The area of triangle BMN is 124.7 square centimeter.
What are similar triangles?Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.
Analysis:
AB = AC = BC = 50cm
AH = AC/2 = 50/2 = 25cm
From Δ ABH, using Pythagoras theorem to find BH.
[tex](BH)^{2}[/tex] = [tex](AB)^{2}[/tex] - [tex](AH)^{2}[/tex]
[tex](BH)^{2}[/tex] = [tex]50^{2}[/tex] - [tex]25^{2}[/tex]
[tex](BH)^{2}[/tex] = 2500 - 625
[tex](BH)^{2}[/tex] = 1875
BH = [tex]\sqrt{1875}[/tex] = 43.3cm
ΔBMN and BHC are similar,
so, BM/BH = MN/HC
BM/43.3 = 12/25
25BM = 12 X 43.3
BM = 519.6/25 = 20.78cm
Area of ΔBMN
= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter
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Come up with two examples of ratio relationships that are interesting to you.
In mathematics a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
Answer:
1:3 is an example and for every two boy there are 5 girls is another example
Edited: I go out Five times as much as My sister does. My sister goes out only 3 times. Which is 15:1
I see 5 blue cars for every 6 red cars. Which is 5:6
Ratio is always represented in terms of ':' like a:b
Examples
#1
Sam has 2 apples Jane has 4 applesThe ratio of apples is 2:4 or 1:2
#2
dummy stars present at your home =10Stars present in Big dipper =7The ratio is 10:7
An italian restaurant receive a shipment of 86 veal cutlet.if it takes to make a dish,how many cutlet will the restaurant have left over after making as many dishes as possible?
Answer:
They have none left over and they can make 43 dishes
Step-by-step explanation:
which 2 number have the mean of 10 and range of 4
Answer:
12 and 8
Step-by-step explanation:
→ Set up two equations
x - y = 4
[tex]\frac{x+y}{2} =10 \\ \\x + y = 20[/tex]
→ Add the 2 equations together
2x = 24
→ Solve for x
x = 12
→ Substitute into original equation
12 - y = 4
→ Solve
y = 8
What QUANTITY does 25.0 m represent?
length
millimeters
meters
milliliters
Answer:
Step-by-step explanation:
m represents the meters.
P is a rectangle with a length of 40 cm and a width of x cm q is a rectangle with a width of y cm the length of q is 25% more than the length of p the area of q is 10% less than the area of p work out the ratio of x:y
In rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
The area of a rectangle is the product of its length and its width.
In the question, we are given two rectangles:-
Rectangle P:
length = 40 cm,
width = x cm,
Thus, the area = length * width = 40x.
Rectangle Q:
length = 25% more than the length of P = 40 + 25% of 40 = 40 + 0.25*40 = 40 + 10 = 50 cm.
width = y cm,
Thus, the area = length * width = 50y.
Now, we are given that, the area of rectangle Q is 10% less than the area of rectangle P.
Thus, we can write that,
Area of rectangle Q = Area of rectangle P - 10% of the area of rectangle P,
or, 50y = 40x - 10% of 40x,
or, 50y = 40x - 0.10*40x,
or, 50y = 40x - 4x,
or, 50y = 36x,
or, y = 36x/50.
We are asked to find the ratio of x:y = x/y.
Substituting y = 36x/50, we get,
x/y = x/(36x/50) = 50x/36x = 25/18.
Thus, the ratio x:y = 25:18.
Thus, in rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
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If n(A) equals 100 and n(B) is equals to 120 and A is the subset of B, find the value of an n(A union B)
Answer:
200
Step-by-step explanation:
Solution,
Given,
n(A)=100
n(B)=120
A⊂B
n(A∩B)=20
n(A∪B)=n(A)+n(B)-n(A∩B)
n(A∪B)=100+120-20
n(A∪B)=200
n(A union B) is equal to the number of elements in set B, which is 120.
How to find n(A union B)If A is a subset of B, it means that every element in set A is also an element of set B.
In this case, n(A) represents the number of elements in set A, which is 100, and n(B) represents the number of elements in set B, which is 120.
To find the value of n(A union B) (the number of elements in the union of sets A and B), we need to consider that the union of two sets includes all the elements that are in either set A or set B, or both.
Since A is a subset of B, all the elements in set A are already included in set B. Therefore, the union of sets A and B will be equal to set B itself.
Thus, n(A union B) is equal to the number of elements in set B, which is 120.
