In the diagram below, BC= QR=2, AC= PRy, and triangle PQR is a right
triangle. Use the drop-down menus to complete the proof that if the equation
2²+y=22 is true of the side lengths in triangle ABC, then triangle ABC must be a
right triangle.
R
Triangle PQR is a right triangle
Click the arrows to choose an answer from each menu.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to
determine that Choose....
It is given that a² + y² = 22 in triangle ABC, so
Choose....
This information shows that the triangles are congruent
because their three sides are congruent. Therefore, to show that triangle PQR is a right triangle,
we can use corresponding parts of the congruent triangles to show that
Choose...
X
We get PQR≅ ABC by using the Pythagorean theorem. Consequently, we would have: ∠ACB = ∠PRQ = 90°.
What is pythagorean theorem ?According to the Pythagorean Theorem, the square of a right triangle's longest side (hypotenuse) is always equal to the sum of the squares of its other two sides (legs).
Knowing that PQR is a right triangle, the following follows:
x² + y² = PQ²
Additionally, we are informed that x² + y² = PQ² , therefore by substitution, we get [tex]Z^{2} = PQ^{2}[/tex] Both triangles have corresponding congruent sides since , ΔPQR ≅ΔABC.
We can deduce the following from the congruent triangles' corresponding parts: ΔACB = ΔPRQ = 90°.
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Terry's mother combines four 1.5-liter bottles of juice with two 0.25-liter cans of sparkling water to make punch. Part A: What is the total amount of punch Terry's mother makes? Part B: The punch is served in 0.25-liter servings. All the servings were served. How many servings were served?
Answer:
A. 6.5 liters
B. 26 servings
Step-by-step explanation:
Part A:
(4 × 1.5) + (2 × .25) = 6.5 liters
Part B:
6.5 liters ÷ .25 liters/serving = 26 servings
I would like to cover a box with contact paper. The box is 18in X 1'1 in x ain How much square in of Contact paper will be used.
The total amount contact paper required will depend on total surface area of the box which will be 778 square inches.
As per the question statement, we are given a box with dimensions
(18in x 1ft 1in x 5 in) and we are supposed to find the total amount contact paper required to cover it.
The total amount contact paper required to cover it will depend on the total surface area of the box.
Given length(L) = 18 inches
Given width(W) = 1 ft 1 in = 13 inches
Given height(H) = 5 inches
Total Surface Area of the box is given by the formula
Area = 2(LW + WH + HL)
Area = 2(18*13 + 13*5 + 5*18)
Area = 2*389
Area = 778 square inches
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the length of a rectangle is given by 6t 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. find the rate of change of the area with respect to time.
Answer:
I am stuck on it too can some one help me please.
Please help!!!
explain why a + b = d
Write equations for the vertical and horizontal lines passing through the point (-9, 5).
Answer:
the vertical line is:
x = 5
The horizontal line is:
y = -9
Step-by-step explanation:
A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.
Then we can write a vertical line as:
x = a
and a horizontal line as
y = b
Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:
x = 5
Step-by-step explanation:
An artist has been commissioned to make a stained glass window in the shape of a regular octagon. the octagon must fit inside an square space. determine the length of each side of the octagon. round to the nearest hundredth of an inch.
Using an assumed value that the octagon must fit inside an 11 inch square space, tthe length of each side of the octagon would be 8.23 inches.
Since an assumed side of the square is 11 inches
Here, y is the two equal sides of the right-angle triangle
So y + x + y = 11
Using Pythagoras's theorem for the right angle triangle
y² + y² = x²
2y² = x²
y² = (x²)/2
y = x /√2
So substitute the value of y = x /√2 in the equation
x /√2 + x + x /√2 = 11
2x /√2 + x = 11
2x /√2 + x√2 /√2 = 11
x[2/√2 + √2 /√2] = 11
x[(2 + √2) /√2] = 11
x(2 + √2) = 11√2
x = 11√2/(2 + √2)
x = 15.5563/3.4142 = 12.1421
Round to the nearest hundredth of an inch
x = 12.1
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What is the total attendance at the food festival from 2014 to 2017?
The total attendance at the food festival from 2014 to 2017 is 16648.
How to calculate the total number?It should be noted that a graph is simply used in Mathematics to illustrate the information given for a data.
In this case, the graph shows the attendance for the years that are given. Therefore, the total attendance at the food festival from 2014 to 2017 will be:
= 2118 + 3391 + 4785 + 6354
= 16648
The attendance is 16648.
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Which graph represents the solution set of the system of inequalities?
