The correct statements of the triangle are; AC = 5 cm; BA = 4 cm; The perimeter of triangle ABC is 12 cm.
What are the correct statements of the Triangles?As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.
Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.
Using Pythagoras theorem in ΔACF :
AC² = FA² + CF²
Thus;
AC² = 3² + 4²
AC = √25
AC = 5
Using Pythagoras theorem in ΔDAB, we have;
BA = √(5² - 3²)
BA = 4 cm
Using Pythagoras Theorem, we have;
CB = √(5² - 4²)
CB = 3 cm
Perimeter of ΔABC = Side AB + Side CB+ Side AC
Perimeter of ΔABC = 4 + 3 + 5
Perimeter of ΔABC = 12 cm
Area of ΔABC = (1/2) * 4 * 3 = 6 cm²
Area of ΔDEF = (1/2) * 8 * 6 = 24 cm²
Area of ΔABC = (6/24) * Area of ΔDEF
Area of ΔABC = (1/4) * Area of ΔDEF
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Given the information provided, we can determine the lengths of the sides of triangle ABC and its perimeter and area.
Explanation:Given that points A, B, and C are midpoints of the sides of right triangle DEF, we can determine the lengths of the sides using the information provided.
BC = 6 cmAC = 5 cmBA = 4 cmDE = 10 cmFD = 6 cmFE = 8 cmTo find the perimeter of triangle ABC, we sum the lengths of all three sides: AB + BC + CA. Substituting the given lengths, AB = BA = 4 cm, BC = 6 cm, and CA = AC = 5 cm, the perimeter is 4 cm + 6 cm + 5 cm = 15 cm.
The area of triangle ABC can be determined using the formula A = bh, where b is the base and h is the height. Triangle ABC and triangle DEF are similar triangles, so their areas are proportional. Since point A is the midpoint of DE, half the base of triangle DEF is equal to the base of triangle ABC. Substituting the given length of DE = 10 cm, the base of triangle ABC is 10 cm / 2 = 5 cm. The height of triangle ABC is equal to the length of AC = 5 cm. Therefore, the area of triangle ABC is A = 5 cm * 5 cm = 25 cm².
-3 x f(-8) +7 x g(2)
The composite function -3 x f(-8) +7 x g(2) has a value of 53
How to evaluate the composite function
From the question, we have the following parameters that can be used in our computation:
f(x) = 2x + 3 and g(x) = x
Calculating f(-8) and g(2), we have
f(-8) = 2 * -8 + 3 and g(2) = 2
Evaluate
f(-8) = -13 and g(2) = 2
Using the above as a guide, we have the following:
-3 x f(-8) +7 x g(2) = -3 * -13 + 7 * 2
Evaluate
-3 x f(-8) +7 x g(2) = 53
Hence, the composite function has a value of 53
Question
Evaluate the expression -3 x f(-8) +7 x g(2) if f(x) = 2x + 3 and g(x) = x
how many ounces of a 12 alcohol solution must be mixed with 6 ounces of a 20% alcohol solution to make a 16% alcohol solution?
Answer:
6 ounces
Step-by-step explanation:
So set your equation up as
12(x)+20(6)=16(x+6)
You set it up this way because with the first number you know the percet but not the ounces so your ounces would be x. The second set you know percet and ounces (the percent will alway go outside the parenthesis). then the last number is waht it wil equal; again we know the percent but not the product. We put x+6 in the parenthesis because you are adding the ounces your don't know(x) wiht the ones you do (6).
To solve distribute
12x+120=16x+96
Now all you have to do is solve for x. Subtract the 96 over then subtract the 12x over, so it would look like this.
12x+120=16x+96
-96 -96
12x+24=16x
-12x -12x
24=4x Now simply divide by 4 and you get 6=x
There should be 6 ounces mixed in order to get the required solution.
Let the number of ounces be represented by x.
Based on the equation, the equation to use will be:
12(x) + 20(6) = 16(x + 6)
Expand the equation
12x + 120 = 16x + 96
Collect like terms
16x - 12x = 120 - 96
4x = 24
Divide both side by 4
4x/4 = 24/4
x = 6
Therefore, the number of ounces will be 6 ounces.
