If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
A. Triangle ABC is scalene because all side lengths of the triangle are different.
B. Triangle ABC is isosceles because two sides of the triangle are equal in length.
C. Triangle ABC is equilateral because all sides of the triangle are equal in length.
D. Triangle ABC is acute because all angles of the triangle are acute angles.
Answers
Answer: A
Step-by-step explanation:
Using the distance formula,
[tex]AB=\sqrt{(5-1)^{2}+(-4-2)^{2}}=\sqrt{16+36}=2\sqrt{13}\\BC=\sqrt{(-3-5)^{2}+(-4-2)^{2}}=\sqrt{64+36}=10\\AC=\sqrt{(-3-1)^{2}+(2-2)^{2}}=4[/tex]
From this, we can conclude that ABC is scalene.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The length of different sides are:
[tex]AB = \sqrt{(5-1)^2+(-4-2)^2} = \sqrt{16+36} = \sqrt{52}\rm\ units[/tex]
[tex]BC = \sqrt{(-3-5)^2+(2+4)^2} = \sqrt{64+36} = 10\rm\ units[/tex]
[tex]AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units[/tex]
Since the length of all the sides of the triangle is not equal it is a scalene triangle.
Hence, the correct option is A.
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Related Questions
Please help me for a treat lol
Answers
Step-by-step explanation:
a) Jill ended her scooter at her house
b) 2/3 or 0.67
c) The domain is [0,19] , The domain tell about the Elapsed Time of the Jill's scooter ride
d) The range is [2,6] , The range tell about the Distance travelled from Jill's House
I hope it helps you
Treat Please :)
Mitra created a mosaic design using square 2x2 cm white tiles and 2x3 cm rectangular centimeter black tiles. She used twice as many white tiles as black tiles. The finished pattern was 1092 square centimeters in area. How many rectangular tiles did she use?
Answers
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of white tiles and y represent the number of black tiles.
Area of white tiles = 2 cm * 2 cm = 4 cm²
Area of black tiles = 2 cm * 3 cm = 6 cm²
She used twice as many white tiles as black tiles. Hence:
x = 2y (1)
Also, the finished pattern was 1092 square centimeters in area. Hence:
4x + 6y = 1092 (2)
From both equations:
x = 156, y = 78
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
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Find the volume (to the nearest cubic foot) of a cone with base radius 4 ft. and height 8 ft.
Answers
Answer:
135 ft^3
Step-by-step explanation:
The volume of a cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]. The radius is 4 and the height is 8, so these values can be plugged in:
[tex]V = \frac{1}{3} \pi \times 4^{2} \times 8[/tex]
[tex]V = \frac{128\pi }{3}[/tex]
This is about 134.041286553 which rounds to 135 ft^3.
N(-2,-2) After a rotation 90 degrees counterclockwise
Answers
Answer: (2,-2)
Step-by-step explanation:
Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)
Sum of 1 OK. Now, think of two numbers with a sum of 1.
Answers
Answer:
0+1
Step-by-step explanat
Any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
What is sum?The result we get after adding some quantity is called the sum of the data.
Given we need to find two numbers whose sum is 1,
So, we can consider in this case two consecutive numbers of opposite sign the greater number should have a positive sign and the smaller number should have negative sign,
For example =
-4+5 = 1
-3+4 = 1
-2+3 = 1
-9+10 = 1
So, any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
Hence, there can be many numbers which can give sum of 1.
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Help please…………………..
Answers
2. vertical
3. x = 0
4. all real numbers
5. Continuous
6. 0 to infinity
That’s all I have without seeing the drop down menu options
4. The diameter of a circle is 10 in. What is the approximate circumference? Show your work to receive
full credit. **You must include the units of measurement to receive full credit.**
Show work :))
Answers
Answer:
31.4 in
Step-by-step explanation:
The circumference of of a circle given the diameter is πd :
C = π×d = 10π = 31.4159....
C ≈ 31.4
The units will still be in as this is a length not an area .
Hope this helped and brainliest please
1) FILL IN THE SPACES:
a. 2.5 liters (L) = ______ml
b. 1320g = ________kg
c. 1.2g = _________mg
d. 1025mcg =_______mg
and. 2TBS=_______tsp
F. 1 TBS =_______ml
g. 2 fl oz =_______ml
h. 75kg =________pounds (lb)
PROBLEMS
1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
2) Express the amount of 1.243 g as:
mg ________
kg ________
mcg _______
3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg?
Answers
Benjamin finds some nickels and quarters under the couch cushions. How many
coins does he have if he has 8 nickels and 12 quarters? How many coins does he have
if he has a nickels and y quarters?
Answers
Benjamin has 340 cents or $3.40.
What is Proportion?Proportion in Mathematics is an equation where two or more ratios are made to be equal.
If a : b = c : d, then we can write a/b = c/d
We know that,
1 nickel = 5 cents
8 nickel = x cents
Using ratio and proportion,
1 : 5 = 8 : x
x = 8 × 5 = 40 cents
Similarly,
1 quarter = 25 cents
12 quarters = 12 × 25 = 300 cents
Total cents Benjamin has = 300 + 40 = 340 cents = $3.40
Hence, Benjamin has a total of $3.40.
