No, angle B or angle C can't be obtuse.
Step-by-step explanation:It is given that:
Angle A in triangle ABC is obtuse.
This means that:
∠A > 90°
Now, let us assume that:
Angle B is obtuse.
i.e. ∠B > 90°
Hence, we get that the sum of two angle is greater than 180 degree.(i.e. ∠A+∠B > 180° )
hence, the sum of all the three angles will be greater than 180 degrees.
But we know that in order to form a triangle the sum of all the three angles must be equal to 180 degree.
No, angle B and angle C cannot be obtuse if angle A is obtuse because the sum of angles in a triangle is always 180 degrees, and if one angle is obtuse, the other two must be acute to satisfy this rule.
We have,
In a triangle, the sum of all angles is always 180 degrees.
If angle A in triangle ABC is obtuse, it means it measures more than 90 degrees (greater than a right angle).
For the sum of the angles to be 180 degrees, angles B and C must be acute (measuring less than 90 degrees).
This is because if either angle B or angle C were obtuse, the sum of the angles would exceed 180 degrees, which is not possible in a triangle.
So, angle B and angle C cannot be obtuse if angle A is obtuse.
Thus,
No, angle B and angle C cannot be obtuse if angle A is obtuse because the sum of angles in a triangle is always 180 degrees, and if one angle is obtuse, the other two must be acute to satisfy this rule.
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Angelo read 1 1/2 pages in 3 minutes. Find his reading speed in pages per hour.
Answer:
30 Pages.
Step-by-step explanation:
We know that there are 60 minutes in an hour, and that 3 goes into 60 20 times (3/60 = 20). Multiply 1 1/2 x 20, and that equals 30 pages.
You can also set it up in fraction form - multiply 1.5/3 times x/60. cross multiply and solve for x. in this case x = 30.
PLEASE HELP ITS EASY
The following table represents a relation. Identify the set of numbers that makes up the range in the relation.
x y
5 -3
4 0
2 1
4 2
-3 3
A. -3, 2, 4, 5
B. -3
C. 0, 1, 2, 3
D. -3, 0, 1, 2, 3
Final answer:
The range of a relation is the set of all possible y-values. For the given table, the range is -3, 0, 1, 2, and 3, which corresponds to answer D.
Explanation:
You're asking to identify the set of numbers that makes up the range in the given relation. The range of a relation refers to all the possible values of y that you can get when you input various values of x. For your table, the y-values are -3, 0, 1, 2, and 3. So, the range is the set of these y-values. Therefore, the correct answer is D. -3, 0, 1, 2, 3.
In general, to find the range, you look at all the second numbers in the ordered pairs of a relation or function. When plotted on a graph, this shows the dependence of y on x.
Suppose your teacher offers to give the whole class a bonus if everyone passes the next math test. The teacher
says she will 1)give a 10-point bonus and (2) increase everyone's grade by 9% of their score. a. Let x represent the original test scores.Write statements (1) and (2) as the functions f (x) and g(x) respectively.b. Explain the meaning of f(g(x)). Evaluate f(g(75)).c. Explain the meaning of g (f(x)). Evaluate g (f(75)). d. Does g(f(x))=f(g(x)).
Answer:
See explanation
Step-by-step explanation:
A. Let x represent the original test scores.
(1) The teacher will give a 10-point bonus, then the score will be x + 10. Hence,
[tex]f(x)=x+10[/tex]
(2) The teacher will increase everyone's grade by 9% of their score, then the score will be x + 0.09x = 1.09x. Hence,
[tex]g(x)=1.09x[/tex]
B. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then
[tex]f(g(x))=g(x)+10=1.09x+10[/tex]
Meaning: the teacher increased by 9% the score and then increased the result by 10 points.
[tex]f(g(75))=1.09\cdot 75+10=91.75[/tex]
C. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then
[tex]g(f(x))=1.09f(x)=1.09(x+10)[/tex]
Meaning: the teacher increased by 10 points the score and then increased the result by 9%.