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Can anyone please answer this question !!!
Max wants to paint a wall that measures 2.1 m by 5.2 m. A tin of paint states that it will cover 3.5 m?. If the tin contains exactly 0.5 litres of paint, and all other measurements are correct to 1 d.p., find the maximum volume of paint needed to paint the wall.
Final answer:
The maximum volume of paint required is 2 liters.
Explanation:
To calculate the maximum volume of paint needed to paint the wall, we need to first determine the area of the wall. The wall measures 2.1 m by 5.2 m, so the area is:
Area = Length × Width = 2.1 m × 5.2 m = 10.92 m²
Now, we know that one tin of paint covers 3.5 m² and contains 0.5 liters of paint. To find the number of tins needed, we divide the total area by the area covered by one tin:
Tins needed = Total area / Area per tin = 10.92 m² / 3.5 m²
Tins needed = 3.12
Since we cannot buy a fraction of a tin, we need to round up to the nearest whole number, which means Max needs 4 tins of paint. To find the total volume of paint, we multiply the number of tins by the volume of one tin:
Total volume = Tins needed × Volume per tin = 4 × 0.5 L = 2 L
Therefore, the maximum volume of paint Max will need is 2 liters.
How many unique triangles can be drawn with given side lengths of 8 inches, 10.3 inches, and 13 inches?
Answer:
1
Step-by-step explanation:
Three side lengths uniquely specify one triangle.
__
Additional comment
All triangles formed with the same three specific side lengths are considered to be congruent. However, the sides can be arranged smallest-to-largest in CW or CCW order. If the triangle is scalene, the different ordering will result in congruent triangles that will not overlay one another.
Only one unique triangle can be formed
Triangle
A triangle is a three-sided polygon with three vertices and three edges. It is a fundamental geometric shape.
How many unique triangle with given side lengths of 8 inches, 10.3 inches, and 13 inches?
only one unique triangle can be formed with sides length of 8 inches, 10.3 inches, and 13 inches
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Use the quadratic formula to determine the solutions to the quadratic equation. Write your answers as decimals, and round to the nearest hundredth (2 decimal spots).
6x2+4x−3=0
Answer:
x1 = 0.45 and x2 = -1.12
Step-by-step explanation:
To solve the equation 6x2+4x−3=0 using the quadratic formula, we use the following equation:
x = [-b ± √(b2 - 4ac)] / 2a
Where a, b and c are coefficients of the quadratic equantion (in our case, a = 6, b = 4 and c = -3)
So we have that:
x1 = [-4 + √(16 + 72)] / 12 = (-4 + 9.3808) / 12 = 0.4484
x2 = [-4 - √(16 + 72)] / 12 = (-4 - 9.3808) / 12 = -1.1151
Rounding to nearest hundredth, we have x1 = 0.45 and x2 = -1.12
find the measure of angle b
Answer:
36 degrees
Step-by-step explanation:
The radius of a circle is 2.7 feet. Find the diameter
Answer:
5.4 ft.
Step-by-step explanation:
Radius is half of the diameter, so multiply 2.7 by 2 to get the full distance, and you get 5.4 ft.
Answer:5.4
Step-by-step explanation: 2.7x2= 5.4
Radius is just half of the diameter so when given radius X2 when given diameter divide by 2
what is the coefficient for x2 -5x+6
The coefficient for x² in the equation x² - 5x + 6 is 1, as it is the implied coefficient when no numerical coefficient is written before a term in a polynomial.
Explanation:The coefficient for x2 in the polynomial equation x2 - 5x + 6 is implied to be 1. When a term in a polynomial has no numerical coefficient written, it is understood that the coefficient is 1. In any polynomial equation of the form ax2 + bx + c = 0, the coefficient of x2 is represented by a. In the given expression, since there is no number in front of x2, a is 1. Therefore, the coefficient of x2 in the equation x2 - 5x + 6 is 1.
