Answer:
It is not a right triangle.
Step-by-step explanation:
If the triangle were a right triangle, then the Pythagorean theorem would apply.
The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]
If A = 10, B = 16, and C = 20, then [tex]10^{2} + 16^{2} = 20^{2}[/tex].
[tex]10^{2} + 16^{2} = 100 + 256 = 356[/tex]
[tex]20^{2} = 400[/tex]
In conclusion, [tex]356 \neq 400[/tex], so this triangle is not a right triangle.
What is the solution set of the inequality?
Answer:
the fourth one is the right one
What is the radical form of each of the given expressions? Drag the answer into the box to correctly match each expression.
2 2/3 -
3 1/3 -
3 3/2 -
2 1/2 -
The radical form of each of the given expressions are;
1) 2^(2/3) = ∛(2²)
2) 3^(1/3) = ∛3
3) 3^(3/2) = √3³
4) 2^(1/2) = √2
What is the radical form of the exponent form?The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]
Thus, we can solve each of the given expressions;
1) We are given the expression as 2^(2/3).
Thus;
x = 2 and y = 3 and we have; ∛(2²)
2) We are given the expression as 3^(1/3).
Thus, x = 1 and y = 3 and so we have;
∛3
3) We are given the expression as 3^(3/2). Thus;
x = 3 and y = 2 and so we now have; √3³
4) We are given the expression as 2^(1/2). Thus;
x = 1 and y = 2 and so we now have; √2
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2/7 x 2 1/4 write your answers in simpliest form
Answer:
the answer is 9/14
Step-by-step explanation:
2/7× 2 1/4 = 2/7× 9/4
= 2 × 9 / 7 × 4
= 18/28
= 9/14
Can somebody please answer these 3 questions please and thank you
[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]
Answer:
x = 30
y = 60
Step-by-step explanation:
First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.
Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.
Lastly, corresponding angles on parallel lines are congruent.
By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.
[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]
Answer:
x = 65
Step-by-step explanation:
From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.
We also know there are 180 degrees in a triangle.
Lastly, we know that alternate interior angles are congruent.
Using this knowledge, we can decide that x = 65.
[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]
Answer:
x = 30
Step-by-step explanation:
Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.
After placing vertical angles down from the given information, we can fill in more using corresponding angles.
Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.
Using this information, we can decide that x = 30.
a party rental company has chairs and tables for rent. the total cost to rent chairs and tables is . the total cost to rent chairs and tables is . what is the cost to rent each chair and each table?
If the total cost to rent 2 chairs and 12 tables is $107 and the total cost to rent 5 chairs and 3 tables is $38, then the costs to rent each chair and table are $2.5 and $8.5 respectively. We can solve this question using elimination and substitution methods.
How do you prove that?Elimination and substitution methods are involved in solving this problem. We're going to use the variables x for the cost of a chair and y for the cost of a table. The total cost to to rent 2 chairs and 12 tables is $107, so the equation can be written as 2x + 12y = 107. The total cost to rent 5 chairs and 3 tables is $38, so the equation can be written as 5x + 3y = 38.
To find the value for x, we need to eliminate the variable y first. Start by multiplying each term in the second equation by 4.
5x · 4 + 3y · 4 = 38 · 4
20x + 12y = 152
Then, subtract the terms in the second equation from their counterparts in the first equation.
2x + 12y = 107
20x + 12y = 152 -
-18x + 0 = -45
Finally, with a little bit of algebraic manipulation, we've got x = 2.5, hence $2.5 is the cost in to rent a chair.
-18x = -45
x = -45/-18
x = 2.5
What about the cost to rent a table? Well, we can substitute 2.5 for x in either of the equations to get the value for y. For instance, we can pick the equation 2x + 12y = 107 and substitute x with 2.5 to isolate the variable y, like this:
2(2.5) + 12y = 107
5 + 12y = 107
12y = 107 - 5 = 102
y = 8.5
The value for y turns out to be 8.5. So the cost to rent a table is $8.5.
Your question is incomplete, but it was most probably "A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 12 tables is $107. The total cost to rent 5 chairs and 3 tables is $38. What is the cost to rent each chair and each table?"
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The side lengths of triangle ABC are written in terms of
the variable p, where p > 3.
A
p+4
C
4p-1
3p
B
Which is correct regarding the angles of the triangle?
Om/A> m2C> mzB
OmZB> mzA> mZC
Omzc>m mZB
O mzC> m2B> MZA
m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.
What is the angle of the triangle?
While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.
Here, we have
In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.
AB=4p-1 , AC=p+4 , BC=3p
where p+4 < 3p [as p≥3]
3p < 4p-1 [as p≥3]
⇒ 4p-1> 3p > p+4
⇒AB > BC > AC
Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.
m∠C > m∠B > m∠A [∵Angle opposite to greater side is greater]
Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.
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A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint?
The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.
So, the ratio of gallons of blue paint to gallons of yellow paint is
= 5 to 9 or 5:9
Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint
= 1- 5/9
=4/9
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the superintendent of schools in a small town in ohio made many policy changes to the way school administration worked in his district. a researcher at a nearby university wanted to look at what teachers in his district thought about the changes. the researcher made a list of all the schools in the district and used a random number generator to select a sample of five schools from the district. then the researcher interviewed every teacher at each of those five schools. which sampling method did the researcher use?
Answer:
The number to the ration
Step-by-step explanation:
the sum of the measures of the angles in the triangle is 180 degrees. what is the measure of each angle? write and solve an equation
If sum of the measures of the angles in the triangle is 180 degrees then
measures of each angle is 60 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The sum of the measures of the angles in the triangle is 180 degrees
By angle sum property, sum of the measures of the angles in the triangle is 180 degrees
Let the measure of angle be x
x+x+x= 180 degrees
3x=180
Divide both sides by 3
x=180/3
x=60
Hence each angle measures 60 degrees.
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Find the perimeter of this semi-circle
with diameter, d = 84cm.
Give your answer as an expression in
terms of π.
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
What is the equation for a semicircle?The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.
How do you calculate the circumference of a half-semicircle?With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.
According to the given data:Diameter of the semi-circle = 84cm
Now,
the circumference of the semi-circle = πr + 2r
Substituting the value of r in the given formula:
the circumference of the semi-circle = πr + 2r
= πr + 2r
= 48π + 42
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
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What is the name of the bolded part of this shape?
Answer:
A right-angled triangle
Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference.
5, 4, 3, 2, ...
Is this an arithmetic sequence?
Ο No
O Yes
Select the correct choice and fill in any answer boxes in your choice below.
O A. The common difference is
O B. There is no common difference.
Answer:
Is this an arithmetic sequence?
Yes.
Is there a common difference and if so, what is it?
Yes, there is a common difference : 1
The common difference is 1
The distance from Jose’s home to school is 1. 85 miles. The school is 2. 34 miles from the local library, which is 1. 9 miles from Jose’s home. If Jose goes from his home to school, from school to the library, and then home, how far did he travel?
The Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.
Define the term total distance?Distance is defined as an object's entire movement without regard for direction. Distance can be defined as how much ground any object has covered regardless of its originating or ending place.The distance between Jose's house and school is 1.85 miles.
The school is 2.34 miles from the nearest library, which is 1.91 miles away from Jose's house.
Total distance = Jose’s home to school + school to library
Total distance = 1.85 + 2.34
Total distance = 4.19 miles.
Thus, the Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.
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Write down the inequality shown on the number line below.
Answer:
- 0.5 ≤ x ≤ 3.5
Step-by-step explanation:
since both ends of the interval are closed circles. This indicates that x can equal both - 0.5 and 3.5 and the values between , then
- 0.5 ≤ x ≤ 3.5
The inequality shown on the number line is -0.5 ≤ x ≤ 3.5.
Given is a number line where a value starts from -0.5 and end at 3.5, we need to write down the inequality shown on the number line,
To write down the inequality shown on the number line starting from -0.5 and ending at 3.5, we need to determine the range of values represented by the line segment.
The left endpoint of the line segment is -0.5, which means the value represented by that point is greater than or equal to -0.5.
We can express this as:
x ≥ -0.5
The right endpoint of the line segment is 3.5, which means the value represented by that point is less than or equal to 3.5.
We can express this as:
x ≤ 3.5
Combining these two inequalities, we have:
-0.5 ≤ x ≤ 3.5
This inequality represents all the values on the number line between -0.5 and 3.5, inclusive.
Hence the required inequality is -0.5 ≤ x ≤ 3.5.
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Over which of the following intervals would the function h(x)=|x-2|+6 be decreasing only?
We have an absolute value function that opens upwards. The interval where it is decreasing only is:
(-∞, 2)
Over which interval is the function decreasing only?All absolute value equations of the form:
y = |x - a| + b
have graphs that open upwards, and a vertex in the point (a, b).
While ones of the form:
y = -|x - a| + b
have graphs that open downwards, and again, a vertex in the point (a, b).
In this case we have one that open upwards:
h(x)=|x-2|+6
With a vertex at (2, 6)
The function will be decreasing on the left side of the vertex, so the interval where the function is only decreasing is:
(-∞, 2)
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What else must you know to prove the triangles congruent by SAS?
D
B
OA AB CD
OB. AD AC
O CAB DC
OD AD BC
As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.
In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),
And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.
Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.
Among our concerned triangles, ΔABC and ΔADC, already given that,
(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,
And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.
At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.
Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and (ΔABC and ΔADC) can be proved to be congruent triangles.
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Given that x is a nonnegative number, a student conjectured that a +5 < x²
Which value of x is a counterexample to the student's conjecture?
A.) x = -1/
5
B.)x = -5
C.)x = 0
D.) x = 5
Option B, x = -5 is correct answer, x = -5 is the counter example to the student's conjecture.
What is inequality?
A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Given inequality in the question is:
x +5 < x²
We will check each option given I question by putting value of x,
putting x = -1/5
x + 5 < x²
-1/5 + 5 < (-1/5)²
24/5 < 1/25
4.8 < 0.04
This is wrong inequality , Therefore, x is not equal to -1/5
putting x = -5
x + 5 < x²
-5 + 5 < (-5)²
0 < 25
This is satisfying the inequality ,
Therefore, x is equal to -5
Hence, correct answer is x = -5
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The equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5). What is the equation of line k?
The equation of line k is y = 1/2x - 1.
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.
Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)
When two lines are parallel their slope are equal, so solving for c,
-5 = 1/2*-8 + c
c = -1
The equation will be,
y = 1/2x - 1
Hence, The equation of line k is y = 1/2x - 1.
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I need help like asap !!!
only numbers and decimal points
a wooden cube nn units on a side is painted red on all six faces and then cut into n^3n 3 unit cubes. exactly one-fourth of the total number of faces of the unit cubes are red. what is nn?
After being painted red on all six faces, a hardwood cube with nn units on each side is chopped into n3n 3-unit cubes. The unit cubes have exactly one-fourth of their faces be red, therefore nn equals 4.
On each face of the large wooden cube, there are tiny faces that have been painted red.
There are few faces overall because each unit cube has faces.
Given that one-fourth of the little faces are red,
[tex]6n^2/6n^3[/tex] [tex]= 1/4[/tex]
[tex]1/n = 1/4[/tex]
[tex]N=4[/tex]
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The half-life of a substance is the time it takes for half of that substance to break down or decay. The half-life of an unknown element is 1 day.
Write an equation for the amount remaining from a sample of 100 grams of the element after x days. How much of the substance will be left after 3 days? Where is the
asymptote?
Answer:
See below
Step-by-step explanation:
Amount = 100 (1/2)^x
after 3 days
amount = 100 ( 1/2)^3 = 12.5 gm left
relative maxima and relative minima of the function f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
The relative maxima and relative minima of the function
f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
the relative maxima is -1.871the relative minima is 1.518How to fine the relative maxima and minimaThe relative minima and maxima is calculated
by differentiating the given function find the critical values or roots of the equationdifferentiate the second tiesubstitute the critical value that are real numbersthe critical value that gave a negative value is the maximathe critical value that gave a positive value is minimaThe procedure is done as follows
x^5 - 4x^3 + 3x^2 - 8x - 6
differentiating gives
5x^4 - 12x^2 + 6x - 8
solving the equation for the critical values are
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
The second derivative
5x^4 - 12x^2 + 6x - 8
differentiating gives
20x^3 - 24x + 6
substituting x = 1.58
20 * 1.58^3 - 24 * 1.58 + 6
= 46.966 (positive hence minima)
substituting x = -1.871
20 * -1.871^3 - 24 * -1.871 + 6
= -169.9 (negative hence maxima)
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Solve for n. −2(n − 5.5) > 21 PLEASE HELP MEEEEEEE
Answer:
Step-by-step explanation:
1. Divide by -2 and thus flip the inequality
2. (n-5.5)<21/-2
3. Add 5.5 to both sides
4. n<-5
5.Check by plugging in any number less than -5 and see if the inequality is true
6. Example: plug in -10
Is -2(-10-5.5)>21?
Yes
31>21 your solution is n<-5
On solving the linear inequality −2(n − 5.5) > 21 for n, we get n < -5.
Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'.
Given in the question,
-2(n - 5.5) > 21
Solving the inequality,
-2n + 11 > 21
-2n > 21 - 11
-2n > 10
-n > 5
n < -5
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.
How to derive a quadratic equation by factorizationIn this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:
y = (x - r₁) · (x - r₂)
y = (x + 2) · (x - 2)
Second, expand the expression derived in the previous step by algebra properties:
y = (x + 2) · x - (x + 2) · 2
y = x² + 2 · x - 2 · x - 4
y = x² - 4
Third, write the resulting expression:
y = x² - 4
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suppose the insect population doubled after 15 hours. how long (in hours) will it take the insect population to grow to eight times its initial size? (simplify your answer completely.)
Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.
What is growth and decay modeling?The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.
Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:
n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.
Suppose an initial number of insects is x and after 15 hours it becomes 2x.
2x = x[tex]e^{15r}[/tex]
[tex]e^{15r}[/tex] = 2
Take the log of both sides of the equation
ln [tex]e^{15r}[/tex]= ln 2
15r = ln 2
r = 0.693147/15
Now, population after 1-hour = x [tex]e^{r}[/tex]
= 1.047
≈ 1.05
Hence the population of insects after 1 hour will be about 1.05 times.
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I NEED HELP ME PLEASE!!!
Answer:
I hope this is right
TG = 34 TG=34 inches
From the figure
PQR is a triangle
PS, QT are medians of the triangle
G is the centroid
Step 1: Calculate the segment of the median (TG = ? )
We know that
Each median is divided into segments with a 2:1 ratio by the triangle centroid.
\therefore \frac{TG}{GQ} = \frac{2}{1} ∴
GQ/TG = 1/2
TG = 2 GQ TG=2GQ
TG = 2 * 17 TG=2∗17
TG = 34 TG=34
Hence, segment of the median TG = 34 inches
The amount of seed in a bird feeder decreased 11 1/4 ounces in 5 days. The amount of seed decreased the same amount each day. What was the change in the amount of seed in the bird feeder after 7 days?
The change in the amount of seed in the feeder after 7 days is 78.75 ounces.
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.
For example, if you ran 80 meters in 10 seconds, you ran on average 8 meters in 1 second
To find the rate at which the amount of seed decreases.
11 1/4 ounces = 5 days
Dividing both sides of the equation by 5.
11 1/4 ounces = 1 day
Multiplying 7 on both sides to get the number for 7 days
7 x 11.25 ounces = 7 days
78.75 ounces = 7 days
If the amount of seed in a bird feeder decreases by 11 1/4 ounces in 5 days, the amount of seed decreases by 78.75 ounces.
The change in the amount of seed in the feeder in 7 days is 78.75 ounces.
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Write the domain as an equality
The domain of the inequality is from zero to negative infinity
[ -∞, 0)How to determine the domain of the inequalityThe domain refers to the values in the input of a function, these values are in the x direction.
The domain says the extents the values of the input is therefore no all the input values must be in the domain
Examining the graph shows that the graph reached the point x = 0 and returned with an arrow.
The arrow means that the values continued limitlessly, such limitless values are represented by infinity with symbol ∞.
The infinity is in the negative direction
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2. Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000. Last year
Maria made $40,000 in sales. How much did Maria earn in salary plus commission?
Last year, Maria earned $54,000
In this question, we have been given Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.
Last year Maria made $40,000 in sales.
This means, she got 10% commission
We find the 10 percent of 40000.
40000 * (10/100) = 4000
Her total earning would be,
$50,000 + $4000(commission) = $54,000
Therefore, Maria earned $54,000
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Can someone please help me this is due tomorrow!
Answer:
I can use the given (algebraic expression) 24c+12 to find the total cost of the order
The expression has two (terms). They are 24c and 12
In 24c the number 24 is the (coefficient) and the letter c is the (variable).
The term 24c represents a (product)
To find the total cost of the order I can (evaluate) the given expression
I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression
24c+12
24(6)+12
144+12
156
The total cost is 156
Hope this helps :)