Answer:
B) Isosceles
Step-by-step explanation:
The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).
We must first determine the length of the sides of the triangle, before we can classify it.
We apply the distance formula to find length of the sides.
[tex]|AB|=\sqrt{(4--1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{5^2+(0)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{25}[/tex]
[tex]\Rightarrow |AB|=5 units[/tex].
The length of side BC
[tex]|BC|=\sqrt{(3-4)^2+(-1-2)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{1+9}[/tex]
[tex]\Rightarrow |BC|=\sqrt{10}[/tex]
The length of side AC
[tex]|AC|=\sqrt{(3--1)^2+(-1-2)^2}[/tex]
We simplify to obtain;
[tex]|AC|=\sqrt{(3+1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{16+9}[/tex]
[tex]|AC|=\sqrt{25}[/tex]
[tex]|AC|=5\:units[/tex]
Since [tex]|AC|=5\:units=|AB|[/tex], the given triangle is an isosceles triangle.
The correct answer is
Answer:
B) isosceles
Step-by-step explanation:
What is the slope of the line passing through the points (0,4) and (-8,-1)
how do you solve this question
2(x-2)+3(x+1)=9
2(x - 2) + 3(x + 1) = 9
2x - 4 + 3x + 3 = 9 distributed the 2 and 3 on the left side
5x - 1 = 9 added like terms (2x + 3x) and (-4 + 3)
5x = 10 added 1 to both sides
x = 2 divided 5 from both sides
Answer: x = 2
If the triangle TSR is similar to triangle TNM, what is the length of x?
Answer:
120:240, 1:2
1:2, 70:140
Answer: x=140
Step-by-step explanation:
A fish tank that holds 80 gallons of water is 55 % full. how many gallons are in the tank now?
Answer:
[tex]44\ gallons[/tex]
Step-by-step explanation:
we know that
A fish tank holds [tex]80[/tex] gallons of water
so
By proportion
Find how many gallons represent [tex]55\%[/tex] of the total tank capacity.
[tex]\frac{80}{100}\frac{gallons}{\%} = \frac{x}{55}\frac{gallons}{\%}\\ \\x=55*80/100\\x= 44\ gallons[/tex]
There are 44 gallons of water in the tank. This is calculated by converting the percentage full into a decimal (0.55) and multiplying it by the total capacity of the tank (80 gallons).
Explanation:The question is asking how many gallons are currently in the fish tank that is 55% full and has a total capacity of 80 gallons.
First, you need to convert the percentage of the tank that is full (55%) to a decimal. To do this, you divide the percentage by 100.
So, 55 divided by 100 equals 0.55.
Next, you multiply this decimal by the total capacity of the tank to find out how many gallons are currently in the tank. 0.55 times 80 equals 44. Therefore, there are 44 gallons of water in the fish tank now.
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The value of the digit in the hundredths place is——— times as much as the digit in the tenths place.
Answer:
the answer is 10
Step-by-step explanation:
compare and contrast subtracting integers and subtracting whole numbers
Subtracting whole numbers does not include subtracting negative numbers, whereas when subtracting integers you can include negative numbers.
Answer:When subtracting whole numbers it is like normal addition whereas in subtraction of integers you can include any integers including negative ones
Step-by-step explanation:
alex is going to share a bag of 24 jelly beans with his friend austin . alex gives some of the jelly beans to austin but , when they do a count , alex has three times as many jelly beans as austin . how many jelly beans do they each have ?
Can u tell me what math book this was from ?
Step-by-step explanation:
Which expression is 8y - 5x + 13y equivalent to after being simplified?
A. 21y - 5x
B. 16y
C. 5x + 21y
D. 8y + 8x
Combine the like terms (8y and 13y) in the given algebraic expression (8y - 5x + 13y), which equals 21y. Thus, after simplifying, the equivalent expression is 21y - 5x.
Explanation:The given expression is 8y - 5x + 13y. In order to simplify it, combine the like terms. The like terms here are 8y and 13y because they both include the variable 'y'. By adding 8y and 13y, we get 21y. Thus, the simplified version of the given expression is 21y - 5x. So, the correct answer is Option A: 21y - 5x.
