By adding the squares of the triangle's two smaller sides and comparing the result to the square of a largest side, you may determine whether triangle is acute, obtuse, or right.
Define the type of triangle?Equilateral triangle:The equilateral triangle comes first. All three sides of this triangle are the same length, and each angle measures exactly 60 degrees. An equilateral triangle is Triangle A.
A right triangle:This triangle has two acute angles, which are angles smaller than 90 degrees in length, but one right angle (as well as angle which measures 90 degrees). A right triangle is triangle B.
Isosceles triangle:The isosceles triangle is another. This triangle has two sides that are the same length.
Scalene triangle:The scalene triangle comes next. This triangle has three different lengths for its three sides.
Acute triangle:The acute triangle is the next type of triangle and has three acute angles.
Obtuse triangle:The obtuse triangle is the last triangle. Two of the angles of this triangle are sharp, and one of the angles is obtuse, which is defined as being more than 90 degrees.
Thus, by adding the squares of the triangle's two smaller sides and comparing the result to the square of a largest side, you may determine whether triangle is acute, obtuse, or right.
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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
Answer:
[tex]C)~A+ \frac{B}{x-3} +\frac{c}{(x-3)^2}[/tex]Step-by-step explanation:
→ [tex]\frac{(7x^2-40x+52)}{(x^2-6x+9)}[/tex]
→ [tex]\frac{7x^2-40x+52}{x^2-2.3x+(3)^2}[/tex]
→ [tex]\frac{7x^2-40x+52}{(x-3)^2}[/tex]
So, your answer is C
[tex]----------[/tex]
hope it helps...
have a great day!!
The partial fractions is to start with the simplified, and "decompose" the expression into initial polynomial fractions, and the calculation is as follows:
Partial fractions:The degree of the fraction must be strictly less than the degree of the denominator required to conduct partial fractions. It's critical to keep that in mind. So, once we've established that partial fractions are possible, we factor the denominator to the greatest extent possible.[tex]\to \frac{7x^2-40x+52}{x^2-6x+9}\\\\\to \frac{7x^2-40x+52}{x^2-(3x-3x)+9}\\\\\to \frac{7x^2-40x+52}{x^2-3x+3x+9}\\\\\to \frac{7x^2-40x+52}{x(x-3)+3(x+3)}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to A+ \frac{B}{(x-3)}+\frac{C}{(x-3)^2}\\\\[/tex]
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Mrs. Freeman is trying to determine if her new desk will fit through her classroom door. Her desk of her is 59 inches wide. She knows that the height of the door is 80 inches and the diagonal measure of the door is 100 inches. Determine the width of her door de ella and whether or not her new desk will fit. Justify your conclusion.
Answer: x = 60
Step-by-step explanation:
the equation is a^2 + b^2 = c^2.
If you draw out the problem, you plug in the information into the formula, so it would be...
x^2 + 80^2 = 100^2.
80^2 = 6,400 and 100^2 = 10,000.
x^2 + 6,400 = 10,000.
You subtract 6,400 from itself and 10,000 and then you get...
x^2 = 3,600.
You square both of those and your final answer will be x = 60.
An isosceles trapezoid has a perimeter of 38 ft and a leg measuring 8 ft. A similar trapezoid has a leg measuring 3ft. Find its perimeter.
The perimeter of a trapezoid is 28ft.
An isosceles trapezoid is a trapezoid whose non-parallel sides (the legs) are equal in length.
The perimeter of an isosceles trapezoid (P) = a + b+ 2c
where a is the top, b is the bottom, and c is the leg of the trapezoid
According to the question,
perimeter = 38ft
leg of an isosceles trapezoid = 8ft
38 = a +b +2 × 8
⇒ 38 = a+b +16
⇒a +b = 38 -16
⇒a +b = 22
Another similar trapezoid has a leg measuring 3ft.
Perimeter of this trapezoid is =( 22 + 2× 3) ft
= (22 +6)ft
= 28 ft
So, the perimeter of a trapezoid is 28ft.
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At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
c = the number of courses served during dinner
f = the number of forks set out by the hostess
Which of the variables is independent and which is dependent?
Answer:
c is the independent variable and f is the dependent variable
Step-by-step explanation:
A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error
The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.
What is a confidence interval with an example?In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
First we need to name some of the variables we are given:
n = 38 the sample size
x = 6.88 the sample mean
= 1.86 the population standard deviation
We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:
= 1-.90 = .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
This can give us a probability expression:
P(-1.645 < z < 1.645) = .90
The margin of error is calculated with the formula: E = z(/2)(/√n)
E = 1.645(1.86/√38) = $.4963(300) = $148.89
Then to calculate the upper and lower limit we add and subtract E from x:
lower limit = 6.88 - .4963 = $7.38(300) = $2214
upper limit = 6.88 + .4963 = $6.38(300) = $1914
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3 divided by 3/4 (three divided by three fourths) | HELP ASAP!
