trueeeeeeeeeeeeeeeee
A playground is in the shape of a right triangle with an area of 294 yd^2. The shortest side of the playground (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the playground (the hypotenuse). How long would the path be?
Show your work.
Don't forget to label the answer.
Answer:
Answer: The length of the path would be 35 yds.
Step-by-step explanation:
We can use the formula for the area of a right triangle to find the length of the other leg. Once we know the lengths of both legs, we can use the Pythagorean theorem to find the length of the hypotenuse.
Let's call the length of the shortest side (the leg) "a", and let's call the length of the other side (the other leg) "b". We know that a = 21 yd and the area of the triangle is 294 yd^2. So we can use the formula for the area of a right triangle to solve for b:
area = (1/2) * a * b
294 = (1/2) * 21 * b
b = (2 * 294) / 21
b = 28
Now we know that a = 21 yd and b = 28 yd. We can use the Pythagorean theorem to find the length of the hypotenuse (c):
c^2 = a^2 + b^2
c^2 = 21^2 + 28^2
c^2 = 441 + 784
c^2 = 1225
c = sqrt(1225)
c = 35
Therefore, the length of the path along the longest side of the playground would be 35 yds.
Answer:
35 yards.
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let's call the other leg of the triangle "x" and the length of the hypotenuse (the path the council would like to add) "c". Then we have:
Area of triangle = (1/2) * base * height
294 = (1/2) * 21 * x
x = 28
Now we can use the Pythagorean theorem to find "c":
c^2 = 21^2 + 28^2
c^2 = 441 + 784
c^2 = 1225
c = sqrt(1225)
c = 35
So the length of the path the council would like to add is 35 yards.
??? HELP im confused
Answer:
a=3
Step-by-step explanation:
the sum of anterior angle of a triangle is =180
57+81+14a=180
138+14a=180
42=14a
42/14=14a/14
3=a
therefore a=3.
please mark me the brainliest.
your friend bought a new pair of shoes. He said the regular price was 75$ but that he got them for a 40% discount. What is the sale price of the shoes?
The sale price of the shoes is $45.
Your friend bought a new pair of shoes that had a regular price of $75. The regular price is the original or full price of the item before any discounts or promotions are applied.
Your friend said that he got a 40% discount on the shoes. A discount is a reduction in price from the regular price, often as a promotion or incentive to encourage customers to purchase the item. In this case, the discount is 40% of the regular price.
To calculate the sale price of the shoes, we need to subtract the discount amount from the regular price. The discount amount is 40% of $75, which is:
Discount amount = 40% x $75
Discount amount = $30
Now, we can find the sale price by subtracting the discount amount from the regular price:
Sale price = Regular price - Discount amount
Sale price = $75 - $30
Sale price = $45
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Does the Laplace Transform Method apply to the following equations?
a.)y′′′+4y′′−3y′+8y=sin(3t)
b.)3y′′+5y′−10y=0
c.)3y′′+2y′−3y=cos(t)
d.)(e^t)y′′+ty′−5(t^2)y=0
e.)yy′=sin(t)
f.)yy′′+5y′=5
g.)y′=sin(y)
h.)2y′+5y=sin(t)
The Laplace Transform Method can be used to solve all of these equations except for equation (e).
a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.
b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.
c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.
d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.
e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.
f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.
g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.
h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.
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how much is 40 lb to kg
40 pounds (lb) is equivalent to 18.14 kilograms (kg). To convert pounds to kilograms, you need to use the conversion factor of 0.45359237 kg per pound.
This means that you can multiply the number of pounds by this conversion factor to get the equivalent weight in kilograms.
The conversion from pounds to kilograms is important when it comes to international trade and travel, where weight measurements are typically done in the metric system. Knowing how to convert between different units of measurement is also useful in scientific and engineering fields, where calculations may require using units from different systems.
It's important to note that weight and mass are not the same thing. Weight is a measure of the force exerted on an object by gravity, while mass is a measure of the amount of matter in an object. The conversion from pounds to kilograms assumes that the force of gravity is constant, but this may not always be the case in different parts of the world.