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Ten out of 50 participants scored between 65 and 75 on a test. What is the relative frequency of the class interval 65-75
The relative frequency of the class interval 65-75 is .20.
What is relative frequency?The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else.
Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.
Given that: 50 participants scored between 65 and 75 on a test.
Hence,
The relative frequency of the class interval 65-75 = 75 - 65 = 20
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What 3D shape does this make? I think it's a cube but the only options are rectangular prism, rectangular pyramid, triangular prism, or no shape. Please help!
Answer:
the answer would be no shape.
Step-by-step explanation:
imagine you have the paper in your hands, if you start from the left you would have to fold the paper 3 times, then when it comes to the last 2 squares, you wouldnt be able to close the cube. hope this helps
Answer:
an open cube
Step-by-step explanation:
your welcome
An 11 3/8-inch wide board can be cut into how many strips of width 5/8 inch, if each cut takes 1/8 inch of the width? (Must the answer be a whole
number?)
Answer:
15.
Step-by-step explanation:
Width of the strip + cut = 5/8 + 1/8 = 3/4.
11 3/8 / 3/4
= 91/8 / 3/4
= 91/8 * 4/3
= 91/6
= 15 1/6
So the answer is 15
Find the area of the trapezoid
Answer:
294.84 ft²
Step-by-step explanation:
A = (B + b)h/2
A = (28.5 ft + 18.3 ft)(12.6 ft)/2
A = 294.84 ft²
Answer: 294.84 ft^2
Step-by-step explanation:
Area of trapezoid=((a+b)/2)*h
here
a=28.5 ft
b=18.3 ft
h=12.7 ft
Area=((28.5+18.3)/2)*(12.7)
Area=294.84 ft^2
For the following exercises, determine whether the functions are even, odd, or neither.
19. Solve |2x − 3 | = 17.
Answer:
The solutions of the equation |2 x-3|=17
are x=10
and x=-7
Step-by-step explanation:
Given equations is |2 x-3|=17.
It is required to find out the values of x satisfying the given equation.
To find it out, use the fact that the solution of this type of equation is 2x-3=17.
Or 2x-3=-17 and simplify the equations using simple mathematical operations.
Step 1 of 2
Solve the equation 2x-3=17,
Add 3 on both sides of the equation 2x-3=17,
2x-3+3=17+3
2x=20
Divide by 2 on both sides of the equation 2x=20,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{20}{2} \\&x=10\end{aligned}$$[/tex]
Step 2 of 2
Solve the equation 2x-3=-17,
Add 3 on both sides of the equation 2x-3=-17,
[tex]$2 x-3+3=-17+3$\\ $2 x=-14$[/tex]
Divide by 2 on both sides of the equation 2x=-14,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$[/tex]
Could use some Geometry help
I am not 100% sure but I think it is 85 degrees
DO NOT take my word for it
Step-by-step explanation:
I'm not sure but I think it is 75 degree
Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.
(, )
The location of the fountain based on the information given is (-1, 0.5).
How to illustrate the location?From the graph, the coordinates are (4, 2) and (-4, -2).
The ratio is given as 5:3.
The coordinates of the fountain will be:
[(5 × -4 + 3 × 4)/(5 + 3), (5 × -3 + 3 × 2)/(5 + 3)]
= (-1, -0.5)
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Mary wants to fence in a rectangular run for her dogs. She has decided that the run will be 5 yards wide. A rectangle with a width of 5 yards and height of x. Which statement best describes the possible lengths of the run if she can use no more than 40 yards of fencing? at most 8 yards at most 15 yards more than 8 yards more than 15 yards Mark this and return
The length of the run is at most 15 yards
How to determine the true statement?The given parameters are:
Width = 5 yards
Height = x
Perimeter = Not more than 40 yards
The perimeter is calculated as:
P = 2 *(Width + Height)
So, we have:
2 *(5 + x) ≤40
Divide by 2
5 + x ≤ 20
Subtract 5 from both sides
x ≤ 15
This implies that the length of the run is at most 15 yards
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Miguel's coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $ per pound, and Type B coffee costs $ per pound. This month's blend used three times as many pounds of Type B coffee as Type A, for a total cost of $. How many pounds of Type A coffee were used
The amount of Type A coffee that was used is 40 pounds.
From the given information;
Type A coffee costs Miguel $5.95 per pound
Type B coffee costs $4.65 per pound.
