The standard form of a given number is scientific notation which is given by the form of exponents of ten and written as 5.67 ×10⁵.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
What is the standard form?Standard form is a way of writing down in the easy form very large or very small numbers.
Let E is the standard form of a given number
E = 567000
E = 500000 + 67000 + 7000
E = 0.567 × 10⁶ = 5.67 ×10⁵
E = 5.67 × 10⁵
Hence, the standard form of a given number is 5.67 ×10⁵.
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EXTENDED RESPONSE Triangle A B C has vertices A(-3,-5), B(-1,-1) , and C(-1,-5) ,
Triangle X Y Z has vertices X(5,-5), Y(3,-1) , and Z(3,-5) ,
c. Write a logical argument using coordinate geometry to support your conjecture.
The corresponding sides have the same measure and are congruent. So, ΔABC ≅ ΔXYZ by SSS.
What in mathematics is the Pythagoras Theorem?
According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c2 = a2 + b2, where c is the hypotenuse and a and b are the triangle's two legs.Observe the graph, the triangles are right triangles. In triangle ABC, AC = 2 and BC = 4. Use the Pythagorean
Theorem to find AB.
AB² = AC² + BC²
AB = √ AC² + BC²
AB = √ 2² + 4²
AB = √4 + 16
AB = √20
Similarly In triangle XYZ, ZX = 2 and ZY = 4. Use the Pythagorean Theorem to find XY
XY² = XZ² + ZY²
XY = √ XZ² + ZY²
XY = √ 2² + 4²
XY = √4 + 16
XY = √20
The corresponding sides have the same measure and are congruent. So, ΔABC ≅ ΔXYZ by SSS.
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Determine the length of the leg of a 45°-45°-90° triangle with a hypotenuse, length of 11 .
The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]
Since two of the angles in this triangle are 45 degrees and it has a 90 degree angle. It is a right isosceles triangle. An isosceles triangle has two sides the same, which have to be the two legs in this triangle because a triangle can not have two hypotenuses.
According to the Pythagorean Theorem:
[tex]a^{2}+b^{2} =c^{2}[/tex]
where a and b are the legs and c is the hypotenuse.
Since two legs in this right triangle are the same , the formula can be altered to be:
[tex]a^{2}+a^{2} =c^{2}[/tex]
[tex]2a^{2} =c^{2}[/tex]
Putting the value of c is 11
[tex]2a^{2} =11^{2}\\ \\ 2a^{2} = 121\\ \\a^{2} = \frac{121}{2\\}\\ a =\sqrt{\frac{121}{2} }[/tex]
[tex]a =\frac{121}{\sqrt{2} }\\ \\a =\frac{11\sqrt{2} }{2}[/tex] ~ [tex]7.78[/tex]
Hence, The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]
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Help help help help help help help
Answer:
Step-by-step explanation:
need bigger image cant see
Find the area of polygon with A(-5,-2) ,B (4,-2), C (4,-7) , D (-5,-7))?
Answer:
A=45
Step-by-step explanation:
Area of a rectangle equation: A=L*W
A=9*5=45
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=2 x-33 for x=9
f (9) = 15 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= 2 x - 33
Put x = 9 ⇒ 2 × 9 - 33
⇒ 18 - 33
⇒ 15
Therefore f (9) = 15
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2) 1, 3, 9, 18, 54, ...
What is the common ratio?
Answer: times 3 each time or 3
Step-by-step explanation:
1 is the first value
1x3=3
3x3=9
18x3=54
Determine a series of transformations that would map Figure B onto figure C
The words that complete the drop down menus are
RotationTranslationThis is further explained below.
What is Translation?In geometry, a translation is a transformation that involves moving every point in a figure, shape, or space by the same distance in a specific direction.
A translation may either be seen as the addition of a constant vector to each point or as the movement of the origin of the coordinate system. Both of these interpretations are valid.
Generally, You need to turn the ship such that all of the sides are aligned parallel to one another.
Move the vertices around in the shape until they are aligned properly.
The rotation should be somewhere about ninety degrees, and the translation should move the form up in a diagonal direction.
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130 2/3 divided by 10 1/2
Answer:
12.44 repeated
Step-by-step explanation:
Answer:
112/9
12.4
12 4/9
Evaluate each expression for a=3 and b=-5 . b(2 b-a)
Evaluating the expression b(2b - a) for a = 3 and b = -5 is equal to 65.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression b(2b - a), substitute the value of the variable a and the value of variable b.
b(2b - a)
-5[2(-5) - (3)]
Performing the arithmetic operations, we can have the value of the expression.
-5[2(-5) - (3)]
= -5(-10 - 3)
= -5(-13)
= 65
Hence, the expression b(2b - a) when a = 3 and b = -5 is equal to 65.