In summary, 40 pounds is equal to 18.14 kilograms, and knowing how to convert between different units of measurement is an important skill in various fields of study and in everyday life.
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7. What is the range of the function
F(x) = 3/4 x - 5 with a domain of -2,0, and 4?
Range of the function is the set {-6.5, -5, -2}.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Domain of the function is the input values of the function and Range of the function is the output values.
Given function is,
F(x) = 3/4 x - 5
Domain of the function is -2, 0 and 4.
F(-2) = (3/4 × -2) - 5 = -13/2 = -6.5
F(0) = (3/4 × 0) - 5 = 0 - 5 = -5
F(4) = (3/4 × 4) - 5 = 3 - 5 = -2
Range = {-6.5, -5, -2}
Hence the required range of the given function is {-6.5, -5, -2}.
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4(3p+3)=60 what does p mean
Answer: p = 4
Step-by-step explanation:
Because 3 * 4 + 3 = 15 which is then multiplied by 4 equaling 60
Answer:
p=4
Step-by-step explanation:
4(3p +3) = 60
12p + 12 = 60
-12 -12
___________
12p = 48
p = 4
hich one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam? (a) It means that you missed two questions on the exam. (b) It means that you got twice as many questions correct as the average student. (c) It means that your grade was 2 points higher than the mean grade on this exam. (d) It means that your grade was in the upper 2% of all grades on this exam. (e) It means that your grade is 2 standard deviations above the mean for this exam.
Answer:
(e) It means that your grade is 2 standard deviations above the mean for this exam.
Step-by-step explanation:
Z-score describes the number of standard deviations away from the mean. In this case, a z-score of +2.0 would be 2 standard deviations above the mean.
ABCD is a parallelogram and EF is parallel to AB. Select all triangles are similar to triangle AEX?
In the parallelogram ABCD the triangles that are similar to ΔAEX is -
Option 1: ΔCFX, Option 2: ΔADC, and Option 5: ΔCBA
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
The parallelogram ABCD is given.
AC is the diagonal of the parallelogram and EF is a line segment parallel to AB and CD in the parallelogram.
In ΔAEX and ΔADC -
m ∠AEX ≅ m ∠ADC, since they are corresponding angles.
m ∠A ≅ m ∠A, since they are reflexive angles.
So, ΔAEX ~ m ∠ADC, by AA similarity.
Similarly, in ΔAEX and ΔCFX -
m ∠EAX ≅ m ∠XCF, since they are alternate interior angles.
m ∠AXE ≅ m ∠CXF, since they are vertical angles.
So, ΔAEX ~ m ∠CFX, by AA similarity.
Now, in ΔAEX and ΔCBA -
Since, EF is parallel to AB then AEFB is also a parallelogram because ABCD is a parallelogram.
Then m ∠E ≅ m ∠B, since they are opposite angles of parallelogram AEFB.
m ∠EAX ≅ m ∠ACB, since they are alternate interior angles.
So, ΔAEX ~ m ∠CBA, by AA similarity.
Therefore, the similar triangles are ΔADC, ΔCFX, ΔCBA.
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solve for x 4(x + 4) + 2x = 52
Answer:
x = 6Step-by-step explanation:
solve for x 4(x + 4) + 2x = 524(x + 4) + 2x = 52
4x + 16 + 2x = 52
6x = 52 - 16
6x = 36
x = 36 : 6
x = 6
Answer:
[tex] \sf \: x = 6[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 4(x + 4) + 2x = 52
Then the value of x will be,
→ 4(x + 4) + 2x = 52
→ 4x + 16 + 2x = 52
→ 6x + 16 = 52
→ 6x = 52 - 16
→ 6x = 36
→ x = 36 ÷ 6
→ [ x = 6 ]
Hence, the value of x is 6.
x² at x = 3 what is the answer pleas help
Answer: 9
Step-by-step explanation:
First plug in 3 for x.
Then you get 3^2
Now you solve and you get 9. Its the same as saying 3 * 3 = 9.
how do I find the % difference between two numbers
Answer: Use the formula C (percent change/ percent difference) = x (the final value)-Y (the initial value) / Y, or C= x-y/y
Step-by-step explanation: This is the official formula. I found that it's easier to use the bigger value in the top x-y first, so you don't have to calculate the absolute value, but other than that the formula is correct.
help
For the factor family 7,8 and 15 write two addition and subtraction facts
Answer:
Addition:
7+8=15
8+7=15
Subtration:
15-8=7
15-7=8
Step-by-step explanation:
You just have to include all numbers and make an equation that involves all three digits
If pp is inversely proportional to the square of qq, and pp is 24 when qq is 7, determine pp when qq is equal to 2.
The value of pp when qq equals 2 is: 294
What is the value of pp when qq equals 2?If pp is inversely proportional to the square of qq, it means that pp*qq²=k, where k is the constant of proportionality.
Given that pp is 24 when qq is 7, we can find the value of k:
24*7² = k
k = 1176
Now, we can use this value of k to find pp when qq is equal to 2:
pp*2² = 1176
pp*4 = 1176
pp = 1176/4
pp = 294
Therefore, when qq is equal to 2, pp is equal to 294.
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Which expression is equivalent to |x| < 11?
Responses
x > –11 or x < 11
x > –11 or x < 11
x < –11 and x > 11
x < –11 and x > 11
x < –11 or x > 11
x < –11 or x > 11
x > –11 and x < 11
Answer:
x > -11 and x < 11
Step-by-step explanation:
Find the absolute value of a number gives you its distance from zero, which is just the numerical parts of it. From this we can reason that the numbers between -11 and 11 have an absolute value less than 11, as they are the numbers that are less than 11 away from zero. This can be represented as -11 < x < 11, and can be separated into x > -11 and x < 11 (the "and" is because x has to fulfill both conditions of being greater than -11 and less than 11).
whats the common denominatior of 1/2 3/4 3/7
Answer:
28
Step-by-step explanation:
Smallest common multiple of 2, 4 and 7 -> 28
Write an expression that is equivalent to 734+356 − 134that uses addition instead of subtraction.
The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:
734 + 356 + (-134)
Answer:
706+350 = 956
Solve the inequality from part A for x. Then use the drawing tools to graph the solution set on the number line.
On the number line, mark the endpoint at 10 with a closed circle.
Next, draw a ray to the right of 10.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Next, we would collect like-terms and rearrange the expression as follows;
1,558 + 60x ≥ 2,158
60x ≥ 2,158 - 1,558
60x ≥ 600
x ≥ 10
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Complete Question:
Solve the inequality from part A for x. 1,558 + 60x ≥ 2,158.
Then use the drawing tools to graph the solution set on the number line.
On the number line, ________________.
Next, draw a ray to the ____ of 10.
Please help will give Brainly
Answer:
410 is the outlier.
What is an outlier?
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.
In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.
Step-by-step explanation:
Hope it helps! =D
pls helpp dilation of 1.5 about the origin
F(1, -1), G(0, 2), H(1, 2)
The Coordinates after dilation of 1.5 about the origin is
F'(1.5, -1.5)
G'(0, 3)
H'(1.5, 3)
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
Given:
We have the Coordinates F(1, -1), G(0, 2), H(1, 2).
As, the Dilation Rule for point (x, y) about origin with scale factor h
h(x, y)------>(hx, hy)
Applying the Dilation Rule we get
F(1, -1)-----> 1.5 F'(1, -1)-----> F'(1.5, -1.5)
G(0, 2)-----> 1.5 G'(0, 2)-----> G'(0, 3)
H(1, 2) -----> 1.5 H'(1, 2)-----> H'(1.5, 3)
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What is F(1) (evaluate the function
F(1) is equal to 0 for the given function F(x).
According to given condition :In order to evaluate a function at a specific value, you simply substitute that value for the input variable in the function and simplify the resulting expression.
If you are given a specific function F(x) and are asked to evaluate it at a specific value, say F(1), then you would substitute x=1 in the function F(x) and simplify the expression.
For example, if [tex]F(x) = x^2 + 2x - 3[/tex], then to evaluate F(1), we substitute x=1 in the expression:
[tex]F(1) = (1)^2 + 2(1) - 3[/tex]
Simplifying the expression, we get:
F(1) = 1 + 2 - 3 = 0
Hence, F(1) is equal to 0 for the given function F(x).
What is function ?A function is a mathematical rule that takes an input value, processes it, and produces an output value. The input value is called the independent variable, and the output value is called the dependent variable, because its value depends on the input.
A function can be represented in various ways, such as an algebraic expression, a graph, a table, or a verbal description. For example, the function f(x) = 2x + 1 is an algebraic expression that represents a linear function, where the independent variable is x and the dependent variable is f(x).
Functions are used to describe and model relationships between variables in various fields of mathematics, science, engineering, economics, and other disciplines. They are important tools for analyzing and solving problems, and they can be used to make predictions, optimize processes, and design systems.
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I need help figuring out This problem .
The value of x in the two congruent triangles is 3.9 and length CB is 53.9.
What is the value of x in the given triangle?The value of x can be determined by applying the principle of congruent theorem.
The congruent theorem states that, if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.
( 11x + 11 ) / 77 = 21 / 30
11x + 11 = 53.9
11x = 53.9 - 11
11x = 42.9
x = 42.9 / 11
x = 3.9 units
The length of CB = ( 11 x 3.9 ) + 11 = 53.9
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i need someone smart to answer this question
The other two exterior angles are the ones in option 4.
105° and 115°
How to find the other two exterior angles of a triangle?Remember two things:
The sum of the exterior angles of any triangle is equal to 360°The sum between an interior angle and the correspondent exterior angle is equal to 180.You can use any of these two to find the answer, I will use the first one.
If one of the exterior angles is 140°, then the only option that adds up to 360° is the lastoption
140° + 115° + 105° = 360°
So that is the correct option.
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Tallulah's family took a road trip to the Grand Canyon. Tallulah slept for the last 129 miles of the trip. If the total length of the trip was 300 miles, what percentage of the total trip had they travelled when Tallulah fell asleep?
43% of the total trip had they travelled when Tallulah fell asleep
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Tallulah's family took a road trip to the Grand Canyon.
Tallulah slept for the last 129 miles of the trip.
the total length of the trip was 300 miles
We have to find the percentage of the total trip had they travelled when Tallulah fell asleep
x/100×300=129
3x=129
Divide both sides by 3
x=43%
Hence, 43% of the total trip had they travelled when Tallulah fell asleep
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what is the distance between point p and q 2,4 /2-,3
The value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.
What does the coordinate geometry distance formula mean?
In coordinate geometry, the distance formula is used to compute the distance between two specified points.
The distance formula is D=
It is used to determine the distance between two locations (x1,y1)(x1,y1)) and (x2,y2)(x2,y2).
Given: Points P and Q are separated by 17 units. The coordinates of point P are (5, 5) and point Q are (-3,y).
Using the distance formula,
PQ = [tex]\sqrt{(x2-x1)^{2} +(y2 - y1)^{2} }[/tex]
17² = 64 - y² +25 +10y
289-64-25 = - y² + 10y
y² + 10y - 200 = 0
On solving the quadratic equation we get,
y = -20, 10
Therefore, the value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.
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A quarterback completes of passes during the first three quarters of a football game. He completes e pass in the fourth quarter and of his passes for the entire game. How many passes does the quarterback throw in the fourth quarter?
Rounding up to the nearest whole number, the quarterback throws 3 passes in the fourth quarter to complete all of them.
Let's first find out how many passes the quarterback completed in the first three quarters:
18 passes completed out of 33 attempts in the first three quarters
= 18/33 = 0.545 (rounded to three decimal places)
We can then find the total number of passes attempted in the first three quarters by using the fact that the completion rate is the number of completions divided by the number of attempts:
0.545 = 18/x, where x is the total number of attempts in the first three quarters
Solving for x, we get:
x = 18/0.545 = 33
So the quarterback attempted 33 passes in the first three quarters.
Next, we can find the total number of passes attempted in the game by using the completion rate for the entire game:
0.625 = (18 + passes completed in the fourth quarter) / (33 + passes attempted in the fourth quarter)
Multiplying both sides by the denominator:
0.625 × (33 + passes attempted in the fourth quarter) = 18 + passes completed in the fourth quarter
20.625 + 0.625 × passes attempted in the fourth quarter = 18 + passes completed in the fourth quarter
Subtracting 18 and 0.625 × passes attempted in the fourth quarter from both sides, we get:
2.625 = passes completed in the fourth quarter - 0.625 × passes attempted in the fourth quarter
Adding 0.625 × passes attempted in the fourth quarter to both sides, we get:
passes completed in the fourth quarter = 2.625 + 0.625 × passes attempted in the fourth quarter
We don't know the exact number of passes attempted in the fourth quarter, but we can see that for every 1 pass attempted, the quarterback completes 0.625 - 0.545 = 0.08 more passes than in the first three quarters. So to complete all of his passes in the fourth quarter, he needs to attempt:
0.08 × x = 0.08 × 33 = 2.64
Question - A quarterback completes 18 of 33 passes during first three quarters of a football game. He completes every pass in the fourth quarter and 62.5% of his passes for the entire game. How many passes does the quarterback throw in fourth quarter?
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calculate 10% of 360km
Answer:36
Step-by-step explanation:360 * 0.1 = 36 or 360/10 = 36
What is the conversion of 2.25 inches to mm ?
In metric system length measured by using kilometres, milimter and miles etc. Thus, the conversion of 2.25 inches to mili meters is equals to the 57.15 mm.
Inches (also called in. ) is a unit of measurement used in US customer measurement systems. It is also part of the imperial measurement system. A millimeter (abbreviation mm) is a unit of measurement in the metric system. Like the inch, it is used to measure the length of an object, especially small ones. "Millimetre" is the US spelling, while in the UK it is spelled "millimetre". To convert from one measurement unit to another, multiply by the conversion factor. Formula to convert inches to millimeters, [X] mm = 25.4 × [Y] in ---(1)
where [X] is the result in mm and [Y] is the amount in we want to convert.We need to convert 2.25 inches to millimeters. So using the formula, millimeter = 25.4 × 2.25 inches
= 57.15
Hence, required value is 57.15 mm.
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After 35 games of a football season, Manchester United won 14 games and lost 21 games at this rate how many games will they win in a 54 game season
The number of games they win is 22 games for 54 game season.
What is proportion?
In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities or values, usually expressed as a fraction. For example, the ratio of boys to girls in a class might be expressed as 3/5, meaning that for every 3 boys in the class there are 5 girls.
Explanation:
Assuming that Manchester United's winning and losing rates remain the same throughout the season, we can use a proportion to estimate how many games they would win in a 54 game season:
wins / total games = winning rate
Using the data given in the problem, we can find the winning rate as:
14 / 35 = 0.4
So, Manchester United's winning rate is 0.4, or 40%.
To estimate how many games they would win in a 54 game season, we can set up a proportion:
wins / total games = winning rate
x / 54 = 0.4
Solving for x, we get:
x = 54 * 0.4 = 21.6
Rounding to the nearest whole number, we get an estimate of 22 games that Manchester United would win in a 54 game season, assuming their winning and losing rates remain the same as the first 35 games.
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conversion a) 192 km b) 15500 dam c) 85000 m d) 3360 hm e) 860000 dm
The given length measurements are converted and given below.
What is unit conversion?Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.
Given is to convert the given measurements as -
a) 192 km
b) 15500 dam
c) 85000 m
d) 3360 hm
e) 860000 dm
We can write the measurements as -
a) 192 km
192 Km = 192000 meters
b) 15500 dam
15500 dam = 15500 x 10 = 155000 meters
c) 85000 m
85000 m = (85000/1000) Km = 85 Kilometers
d) 3360 hm
3360 hm = 3360 x 100 = 336000 meters
e) 860000 dm
860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter
Therefore, the given length measurements are converted and given above.
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