The trapezoid's area if its height is 8 is 156.
What is trapezoid area?Trapezoid area is the area of a four-sided flat shape with two sides that are parallel. It is a type of quadrilateral with two non-parallel sides. To calculate the area of a trapezoid, you need to multiply the sum of the lengths of the two parallel sides by the height of the trapezoid and then divide by two. The formula for trapezoid area is A = (a + b) * h / 2, where a and b are the lengths of the two parallel sides and h is the height of the trapezoid.
The area of a trapezoid is calculated by multiplying the height by the average of the two bases. Therefore, the area of the trapezoid in question is 8 multiplied by the average of 12 and 27, which is 19.5. The final answer is then 156.
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If P = (5, 4), Find:
r90° (P)
Answer:
r90° (P) = (4, -5).
Step-by-step explanation:
The point P is (5, 4). To find the image of P after rotating it 90° counterclockwise, we use the transformation matrix for a 90° counterclockwise rotation:
[[0, -1], [1, 0]]
The coordinates of the image of P after rotating 90° counterclockwise are given by:
[[0, -1], [1, 0]] * [5, 4] = [4, -5]
So, r90° (P) = (4, -5).
please help! lengths and angle
The given sides 5.25, 7 , 8.25 doesn't not constitute a right angled triangle.
What is right angled triangle?The foundation of trigonometry is a right-angled triangle, one of the most significant geometric shapes. The "base," "hypotenuse," and "height" of a right-angled triangle are three-sided triangles with a 90° angle between the base and the height. A right triangle's area is the portion of the triangle that is contained within the triangle's edge.
An angle that is the same as another is known as a right angle (90 degrees). Simply referred to as a right triangle. A right-angled triangle has three sides, the hypotenuse, the leg, and the right angle, which is known as the leg. The two legs are described by the terms "base" and "height," which are interchangeable.
Applying the Pythagoras theorem we can find id the given sides make a right angled triangle or not.
Pythagoras theorem is
c² = a² + b²
c, the hypotenuses and the longest side
a and b rest of the two legs
Given sides, 5.25, 7 , 8.25
8.25² = 5.25² + 7²
68.0625 ≠76.5625
Thus, The given sides 5.25, 7 , 8.25 doesn't not constitute a right angled triangle.
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How do you solve a 30 60 90 problem?
To solve a 30-60-90 triangle problem, you can use the ratios of the sides of a 30-60-90 triangle. The ratios are:
The hypotenuse is opposite the 60 degree angle, and it is always twice the length of the shorter leg.
The longer leg is opposite the 90 degree angle, and it is always √3 times longer than the shorter leg.
The shorter leg is opposite the 30 degree angle, and it is always equal to x where x is the value of the shorter leg.
So, you can use these ratios to find the missing side length(s) of a 30-60-90 triangle, given the length(s) of the other side(s). For example, if you know the length of the hypotenuse, you can find the lengths of the other two sides by dividing the hypotenuse by 2 and √3, respectively.
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rewrite the quadratic equation in the y=a(x-h)^2 +k y=5x^2 -30x+95
The required equation in the given format is given as y = 5(x - 1)² + 90.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given equation,
y=5x² -30x+95
Take 5 commons from terms 5x² and 30 and put it in parenthesis, in the parenthesis add and subtract 1
y = 5[x² - 2x + 1 - 1]+ 95
y = 5 (x - 1)² - 5 + 95
y = 5(x - 1)² + 90
Thus, the required equation in the given format is given as y = 5(x - 1)² + 90.
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What is the factored form of 9x² 12x 4?
The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).
The given expression is 9x² - 12x + 4
By splitting the middle term, let us factor this polynomial.
To identify the factors we have to consider factors of 36 as (9 × 4)
9x²- 6x - 6x + 4
=3x(3x - 2) - 2(3x - 2)
=(3x - 2)(3x - 2)
Another example of a quadratic polynomial can be taken to demonstrate similar factorization:
x² + 9x + 20
= x² + 5x + 4x + 20
= x × (x + 5) + 4 × (x + 5)
= (x + 5)(x + 4)
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is this correct?
just making sure...
Answer:
you are right bro keep up
I can’t figure out where to put it
The angle be 5x - 12 and 3x - 8 then the value of x = 25.
What is meant by measure of angle?The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.
Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner."
A protractor is a precision tool for measuring angles. Angles are measured in degrees, therefore the term "degree measure." Because one full revolution is equivalent to 360 degrees, it is divided into 360 segments.