For this month, the equation can be expressed as:
A + 3A
Thus;
5.95A + 3(4.65)A = 796.00
5.95A +13.95A = 796.00
19.9A = 796.00
A = 796.00/19.9
A = 40
Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.
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Use the following information to answer the question.
Triangle ABC has side lengths AB=16, BC=13, and AC=7.
Triangle DEF has side lengths DE=4, EF=3.25, and DF=1.75.
Janna needs to prove △ABC∼△DEF.
Which methods can she use to help her prove the triangles are similar by the SSS Similarity Theorem?
Select all that apply.
(The choices are in the image)
For Janna to prove that △ABC∼△DEF by the SSS similarity theorem, she will use: B. DE/AB = EF/BC = DF/AC = 1/4.
What is the SSS Similarity Theorem?According to the SSS similarity theorem, if the ratio of the corresponding sides of two triangles are equal, then both triangles are similar.
The ratio of the corresponding sides of the triangles given are:
DE/AB = 4/16 = 1/4
EF/BC = 3.25/13 = 1/4
DF/AC = 1.75/7 = 1/4
Therefore, what Janna needs is:
B. DE/AB = EF/BC = DF/AC = 1/4
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Question 5 of 10
What is the first step in solving a quadratic equation of the form given below?
(ax+ b)² = c
O A. Divide both sides by c
OB. Factor out a common factor
OC. Use the zero product rule
OD. Take the square root of both sides
Answer:
D
Step-by-step explanation:
(ax + b)² = c
step 1 : take square root of both sides
ax + b = ± [tex]\sqrt{c}[/tex]
step 2 : subtract b from both sides
ax = - b ± [tex]\sqrt{c}[/tex]
step 3 : divide both sides by a
x = - [tex]\frac{b}{a}[/tex] ± [tex]\frac{\sqrt{c} }{a}[/tex]
Answer:
D. Take the square root of both sides
Step-by-step explanation:
Given quadratic equation:
[tex](ax+b)^2=c[/tex]
To solve, square root both sides:
[tex]\implies \sqrt{(ax+b)^2}=\sqrt{c}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{n^2}=n, \quad \textsf{assuming }n \geq 0:[/tex]
[tex]\implies ax+b=\pm\sqrt{c}[/tex]
Subtract b from both sides:
[tex]\implies ax=-b\pm\sqrt{c}[/tex]
Divide both sides by a:
[tex]\implies x=\dfrac{-b\pm\sqrt{c}}{a}, \quad a\neq 0[/tex]
What's the equation of a line that passes through points (–1, –5) and (1, 3)? Question 20 options: y=-2x
y=1/4x-2
y=-x+4
y=4x-1
Which model represents the factors of 4x^2-9
The model (x+a)(x-a) will represents the factors of 4x²-9 as (2x+3)(2x-3).
What are the quadratic equations in one variable completing the squares method?The "completing the squares" method aims to construct a quadratic equation of the form where the x variable is entirely covered by a single squared term, which is the square of a linear expression in x, as the name suggests.
The quadratic equation can resemble this:
x²-a² = (x+a)(x-a)
Given equation;
⇒4x²-9
⇒(2x)²-3²
The equation can be modeled as;
(2x+3)(2x-3)
Hence the model (x+a)(x-b) will represents the factors of 4x²-9 as (2x+3)(2x-3).
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How do I solve quadratic equations for example,h(t) = – 0.07t2 + 0.007t + 5
Answer:
x ≈ -8.402, 8.502
Step-by-step explanation:
The usual methods of solving quadratic equations apply to this one. Any of them can be used: graphing, factoring, completing the square, quadratic formula.
SolutionOften, when the coefficients are non-integers and have no obvious relationship to each other, the most convenient method of solution is the quadratic formula. It tells you the solution to ax²+bx+c=0 is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Your equation has the coefficients, a = -0.07, b = 0.007, c = 5, so the solutions are ...
[tex]x=\dfrac{-0.007\pm\sqrt{0.007^2-4(-0.07)(5)}}{2(-0.07)}=\dfrac{-0.007\pm\sqrt{1.400049}}{-0.14}\\\\x=0.05\pm\sqrt{\dfrac{200007}{2800}}=0.05\pm\sqrt{71.4310\overline{714285}}\\\\\boxed{x\approx\{-8.40169,\,8.50169\}}[/tex]
Answer:
[tex]t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]
Step-by-step explanation:
Quadratic equations are in the form [tex]ax^2+bx+c=0[/tex], where [tex]a\neq 0[/tex].