2/3 × 6 + 2/3 × n for n = 2
Answer:
16/3 or 5 1/3
Step-by-step explanation:
Plugging in 2 for n, you get(2/3*6)+(2/3*2)=4+4/3=16/3= 5 1/3. Hope this helps!
Please look at the image , they all need to be factored using DOTS moi
Hope this will help u....:)
Look at the attached picture ⤴⤴
with process Plz！！Thank you very much
Step-by-step explanation:
In circle with centre O.
[tex]OA \cong OB.. (Radii\: of \:same \:circle) \\
\therefore m\angle OAB = m\angle OBA =28°\\
(m \angle 's \:opposite \:to \:congruent \:sides \:\\are \:equal) [/tex]
[tex] m \angle AOB = 180°-(m\angle OAB + m\angle OBA)\\
\therefore\: m \angle AOB = 180°-(28° + 28°)\\
\therefore\: m \angle AOB = 180°-56°\\
\therefore\: m \angle AOB = 124°\\
m \angle ACB = \frac{1}{2} \times m \angle AOB[/tex]
[tex](m\angle\: formed\: on\: the \:circle \:\\is\: half\: the\:\angle\: formed\: at\: the \:center\: \\of \:the \:circle)[/tex]
[tex] \therefore\: m \angle ACB = \frac{1}{2} \times 124°\\
\therefore\: m \angle ACB = 62°\\[/tex]
A circle with radius 3 has a sector with central angle 1/9 pi radians what is the area of the sector
Answer:
The area of the sector is [tex]\frac{\pi}{2}\ units^2[/tex]
Step-by-step explanation:
step 1
Find the area of complete circle
[tex]A=\pi r^2[/tex]
we have
[tex]r=3\ units[/tex]
substitute
[tex]A=\pi 3^2\\A=9\pi\ units^2[/tex]
step 2
Find the area of the sector
we know that
The area of complete circle subtends a central angle of 2π radians
so
using proportion
Find out the area of a sector by a central angle of 1/9 pi radians
[tex]\frac{9\pi}{2\pi}=\frac{x}{\frac{1}{9}\pi} \\\\x=9\pi(\frac{1}{9}\pi})/2\pi\\\\x=\frac{\pi}{2}\ units^2[/tex]
Simplify the expression below.
(6-3)(66)
Answer:
198
Step-by-step explanation:
(6-3) x 66 subtract
3x66 multiply
198
Write two polynomials with a difference of 2x2 + x + 3
Answer:
The two polynomial CAN be [tex]5x^4+5x^3+8x^2+x+6[/tex] and [tex]5x^4+5x^3+8x^2+2x+13[/tex].
Step-by-step explanation:
Step 1: Simplify the expression:
[tex]2*2 + x + 3[/tex]
[tex]4+x+3[/tex]
[tex]x+7[/tex]
Step 2: Think of a random polynomial:
[tex]5x^4+5x^3+8x^2+x+6[/tex]
Step 3: Either add your "random polynomial" by [tex]x+7[/tex] or subtract it.
I want to add it so...
[tex]5x^4+5x^3+8x^2+x+6+x+7[/tex]
= [tex]5x^4+5x^3+8x^2+2x+13[/tex]
Check by subtracting [tex]5x^4+5x^3+8x^2+x+6[/tex] and [tex]5x^4+5x^3+8x^2+2x+13[/tex].
[tex]5x^4+5x^3+8x^2+2x+13[/tex]
- [tex]5x^4+5x^3+8x^2+x+6[/tex]
_____________________
[tex]0x^4 - 0x^3 -0x^2 +x +7[/tex] or [tex]x+7[/tex]
What is the probability of spinning the spinner and the arrow landing on the number ‘1’ and then spinning it a second time and it landing on ‘2’ the second time?
Answer:
There isn't a picture, but i'm guessing they are on opposite ends. If so, it would be 50-50.