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What is the name of the expression under the radical symbol in a radical function?
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.
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What is the solution to the following system of equations? (2 points) y = x2 + 10x + 11 y = x2 + x − 7
Answers
Answer:
y=x^(2)+10x+11,y=x^(2)+x-7
Step-by-step explanation:
I think so bro
Step-by-step explanation:
I assume you mean
y = x² + 10x + 11
y = x² + x - 7
well, I subtract equation 2 from equation 1 :
0 = 9x + 18
9x = -18
x = -2
y = x² + x - 7 = (-2)² - 2 - 7 = 4 - 2 - 7 = -5
the solution (the intersection point of both graphs) is the point (-2, -5).
The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?
Answers
Answer:
-7/2 or 2 are inputs that give 19 as output.
Step-by-step explanation:
The problem gives us a quadratic function [tex]\displaystyle \large{f(x)=2x^2+3x+5}[/tex]. When its output is 19, we want to know the input value(s).
Since an output which is f(x) = 19. Therefore:
[tex]\displaystyle \large{19=2x^2+3x+5}[/tex]
Rearrange the expression in quadratic equation.
[tex]\displaystyle \large{0=2x^2+3x+5-19}\\\\\displaystyle \large{0=2x^2+3x-14}\\\\\displaystyle \large{2x^2+3x-14=0}[/tex]
Factor the expression.
[tex]\displaystyle \large{(2x+7)(x-2)=0}[/tex]
Solve like linear equation which we get:
[tex]\displaystyle \large{x=-\dfrac{7}{2}, 2}[/tex]
If you input these x-values in the function, you will get 19 as the output which satisfies the condition.
Hence, inputs are -7/2, 2
Answer:
[tex]x=2, \quad x=-\dfrac{7}{2}[/tex]
Step-by-step explanation:
Set the function to 19:
[tex]\implies 2x^2+3x+5=19[/tex]
Subtract 19 from both sides:
[tex]\implies 2x^2+3x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]: 7 and -4
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2x^2-4x+7x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(x-2)+7(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (2x+7)(x-2)=0[/tex]
Therefore the function's input values that when evaluated give a value of 19 are:
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}[/tex]
[tex](x-2)=0 \implies x=2[/tex]
A die is tossed. Find the odds against rolling a number greater than 4.
Answers
Reason:
There are 4 outcomes we don't want (rolling 1,2,3 or 4) and 2 outcomes we do want (rolling 5 or 6)
This gives the odds against ratio of 4:2 or 2:1
This can be written out as "2 to 1" or "two to one".
Having 2 to 1 odds means that we're twice as likely to get something we don't want vs something we do want.
Side note: the odds in favor will have us flip the ratio.
Question 4
(Essay Worth 10 points)
(06.05 MC)
a Iris is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is
seeds she planted. The function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points) (2
Part C: Evaluate the composite function in Part A for 30 weeks. (4 points)
Answers
A) Composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks is f[s(w)] = 50w + 25.
B) The unit of measurement for the composite function is flowers.
C) Number of the flowers for 30 weeks will be 1525.
What is a composite function?A function is said to be a composite function when a function is written in another function. The composite function that represents the number of flowers is f[s(w)] = 50w + 25. and the number of flowers for 30 weeks is 1525.
Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks.
From the given data we will find the function for the number of flowers with time.
f(s) = 2s + 25
We have s(w) = 25w
f[(s(w)]=2s(w) + 25
f[(s(w)] = 2 x ( 25w ) +25
f[s(w)] = 50w + 25.
Part B: What are the units of measurement for the composite function in Part A
The expression f[s(w)] = 50w + 25 will give the number of the flowers blooming over a number of the weeks so the unit of measurement will be flowers.
Part C: Evaluate the composite function in Part A for 30 weeks.
The expression f[s(w)] = 50w + 25 will be used to find the number of flowers blooming in 30 weeks put the value w = 30 to get the number of the flowers.
f[s(w)] = 50w + 25.
f[s(w)] = (50 x 30) + 25.
f[s(w)] = 1525 flowers.
Therefore the composite function is f[s(w)] = 50w + 25. unit will be flowers and the number of flowers in 30 weeks will be 1525.
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I paid $8000 to burrow $50000 for 2 years. What was the rate of simple interest charged?
[make brainliest if got correct and 20pts]
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]
please help meeeee will mark them brain
from biggest to smallest
Answers
0.83 (5/6), 0.77 (7/9), 0.75 (3/4), 0.66 (2/3), 0.583 (7/12), 0.5 (1/2).
can you please help me with this two questions
Answers
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
Question 2
ΔABC and ΔCDA are congruent because:
they are both right trianglesthey share one side (AC)their hypotenuse are parallel (marked by the arrows)This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
Question 3
The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
If x = -3, then x 2 - 7x + 10 equals
37
40
22
Answers
40
Step-by-step explanation:
[tex]{ \red{ \tt{given \: }}} \: :- \: { \green{ \tt{x = - 3}}}[/tex]
Then, Substitute the value of "x" in this below equation..