There are three basic methods to solve quadratic equations algebraically:
FactoringCompleting the SquareQuadratic FormulaGiven quadratic equation:
[tex]h(t)=-0.07t^2+0.007t+5[/tex]
Method 1 - Factoring
If the trinomial is able to be easily factored, set the equation equal to zero and factor. Set each factor equal to zero and solve.
As the given example is not easily factored, factoring is not the best method to use on this occasion.
Method 2 - Completing the Square
If the quadratic expression is not able to be easily factored, try completing the square.
Divide all terms by [tex]a[/tex] (-0.07):
[tex]\implies t^2-\dfrac{1}{10}t-\dfrac{500}{7}=0[/tex]
Move the constant to the right side:
[tex]\implies t^2-\dfrac{1}{10}t=\dfrac{500}{7}[/tex]
Add the square of half the coefficient of t to both sides:
[tex]\implies t^2-\dfrac{1}{10}t+\left(-\dfrac{1}{20}\right)^2=\dfrac{500}{7}+\left(-\dfrac{1}{20}\right)^2[/tex]
[tex]\implies t^2-\dfrac{1}{10}t+\dfrac{1}{400}=\dfrac{200007}{2800}[/tex]
Factor the perfect trinomial:
[tex]\implies \left(t-\dfrac{1}{20}\right)^2=\dfrac{200007}{2800}[/tex]
Square root both sides:
[tex]\implies t-\dfrac{1}{20}=\pm\sqrt{\dfrac{200007}{2800}[/tex]
Add 1/20 to both sides:
[tex]\implies t=\dfrac{1}{20}\pm\sqrt{\dfrac{200007}{2800}[/tex]
As decimals to 2 decimal places:
[tex]\implies t=8.50, -8.40\:\:\sf(2 \:d.p.)[/tex]
Method 3 - Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
This can be used to find both real and imaginary or complex solutions.
Identity the variables:
[tex]a=-0.07, \quad b=0.007, \quad c=5[/tex]
Substitute the values into the quadratic formula and solve for t:
[tex]\implies t=\dfrac{-0.007 \pm \sqrt{0.007^2-4(-0.07)(5)} }{2(-0.07)}[/tex]
[tex]\implies t=\dfrac{-0.007 \pm \sqrt{1.400049}}{-0.14}[/tex]
[tex]\implies t=\dfrac{0.007 \pm \sqrt{1.400049}}{0.14}[/tex]
[tex]\implies t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]
Finally, a non-algebraic method of solving a quadratic equation is by graphing using a graphical calculator (see attached). The solutions are the points at which the curve intercepts the x-axis.
y = 4x - 10
y = 2
What is the solution to the system of equations?
(3, 2)
(2, 3)
(-2, 2)
(2,-2)
Answer:
x= 3
y=2
Step-by-step explanation:
Let's solve your equation step-by-step.
2=4x−10
Step 1: Flip the equation.
4x−10=2
Step 2: Add 10 to both sides.
4x−10+10=2+10
4x=12
Step 3: Divide both sides by 4.
4x/4=12/4
x=3
Answer:
since y=2 substitute y into y=4x-10
2=4x-10
2+10=4x
12=4x
Divide both sides by 4
12/4=4x/4
x=3
Therefore the answer is (2,3)
Checky= 4x-10
2= 4×3-10
2= 12-10
2=2
Triangles G H L and K H J are connected at point H. Angles Angles L G H and H K J are congruent. Sides G H and H K are congruent.
Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
SSS
ASA
SAS
AAS
The congruence theorem that can be used is: B. ASA
What is the ASA Congruence Theorem?If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.
Therefore, triangles GHL and KHL in the image given are congruent triangles by the ASA congruence theorem.
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Answer: Option 2 or B. ASA
Step-by-step explanation: Trust me!
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone! :)
Question 5
Sam wants to build a toy box in the shape of a rectangular prism that will
hold 36 cubic feet. If the height needs to be 1 foot less than the width and
the length is twice the width, find the height of the toy box.
Considering the volume of the given rectangular prism, the height is of 5.03 feet.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, we have that:
h = w - 1 -> w = h + 1.l = 2w = 2(h + 1) = 2h + 2.The volume is of 365 cubic feet, hence:
lwh = 365
(2h + 2)(h + 1)h = 365
(2h² + 4h + 2)h - 365 = 0
2h³ + 4h² + 2h - 365 = 0.
Using a cubic equation calculator, the height is of h = 5.03 feet.
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the table shows a proportional relationship between the distance a snall travels and the time it takes what is the proportional constant in centimeters per minute
The constant of proportionality in centimeters per minute is: 5.5.
How to Find the Constant of Proportionality?To find the constant of proportionality of the table shown in the image attached below, use one pair of points, (12, 66).
Constant of proportionality, k = y/x, therefore, the proportional constant in centimeters per minute would be:
k = 66/12 = 5.5 cm per min.
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Please help ill give whoever answers the best the brainliest answer :))
Answer:
Step 3 is wrong and the answer should be 576
Step-by-step explanation:
Step 1 and step 2 are correct
Step 2: 4 × 12^2
You don't multiply 12 by 4, you first complete the exponent since, in PEMDAS, Exponent is before Multiplying.
Step 3 should be: 4 × (12×12)
= 4 × 144
= 576
The price of a roll of fabric is reduced by 20%
to £60.
What was its original price?
The original price is £75
How to determine the original price?Let the original price be x.
The reduced price is given as:
Reduced =60
So, we have:
Reduced = Original price * (1 - discount)
This gives
x * (1- 20%) = 60
Evaluate the difference
x * 0.8 = 60
Divide by 0.8
x = 75
Hence, the original price is £75
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Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?
Verbal
4. Are one-to-one functions either always increasing or
always decreasing? Why or why not?
Answer:
If a function is continuous and one - to - one then it is either always increasing or always decreasing.
Step-by-step explanation:
An easy way to see this on a graph is to draw a horizontal line through the graph . If the line only cuts the curve once then the function is one - to - one.
Answer:
If a one-to-one function is not continuous, it is sometimes increasing or decreasing. If a one-one function is continuous, it is always increasing or always decreasing.
For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]
This function is one-to-one and it is not always increasing or decreasing.
Step-by-step explanation:
A statement that are one-to-one functions either always increasing or always decreasing is given.
It is required to explain the given condition.
To explain the given condition, consider a continuous and a not continuous function then explain about the one-to-one function.
If a one-to-one function is not continuous, it is sometimes increasing or decreasing.
For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]
This function is one-to-one and it is not always increasing or decreasing.
If a one-one function is continuous, it is always increasing or always decreasing.
For example, if f(x)=x-3. It is a continuous function and it reaches a minimum value at some values of x and it then keeps increasing.
There will be the same output value for different input values. It does not pass the horizontal line test and so it is not a one-to-one function.
Which pair of equations generates graphs with the same vertex?
The pair of equations that generates graphs with the same vertex is
B) y = –4x2 and y = 4x2
What is vertex ?A vertex serves as angular point that allows the meeting of two or more lines .
To express a quadratic equation we can use :
[tex][y = a(x - h) ^{2} + k][/tex]
where vertex is (-h , k)
If we look at first option, the the vertices are [tex](-4 , 0) and (4 , 0)[/tex]
Then the second option, graphs' vertices are the same thing which is ,[tex](0 , 0).[/tex]
Therefore, the pair of equations that generates graphs with the same vertex is B) y = –4x2 and y = 4x2
CHECK THE COMPLETE QUESTION BELOW:
Which pair of equations generates graphs with the same vertex?
A) y = –(x + 4)2 and y = (x – 4)2
B) y = –4x2 and y = 4x2
C) y = –x2 – 4 and y = x2 + 4
D) y = (x – 4)2 and y = x2 + 4
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GUYS HELP QUICK!!!!
Ella completed the following work to test the equivalence of two expressions.
2 f + 2.6. 2 (0) + 2.6. 0 + 2.6. 2.6. 3 f + 2.6. 3 (0) + 2.6. 0 + 2.6. 2.6.
Which is true about the expressions?
The expressions are equivalent because Ella got different results when she substituted zero for f.
The expressions are equivalent because Ella got the same result when she substituted zero for f.
The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
The expressions are not equivalent, even though Ella got the same result when she substituted zero for f. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
Ella completed the following work to test the equivalence of two expressions.
First expression, Second expression
⇒ 2f + 2.6 ⇒ 3f + 2.6
⇒ 2(0) + 2.6 ⇒ 3 (0) + 2.6
⇒ 0 + 2.6 ⇒ 0 + 2.6.
⇒ 2.6 ⇒ 2.6
The expressions are not equivalent, even though Ella got the same result when she substituted zero for f.
Then the correct option is C.
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