[tex]g(f(75))=1.09(75+10)=92.65[/tex]
D. [tex]g(f(x))\neq f(g(x))[/tex] because [tex]1.09(x+10)\neq 1.09x+10[/tex]
the smoothie shop sold 35 banana smoothies, 48 strawberry smoothies, and 25 orange smoothies. how many smoothies were sold in all?
Answer:
35
+ 48
25
= 108
The smoothie shop sold a total of 108 smoothies.
Explanation:To find the total number of smoothies sold, we add up the number of banana smoothies, strawberry smoothies, and orange smoothies. The smoothie shop sold 35 banana smoothies, 48 strawberry smoothies, and 25 orange smoothies. Therefore, the total number of smoothies sold is 35 + 48 + 25 = 108 smoothies.
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Rearrange to make x the subject
a = 7x/k -r
Help me pls
Final answer:
To make x the subject of the equation a = 7x/k - r, add r to both sides, multiply by k, and then divide by 7, resulting in x = k(a + r)/7.
Explanation:
To rearrange the equation a = 7x/k - r to make x the subject, we need to perform a series of algebraic manipulations. Firstly, we add r to both sides of the equation, giving us a + r = 7x/k. Following this, we multiply both sides by k to get rid of the denominator, which results in k(a + r) = 7x. Finally, we divide both sides by 7 to solve for x, which gives us x = k(a + r)/7. This rearrangement shows x as the subject of the original equation.
On a piece of paper, graph the system of equations. Find the solution to the system y=2x-5 and y=x+4
Answer:
[9, 13]
Step-by-step explanation:
{y = x + 4
{y = 2x - 5
Since we have two expressions set equal to y, use the Substitution Method:
[tex]x + 4 = 2x - 5[/tex]
-2x -2x
___________________
-x + 4 = -5
- 4 - 4
__________
-x = -9
x = 9 [Plug this back into both equations to get the y-coordinate of 13]; 13 = y
I am joyous to assist you anytime.
bart ran 500 meters from the cops and a speed of 6 meters/second before he got caught. how long did he run?
Answer:
He ran for 83.333 seconds before he was caught.
Hope this help.
Karen had a roll of ribbon 48 1/2 metres long. How many pieces of ribbon of length 1 1/5m can she cut from the roll? How many metres of ribbon will be left?
Answer:
40 and 0.5
Step-by-step explanation:
48 and 1/2 metres = 48.5 metres
1 and 1/5 metres = 1.2 metres
Take 48.5 and divide it by 1.2 and you will get 40.41666667...
Since the maximum whole number you can get is 40, you can cut 40 pieces of 1.2 metres of ribbon off.
Remainder = 48.5 - (40 x 1.2) = 0.5 metres left
The number of pieces of ribbon can be cut from roll is 40 and 0.5 m of ribbon left.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
We have,
Karen had a roll of ribbon 48 1/2 m long.
= 48.5 m long
and, 1 and 1/5 m = 1.2 m
Now, the number of pieces of ribbon can be cut from roll is
= (48.5) / (1.2)
= 40.416
and, the amount of ribbon left
= 48.5 - (40 x 1.2)
= 0.5 m
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-9.25 is rational or irational
Answer:
It is rational.
Step-by-step explanation:
A rational number is a number that can also be written as a fraction or ratio. -9. 25 is also equal to -9 1/4. Therefore, it is rational.
Answer:
-9.25 is rational
Step-by-step explanation:
What is the equation that represents the line that passes through the point (2,6) and has a slope of -5?
Answer:
y = - 5x + 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 5, thus
y = - 5x + c ← is the partial equation of the line
To find c substitute (2, 6) into the partial equation
6 = - 10 + c ⇒ c = 6 + 10 = 16
y = - 5x + 16 ← equation of line
The product of 4 and a number plus 17 is 5
The required solution is -63/4.
It is required to find the number.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications
Given :
Step 1: Write down the question as an algebra problem, with the unknown as X
The unknown is a number plus 17, so we write it as (X+17). The product is four times (X+17), so we write it as 4(X+17). Set it equal to 5, as per the question,
4(X+17)=5
Step 2: Divide both sides by 4
4(X+17)/4=5/4
X+17=5/4
Step 3: Isolate X by subtracting 17 from both sides
X= 5/4-17
X= 5/4- (17*4)/4
X= 5/4-68/4
X=-63/4
Therefore, the required solution is -63/4.