Let the two angle be 5x - 12 and 3x - 8
5x + 3x - 12 - 8 = 180
Add similar elements: 5x + 3x = 8x
8x - 12 - 8 = 180
Subtract the numbers: -12 - 8 = -20
8x - 20 = 180
Move 20 to the right side
8x = 200
Divide both sides by 8
= 8x / 8 = 200 / 8
x = 25
Therefore, the value of x = 25.
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if the racetrack publishes that the odds in favor of a horse winning a race are 2 to 4, what is probability that the horse will not win the race?
The probability that the horse will not win the race is 0.5. The result is obtained by subtracting the probability of winning from 1.
How to calculate probability?Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceWhile, the probability for the opposite event is
P(not A) = 1 - P(A)
If the probability that a horse will win the race is 2/4, find the probability that the horse won't win the race!
The probability that the horse will win the race is
P = 2/4 = 0.5
The probability that the horse will lose is
P = 1 - P(A) = 1 - 0.5 = 0.5
Hence, the horse will lose with the probability of 0.5.
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Select the pairs of ratios that form a true proportion. Choose all that apply.
a. 3:6 and 5:10
b. 4/12 and 6/18
c. 20/5 and 10/3
d. 24:36 and 8:9
the pairs of ratios that form a true proportion: a and b
What is true proportion?An equation proving the equality of two ratios is a genuine proportion. Knowing one ratio in a percentage can be used to determine values in the other equal ratio.
Where x is the number of successes and n is the sample size, p′ = x / n. The variable p′ represents the proportion of the sample and acts as a point estimate for the proportion of the genuine population.
Now, given that -
a. 3:6 and 5:10
= 1:2 and 1:2
Thus, it is a true proportion.
b. 4/12 and 6/18
= 4:12 and 6:18
= 1:3 and 1:3
Thus, it is a true proportion.
c. 20/5 and 10/3
= 20:5 and 10:3
= 4:1 and 10:3
Thus, it is not a true proportion.
d. 24:36 and 8:9
= 2:3 and 8:9
Thus, it is not a true proportion.
So, correct pairs of ratios that form a true proportion is: a and b.
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How do you find the distance between two lines?
Assume that y = mx+c1 and y = mx+c2 are two parallel lines. D = |(c2-c1)/(1 + m2)| calculates the distance between the lines.
What is meant by parallel lines?Parallel lines are coplanar, infinite straight lines in geometry that don't cross at any point. Planes in the same three-dimensional space that never cross each other are said to be parallel. The minimal distance between two parallel curves prevents them from touching or intersecting. Two lines in the same plane that are equally spaced apart and never cross each other are referred to in geometry as parallel lines. Both vertical and horizontal can be used. A zebra crossing, rows of notebooks, and nearby railroad tracks are just a few instances of parallel lines that we encounter every day.Lines in a plane that consistently have the same separation are said to be parallel. Nothing can cross a parallel line.To learn more about parallel lines refer to:
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Two angles of a quadrilateral measure 74° and 231°. The other two angles are in a ratio of 2:3. What are the measures of those two angles?
Answer:
22° and 33°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
the ratio of the other 2 angles = 2 : 3 = 2x : 5x ( x is a multiplier )
sum the 4 angles and equate to 360
2x + 3x + 74 + 231 = 360
5x + 305 = 360 ( subtract 305 from both sides )
5x = 55 ( divide both sides by 5 )
x = 11
then
2x = 2 × 11 = 22°
3x = 3 × 11 = 33°
the other 2 angles have a measure of 22° and 33°
8. Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
Direct And Indirect Proportions
Answer:
She would've traveled 4cm on the map
Step-by-step explanation:
If 1cm=18km in the map and Rashmi drove 72km, we just have to divide 72 by 18 to get the distance she traveled on the map.
72÷18=4
show how to write each phrase as multiplication expression. 1 tenth of 3: 1 tenth of 0.3:
The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The expressions are given below.
1/10 of 3 and 1/10 of 0.3
Then the multiplication of the expression is given by putting a cross sign between them. Then we have
⇒ [(1/10) x 3] x [(1/10) x 0.3]
⇒ 0.3 x 0.03
⇒ 0.009
The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.
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There are 12 6th grades and s 7th graders on the soccer team. How many students are on the team? write an algebraic expression
Answer:
12 + s
Step-by-step explanation:
You want the total of 6th and 7th graders on the soccer team if there are 12 6th graders and 's' 7th graders on the team.
SumThe sum of 12 and s is written as ...
12 + s
How do you graph y equals 1?
y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.
To see the graph of y = 1
Now, According to the question:
What is called graph?
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Hence, y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.
