The value of the legs of the triangle would be hypotenuse/√2.
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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use substitution to solve each system of equations
2. y= 4x+5
2x+y=17
6. 3x +4y= -3
x+2y= -1
8. -1=2x - y
8x-4y=-4
10. y= -4x + 11
3x + y=9
15. -5x+4y=20
10x-8y= -40
I think it's answer this .
Unit 1 geometry basics Homework 2
pls help! i’ll mark brainliest
The value of AB= 24 BD is congruent to BC. BD=BC
BD = 5x – 26, BC = 2x + 1, and AC = 43
How to find value of AB?From the diagram , AC=AB+BCTo find out , we need to find BC first . For that we have to find out xWE know that BD=BC, using that we solve for x5X-26=2X+1SUBSTRACT 2X3X-26=1ADD 263x=27x=9Now we plug in 9 for x and find out BCBC=2x+1BC=2(9)+1BC=19We know AC= 43AC=AB+BC43=AB+19subtract 19AB=24To learn more about find value of AB refers to:
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The first 5 terms of a certain sequence are 6. 12, 24, 48, and 96.
Which two statements about this sequence are true?
This is a geometric sequence.
This is an arithmetic sequence.
The function f(n)2(6)"
The function f(7) = 6(2)"
The function f(n) = 6 -6(n
represetits this sequence, where is a positive whole
represents this sequence, where is a positive whole r
1) represents this sequence, where n is a positive wh
Answer:
see explanation
Step-by-step explanation:
there is a common ratio between consecutive terms, that is
12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2
this indicates the sequence is geometric
the nth term of a geometric sequence is
f(n) = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 6 and r = 2 , then
f(n) = 6 [tex](2)^{n-1}[/tex]
A cereal box is designed to hold a volume of 4096 cubic centimetres of cereal.
What dimensions will minimize the cost of producing the box?
Answer:
Refer to the step-by-step
Step-by-step explanation:
To minimize the cost of producing the box, we would want the box to be a cube.
Where the volume, [tex]V=s^{3}[/tex], where s is the length of one side of the box.
We were given the value, [tex]V=4096 cm^{3}[/tex], plug this into the equation above so we can find the dimensions of the box...
[tex]4096=s^{3} = > s=\sqrt[3]{4096} = > s=16[/tex]
Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.
Please help me on this :/
Answer
8. b
9.C
10.a
11.a
12. c
13. b
brainliest pls <3
Put the letters into the correct order to make worlds. Then match them to the definitions
oiffce psorin hlostipa ctotgae fcatyor gtues-hsoue
1. A room or building where people work at desks……..
2. A small hotel that is not very expensive………
3. A building where people are sent if they have committed a crime……..
4. A building where people go if they ill……..
5. A building where people make things, often using machines………
6. A small attractive house in the country……….
*************
1. A: Excuse me, can you tell me (1) the way to how far for the station?
B: Yes, sure. (2) Take/Turn left at the traffic lights and you'll see the station (3) in front / by
front of you.
2. A: Excuse me, (4) is it far / can you direct to the museum?
B: No. Just go (5) straight off / straight on for about half a kilometre and the museum is
(6) on / at your right.
Answer:
Step-by-step explanation:
A DVD player had a $108. Price tags the store gave a 25% discount. What was the amount of the discount?
Answer:
$27
Step-by-step explanation:
If we know that %25 is equal to 1/4, or 0.25, then we can use an equation that look like this:
108 × 0.25 = 27
Therefore, the amount of the discount was $27
How can you solve for percentages?Solving for percentages can be tricky, and you may need help on trying to solve a problem including one. If you need to find a percentage of a number, the easiest way to do that is to convert the percentage into a fraction or decimal and multiply the total by that number.
For ex.
What is 15% of 60?
To do this, convert the percentage into a decimal.
15% converted into a decimal is 0.15.
Now multiply 60 by 0.15.
60 ÷ 0.15 = 9
So, the answer to this example would be 9.
Level 3: What is the sum of the polynomials?