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Estimate the square root of 0.39 to the nearest 10th Place
Answer:
0.62
Step-by-step explanation:
A cruise ship travels 20 miles in 50 minutes. How far does it travel in one minute?
Answer:
0.4 miles
Step-by-step explanation:
Answer:just do 50 divided by 20
Step-by-step explanation:
50 divided by 20
Let p: x < −3
Let q: x > 3
What is represented by p ∨ q?
Answer:
Step-by-step explanation:
p ∨ q : x < −3 or x > 3
Lina packs 3-inch cups into boxes
measuring 12 inches by 15 inches.
How many cups fit in one box?
The division is one of the four fundamental arithmetic operations. The number of cups that Lina can feel in the box is 20.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Lina packs 3-inch cups into boxes measuring 12 inches by 15 inches. Since the bottom of the cup is circular, therefore, will cover a square area as shown in the image below.
Therefore, the number of cups that can fit in the bcan be written as,
Number of cups= (12 inches × 15 inches)/(3 inches × 3 inches)
= 20 cups
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Find the range of f(x) =3x-5 for the domain {-1.5,2,4}
Answer:
Step-by-step explanation:
calculate :
f(-1) =3(-1)-5 = - 8
f(5) =3(5)-5 = 10
f(2) =3(2)-5 = 1
f(4) =3(4)-5 = 7
the range is : E = {-8.10,1,7}
Which letter represents the point (4, -5)?
P
Q
R
S
You purchase n cartons of tennis balls at $25 per carton from an online retailer that charges 8% tax and $17 in shipping costs. The expression 25n +0.08(25n) + 17 can be used to represent the total cost.
Answer:
The expression is [tex]\$(27n+17)[/tex]
Step-by-step explanation:
The question is Simplify the expression and identify the units
we have
[tex]25n+0.08(25n)+17[/tex]
Find the product between 0.08 and 25n
[tex]0.08(25n)=2[/tex]
substitute
[tex]25n+2n+17[/tex]
Groups terms that contain the same variable
[tex](25n+2n)+17[/tex]
Combine like terms
[tex]27n+17[/tex]
The expression above represent the total cost
therefore
the unit is in dollars ($)
Write a quadratic equation with roots of 3/4 and -4
Answer:
(x-3/4)(x+4)
any quadratic can be written as (x-root)(x-root) if you need standard form then multiply
Evaluate the
expression:
2,322 - 27
Answer:
the answer is 2295
Step-by-step explanation:
of that doesn't work then put it in a calculator
[tex] {x}^{3} \times {x}^{4} [/tex]
Answer:
[tex]x^{7}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex], thus
x³ × [tex]x^{4}[/tex] = [tex]x^{(3+4)}[/tex] = [tex]x^{7}[/tex]
Answer:
[tex]x^{7}[/tex]
Step-by-step explanation:
[tex]x^{n}[/tex]×[tex]x^{m} = x^{n+m}[/tex]
a group of hikers find a fallen tree in a forest. he dead tree trunk is covered by mushrooms and other fungus. the apples are all rotten and decayed by bacteria. which statement best summarizes how these fungus and bacteria organisms are obtaining their food energy
Answer:
Step-by-step explanation:
Answer: D. The fungus and bacteria organisms are obtaining the energy they need by decomposing organic matter like dead trees and old apples.
Fungi is the primary decomposer of biological waste in forest ecosystem. Fungi grows on the branching network of hyphae which provide it more penetration potential towards the litter. Wood decaying fungi has enzymes required for decomposition of lignin, a chemical substance found in wood. Fungi decompose organic matter by releasing enzymes which breaks down the decaying matter, after that they absorb the nutrients in the decaying material. The left residue in the organic matter includes sugars and amino acids are degraded and decomposed by the bacteria.
Answer:
D) the fungus and bacteria organisms are obtaining the energy they need by decomposing organic matter like dead trees and old apples
Step-by-step explanation:
Who on here is from Connections Academy?
Answer:
not me
Step-by-step explanation:
I am not from Connections Academy, but I am in Ohva.