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Forty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
Here's the question: You have an electrical circuit with various components, all of which are in series. The current (I) through the system is (5.772 - 5.323i) milliamperes (mA). The impedance (Z) in that same system is (3.342 + 4.176i) kilohms (kΩ). Please tell me the magnitude of the voltage in the circuit.
Answer:Magnitude of voltage is 41.9963 volts
Step-by-step explanation:
Given that current I =5.772-5.323i mA
and impedance, Z=3.342+4.176i kilo ohms
Then voltage in the circuit = IZ
[tex]=(5.772-5.323i)X10^{-3}X(3.342+4.176i)X10^{3}[/tex]
[tex]V=(5.772-5.323i)X(3.342+4.176i)[/tex]
[tex]V=19.290024+24.103872i-17.789466i-23..5148848i^{2}[/tex]
[tex]V=41.518892+6.314406i[/tex]
Magnitude of V = [tex]\sqrt{41.518892^{2} +6.314406^{2} }=\sqrt{1763.6901}=41.9963volts[/tex]
the sum of 367 and 863 is equal to the sum of 863 and another number. what is that number?
Answer:
Sum of 367 and 863 is equal to the sum of 863 and 367. Thus, 367 is the required number.
Step-by-step explanation:
Commutative property of Addition
Let a and b be two real numbers. Then commutative property of addition states that the sum of a and b is equal to the sum of b and a that is
[tex]a + b = b + a[/tex]
Similarly, we a re given here,
[tex]367 + 863 = 1230\\1230 = 863 + 367[/tex]
Thus, sum of 367 and 863 is equal to the sum of 863 and 367.
Thus, 367 is the required number.
Commission earned is 6% at a show store; original cost of shoes: $125
125 x .06 = 7.5
6% of $125 is $7.50
In 6th grade , the ratio of boys to girls is 4 to 5
If there are 145 girls how many boys are there?
https://socratic.org/questions/the-ratio-of-boys-to-girls-at-a-college-is-4-5-how-many-boys-and-are-there-if-th
there would be 124 boys in the class
of 350 male athletes at a high school, some play only basketball, some play on baseball, and some do both. If 250 of the males play basketball, and 120 play both sports, how many of the males play baseball
250 and 120 both adds up to 370 but 350 of the male play sports. So u answer can't be sloved
One hundred male athletes in the school play baseball only. This is determined by subtracting the number of males who play both sports and who play only basketball from the total number of male athletes.
Explanation:The question states there are 350 male athletes in total at the high school. We know that 250 males play basketball and that 120 males play both sports. To figure out the amount of males who play baseball, we first subtract the number of males who play basketball and both sports from the total number of male athletes.
Therefore, the calculation would be as follows:
First, subtract the number of students who play both sports (120) from the number of students who play basketball (250). This gives you the number of students who only play basketball. 250 - 120 = 130. Then subtract the number of students who only play basketball (130) and the number of students who play both sports (120) from the total number of male athletes (350) to get the number of students who only play baseball. 350 - 130 - 120 = 100.
So, there are 100 males that only play baseball according to the given information.
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Stanley ran a 5 kilometer race in 30 minutes. what was his speed in kilometers per hour? round to the nearest tenth
Solve for x.
78(−32−48x)+36=23(−33x−18)−10x
Answer:
2
Step-by-step explanation:
A shoe manufacture reported negative earnings of $453,000 for 2012. In 2013 the company reported earnings of $813,000, and in 2014 the company reported earnings of $384,000. How much more money did the company earn in 2014 than 2012? A) $360,000
B) $429,000
C) $744,000
D) $837,000
The answer is D for the quick answer
Please explain so i could understand
The domain is the input values ( x values).
These would be the numbers that the arrows are pointing away from.
The domain is (-2, 0 , 1, 3 , 5)
write an equation for twelve times h equals one hundred and twenty minus thirty-six
we will always start order of operation from left to right
Left most is :
twelve times h
so, [tex]12 \times h[/tex]
Right side is :
one hundred and twenty minus thirty-six
[tex]120-36[/tex]
now, we can set them equal
we get
[tex]12 \times h=120-36[/tex]
so, the equation is
[tex]12 \times h=120-36[/tex]................Answer
A particular computer takes 15 minutes to download a 45 minute tv show . How long will it take the computer to download a 1.5 your movie?