Now, To see the representation of graph y = 1
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PLEASE HELP ASAP!!!!! Verify that f and g are inverse functions. f(x)=5x+2 and
g(x)=(x-2)/5
The inverse equations are F(x)⁻¹ = ( x - 2 ) / 5and F(x)⁻¹ = 5x + 2.
What is an inverse function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x and y are interchanged, and then the value of y is given an inverse function.
Given that the two equations are y= 1/2X+10 and y= -8X+3. The value of inverse functions will be calculated by replacing the x and y values and solving for y,
f(x)=5x+2
x = 5y + 2
y = ( x - 2 ) / 5
The inverse of the second equation is calculated as,
g(x)=(x-2)/5
x = ( y - 2 ) / 5
y = 5x + 2
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The circumference of a circle is 22π m. What is the area, in square meters? Express your answer in terms of π.
The area, in square meters is 121π m²
How to determine the areaThe formula for calculating the area of a circle is expressed as;
A = πr²
Where;
A is the area of the circler is the radius of the circleAlso, the circumference of the circle is expressed as;
Circumference = 2πr
Now, substitute the value of the circumference, we have;
22π = 2πr
Make 'r' the subject of formula, we get;
r = 11
Now, subsitiute into the formula for area;
Area = π(11)²
Find the square
Area = 121π m²
Hence, the value is 121π m²
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The area of the circle in terms of π is 121π metres square.
How to find the area of a circle?The circumference of the circle is 22π metres. The circumference of a circle is the perimeter of the circle.
Therefore,
circumference of a circle = 2πr
where
r = radiusHence,
circumference of the circle = 22π metres
22π = 2πr
r = 22π / 2π
r = 11 metres
Let's find the area of the circle.
Therefore,
area of the circle = πr²
where
r = radiusTherefore,
area of the circle = 11² × π
area of the circle = 121π metres²
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What is the factor of 4x² 28x 49?
The factors of the given expression 4x² + 28x + 49 is (2x + 7)(2x + 7).
Given polynomial is 4x2 + 28x + 49
Factoring polynomials is done in many ways. The four significant methods of factoring polynomials are as follows.
Method of Common Factors
Grouping Method
Factoring by splitting terms
Factoring Using Algebraic Identities
Let us operate the algebraic identity to factor this.
⇒ 4x² + 28x + 7²
⇒ 4x² + 2(14)(x) + 7²
⇒ (2x)² + 2(2x)(7) + 7²
This is similar to a² + 2ab + b² = (a + b)²
⇒ (2x + 7)²
⇒ (2x + 7)(2x + 7)
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Show that Area A + Area B = Area C
Area a + b + c = Area of Semi-circle on BC (radius 5). = Area c + d ... Shaded area = Sum of semi-circles on AC and AB – Semi-circle on BC + Triangle Area.
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in cm², also known as square centimeters.Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.To learn more about three-dimensional object refer to:
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4/5 of 3/4= __/__ x __/___= ___/___=___/___
___ is a blank box for a number
___/___ is a blank fraction
The required evaluation of the given fraction 4/5 of 3/4 is 3/5.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
Arithmetic operations can also be specified by the addition, subtract, dividing, and multiplying built-in functions.
We have to determine the evaluation of 4/5 of 3/4
As per the question, we have
⇒ 4/5 of 3/4
This can be also rewritten as:
⇒ (4/5) × (3/4)
Apply the multiplication operation,
⇒ 12/20
Reduce the above fraction into the simplest form,
⇒ 3/5
Thus, the required evaluation is 3/5.
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Write the opposite of the reciprocal of -2.4
Answer:
0.42
Step-by-step explanation:
- 2.4 = - 12/5
The opposite of the reciprocal of – 2.4 is
+ 5/12 ≈ 0.42
Answer: 5/12
Step-by-step explanation:
if -2.4 in fractions is 12/5 the opposite reciprocal is the fraction and sign fliped which is 5/12
An animal shelter has a total of 65 abandoned cats and dogs. The ratio of cats and dogs is 6:7. How many cats are in the shelter. How many dogs are in the shelter?
The animal shelter has a number of 35 dogs.
How to determine the number of dogs in an animal shelter
According to the statement, the animal shelter has a total of 65 abandoned cats and dogs and cats to dogs ratio is 6 : 7. We are asked to find the number of abandoned dogs in the shelter:
D = [d / (c + d)] · N
Where:
N - Number of animals.d - Dog number in ratio.c - Cat number in ratio.D - Number of abandoned dogs.If we know that d = 7, c = 6 and N = 65, then the number of abandoned dogs is:
D = (7 / 13) · 65
D = 35
There are 35 dogs in the animal shelter.