A box contains 13 3/4 ounces of spaghetti.A serving size is 1 1/4 ounces. How many servings are in one box of spaghetti?
Answer:
11 servings
Step-by-step explanation:
13 3/4 ÷ 1 1/4 = 11
There are 11 servings in one box of spaghetti.
What is division?Division is breaking a number up into an equal number of parts.
Given that, A box contains 13 3/4 ounces of spaghetti. A serving size is 1 1/4 ounces.
55/4÷5/4 = 11
Hence, There are 11 servings in one box of spaghetti.
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(4v3 + 3v - 8v4) + (4V - 8v4 - 7)
Answer:
-21v-7
Step-by-step explanation:
1st remove parentheses: 4v*3+3v-8v*4+4v-8v-7
2nd Add similar elements: 3v+4v-8v= -v
=4*3v-v-8*4v-7
3rd Multiply the numbers: 4*3=12
12v-v-8*4v-7
4th Multiply the numbers: 8*4=32
=12v-v-32v-7
5th Add similar elements: 12v-v-32v=-21v
= -21v-7
you're laying plumbing on a construction site. The blueprints call for 8 sections of 5 3/4 inch long piping. how many inches of piping will use
Hey!
---------------------------
Solution:
8 = 8/1
5 3/4 = 23/4
23/4 * 8/1 = 184/4
184/4 = 46
---------------------------
Answer:
He will use 46 inches of piping.
---------------------------
Hope This Helped! Good Luck!
Answer:
46
Step-by-step explanation:
8*5.75= 46
F(1)=192
192,48,12,3
The sequence shown is
Answer:
Geometric
an=an-1₋(.25);a₁=192
an=192(.25)^n-1
7.32421875*10^−4
Step-by-step explanation:
Answer:
The sequence shown is geometric
Recursive function:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function: [tex]a_n = 192 \times 0.25^{n-1} [/tex]
10th term: 0.000732421876
Step-by-step explanation:
In a geometric sequence the n+1 term divide by the n term is constant
48/192 = 0.25
12/48 = 0.25
3/12 = 0.25
From this result we can deduce the recursive function:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function:
[tex]a_n = a \times r^{n-1} [/tex]
where a is the first term in the sequence (= 192) and r is the common ratio (= 0.25). Replacing:
[tex]a_n = 192 \times 0.25^{n-1} [/tex]
The 10th term is:
[tex]a_{10} = 192 \times 0.25^9 = 0.000732421876 [/tex]
what is the explicit formula for this gemoetric sequence 8 4 2 1
Answer:
an = 8·(1/2)^(n-1)
Step-by-step explanation:
The first value is a1 = 8 and the common ratio is r = 1/2, so the formula is ...
an = a1·r^(n-1)
an = 8·(1/2)^(n-1)
an = 2^(4-n) . . . . . . more compact version
Ryan feeds his dog 2/3 pounds of dog food for each meal. Ryan has just bought 18 pounds of dog food. For how many meals will the food last?
Answer:
Step-by-step explanation:
30 meals
Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last
skater. Then, they try to decide whether or not Oliver should be the first skater in the race.
Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race?
A = {MOPN, PMON}
A = {OPMN, OMPN)
A = {MOPN,MPON, OPMN, POMN)
A = {MOPN. MPON, PMON, POMN)
Answer:
A = {MOPN, MPON, PMON, POMN}
Step-by-step explanation:
Everyone has already agreed that Naim would be the last skater, so we have to make sure that the result has 'N' in each last place. As we can see, they all have this.
Now, we also have to make sure Oliver not first, because although they're trying to decide, the problem asks for the complement in which "Oliver is the first skater in the race."
A complement is all the values that are NOT in the set, so it cannot be A = {OPMN, OMPN) or A = {MOPN,MPON, OPMN, POMN), because they both have at least one case where 'O' is first.
A complement is ALL other values of the set, so it cannot be A = {MOPN, PMON}, because that set only shows two possible values.
Therefore, A = {MOPN, MPON, PMON, POMN} is your answer.
Answer:A=OPMN,OMPN
Step-by-step explanation:
we know oliver is first in the race and naim is last so the other racers are in between