{y>−2x−2y≤x+4
The graph represents the solution set of y > -2x - 2 and y ≤ x + 4 is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the system of inequalities graphically?The system of inequalities is given as
y > -2x - 2
y ≤ x + 4
Next, we plot the system of inequalities on a graph (see attachment)
From the attached graph, we have both lines of the graph intersect at (-2, 2)
Also, we can see that the graph has two lines (one shaded and one closed line)
By comparing the attached graph and the graphs in the list of options, we can see that the graph represents the solution set of the system of inequalities is graph (a)
Hence, the graph represents the solution set of the system of inequalities is graph (a)
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what is the following solution to this absolute value equation?
6|-f + 3| + 7 >7
The solution of this absolute value equation is f<3
What is absolute value?Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
On subtracting 7 from both sides
=6|-f + 3| + 7 - 7 > 7 - 7
=6|-f + 3| > 0
Now diving both sides by 6
|-f + 3| > 0
Now, this results in two condition
1.) -f+3>0
So,
f<3
2.) -(-f+3)<0
So,
3-f<0
f<3
Therefore, f can accept any value that satisfies the equation f<3.
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Jose used to budget $500 each month for groceries. He decided to change his budget
for groceries to $425 this month. By what percentage was Jose's budget for groceries
reduced this month?
Answer:
15 percent change
Step-by-step explanation:
1) 500 - 425 = 75
2) 75 / 500 = 0.15
3) 0.15 * 100= 15
PQRST is a rectangular-based pyramid with a height of 10 cm.
P
4 cm S
10 cm
R
Find the angle between the line PT and the plane PQRS.
Give your answer correct to 1 decimal place.
The angle between the line PT and the plane PQRS is 63.4°
In this question, we have been given a rectangular based pyramid PQRST.
A pyramid has height of 10 cm.
We need to find the angle between the line PT and the plane PQRS.
We know that the angle made by triangular plane TPS with the rectangular plane PQRS is same as the angle between the line PT and the plane PQRS.
If we draw a perpendicular through point T and intersects the plane PQRS at point M.
Let R be the midpoint of side PS
Consider a right triangle RMT.
We need to find angle TRM.
Here, MT = 10 cm, MR = 5 cm (1/2 × length of the rectangle)
Consider the tangent of the angle TRM
tan(∠TRM) = TM / RM
tan(∠TRM) = 10 / 5
∠TRM = tan^(-2)[2]
∠TRM = 63.4°
Therefore, the angle between the line PT and the plane PQRS is 63.4°
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Evaluate the following expressions.
Answer:
[tex]a.[/tex] [tex]\frac{49}{50}[/tex]
[tex]b.[/tex] [tex]8[/tex]
Step-by-step explanation:
[tex]a.[/tex] [tex]\frac{1}{2} +\frac{2}{5} +\frac{2}{25}[/tex]
To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).
To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
25: 25, 50
The LCM is 50.
Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.
To do this, we multiply the numerator and the denominator by the same number.
[tex]\frac{1}{2} *\frac{25}{25} =\frac{25}{50}[/tex]
[tex]\frac{2}{5} *\frac{10}{10} =\frac{20}{50} \\[/tex]
[tex]\frac{2}{25} *\frac{2}{2} =\frac{4}{50}[/tex]
Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.
[tex]\frac{25}{50} +\frac{20}{50} +\frac{4}{50} \\\\=\frac{49}{50}[/tex]
_______________________________________________________
[tex]b.[/tex] [tex]\frac{2}{3} *\frac{30}{7} *\frac{14}{5}[/tex]
To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.
[tex]2*30*14=840\\3*7*5=105[/tex]
[tex]\frac{840}{105} =\frac{8}{1}[/tex]
Which graph does not represent a function?
hler
Intro
Done
Answer:
The third one (the elliptical shape) is not a function
Step-by-step explanation:
Every x value of a function must be paired to a single y value. One really easy way to tell of a graph is a function is called the "vertical line test." This says that if a vertical line drawn anywhere in the graphed area passes through more than one point, it is not a function.
There are 80 houses in the neighborhood 1/4 of the houses have a chain-link fence in the backyard 2/5 of the houses have a privacy fence in the backyard the rest of the houses have no fence how many houses have no fence in the backyard
Based on the number of houses in the neighborhood and those that have a chain-link fence and a privacy fence, the number of houses with no fence in the backyard are 28 houses
How to find the number of houses with no fence?First, find the number of houses in the neighborhood that have a chain-link fence:
= Number of houses x Proportion with a chain-link fence
= 80 x 1/4
= 20 houses
Then find the number of houses in the neighborhood that have a privacy fence:
= Number of houses x Proportion with a privacy fence
= 80 x 2/5
= 160 / 5
= 32 houses
The number of houses in the neighborhood that have no fence is:
= Total number of houses - Houses with a chain-link fence - Houses with a privacy fence
= 80 - 20 - 32
= 28 houses with no fence
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The Tiny family is purchasing a coat for $ 1.3 x10-5 a pair of boots for $ 2.1 x 10-5 and a pair of gloves for $ 7.6 x 10-6. The Tiny family paid with $5.0 x 10-4
What is the Total:______________________________________________________
How much change :
___________________________
The total cost for the items which the Tiny family purchased is $41.6 × 10⁻⁶ while their change is equal to $45.84 × 10⁻⁵.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to determine the total cost, we would add all of the costs incurred by Tiny family as follows:
Total cost = 1.3 × 10⁻⁵ + 2.1 × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = (1.3 + 2.1) × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = 3.4 × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = $41.6 × 10⁻⁶
Next, we would calculate the change as follows:
Change = Amount paid - Total cost
Change = $5.0 x 10⁻⁴ - $41.6 × 10⁻⁶
Change = $45.84 × 10⁻⁵
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⚠URGENT!!!⚠Find the volume of the figure shown.
Volume=_________cm^3
By using the concept of composite solid, the volume of the entire figure is equal to 566 cubic centimeters.
What is the volume of the figure shown in the picture?
In this question we find a composite solid formed by the following components:
Two prisms with a rectangular base.Two prisms with a right triangular base.Please notice that the volume of a prism is equal to the product of the area of the transversal area and the height of the prism. Now we proceed to determine the volume of the entire figure:
V = V₁ + V₂ + 2 · V₃
V = (19 cm) · (2 cm) · (7 cm) + (10 cm) · (4 cm) · (7 cm) + 2 · [(1 / 2) · (5 cm) · (4 cm)]
V = 566 cm³
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Math translation/shrink problem
The rule of g(x) after the transformation is g(x) = 3(x + 4)^2 + 3(x + 4)
How to determine the image of the transformation?The function is given as
f(x) = x^2 + x
The transformations are given as:
Translation 4 units leftHorizontal shrink by 1/3The rule of the above transformations are :
Translation 4 units left: (x + 4, y)Horizontal shrink by 1/3: (3x, y)When the above transformations are combined, we have
Translation 4 units left: (x + 4, y)Horizontal shrink by 1/3: (3(x + 4), y)This means that
g(x) = 3f(x + 4)
So, we have
g(x) = 3(x + 4)^2 + 3(x + 4)
Hence, the function g(x) is g(x) = 3(x + 4)^2 + 3(x + 4)
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write an equation that passes through the point -9, 4 and is parallel to y=2/3x+19
The equation of the line that is parallel to y = 2/3x + 19 and passes through (-9, 4) is: y = 2/3x + 10.
How to Write the Equation of Parallel Lines?Two lines that are parallel have equal slope (m).
In the slope-intercept form of the equation of given line, y = mx + b:
m = slope of the lineb = y-intercept of the line.Given:
A point (-9, 4)
Equation, y = 2/3x + 19.
The slope (m) = 2/3.
The line that passes through (-9, 4) and is parallel to y = 2/3x + 19 would also have a slope (m) = 2/3.
Substitute (x, y) = (-9, 4) and m = 2/3 into y = mx + b to find the value of b:
4 = 2/3(-9) + b
4 = -6 + b
4 + 6 = b
b = 10
To write the equation, substitute m = 2/3 and b = 10 into y = mx + b:
y = 2/3x + 10.
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Which equation has the correct sign on the product?
OA. (-8)(-8)= -64
OB. (-18)4 = -72
OC. 13-3-39
OD. 45(-4)= 180
Hi please help me if you do I would be happy
2 If x and y vary directly and y=32 when x=18, then which of the following equations correctly represents
the algebraic relationship between x and y?
(A)y=16/9x
(B)y=x+14
(C) x+y=50
(D)y=9/16x
The equation would be y = 16/9x which represents the algebraic relationship between x and y which is the correct answer would be an option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given that x and y vary directly and y = 32 when x = 18
Direct variation equation can be written as:
y = kx where "k" is a constant.
Substitute the values of y = 32 and x = 18 in the direct variation equation and solve for k:
⇒ 32 = k(18)
⇒ k = 32/18
⇒ k = 16/9
The direct variation equation :
⇒ y = 16/9x
Therefore, the equation would be y = 16/9x which represents the algebraic relationship between x and y.
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please help me solve these as much as possible urgent neeeddd.
i think its easy but im just not smart
solve as many as you can. one is enough (but more is better)
Answer:
7. 45
8. 19
9. 15
10. 24
11. 23
12. 6
13. 8
14. 15
15. 12
16. 3
17. 26
18. 12
19. 21
20. 34
21. 2
hope this helps!:)
Nora and her little brother, Finn, spent all afternoon raking leaves. They filled b bags with leaves. When Nora wasn't looking, Finn emptied 4 of the bags to make a leaf pile! Luckily, Nora caught Finn before he got to the remaining 7 bags
Based on the number of bags of leaves that Finn emptied and the number of bags remaining, the total number of bags that Nora and Finn filled up is 11 bags.