Step-by-step explanation:
no picture;;
Answer:
50-50
Step-by-step explanation:
What is 10b +19 when b= -2
Answer:
-1 i hope this helps! :)
Step-by-step explanation:
you are given both 10b + 19 and b = -2
lets plug in the value of b
10b(-2) + 19
multiply the 10b and the -2
-20b + 19
-20 + 19 = -1
-1
A graph titled Arnie's Airplane has time (minutes) on the x-axis and distance (miles) on the y-axis. A line goes through points (0, 0) and (2, 10). A 2-column table with 3 rows titled Bernie's Biplane. Column 1 is labeled Time (minutes) x with entries 3, 5, 8. Column 2 is labeled Distance (miles) y with entries 21, 35, 56.
Find each slope from the graph and table to compare the constant speeds of the two airplanes.
What is the constant speed (slope) of Arnie’s airplane?
What is the constant speed (slope) of Bernie’s biplane?
Who flew faster?
Answer:
its 5 7 bernie
Step-by-step explanatioi just did it
Answer:
5, 7, bernie
Step-by-step explanation:
I got it right
Describe two different ways to write 7/3 as a mixed number.
A basket contains apples and oranges in the ratio of 4:1. How many apples are there if the total amount of fruits is 40?
Answer:32
Step-by-step explanation:
u fist find the total ratio 4+1 =5then the ratio belonging to apple is four
so u divide 4 by 5 then multiply to the total no of fruit
and that will give u 32
A ratio shows us the number of times a number contains another number. The number of apples in the basket is 32.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Let the number of apples and oranges in the basket be represented by 4x and x respectively.
Given the total number of fruits in the basket is 40. Therefore, the sum of the number of fruits can be written as,
[tex]4x+x=40\\5x=40\\x=8[/tex]
The number of apples = 4x = 4(8) = 32
Hence, the number of apples in the basket is 32.
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-9x-6y=12 what’s there slope and y intercept
Answer: slope = -3/2
Y intercept = -2
Step-by-step explanation:
15. Sense or Nonsense
cense or Nonsense? Sam and Dave each solve the problem at
e right. Sam says the sum is 4 feet 18 inches. Dave says the sum
e 5 feet 6 inches. Whose answer makes sense? Whose answer is
nonsense? Explain.
Says shouldn’t Say 18 inches because that is 1 ft 6 inches
In ΔDEF, the measure of ∠F=90°, ED = 65, FE = 56, and DF = 33. What is the value of the cosine of ∠D to the nearest hundredth?
Answer:
[tex]cos(D)=0.51[/tex]
[tex]m\angle D=59.49^o[/tex]
Step-by-step explanation:
we know that
In the right triangle DEF
[tex]cos(D)=\frac{DF}{ED}[/tex] ---> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(D)=\frac{33}{65}=0.51[/tex]
using a calculator
[tex]m\angle D=cos^{-1}(\frac{33}{65})=59.49^o[/tex]
To find the value of the cosine of angle ∠D in triangle ΔDEF, use the cosine formula with the given side lengths which is 59.49 degrees.
Explanation:In the given triangle ΔDEF, the measure of angle ∠F is 90°. We are given the lengths of the sides DF, FE, and ED as 33, 56, and 65 units respectively. To find the value of the cosine of angle ∠D, we need to use the cosine formula:
cos(D) = (DF2 + DE2 - EF2) / (2 * DF * DE)
Substituting the known values, we have:
cos(D) = (332 + 652 - 562) / (2 * 33 * 65)
= 59.49
Simplifying this expression gives us the value of the cosine of angle ∠D.
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Anna maria read 40 pages in 60 minutes. What is her unit rate in pages per minute?
Answer:
1.5 pages per minute.
Step-by-step explanation:
Answer:
Anna Maria reads 0.66 (2/3) page per minute
Step-by-step explanation:
Unit rate (speed)=distance/time, so you would divide 40 by 60. that simplifies to 2/3, or .66
If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) in scientific notation.
Answer:
1.08 ⋅ 10 ^8 km
Step-by-step explanation:
Simplify by using Order of operations: 15/1+4 + 6+3/3
To simplify the expression 15/1+4 + 6+3/3, we perform the division operations first, followed by addition, which results in the simplified expression of 26.