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Select the reason that best supports Statement 5 in the given proof.
A={x|x is an even number more than 0 but less than 5}
Three angles fit around a .2 of the angles are 115° and 53° work out the size of the third angle which of the word below describes the third angle right angle obtuse angle reflex angle or acute angle
Three angles fit around a point, two of the angles are 115° and 53° , then the size of third angle would be 192° and it would be a reflex angle.
The sum of the angles around a point is 360 °
If the two angles are 115° and 53° , the sum of the two angles would be 168°
If we reduce the sum of the two angles from the total 360° , we get the size of third angle as 192°
As the size of third angle is more than 180° , so the name of the third angle is reflex angle because right angle is measured 90° , obtuse angle is measured more than 90° but less than 180° , reflex angle is measured more than 180° but less than 360° and acute angle is measured less than 90 °
Correct question is - Three angles fit around a point. Two of the angles are 115° and 53° . Work out the size of third angle and which of the words below describe the third angle
• Right angle
• Obtuse angle
• Reflex angle
• Acute angle
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Tell whether each equation is in slope-intercept, point-slope, or standard form.
d. y-3=4 x
y-3=4 x is in point-slope form, it is neither in slope-intercept form nor standard form.
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
the equation looks like this in point-slope form ⇒ y-2= 4(x-0)
Here, the points are (x, y) and the points the line is passing through is
(0, 2)
y-2= 4(x-0) is in point-slope form, it is neither in slope-intercept form nor standard form.
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Solve each system by substitution.
5m - n = 7 , 3 + 3n = 6m
Using substitution method, the solution of the given system of equations is (2,3)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
5m - n = 7 ............ (1)
3 + 3n = 6m .............. (2)
In equation (1), subtract 5m from both sides:
5m - n - 5m = 7 - 5m
-n = 7 - 5m
Multiply by (-1)
n = 5m - 7 ...... (3)
Substitute n = 5m - 7 into equation (2)
3 + 3n = 6m
3 + 3(5m - 7) = 6m
15m -18 = 6m
9m = 18
m = 2
Substitute back m = 2 into equation (3)
n = 5m - 7
n = 5.(2) - 7 = 3
Hence, the solution is (2, 3)
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Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than kayla’s biking speed. Find kayla’s biking speed
When Kayla rode her bike home from college one weekend, her biking speed is 15 miles per hour
Speed is defined as the ratio between the distance and the amount of time an object traveled.
speed = distance/time
If the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed, we have:
average speed of the bus = 10 mph + biking speed
let x = biking speed
y = average speed of the bus
y = 10 + x
Covering the same distance of 75 miles, calculate the time it took her riding the bus and the bike.
time = distance/speed
time riding the bus = 75 miles/(10 + x)
time riding the bike = 75 miles/x
If it took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike
time riding the bus = time riding the bike - 2
75 miles/(10 + x) = (75 miles/x) - 2
75/(10 + x) = (75 - 2x)/x
Multiplying both sides by x(10 + x),
x(10 + x)[75/(10 + x)] = x(10 + x)[(75 - 2x)/x]
75x = 750 - 20x + 75x - 2x^2
2x^2 + 20x - 750 = 0
x^2 + 10x - 375 = 0
(x - 15)(x + 25) = 0
x = 15 ; x = -25
Since we cannot have negative amount of time, choose x = 15.
Hence, Kayla's biking speed is 15 miles per hour.
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The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
What is the triangle?A triangular is a geometry with 3 sides and three angles. The triangle has angles that sum up to 180 °.
In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.
The sides of the triangle are in ascending order, then we have
WY < YZ < WX < XY < XZ
Then the sequence of the angles is given as,
∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
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Write in point-slope form an equation of the line through each pair of points. (0,-1) and (3,-5)
The equation of the line in point-slope form, which passes through the pair of points located at (0 , -1) and (3 , -5), is y + 5 = -4/3(x - 3).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (0 , -1) and (3 , -5).
m = (y2 - y1)/(x2 - x1)
m = (-5 - -1)/(3 - 0)
m = -4/3
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -4/3 and (x1 , y1) = (3 , -5)
(y - -5) = -4/3(x - 3)
y + 5 = -4/3(x - 3)
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Anyone out there knows how to do math
Step-by-step explanation: I hope this helps.
Answer: the correct answer is 1, 2, and 5
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10 miles in 30 minutes would mean Julia was riding at 20mph.
5 miles in 12 minutes would mean Alex was riding at 25mph which means Alex would've had the greater average speed.
miles per hour is a good measure for this scenario because a hour is 60 minutes and the numbers 12 and 30 go into 60 cleanly.