How to find the number of bags?Finn and his sister, Nora, have been racking leaves and they raked enough to fill up a certain number of bags.
Out of these bags, Finn emptied 4 bags to be able to make a leaf pile. Nora then stopped him from emptying the other 7 bags.
The total number of bags of leaves raked by Nora and Finn is:
= Number of bags remaining + Number of bags emptied by Finn
= 7 + 4
= 11 bags of leaves
Remaining part of question:
How many bags of leaves were raked by Finn and Nora?
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Mr. Mole left his burrow and started digging his way down.
AAA represents Mr. Mole's altitude relative to the ground (in meters) after ttt minutes.
A=-2.3t-7A=−2.3t−7A, equals, minus, 2, point, 3, t, minus, 7
How fast did Mr. Mole descend?
Mr mole descend at the rate of 2.3 meters per minutes.
A rate in mathematics is the comparison of two related values expressed in dissimilar units.
The numerator of the ratio expresses the equivalent rate of change in the other (dependent) variable if the denominator of the ratio is presented as a single unit of one of these quantities and it is expected that this number may be altered systematically (i.e., is an independent variable).Examples of rates that are usually represented as "per unit of time" are speed, heart rate, and flux. An example of a ratio having a non-time denominator is the electric field ratio. Other examples include exchange rates and literacy rates (in volts per meter).The given equation to represent the position of Mr. Mole is
A = -2.3 t - 7
where A denotes the depth and t is the time.
Now the rate can be found out by dividing the change in depth by the change in time.
Differentiating we get
ΔA = -2.3 Δt
or, ΔA / Δt = -2.3
hence the rate of the mole is 2.3 meters per minutes.
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m = -5, passing through (-2, 4)
Y-b=m (x-a)
y- 4= -5 (x+2)
y- 4= -5x -10
y = -5x -6
Jason's square bedroom has an area of 112 square feet. The length of one
of his room is between what two whole numbers?
Multiplying Radicals.
The distance remaining to a destination after t minutes is given by d(t) = 340-0. 85t, measured in miles. The graph of d(t) is shown below.
After how many minutes is the destination reached?
In 400 minutes, it will reach the destination.
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is also frequently used metaphorically to refer to a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial thinking is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalise the majority of these notions of distance, both literal and figurative.
Distance is equal to speed × time. Time is equal Distance/Speed.
we have given, d(t)=340-0.85t
where, t is the time and d(t) is the distance.
when t = 0 we get,
d(t)=340
If we set d(t)=0 we get, 0= 340- 0.85t
add with 0.85t on both side
0.85t=340
t= 340/0.85
t= 400 minutes
Hence, the time taken to reach the destination is 400 minutes.
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Name the subset of the real numbers to which each number belongs 2/3
The given number 2/3 belongs to the subset of rational numbers.
What are subsets?
All numbers on the number line, from negative to plus infinity, are considered to be real numbers. They are breaking up into the following groups:
1. We can count the components of a set using natural numbers.
2. Natural numbers and their opposites in the negative, such as zero, are known as integers.
3. Fractions can be used to express rational numbers.
4. Non-periodic infinite decimals are indicative of irrational quantities.
The answer to the given question is : It belongs to the rational numbers because it is a fraction.
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A theater group made appearances in two cities. the hotel charge before tax in the second city was $500 higher than in the first. the tax in the first city was 6.5% and the tax in the second city was 6% the total hotel tax paid for the two cities was $748.7. how much was the hotel charge in each city before tax?
Using algebraic expression and equation, the hotel charge before tax in each city is $5749.60 and $6249.60, respectively.
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 "=".
Let x = hotel charge before tax in the first city
If the hotel charge before tax in the second city was $500 higher than in the first, then
hotel charge before tax in the second city = $500 + x
If the tax in the first city was 6.5% and the tax in the second city was 6% and the total hotel tax paid for the two cities was $748.7, then
x(0.065) + ($500 + x)(0.06) = $748.7
Solving for x,
x(0.065) + ($500 + x)(0.06) = $748.7
0.065x + $30 + 0.06x = $748.7
0.065x + 0.06x = $748.7 - $30
0.125x = $718.7
x = $5749.60
hotel charge before tax in the first city = $5749.60
hotel charge before tax in the second city = $500 + x
hotel charge before tax in the second city = $500 + $5749.60
hotel charge before tax in the second city = $6249.60
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