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1. Use the diagram and information below to create and solve an equation.
Don’t forget to show all your work and label your answer.
m∠2 = (y + 10)° and m∠4 = (3y – 24)°
What is m∠2?
The measure of angle 2 from the given figure is 27°.
What is vertical angle theorem?Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
Given that, m∠2 = (y+10)° and m∠4 = (3y-24)°.
Here, m∠2=m∠4 (∵ Opposite vertical angles are equal)
(y+10)°=(3y-24)°
3y-y=10+24
2y=34
y=17
So, m∠2 = (y+10)°=27°
Therefore, the measure of angle 2 from the given figure is 27°.
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i need help to solve this
Answer:
I'm pretty sure the answer to the 1st question is 2.46 and the answer to the 2nd question is just 15. (I'm sorry if I'm wrong!)
Using the double number line shown, for the equation 5x + 4 = 14, what is the value of x?
OA. 1
OB. 2
O C. 10
OD. 14
Which situation could be represented by -5x3?
A.
the total cost of 3 notebooks that cost $5 each
B.
the change in value of a bank account from 3 purchases of $5 each
C.
the distance traveled by a fish when it swims 5 meters per second for 3 seconds
D.
the change in temperature if it starts at negative 5 degrees and decreases by 3 degrees
Penelope has a collection of vintage action figures that is worth $350. If the collection appreciates at a rate of 2.8% per year, which equation represents the value of the collection after 5 years?
Equation represents the value of the collection after 5 years is 350(1.03)³ .
What sort of equation would that be?An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
Future value with appreciation can be calculated using the following general formula:
V = P(1+r)ⁿ where
V = Future value
P = Present value
r = appreciation rate
n = number of years
Given P = $350 , r= 2.8%=0.03 , n = 3
Now we substitute the given values in the equation to get:
V=350(1+0.03)³
or, V= 350(1.03)³
or, V= 381.5 dollars approximately .
Hence the required equation is V= 350(1.03)³ .
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Please help! PLEASE GIVE ACTUAL ANSWERS
Answer: write it out then ill answer
Step-by-step explanation:you could at least write it so i know what im answering cuz that shows nothing
What is the sum of the exterior angles of a polygon with 15 sides?
So, the sum of the exterior angles of a polygon with 15 sides is 2340 degrees.
The sum of the exterior angles of a polygon can be found using the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon.
In the case of a polygon with 15 sides, the number of sides (n) is 15. Therefore, the sum of the exterior angles can be found by plugging in 15 for n and solving the equation:
(15-2) * 180 = (13) * 180 = 2340 degrees
Therefore, the sum of the exterior angles of a polygon with 15 sides is 2340 degrees.
It's worth noting that the sum of all exterior angles of a polygon is always 360 degrees less than the sum of the interior angles of a polygon.
The sum of the interior angles of a polygon with n sides is (n-2)*180.
So for a 15 sided polygon the sum of the interior angles is (15-2)*180 = 2340 degrees.
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Given each pre-image and image, determine the scale factor.
*Note: The pre-image is notated by the shaded gray area. Your answer should be given as a whole number or fraction.
The scale factor of the dilation transformation of the pre-image triangle ΔDEF to the image ΔD'E'F', with the origin as the center of dilation is 3.
What is a dilation transformation?A dilation transformation is one in which the lengths of the sides of the pre-image are scaled up by a common factor to get the lengths of the sides of the image.
The coordinates of the vertices of the triangle ΔDEF are;
D(1, 5), E(1, 2), F(3, 2)
The length of the sides of triangle ΔDEF, making use of the difference between the non equal coordinate points, are;
DE = 5 - 2 = 3
EF = 3 - 1 = 2
The length of the side DF can be found using the formula for the distance between two points on the coordinate plane (a form of the Pythagorean Theorem), which is presented as follows;
DF = √((3 - 1)² + (2 - 5)²) = √(2² + (-3)²) = √(13)
The coordinates of the vertices of triangle ΔD'E'F' are; D'(3, 15), E'(3, 6), F'(9, 6)
Therefore; D'E' = 15 - 6 = 9
E'F' = 9 - 3 = 6
D'F' = √((9 - 3)² + (6 - 15)²) = √(6² + (-9)²) = √(9 × 13) = 3·√(13)
The scale factor, s.f. = The ratio of the corresponding sides of the triangles which is found as follows;
D'E'/DE = 9/3 = 3
E'F'/EF = 6/2 = 3
D'F'/DF = 3·√(13)/√(13) = 3
s.f. = D'E'/DE = E'F'/EF = D'F'/DF = 3
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