15 more than a number b
Hello!) this is math :( can you help me please?
As in the first four terms, I assume that means using the equation with 1,2,3,4.
11) if n = 1, the answer would be 3.
If n = 2, the answer would be 10.
If n = 3, the answer would be 17.
If n = 4, the answer would be 24.
12) If n = 1, the answer would be 55.
If n = 2, the answer would be 45.
If n = 3, the answer would be 35.
If n = 4, the answer would be 25.
An explicit formula is used to find any term in a sequence by putting in the number of that term in place of the unknown variable.
In order to find the first four terms, we need to plug values, from 1-4, separately in each of the formulas.
For f(n) = 7(n+1) - 11, put values from 1-4 in place of n:
f(1) = 7(1+1) - 11 = 3 ----> First term
f(2) = 7(2+1) - 11 = 10 ----> Second term
f(3) = 7(3+1) - 11 = 17 ----> Third term
f(4) = 7(4+1) - 11 = 24 ----> Fourth term
For f(n) = 65 - 10n, put values from 1-4 in place of n:
f(1) = 65 - 10(1) = 55 ----> First term
f(2) = 65 - 10(2) = 45 ----> Second term
f(3) = 65 - 10(3) = 35 ----> Third term
f(4) = 65 - 10(4) = 25 ----> Fourth term
it is possible to create a semi regular tessellation using only squares and regular hexagons?
Final answer:
Yes, a semi-regular tessellation can be created using squares and regular hexagons. One example of this is the honeycomb pattern, which consists of hexagons surrounded by squares.
Explanation:
Yes, it is possible to create a semi-regular tessellation using only squares and regular hexagons. A semi-regular tessellation is a pattern that repeats using two or more regular polygons, but with different arrangements around each vertex.
One example of a semi-regular tessellation using squares and regular hexagons is the honeycomb pattern. In this pattern, the squares and hexagons are arranged in such a way that they fill the plane without any gaps or overlaps.
To create the honeycomb pattern, you start by placing a regular hexagon in the center. Then, surround the hexagon with six squares, with each square touching two sides of the hexagon. Finally, place a hexagon on each side of the square, with each hexagon touching two sides of the square and one side of the adjacent hexagon. Repeat this pattern to create a tessellation.
At a school concert,the orchestra plays 8 songs that are 4.25 min long and 3 songs that are twice as long as each of the others.how long is the concert?
Answer: 59.5 minutes.
Step-by-step explanation:
1. You have the following information given in the problem above:
- 8 songs are 4.25 minutes long.
- 3 songs are twice as long as each of the others.
2. Therefore, the total time of 8 songs is:
[tex](8)(4.25min)=34min[/tex]
3. And the total time of the 3 songs is:
[tex](2)(3)(4.25min)=25.5min[/tex]
4. Therefore, you have that the result is:
[tex]34min+25.5min=59.5min[/tex]
The concert is 59.5 minutes long.
Let's break down the problem step-by-step:
The orchestra plays 8 songs that are each 4.25 minutes long.The orchestra also plays 3 songs that are twice as long as each of the 4.25 minute songs.First, we calculate the total time for the 8 songs:8 songs x 4.25 minutes = 34 minutes
Next, we calculate the length of the songs that are twice as long as the 4.25 minute songs:2 x 4.25 minutes = 8.5 minutes per song
We then find the total time for these 3 songs:3 songs x 8.5 minutes = 25.5 minutes
Finally, we add the time for all the songs to get the total duration of the concert:34 minutes + 25.5 minutes = 59.5 minutes
So, the total duration of the concert is 59.5 minutes.
find the slope 3x+5y=29
Answer: [tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
If you solve for y, then it will be in y = mx + b format where m is the slope.