12*5=60
30*2=60
60 minutes=1 hour
Reya says
"The two sequences T(n) = 7 + 5n and
S(n) = 54 - 6n don't have any terms in
common because when I solve T(n) = S(n)
I get n = 4 which isn't an integer.
Give a reason why Reya is wrong.
Answer:
Step-by-step explanation:
4 + 4 = 4 so 9 is equal to 6
is 2^2 equals to -2^2
Answer:
Yes, 2² = -2².
Step-by-step explanation:
Given that,
→ prove that 2² equals to -2².
Let's prove the equation,
→ 2² = -2²
→ 4 = 4
→ [ LHS = RHS ]
Hence, it is proved to be equal.
Find the slope and y -intercept of each line.. y=0.4-0.8 x
The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given: y = -0.8x + 0.4
As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where
m = slope of the linec = y-intercept of the lineOn comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.
Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.
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Draw the two planes determined by the following equations:
2x+3y-z=12
2x-4y+z=8
Both the planes of the given equations,
2x+3y-z=12 (1)
2x-4y+z=8 (2)
They have been drawn in a three-dimensional plane, and the images are attached below.
whos good at algebra bc...
[tex]\displaystyle\\Answer:\ y=-\frac{1}{3} x+5[/tex]
Step-by-step explanation:
Choose two points that belong to this graph: (0,5) (3,4)
Formula for a straight line:
[tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
[tex]\displaystyle\\x_1=0\ \ \ \ \ x_2=3\ \ \ \ \ y_1=5\ \ \ \ \ y_2=4\\\frac{x-0}{3-0} =\frac{y-5}{4-5} \\\\\frac{x}{3}=\frac{y-5}{-1}[/tex]
Multiply both parts of the equation by -1:
[tex]\displaystyle\\-\frac{x}{3}=y-5\\\\ -\frac{x}{3} +5=y-5+5\\\\-\frac{x}{3}+5=y\\\\y=-\frac{1}{3}x+5[/tex]
How many days are there from May 27th to June 5th (include both days)?
Answer: 10
Step-by-step explanation:
its 10 x
may 27, 28, 29, 30, 31, june 1, 2, 3, 4, 5,
1. 2. 3. 4. 5. 6. 7 8 9. 10
A football team needs to sell at least 20,000 tickets to two games to cover expenses. They sell 10,184 tickets to one game and 9,723 tickets to the other. Estimate by rounding to the nearest thousand and by rounding to the nearest hundred. Did the team sell enough tickets?
what is the solution for w in the equation?
equation: w + 1/2 = 1/4w + 2 (the / is for fraction bar)
options:
A: w = 2
B: w = 10/3
C: w = 9/8
D: w = 4
The solution for w in the equation is w = 2. therefore, the correct option is A; w = 2
What is the solution for an equation?An equation represents equality of two or more mathematical expression.
The solution of an equation refers to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
WE have been given the equation: w + 1/2 = 1/4w + 2
Then to solve, Subtract 1/2 from both sides of the equation.
w=1/4w+1 1/2
Then Multiply both sides by 4
4w=w+6
Now Subtract w from both sides
3w=6
Now Divide both sides by 3
w=2
Therefore, the solution for w in the equation is w = 2 , the correct option is A; w = 2
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3
1 point
Find the distance between the pair of points. Round to the nearest tenth, if necessary.
(-7,-8). (4,3)
Answer:
15.6
Step-by-step explanation:
Find the difference between coordinates:
(x2-x1) = (4 - -7) = 11
(y2-y1) = (3 - -8) = 11
Square the results and sum them up:
(11)2 + (11)2 = 121 + 121 = 242
Now Find the square root and that's your result:
Exact solution: √242 = 11√2
Aprox solution: 15.5563
Rounded to nearest tenth: 15.6
Which correctly applies the distributive property?
Answer:
The last one.
Step-by-step explanation:
2(x + 3)
= 2*x + 2*3
= 2x + 6.
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What is the factored form of the expression over the complex numbers? 16x^2+9y^2
Answer:
(4x+3iy)(4x−3iy)
Step-by-step explanation:
We have a^2 + b^2
Over the complex number, this is equal to
(a-bi) (a+bi)
(4x -3yi) (4x+3yi)
Each sequence has eight terms. Evaluate each related series. -13,-14.5,-16, .......,-23.5
Evaluating each series of 8 terms, the result is
∑ = 42
We solve this problem by defining, succession:
What are sequences?A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.
As we can see the variation between each of the terms is:
-14.5 - (-13) = -1.5-16 - (-14) = -1.5The initial number is -13
a1 = -13
The final number is -23.5
an = -23.5
Let's determine the sum of this sequence of numbers
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
-13,-14.5,-16, .......,-23.5
∑ = 8(-13 - (-23.5))/2
∑ = 42
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