[tex]{ \orange{ \tt{ {x}^{2} - 7x + 10}}}[/tex]
[tex]{ \orange{ \tt{ {( - 3)}^{2} - 7( - 3) + 10}}}[/tex]
[tex]{ \orange{ \tt{9}}} \: + \: { \orange{ \tt{21}}} \: + \: { \orange{ \tt{10}}}[/tex]
[tex] = { \orange{ \tt{40}}}[/tex]
which equation has the correct sign on the product
Answers
The equation which has the correct sign on the product is 27(-5) = -135
Sign of product- × - = +
- × + = -
+ × - = -
+ × + = +
Given equations:
27(-5) = -135
(-4)(-4) = -16
(-61) (3) = 183
22 × 4 = -88
Correct equation:
27(-5) = -135
(-4)(-4) = 16
(-61) (3) = -183
22 × 4 = 88
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Factor out the GCF from the given polynomial. 38x-8
Answers
Answer:
2(19x - 1)
Step-by-step explanation:
The GCF of 38 and 8 is 2 :
Now we take a common factor of 2 :
2(19x - 1)
Hope this helped and have a good day
Answer:
2(19x-4)
The gcf of 38 and 8 is 2 so factor it out.
Alejandro and Emila ordered a pizza. Alejandro at 1/3 of the pizza and Emila ate 2/5 of the pizza. How much did they eat together? Was there any pizza left? How much?
Answers
Answer: [tex]\frac{4}{15}[/tex] of the pizza was left
Step-by-step explanation:
lets first get the denominators the same..
[tex]\frac{1}{3} = \frac{5}{15}[/tex]
[tex]\frac{2}{5} = \frac{6}{15}[/tex]
To find the total pizza eaten we add these two fractions
[tex]\frac{5}{15} +\frac{6}{15} =\frac{11}{15}[/tex]
we can think of [tex]\frac{15}{15}[/tex] as 1 pizza because it simplifies to 1
[tex]\frac{15}{15} -\frac{11}{15} =\frac{4}{15}[/tex]
Therefore, [tex]\frac{4}{15}[/tex] of the pizza was left
Answer:Amount left=4/15
Step-by-step explanation:
The solution is in the image
Graph the system of inequalities:
-x + 2y - 4 <0
3x + 4y + 420
Answers
Step-by-step explanation:
draw the graph then use the graph to answer the following questions
im really not sure with my answer, please tell which is the correct choice.
Answers
Answer:
the orange one
Step-by-step explanation:
(10 + 10) : (5-3) =
20 : 2 =
10
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answers
The ratio of the lengths of and is 1: 1
PQ parallel to RS
PR and PS; perpendicular to PQ and RS.
What are the perpendicular lines?
Perpendicular lines are lines that intersect at a 90 degrees angle. Parallel lines are lines that are always the same distance apart.
FOR parallel lines, the perpendicular line joining then is always the same; here the 4 angles formed are all 90°
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Your answer should be an expanded polynomial in standard form.
(7a³-2a-2) + (-5a + 3) =
Answers
Answer:
7a^3-7a+1
Step-by-step explanation:
(7a³-2a-2) + (-5a + 3) =
Combine like terms
7a^3-2a-5a-2+3
7a^3-7a+1
What is the area of the parallelogram?
Answers
Answer:
Area = 120 in²Step-by-step explanation:
follow the formula in the picture
Area = b * h
Area = 15 * 8
Area = 120 in²
Determine the length of side QS.
A) 1.9
B) 3.4
C) 2.4
D) 5.7
Answers
square root 3.4 = 1.84
Answer = A-1.9
Answer: C) 2.4
Given one opposite angle, two known sides and one missing side.
Hence use cosine rule:
[tex]\sf c = \sqrt{a^2 + b^2- 2ab \ cos\theta}[/tex]
insert values
[tex]\sf c = \sqrt{1.2^2 + 1.4^2- 2(1.2)(1.4) \ cos(134)}[/tex]
simplify
[tex]\sf c = 2.3945 \quad \approx \quad 2.4[/tex]
find the area of the shaded regions. give your answer as a completely simplified exact value in terms of π
20 POINTS!!!
WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
V=r^2π => 36π·3/4 = 27π
Help please! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC.
(file is posted below)
Answers
The measure of BD and BC are 7 and 7√2 respectively
Triangular altitude theoremA triangle is a shape with 3 sides and angles.
According to the theorem
CD/BD = BD/DA
From the given figure
CD = DA = 14/2
CD = DA = 7
Substitute
7/BD = BD/7
BD² = 7²
BD² = 49
BD = 7
Determine the measure of BC
sin 45 = BD/BC
sin45 = 7/BC
BC = 7/sin45
BC = 7√2
Hence the measure of BD and BC are 7 and 7√2 respectively
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How to find the average collection period
Answers
Answer:
dividing a company's yearly accounts receivable balance by its yearly total net sales