(-7x2 – 3x4 – 5) + (-3x4 +3+9x²)
Answer:
2x^2-6x^4-2
Step-by-step explanation:
Answer:
Remove parentheses.
−7x²−3[tex]x^{4}[/tex]−5−3[tex]x^{4}[/tex]+3+9x²
Add −7x² and 9x² .
2x²−3[tex]x^{4}[/tex]−5−3[tex]x^{4}[/tex]+3
Subtract 3[tex]x^{4}[/tex] from −3[tex]x^{4}[/tex].
2x²−6[tex]x^{4}[/tex]−5+3
Add −5 and 3.
2x²−6[tex]x^{4}[/tex]−2
Step-by-step explanation:
Ellie ha been training for the Cedar Ridge Off-Road Race. The firt week he trained, he ran 3 day and took the ame two route each day: 2. 5 mile on a path in the wood in the morning and a longer route at the park in the afternoon. By the end of the week, Ellie had run a total of 24 mile. Which equation can you ue to find how many mile, x, Ellie ran each afternoon
The Distance that Ellie ran each evening is 16.5 miles for a entirety week.
How to find the number of miles?We can use the following equation to find how many miles, x, Ellie ran each afternoon:
x + 2.5(3) = 24
Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.
To solve for x, we can start by simplifying the left side of the equation:
x + 7.5 = 24
Then, we can subtract 7.5 from both sides:
x = 16.5
So, Ellie ran 16.5 miles each afternoon.
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What is the radius and diameter of the following circle
Answer:
r=4.2
d=9
Step-by-step explanation:
The radius is 4.2cm
The diameter is d=9
Solution
d=2r=2·4.5=9
Hope this helped!!!!!
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
b
Step-by-step explanation:
The factorization of a trinomial is modeled with algebra tiles.
An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled + x, 2 are labeled negative. 4 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 12 tiles are in the Product spot: 1 is labeled + x squared, 2 are labeled negative x, the 3 tiles below + x squared are labeled + x, and the 6 tiles below the negative x tiles are labeled negative.
Which trinomial is factored?
x2 + 3x – 6
x2 + 5x – 6
x2 + 3x – 2
x2 + x – 6
Answer:
A.) x + 3 and x + 2
Step-by-step explanation:
The trinomial which is factored as described is; x² + x - 6.
Trinomial factorisationAccording to the question;
Factor 1 spot: 1 is labeled + x, 2 are labeled negative.(x -1 -1)
Factor 2 spot: 1 is labeled + x and 4 are labeled +.x + 1 + 1 + 1
Product spot: 1 is labeled + x squared, 2 are labeled negative x, the 3 tiles below + x squared are labeled + x, and the 6 tiles below the negative x tiles are labeled negative.x²-2x +3x -6
Hence, the product of the factors is therefore;
x² + x - 6.From the description of the previous factors; the trinomial which is factored is; x² + x - 6.
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Christina is planning on selling handmade blankets. She has 1,000 blankets to sell and expects the number of blankets sold to be 10 fewer than her total number of blankets for every $1 she
charges for a blanket. What is the equation
The equation is y = 1000 - 10x, where y is the number of blankets sold and x is the price in dollars.
This equation represents the relationship between the number of blankets sold (y) and the price of each blanket (x). The equation starts with the total number of blankets Christina has to sell (1000) and then subtracts 10 for every $1 increase in the price of the blanket. This means that as the price of the blanket increases, the number of blankets sold will decrease by 10 for every $1 increase. For example, if Christina charges $50 for a blanket, the number of blankets sold would be 500 (1000 - (10x50)).
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In the diagram below, PQ is parallel to MN. If PQ, is 22 more than MP, PO=12, and MN=12, find the length of MP. Figures are not necessarily drawn to scale. State your answer in the simplest radical form, if necessary.
The measure of the length MP is equal to 6.
What are similar triangles?Two triangles are similar triangles if they have the same corresponding angle measures and proportional side lengths.
Given is a triangle ΔOMN.
