How many children and how many adults swam at the public pool that day?
Answer:
383 children and 361 adults
Step-by-step explanation:
Let's say there are a adults and c children. Since the total number of people was 744, we can write:
a + c = 744
We also know that children's prices are $1.75 per child and adults' prices are $2 per adult. Since the total is $1392.25, we can write:
1.75c + 2a = 1392.25
Now we have a system of linear equations:
a + c = 744
1.75c + 2a = 1392.25
Multiply the first equation by 2:
2 * (a + c = 744) ⇒ 2a + 2c = 1488
Now subtract the second equation from this one:
2a + 2c = 1488
- 2a + 1.75c = 1392.25
___________________
0a + 0.25c = 95.75
c = 383
Plug this in to find a:
a + c = 744
a + 383 = 744
a = 361
There were 383 children and 361 adults.
Lets use some variables:
x = number of adults
y = number of children
744 total people used the public swimming pool and the number adults and children are unknown, so, we can write an equation like:
x + y = 744
Since $2 are for adults, we can write that as 2x. Since $1.75 are for children, we can write that as 1.75y. Since the total price is $1,392.25, that's what the equation should equal. Equation:
2x + 1.75y = 1,392.25
Now, we have a system of equations.
~Rationalize equations
x + y = 744, 2x + 7/4y = 5569/4
~Isolate x for [ x + y = 744 ]
x + y - y = 744 - y
x = 744 - y
~Substitute with x
2(744 - y) + 7/4y = 5569/4
~Isolate y for [ 2(744 - y) + 7/4y = 5569/4 ]
2(744 - y) * 4 + 7/4y * 4 = 5569/4 * 4
8(744 - y) + 7y = 5569
5952 - 8y + 7y = 5569
5952 - y = 5569
5952 - 5952 - y = 5569 - 5952
-y = -383
-y/-1 = -383/-1
y = 383
~Substitute y with 383 in [ x = 744 - y ]
x = 744 - 383
x = 361
Therefore, there are 361 adults and 383 children.
Best of Luck!
Solve the equation and check your answer. 61 2 = 11 4 + n Which statements are correct? Check all that apply.
Answer:
its the second, third, and fifth one
Step-by-step explanation:
6-9x=6x-10x-24
solve for x
plzz help
Answer: 6
Step-by-step explanation:
The answer is 6 because subtract 6-9x=6x-10x-24
the lines on a coordinate plane are perpendicular.
perpendicular lines form what type of angles?
Final answer:
Perpendicular lines on a coordinate plane intersect to form right angles, which are precisely 90°. The slopes of perpendicular lines are negative reciprocals of each other.
Explanation:
When two lines on a coordinate plane are described as being perpendicular, this means they intersect to form right angles, which are angles of 90°. It's important to recognize that perpendicular lines have slopes that are negative reciprocals of each other. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2. These slopes ensure that the angles formed between the lines are exactly 90 degrees.
In geometry and physics, this concept is further explored with orthogonal vectors, which are two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors. Their importance lies in various applications, such as breaking down a force into components acting along perpendicular axes.
The perimeter of
the rectangular playground shown
below is 160 feet. What is the area of the
playground?
Known :
Perimeter = 160 ft
length = 50 ft
Asked :
Area = ...?
Answer :
Find the width first :
Perimeter = 2 (length + width)
160 = 2 (50 + width)
width = (160 ÷ 2) - 50
width = 80 - 50
width = 30 ft
Now, let's find the Area :
Area = length × width
= 50 × 30
= 1.500 ft²
So, the area of the playground is 1.500 ft²
Hope it helpful and useful :)
What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number? StartFraction 10 Over 121 EndFraction StartFraction 24 Over 121 EndFraction StartFraction 6 Over 11 EndFraction StartFraction 10 Over 11 EndFraction
Answer:
24/121, the 2nd choice on edg
Step-by-step explanation:
4/11 times 6/11 so that becomes 24/121
Answer:
24/121
Step-by-step explanation: