From all the given statements, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.
What is an area of a triangle?
The area of a triangle is half the product of the base of the triangle and the height of the triangle.
Area = 1/2 * base * height
As given the Area of both the big squares of figure 1 and figure 2 are equal because the side of both the squares is equal, therefore, (a+b).
figure 1,
Big square = (a+b)²,
figure 2,
Big square = (a+b)²,
Also, the sides of the 4 triangles are also the same giving the same area for all 8 triangles from Figures 1 and 2.
Figure 1,
area for 1 triangle = ab/2
area for 4 triangle = 4*(ab/2)
area for white square = big square area - 4 triangles area
= (a+b)² - 4*(ab/2)
Figure 2,
area for 1 triangle = ab/2
area for 4 triangle = 4*(ab/2)
area for white square = big square area - 4 triangles area
= (a+b)² - 4*(ab/2)
Hence, the given statement, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.
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The formula for the volume of
a square pyramid is V = 1/3s(2 squared) h.
Rewrite the formula in terms of h.
Then find the height of a square
pyramid with volume V = 400 cm3
and side length s = 10 cm.
Therefore , the height of the given square pyramid is 12 cm.
What is the plain meaning of volume?The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.
Here,
To calculate a square pyramid's volume in terms of h, use the formula h = [tex]\frac{3V}{s^{2} }[/tex]
With V = 400 and s = 10 cm, a square pyramid's height is 12 cm.
The equation for calculating the volume of a square pyramid is:
=> 1/3 [tex]s^{2}[/tex]h =V
=> h = [tex]\frac{3V}{s^{2} }[/tex]
Therefore we can rewrite the formula in terms of h you need to:
=> h = [tex]\frac{3V}{s^{2} }[/tex]
You must substitute these numbers into the following formula to determine the height of a square pyramid with volume V = 400 and side lengths s = 10 cm:
=> h = 3 * 400 / [tex]10^{2}[/tex]
=> 3* 400/100
=> 3*4
=> 12
Therefore , the height of the given square pyramid is 12 cm.
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Help me plssssssssssss
Answer:
(1,3)
Step-by-step explanation:
Substitute in 3x for y in the equation x + y = 4
x + 3x = 4
4x = 4 Divide both sides by 4
x = 1
Substitute 1 for x in either of the 2 original equations
x + y = 4
1 + y = 4 Subtract 1 from both sides
y = 3
(1,3)
Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
The graph of the absolute function g(x) = -|x + 3| - 4 has vertex at (-3, -4) and touches the y -intercept at (0, -7)
Graph of an Absolute FunctionThe graph of an absolute value function is called an absolute value graph. The absolute value graph depicts the distance of a number from the origin. The graph of the absolute value function is symmetric about the y -axis. The graph of the absolute value function makes a right angle at the origin.
In this problem the function given is
g(x) = -|x + 3| - 4
To graph this function, we can use a graphing calculator which will enable us to plot all points accurately.
The graph touches the y -axis at (0, -7)
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[tex]\sqrt{x} (\pi -\sqrt{x} 17)x^{2}[/tex]
The value of [tex]\sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2[/tex] is [tex]\pi x^2 \sqrt{x}-17 x^3[/tex]
[tex]$$\begin{aligned}& \sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2 \\& =x^2 \sqrt{x}(\pi-17 \sqrt{x})\end{aligned}$$[/tex]
Apply the distributive law: [tex]$\quad a(b-c)=a b-a c$[/tex]
[tex]$$\begin{aligned}& a=\sqrt{x} x^2, b=\pi, c=\sqrt{x} \cdot 17 \\& =\sqrt{x} x^2 \pi-\sqrt{x} x^2 \sqrt{x} \cdot 17 \\& =\pi x^2 \sqrt{x}-17 x^2 \sqrt{x} \sqrt{x} \\& 17 x^2 \sqrt{x} \sqrt{x}=17 x^3 \\& =\pi x^2 \sqrt{x}-17 x^3\end{aligned}$$[/tex]
What is distributive law?
The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.
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Complete the two-column proof. Drag the missing statements into the correct order.
Given: ∠1≅∠2 ; JK║AB
Prove: ∆CDL is an isosceles triangle.
By using the property of isosceles triangle, it can be proved that-
∆CDL is an isosceles triangle
What is isosceles triangle?
At first, it is important to know about triangle.
A triangle is a two dimensional three sided figure. A triangle has three sides and three interior angles.
A triangle whose any two sides are equal are called isosceles triangle.
JK || AB [Given]
[tex]\angle 1 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 4[/tex] [Corrosponding angle]
[tex]\angle 1 \cong \angle 2[/tex] [Given]
[tex]\angle 3 \cong \angle 4[/tex] [Transitive property of congruence]
CL [tex]\cong[/tex] DL [Converse of isosceles triangle theorem]
∆CDL is an isosceles triangle [Def. of isosceles triangle]
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If I want to invest my money and turn it into $900 over the course of two and a half years at the rate of 3.5%, how much money will I need to invest?
To turn $900 into $900 over the course of two and a half years at the rate of 3.5%, we can use the following formula:
Copy code
investment = (900 * (1 + 0.035)) ^ (2.5 / 1)
In this formula, investment represents the amount of money you need to invest, 900 represents the final amount you want to end up with, 0.035 represents the interest rate of 3.5%, 2.5 represents the number of years you want to invest for, and 1 represents the number of times per year that the interest is compounded.
Plugging in the values from the problem into the formula, we get:
Copy code
investment = (900 * (1 + 0.035)) ^ (2.5 / 1)
investment = ($900 * 1.035) ^ (2.5 / 1)
investment = $931.75 ^ 2.5
investment = $1434.24
Therefore, to turn $900 into $900 over the course of two and a half years at the rate of 3.5%, you will need to invest $1434.24.
i need help
Cerise waters her lawn with a sprinkler that sprays water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an angle of 300°, as shown by the shaded area in the accompanying diagram.
What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?
Responses
a. 79 ft. 2
b. 94 ft.2
c. 707ft.2
d. 589 ft.2
A sector is a part of a circle that is bounded by an arc and two radii. Thus the area of the lawn is Option D. 589.
What is the circle about?A circle is a figure that is bounded by curved lines called circumference. Some parts of a circle are radius, sector, diameter, chord, circumference, arc etc.
A sector can be defined as a part of a circle which is bounded by two radii and an arc.
The area of a sector can be determined by;
Area of a sector = (θ/360) *r²
where: θ is the measure of the internal angle of the sector
r is the radius of the sector
In the given question, it can be observed that the area of the lawn that receives water from the sprinkler has the shape of a sector.
So that:
Area of the lawn = (300/360)*22/7 * 15²
= 589.2857
Area of the lawn = 589²
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in a regression analysis, the standard error of the estimate is determined to be 4. in this situation, the mse
The mse will be 16 in the given case as mse is the square of standard error.
What is regression analysis ?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").
Given, the standard error = 4
We know that standard error is the square root of mse ( mean squared error ).
So, mse = (standard error)^2
= 4^2
= 16.
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What is the perimeter of the triangle?
Answer:
36 unitsStep-by-step explanation:
it is an isosceles right triangle, we divide it in two parts and we have two right triangles, with the Pythagorean theorem we find the hypotenuse and add it to the other side to get the perimeter (SEE FIGURE)
BC and AC = √(8²+6²)
BC and AC = √(64+36)
BC and AC = √100
BC and AC = 10 units
now we add the sides and find the perimeter
16 + 10 + 10 =
36 units
Use the table to determine the location with the greatest amount of rainfall and the location with the least amount of rainfall.
a. Using complete sentences, identify the city with the greatest amount of rainfall and the city with the least amount of rainfall, and express the ratio of their respective rainfalls as a decimal number, rounded to the nearest hundredth.
b. Describe what this ratio tells you.
The region with the most rainfall is Beaumont, and the region with the least is El Paso.
How can I find the locations with the most and least rainfall?
Making sure to utilize the same units is the first step. Let's convert everything to meters as a result.
Austin equals 0.8687 m
Beaumont = 1.534 meters.
Galveston = 1,095 meters
El Paso equals 0.246 m
Del Rio equals 0.4953 m
South Padre=0.655 meters
Based on this, El Paso has the least amount of rainfall, while Beaumont has the most.
How are the two locations connected?
These locations have a ratio of 1.5 to 0.2, or 1.5/ 2 = 0.7. According to this ratio, the amount of rainfall in these locations varies by 0.7 meters.
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Will thank and rate 5 stars if answers correct
Answer: We use the SSS
Step-by-step explanation:
SSS method or Side Side Side method is when we test to see if the triangles are the same or not. We know this by checking if the sides of the triangles change at the same rate or not!
Let test the YW is 4 and the WY is 8, we see the side multiply by 2
The VX is 5 and the XZ is 10, wee see the sided multiply by 2
So we use the SSS to show that both triangles are equal
HELP ASAP PLS
Reuben added 8 fish to his pond each day for 48 days. what was the total change in the number of fish in the pond
Answer:sd
Step-by-step explanation:
PLS HELP ASSAP
You can buy 56 diapers at Babies-R-Us for $28, and you can buy 112 diapers online for $52. Which is the better deal, and how much will you save per diaper?
Responses
A Online by $0.04Online by $0.04
B Babies R Us by $0.15Babies R Us by $0.15
C Babies R Us by $0.04Babies R Us by $0.04
D Online by $0.15
The correct option is a) online by $0.04.
The better deal is online, by $0.04 will save per diaper.
How do I solve for x in a equation?
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
Cost of 56 diapers at Babies-R-Us = $28
Cost of 1 diaper at Babies-R-Us = [tex]\frac{28}{56}[/tex]
= 0.5
Cost of 112 diapers online = $52
Cost of 1 diaper online = [tex]\frac{52}{112}[/tex]
= 0.46
So, the cost of diapers online is cheaper than that at Babies-R-Us.
Difference between 1 diaper in both case = $0.5- $0.46= $0.04
Online deal is better than and you will save by $0.04 per diaper.
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please help geometry
Answer:
Based on my estimates, Thy answer shall be the letter known as C
Help with is ixl please
Answer:
q=82
Step-by-step explanation:
The line is equal to 180 degrees, and we have three angles and two have numbers, so this will be easy.
Add 58+40 to get 98, now subtract 98 from 180.
180-98=82
A computer store buys a computer system at a cost of $605.25. The selling price was set at $807, but after a year the computer did not sell. The store then advertises a 25% markdown on the $807 computer system. Find the sale price.
PLS HELP
Answer: $605.25
Step-by-step explanation:
100% - 25% = 75%
807 times 0.75 = $605.25
The sale price is $ 605.25
at a grocery store, 4% of the eggs are broken. if you buy a dozen eggs, what is the probability that none are broken?
The probability that none are broken as calculated from the data given is 0.96.
No of eggs = 12
percentage of broken eggs = 4%
=4/100 * 12 = 0.48 eggs
therefore , probability of getting broken egg
= no of favorable outcome/ no of outcomes
=0.48/12
=0.04
hence probability of not getting any broken egg
= 1 - P(broken)
= 1- 0.04
= 0.96
There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.
When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
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Which choice shows (50+30) + 40 correctly rewritten using the associative property and then correctly simplified"
50+40+30= 90+30= 120
(30+50) + 40 = 80+ 40 = 120
50+ (30+40) = 50 + 70 = 120
O 50+(30+40) = 80 + 40 = 120
The required simplified value of the given expression is 120.
Given that the expression as;
(50 + 30) + 40.
What is simplification?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here, we have;
= (50 + 30) + 40
Now, using associative property, in parenthesis 50 + 30 become 80.
= 80 + 40
Then using associative property, 80 + 40 become 120
= 120
Thus, the simplified value is 120.
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Subtracting a number is the same as adding its additive inverse. For which elevation do we need to find the additive inverse? What is the additive inverse of that elevation?
Yes subtracting a number is the same as adding its inverse. We have to find the additive inverse of a function.
What is additive inverse?The additive inverse of a number is the number which when we add to the number results zero.
How to find additive inverse?Complex numbers are made up of both real and fictitious numbers. A + iB, where A is the real number and B is the imaginary number, is a complex number.
The additive inverse of A + iB should now be a value that, when added to a given complex number, produces the result zero. It will therefore be -(A + iB).
Suppose we have to find additive inverse of 5.
Let the additive inverse of 5 be x.
So,5+x=0
x=-5
So the additive inverse of 5 is -5.
Hence to find additive inverse of a positive number we have to just put a negative mark and for a negative number we have put positive mark in front of the number.
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What is the image of (5,-4)(5,−4) after a dilation by a scale factor of 33 centered at the origin?
The new coordinate of point (5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132)(165,132)
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
Given the coordinate (5,-4),(5,-4)
If we apply a scale factor by 33 on any general coordinate (x,y)
Then,
x → 33x and y → 33y
Similarly
5 → 33(5) = 165
-4 → 33(-4) = -132
So the new coordinate will be (165,-132)(165,-132)
Same step apply once more for (5,-4) the coordinate of other is same
Hence "The new coordinate of point (5,-4)(5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132),(165,-132)
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Seven percent of people receiving your email opened it. Two percent of people receiving your email clicked a link. Of those who opened the email, what percent clicked a link?.
Therefore, percentage of those who opened the email , clicked a link is 28.57%
What is percentage ?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Here,
Let the amount of people receiving your email is x
The amount of people receiving your email opened it is 7%
7/100 * x = 0.07x
The amount of people receiving your email clicked a link is 2%
So,
2/100 * x = 0.02x
Therefore,
percent of those who opened the email , clicked a link is
=> 0.02x/0.07x * 100
=> 2/7*100 = 28.57%
Therefore, percentage of those who opened the email , clicked a link is 28.57%
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Help me!
I don’t know what it’s asking and im scared
What do I do in here
Using the scale factor, the length of the new figures are as 21 inches, 21 inches and 36 inches.
How to find the length of the new figure using scale factor?Bill drew a scale drawing of the figure using a scale factor of 3.
A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
The length of the drawing are 7 inches , 7 inches and 12 inches . The length of the new figure can be found as follows.
using the scale factor
length 1 = 7 × 3 = 21 inches
length 2 = 7 × 3 = 21 inches
length 3 = 12 × 3 = 36 inches
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What is the value of r in the equation below? Give your answer as a
decimal.
10r - 1.5 = 12.5
3
1.4 is the value of r in the equation given.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. For solving equations The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
In the given equation,
10r -1.5 = 12.5
Simplifying using PEMDAS
add 1.5 on both sides
10r = 14
divide by 10 into both sides
r = 14/10 = 1.4
Therefore, The value of r in the given equation is 1.4.
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Can anyone help me solve this word problem?
Answer:
A:) T(t) = 305(230/305)^(t/10) +70
B:) T(20) ≈ 243.4 °F
Step-by-step explanation:
You have a pie removed from a 375° oven to a room temperature of 70° that has cooled to 300° after 10 minutes. You want to know its temperature after 20 minutes.
Law of CoolingNewton's law of cooling tells you the rate of change of an object's temperature is proportional to the difference between the object's temperature and that of its surroundings. The differential equation describing this has an exponential function as its solution. That exponential function can be written as ...
temperature = (initial temperature difference)·(cooling factor)^(time/(cooling time)) + (final temperature)
ApplicationHere, the initial temperature difference between the pie and room temperature is ...
initial temperature difference = 375° -70° = 305°
The final temperature is the room temperature:
final temperature = 70°
The cooling factor is the multiplier applied to the temperature difference in the time period "cooling time". Here, the pie is at 300°, a temperature difference of 300° -70° = 230° after a cooling time of 10 minutes. The cooling factor is ...
cooling factor = 230/305
A:) EquationThese values let us write the equation as ...
T(t) = 305(230/305)^(t/10) +70
B:) 20 minutesThe temperature after 20 minutes is found using this equation:
T(20) = 305(230/305)^(20/10) +70 = 305(46/61)^2 +70 = 243 27/61
T(20) ≈ 243.4 . . . . degrees F
__
Additional comment
The cooling factor can be expressed as a value that lets the exponent be t. Often, it is written as (e^k), where ...
k = 1/10·ln(230/305) ≈ -0.0282232
Then the equation is ...
T(t) = 305·e^(-0.0282232t) +70
It could also be written as ...
T(t) = 305(0.972171^t) +70
where 0.972171 = (46/61)^(1/10).
A triangle has vertices at F (6, 3), G (3, 4), and H (1, 7). What are the coordinates of each vertex if the triangle is rotated 180° about the origin counterclockwise?
To rotate a triangle 180° about the origin counterclockwise, we can take each vertex of the triangle and reflect it across the origin. This will produce a new set of coordinates for each vertex that is the same distance from the origin as the original, but on the opposite side of the origin.
For example, the vertex F has coordinates (6, 3). If we reflect this point across the origin, we get the new point (-6, -3). Similarly, the vertex G has coordinates (3, 4), which become (-3, -4) when reflected across the origin, and the vertex H has coordinates (1, 7), which become (-1, -7) when reflected across the origin.
Therefore, the coordinates of each vertex of the triangle after rotating it 180° about the origin counterclockwise are as follows:
F: (-6, -3)G: (-3, -4)H: (-1, -7)Note: When rotating a point about the origin, the direction of rotation (clockwise or counterclockwise) is important. If we had rotated the triangle 180° about the origin clockwise instead of counterclockwise, the new coordinates of each vertex would have been the same as the original, since the triangle would be reflected across the origin and end up in the same position as it started.
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The expression below is the factorization of what polynomial? Write
exponents with the caret (^). For example, enter x2 as x^2.
−1(x − 4)(5x+1)
The required Polynomial equation is − 5x²+ 19x + 4.
Factorization of Polynomials:Factorization is the process of determining the factors of a given value or algebraic statement. The numbers or the algebraic expressions that are multiplied to create the original number or original expressions are known as factors.
If p(x) is polynomial, with factors (x + a) and (x - a) then p(x) will equal to product of (x + a) and (x - a) => p(x) = (x + a)(x - a)
Here we have
The factorization of a polynomial is −1(x − 4)(5x+1)
To find the Polynomial we need to multiply given factors as given below
=> −1(x − 4)(5x+1)
=> −1 [ (x − 4)(5x+1)]
=> −1 [ 5x²−20x + x −4 ] [ add like terms ]
=> − 5x²+ 19x + 4 [ Multiply with − 1 ]
Therefore,
The required Polynomial equation is − 5x²+ 19x + 4.
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In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
please answer soon will give brainiest if correct.
AC:PC.= 3/5, as Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N.
What is Trapezoid?A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides.
The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
A trapezoid is a closed, four-sided, two-dimensional figure that has both a perimeter and an area.
The bases of the trapezoid are the two sides of the shape that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the shortest distance between two parallel sides.
According to our question-
Consider about the triangles ACB and PCN.
These triangles contain
Since angle C is the common angle and the transversal BC cuts two parallel lines PN and AB, angles ABC and PCN are congruent as equivalent angles by virtue of the reflexive property.
In light of the AA Similarity Theorem, triangles ACB and PCN are comparable.
Similar triangles have matching sides that are proportionate, thus
3/8 / 5/8= 3/5
Hence, Due to the fact that Line l AB and goes via point M to intersect Leg BC and the diagonal AC at points P and N, AC:PC.= 3/5.
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solve the following inequality 7x-3/9 ≥ 8 - 2x. Then graph the solution on the number line
does 3+4x is less than or equal to 2(1+2x have a solution
Answer:
NO
Step-by-step explanation:
You need x on one side of the equation.
3+4x ≤ 2(1+2x)
3+4x ≤ 2+4x
-4x -4x
3 ≤ 2
Since there is no x value there is no solution