Now, ΔOMN and ΔOPQ are similar. This means that the side lengths are proportional to each other. We can write -
OP/OM = PQ/MN
12/OM = PQ/MN
12/(OP + PM) = PQ/MN
It is given that -
PQ = MP + 2
12/(OP + PM) = (MP + 2)/MN
12MN = (MP + 2)(OP + PM)
12 x 12 = (MP + 2)(MP + 12)
(MP)² + 12MP + 2MP + 24 = 144
(MP)² + 14(MP) - 120 = 0
Let MP = x, then we can write -
x² + 14x - 120 = 0
(x + 20)(x - 6) = 0
(x + 20) = 0 and (x - 6) = 0
x = - 20 and x = 6
x = 6 {Lengths cannot be negative}
Therefore, the measure of the length MP is equal to 6.
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pls help with question image is linked
The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg
How to determine the amount sold each dayFrom the question, we have the following parameters that can be used in our computation:
Day 2 = Day 1 - 25
Day 3 = 2/7 * (Day 1 + Day 2)
Total weights = 315
Next, we use the following representations
x = Day 1, y = Day 2 and z = Day 3
So, we have the following equations
y = x - 25
z = 2/7(x + y)
x + y + z = 315
Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315
z = 2/7(x + x - 25) = 2/7(2x - 25)
x + y + z = 315 ⇒ x + x - 25 + z = 315
So, we have
z = 2/7(2x - 25)
2x + z = 340
Substitute z = 2/7(2x - 25) in 2x + z = 340
2x + 2/7(2x - 25) = 340
So, we have
7x + 2x - 25 = 1190
Evaluate the like terms
9x = 1215
Divide by 9
x = 135
So, we have
y = x - 25 = 135 - 25 = 110
z = 2/7(x + y) = 2/7 *(135 + 110) = 70
Hence, the amounts are 135 kg, 110 kg and 70 kg
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This is algebra 2, please help.
The vertex and axis of symmetry of the graph is shown in image.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Now,
Since, The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Hence, The points corresponds to x = - 2 and - 4 are;
For x = - 2;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-2 + 6)² - 5
⇒ f (x) = 1/4 (4)² - 5
⇒ f (x) = 4 - 5
⇒ f (x) = - 1
For x = - 4;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-4 + 6)² - 5
⇒ f (x) = 1/4 (2)² - 5
⇒ f (x) = 1 - 5
⇒ f (x) = - 4
Thus, The points are;
⇒ (- 2, - 1) , (- 4, - 4)
And, The vertex of the function is,
⇒ ( - 6, - 5 )
And, The axis of symmetry of the graph is,
⇒ x = - 6
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Describe the transformation from the red figure to the blue figure.
The blue figure is translated ____ units ____ and ____ units ____ from the red figure.
Step-by-step explanation:
The blue figure is translated 2 units down and 6 units across from the red figure.
6. 175 is ___% of 125
7. ___is 120% of 720
Answer:
6. 175/125=x/100
Cross products equal 125x=17500
Solve for x and you get 140%
7. 20% of 720 is 144. You need to find 120% so add the full 720 (100%) to the 144 and you get 864 (120%)
Step-by-step explanation:
Answer:
6. 140% 7. 864
Step-by-step explanation:
Step for #1:
1.) 175 ÷ 125 = 1.4
2.) 1.0=100 0.4=40
3.) 1.4 = 140%
Answer; 140%
Step for #2:
1.) 120% × 720 = ?
2.) 120 x 720 = 86,400
3.) 86,400 ÷ 100 = 864
Answer; 864
Simplify (with steps please:))
√((x+c)^2 + y^2) = x*a/c + a
On solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
√{(x + c)² + y²} = x (a/c) + a
√{(x + c)² + y²} = xa/c + a
√{(x + c)² + y²} = a{x/c + 1}
√{x² + c² + 2xc + y²} = a{x/c + 1}
{x² + c² + 2xc + y²} = ± (a{x/c + 1})²
Now, we can write -
{x² + c² + 2xc + y²} = (a{x/c + 1})² ...... (1)
and
{x² + c² + 2xc + y²} = - (a{x/c + 1})² ......... (2)
Solving (1) as -
{x² + c² + 2xc + y²} = (a{x/c + 1})²
{x² + c² + 2xc + y²} = a²(x/c + 1)²
{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)
{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)
y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}
Solving (2) as -
{x² + c² + 2xc + y²} = - (a{x/c + 1})²
y² = - (a{x/c + 1})² - (x² + c² + 2xc)
y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}
y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}
Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
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Please help me asap!!
Answer:
D
Step-by-step explanation:
If Claire bikes at an average speed of 7 miles per hour how many hours will it take her to ride 28 miles?
Answer:
4 hours
Step-by-step explanation:
28/7 = 4
At the toy store, 4 toy cars cost $3.84. How much does it cost to buy 20 toy cars?
A. $20.20
B. $17.20
C. $19.20
D. $21.20
Whoever gets the correct answer will get a crown!!!
Step-by-step explanation:
To answer this, we need to find the scale factor which is to find how much one individual car is worth.
So we need to divide 3.84 and 4.
3.84 ÷ 4 = 0.96
So each car is $0.96.
To find 20 toy cars, we need to multiply 0.96 and 20.
The answer is:
$19.20
HELP BRAINLIEST FOR FASTEST AND CORRECT NO NEED TO EXPLAIN
Answer:
The answer is 48
Step-by-step explanation:
Answer:
48 students
4*12=48
Which is the equation of the given line?
x = 1 y = 2x y=x y=1 (need help ASAP)
Answer:
y = 1
Step-by-step explanation:
Since the line is a horizontal line through 1, y = 1.
I need to know the steps in order to solve this math problem....Please briefly describe the steps
a) A function w(t) to represent the amount of water in the pool using the two functions is w(t) = -3t + 5.
b) The pool will leak out the water when w(t)=0.
c) It will take 1.67 hours to leak out all the water from the pool.
d) Yes, functions f(t) and d(t) will intersect on the graphs when the pool stops leaking all the water out.
e) The domain of the functions f(t), d(t) and w(t) are 0 ≤ t ≤ 1.67.
What are functions?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Subtract the amount flowing into the pool by the amount being drained out the pool to get the amount of water in the pool .
The given functions are -
Flowing: f(t) = t² + 8t + 9.
Draining: d(t) = t² + 11t + 4.
The amount of water in the pool is -
w(t) = f(t) - d(t)
w(t) = t² + 8t + 9 - t² - 11t - 4
w(t) = -3t + 5.
Therefore, the function obtained is w(t) = -3t + 5.
When the condition is w(t) = 0 then, the pool will have leaked all the water.
Plugging in the values -
-3t + 5 = 0.
3t = 5
t = 1.67.
Therefore, the pool will leak all the water in 1.67 hours.
Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked. The graph is shown below.
The domain of a function is the set that contains all input values of the function. The input is the time in the given situation, so -
Time cannot be negative, hence t ≥ 0.
When all the water has been drained, everything stops, hence t ≤ 1.67.
Therefore, the domain of the function is 0 ≤ t ≤ 1.67.
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F(x)=2(x-3)squared it’s graphing and I forgot how to solve it
The solution of the function f(x) = 2(x - 3)² is at x = 3 as shown in the graph.
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial can be classified based on degree as linear, quadratic, cubic.
Given the function:
f(x) = 2(x - 3)²
The graph of f(x) is plotted. The solution of the graph can be gotten from its x intercept. Hence the solution is at x = 3
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Akira receives a price at a science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foll did it take to cover the trophy including the bottom
Answer:
216 cm^2
Step-by-step explanation:
Solve these for points I got a one in algebra so this would be helpful to my grade
The solution for each system of equations is given as follows:
1) x = -4, y = -8.
2) x = 5, y = -1.
3) x = -7, y = 2.
4) No solution.
5) x = 2, y = -6.
6) x = -3, y = 4.
How to solve the system of equations?The system of equations are solved using the elimination method, writing one variable as a function of another, replacing in the other equation, and then obtaining each variable.
For item 1, we eliminate x, as follows:
x = 12 + 2y.
Hence the solution for y is obtained as follows:
5(12 + 2y) + 3y = -44
60 + 10y + 3y = -44
13y = -104
y = -104/13
y = -8.
Then the solution for x is given as follows:
x = 12 + 2y = 12 + 2(-8) = -4.
For item 2, we have that:
y = 19 - 4x.
Hence:
7x - 2(19 - 4x) = 37
7x - 38 + 8x = 37
15x = 75
x = 5.
Hence the solution for y is of:
y = 19 - 4(5) = -1.
For item 3, we can simplify the second equation by two, hence:
-x + y = 9.
y = 9 + x.
Hence:
3x + 8(9 + x) = -5
3x + 72 + 8x = -5
11x = -77
x = -7.
Hence the solution for y is of:
y = 9 - 7 = 2.
For item 4, we have that:
x = 7 + 3y.
Hence:
2(7 + 3y) - 6y = 12
14 + 6y - 6y = 12
0y = -2. (no solution, division by zero).
For item 5, we have that:
y = -2 - 2x.
Hence:
5x + 3(-2 - 2x) = -8
5x - 6 - 6x = -8
-x = -2
x = 2.
Hence the solution for y is of:
y = -2 - 2(2)
y = -6.
For item 6, we simplify the second equation by two, hence:
2x + y = -2
y = -2 - 2x.
Replacing on the first equation, we have that:
2x + 5(-2 - 2x) = 14.
2x - 10 - 10x = 14
-8x = 24
8x = -24
x = -3.
Hence the solution for y is obtained as follows:
y = -2 - 2(-3)
y = -2 + 6
y = 4.
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PLEASE HELP: Given AC and BD bisect each other, prove that ΔABX≅ΔCDX using the SAS congruence theorem. ??
The ∆ABX and ∆CDX formed after the mutual bisection of AC and BD each other at point X are congruent i.e ΔABX ≅ ΔCDX, by SAS congruance theorem.
SAS congruence theorem: "SAS " stands for "Side-Angle-Side". If there is two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are said to be congruent. We have , A Quadrilateral ABCD, such that AC and BD bisect each other at point X. After bisection there is formed 4 triangles. We have to show ΔABX ≅ ΔCDX by SAS Congruance Rule. Now, as we know that bisect point divides the sides into two equal parts, i.e, AX = CX and DX = BX. So, in ΔABX and ΔCDX
AX = CX ( since X is bisecter point )BX = DX ( from bisection )m∠AXB = m∠CXD ( corresponding angles)As we see ∠AXB is angle in between to two sied AX and BX . Similarly, ∠CXD is in between CX and DX . So, by using SAS congruance theorem ∆ABX is congruent to ∆CDX i.e., ΔABX ≅ ΔCDX.
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Name the property that i hown by each equation. A. 6a 4 = 4 6a
B. 30 60 = 15(2 4)
C. 3(8x 4) = 3(4 8x)
D. 4(6a) = (4 · 6)a
A. Commutative property of addition
B. Distributive property
C. Commutative property of addition
D. Associative property of multiplication
Commutative property of addition: The commutative property of addition says that a change in the order of the numbers being added does not affect the sum. We define a commutative property of addition as adding the numbers in any order that will give the same answer.a + b =b + a
Here, a and b is whole numbers, integers or decimals, or even fractions.
Distributive property: According to this property, multiplying the summation of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. In other words, according to the distributive property, an expression of form A (B + C) can be solved as A (B+ C) = AB + AC.Associative property of multiplication: The associative property of multiplication is defined as that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.Read more about the distributive property:
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The complete question is:
Name the property that is shown by each equation.
A. 6a + 4 = 4 + 6a
B. 30 + 60 = 15(2 + 4)
C. 3(8x + 4) = 3(4 + 8x)
D. 4(6a) = (4 · 6)a