To simplify the expression 15/1+4 + 6+3/3 using the order of operations, we must follow specific rules. The order of operations is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In the absence of parentheses and exponents in this expression, we'll focus on the multiplication/division and addition/subtraction.
First, let's look at the division and multiplication. Since there's no multiplication, we only need to perform the division operations, and we proceed from left to right:
15/1 = 15 (since any number divided by 1 is the number itself)3/3 = 1 (since any number divided by itself is 1)Now we are left with the addition operations:
15 + 4 + 6 + 1 = 26
Therefore, the simplified expression is 26. To generate accurate answers, always follow the order of operations diligently.
The simplified expression is [tex]\( 26 \).[/tex]
To simplify the expression using the order of operations (PEMDAS/BODMAS), we follow these steps:
1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
Given the expression [tex]\( \frac{15}{1} + 4 + 6 + \frac{3}{3} \),[/tex] let's simplify it step by step:
1. Solve the division: [tex]\( \frac{15}{1} = 15 \) and \( \frac{3}{3} = 1 \).[/tex]
2. Now, we have:[tex]\( 15 + 4 + 6 + 1 \).[/tex]
3. Perform addition from left to right: [tex]\( 15 + 4 = 19 \), \( 19 + 6 = 25 \), \( 25 + 1 = 26 \).[/tex]
Therefore, the simplified expression is [tex]\( 26 \).[/tex]
A soccer ball has a 35 cm diameter. what is the volume of the contents of the ?
Answer:
To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don't have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.
Step-by-step explanation:
To find the volume of a soccer ball,the formula is V=4/3 πr^3,where r is the radius and π=3.14. A regulation soccer ball has a radius of 35cm. find the volume of a soccer ball to the nearest cubic centimeter. This is just some to keep in mind.
All I need is the answer please
Answer:
80 dollar tip
Step-by-step explanation:
16 percent of 500=80
Answer: That would be $580.
Step-by-step explanation: The tip is equal to $80 itself self you add the original amount ($500) to the tip (16%=$80) the total will be $580.
Which are examples of Pythagorean Triples
A) 6, 8, 10
B) 8, 10, 12
C) 10, 16, 16
D) 12, 16, 20
E) 14, 18, 20
F) 15, 20, 25
check all the above !!
Answer:
It should be
A
F
D
Step-by-step explanation:
Just do A^2+B^2=C^2 and plug in what the three given numbers are, if A^2+B^2=C^2 and it comes out as correct meaning the sum of A and B is equal to C than boom you have a triple
Answer would be option(A){6, 8, 10}, (D) {12, 16, 20} and (F) {15, 20, 25} are examples of Pythagorean Triples
What is Pythagoras theorem?
Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.
{6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples where any 2 side the sum of the squares adds up to be equal the other side.
We can test this:
6²+ 8² = 10² ⇒ 100=100
12²+16²= 20² ⇒ 400=400
15²+ 20²= 25²⇒ 625=625
Hence, {6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples
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A city is planning to build a square-shaped playscape at a city park.
The table shows several values for A, the area of the playscape, in square feet, and f(A), the length, in feet, of one side of the playscape. The function represented is .
About how many square feet are in the playscape if the length of a side is 63 feet?
4,000
4,160
4,489
4,830
Answer:
4,000
Step-by-step explanation:
if p is 2% of k. What is 50% of k intems of P and k and if 10% of a number is 7. What is 80% of the number?
Answer:
a.p/100
b.56
Step-by-step explanation:
2% of p=k
2/100 ×p=k
2p/100=k
Cross multiply 2p=100k
P=100k/2
p=50k
Let's make k the subject of formula
k=p/50
So 50% of k in terms of p
50/100×k
And k=p/50
So let's substitute
50/100×p/50
P/100
Therefore 50%of k=p/100
Let the unknown number be x
10% of x is 7
10/100×x=7
10x/100=7
Cross multiply
10x=(100)(7)
10x=700
Divide both sides by 10
X=70
So 80% of 70
80/100×70
5600/100
=56
Therefore 80% of 70=56