3x + 5y = 29
-3x -3x
5y = -3x + 29
[tex]\frac{5y}{5} = \frac{-3x}{5} + \frac{29}{5}[/tex]
[tex]y = \frac{-3}{5}x + \frac{29}{5}[/tex]
m = [tex]-\frac{3}{5}[/tex]
To find the slope of the line for the equation 3x+5y=29, rewrite it in slope-intercept form y=mx+b. After isolating y, you'll find that the slope m is -3/5.
Explanation:To find the slope of the line represented by the equation 3x + 5y = 29, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we solve for y:
Subtract 3x from both sides to get 5y = -3x + 29.Divide every term by 5 to isolate y on one side, resulting in y = -3/5x + 29/5.Now, the equation is in slope-intercept form, and we can easily identify the slope as -3/5. This means there is a decrease of 3 on the vertical axis for every increase of 5 on the horizontal axis. Thus, the slope of the line is -3/5.
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow. Which inequality correctly compares the temperatures of the three cities?
A.
Bangkok's temperature < Cape Town's temperature < Moscow's temperature
B.
Bangkok's temperature < Moscow's temperature < Cape Town's temperature
C.
Bangkok's temperature > Moscow's temperature > Cape Town's temperature
D.
Bangkok's temperature > Cape Town's temperature > Moscow's temperature
Answer: The correct option is D.
Explanation:
It is given that in January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow.
Since Bangkok is hotter than Cape Town, it means the temperature of Bangkok is more than or greater than the Cape town.
[tex]\text{Bangkok's temperature}>\text{Cape Town's temperature}[/tex] .... (1)
Since Cape Town is hotter than Moscow, it means the temperature of Cape town is more than or greater than the Moscow.
[tex]\text{Cape Town's temperature}>\text{Moscow's temperature}[/tex] ..... (2)
From equation (1) and (2) we get,
[tex]\text{Bangkok's temperature}>\text{Cape Town's temperature}>\text{Moscow's temperature}[/tex]
Therefore, the correct option is D.
The Correct answer is d
Help PLDAWEKFMWELFEFLE
(7/3)/(9/2)=(14/27)/1
The sum of the prime numbers less than 8 and is equal to 17 what is the sum of the prime numbers
Prime numbers mean that their factors are only the number itself and 1.
2, 3, 5, 7, 11, etc. all fall under this category.
note however, that the numbers have to be less than 8: [2, 3, 5, 7] are your choices
2 + 3 = 5
5 + 5 = 10
10 + 7 = 17
Therefore, {2, 3, 5, 7} are your answers
hope this helps
Answer:
2,3,4,5,7
Step-by-step explanation:
Water stations are placed every 600 meters of a fifteen kilometer race. How many water stations will be needed?
25 water stations, 15000/600 = 25
Given:2PQ=PR prove: Q is the midpoint of PR
Answer:
Using definition of midpoint, Q is the mid point of PR.
Step-by-step explanation:
Given 2PQ=PR
And Q lies on the line PR (It should be given in the problem itself else we have to assume it to prove "Q is the midpoint of PR").
Then PR=PQ+QR using segment addition postulate.
Let us plugin PR in given equation.
2PQ=PQ+QR
Subtract PQ from both sides.
2PQ-PQ=PQ+QR-PQ
PQ=QR
Since Q lies on the line PR and PQ=QR, Q is the mid point of PR.
Hence proved.
In geometry, if 2PQ=PR, point Q is the midpoint of PR. This is because the given condition implies that the length of segment PQ is half of the length of the whole segment PR, meaning Q divides PR into two segments of equal lengths.
Explanation:In Geometry, the statement 2PQ=PR is the given condition. Prior to your question, we are assuming that PQ and QR are line segments. This would imply that P, Q, and R all lie on the same line, with P and R being the endpoints and Q somewhere between them.
Now, the provided condition (2PQ=PR) means that the length of segment PQ is half of the length of the whole segment PR. If we assume segment PQ is 'a' units long, then 2PQ would be '2a' units long. According to the equation, PR is also '2a' units long.
By definition, the midpoint of a line segment is the point that divides the segment into two segments of equal length. Since PQ is half of PR, point Q would divide PR into two equal segments, PQ and QR, both being 'a' units in length. Therefore, Q is the midpoint of PR.
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