Answer:
[tex]3 \div \frac{3}{4 } \\ = 3 \times \frac{4}{3} \\ = 4[/tex]
Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
The third side of the triangle will be less than 35.
What is a triangle?A polygon with three angles, sides and angles is called a triangle.
Given that, Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
We know that, triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, length of the third side < 15+20 < 35
Hence, the third side of the triangle will be less than 35.
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I’ll brainliest you please help me
Answer:
x = 62°
y = 118°
Step-by-step explanation:
Since the sum of interior angles of any quadrilateral is 360°, all of the interior angles in this image will add up to 360°.
Since the shape of the trapezoid is symmetrical, x is equivalent to 62°.
This means 62 + 62 + x + x = 360°
(360-(62+62))/2 = 118°
118 + 118 + 62 + 62 = 360°
x = 62°
y = 118°
What is 5.6 x -0.75
i really need help
Answer:
-4.2
Step-by-step explanation:
your mom < 3 3 3 3 3 3 3
Define negative and positive numbers. Explain.
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
Negative Numbers :-⟹ Numbers that are less than zero are known as negative numbers (or integers). They fall on the left side of the number line.
Positive Numbers :-⟹ Numbers that are greater than zero are known as positive numbers (or positive integers). They fall on the right side of the number line.
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HELP ME I am not really sure how to explain this !!!
Answer:
I'm not good with math lol
Find the value of y
Answer:
y = 4
Step-by-step explanation:
The triangles are congruent.
8y = 6y + 8
2y = 8
y = 4
Mr. Garcia purchased twelve watermelons for the school picnic. Each watermelon cost $4.95. How much did he pay for the watermelons?
Answer:
$59.40
Step-by-step explanation:
Multiply the amount of watermellon (12) by the price (4.95) giving you 59.40
Answer:
$59.40
Step-by-step explanation:
take $4.95 and times it by twelve to get $59.40
Write an absolute value equation that satisfies the following condition.
The equation has only one solution x=-17.
Answer:
x=-17.......................
Step-by-step explanation:
x+17=0
Consider the line x+5y=6
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
[tex]x + 5y = 6[/tex] is perpendicular to [tex]y = 5x + \frac{6}{5}[/tex] and parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex]
Step-by-step explanation:
First, convert the equation to standard form so that y is isolated.
x + 5y = 6 --> x - 6 = -5y (divide both sides by -5) --> [tex]y = -\frac{1}{5}x + \frac{6}{5}[/tex]
A perpendicular line will have a slope that is the opposite reciprocal of the original slope (meaning you flip the numerator and denominator then make it negative).
[tex]-\frac{1}{5}[/tex] is perpendicular to [tex]-(\frac{-5}{1} )[/tex] which simplifies to 5.
A parallel line will have the same slope, but the y-intercept will be different. It can be pretty much any number as long as the original slope is used in the new equation.
[tex]y = -\frac{1}{5}x + \frac{6}{5}\\[/tex] is parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex] just like [tex]y = -\frac{1}{5}x - \frac{100}{23}[/tex].
Evaluate the expression if x = 6
X3 – 10 =
Answer:
8
Step-by-step explanation:
3x6 = 18
18-10 = 8
I need help with my final
Answer:
a
Step-by-step explanation:
Answer:
B is the answer .look at the picture I sent.
An entertainment center is 52 inches wide and 40 inches high. Will a tv with a 60 inches diagonal fit ?
No, a TV with a 60 inch diagonal would not fit in an entertainment center that is 52 inches wide and 40 inches high.
What is diagonal?Diagonal is a line connecting two or more points that are not in a straight line. It is used to describe the shape of a polygon and also used in mathematics to refer to lines, angles, and shapes. It can also refer to a line, or direction, that is not parallel or perpendicular to something else. In geometry, diagonal lines are used to divide shapes into equal parts, and are used in the construction of polygons. In linear algebra, diagonal lines are used to calculate the determinant of a matrix.
The diagonal measurement of a TV is the length of a line drawn between the opposite corners of the TV. For a 60 inch diagonal TV, the width of the TV would be around 52 inches and the height would be around 33 inches. As the entertainment center is only 40 inches high, the TV would not fit in it.
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If h = 18 units and r = 9 units, then what is the volume of the cone shown above
A. 234 cubic units
B. 1,458 cubic units
C. 972 cubic units
D. 486 cubic units
Answer:
Volume = 1526.04 cubic units
Step-by-step explanation:
Formula for volume of a cone:
V = πr²h/3
If we use 3.14 for pi, we get 1526.04:
V = 3.14(9)^2(18)/3
V = 1526.04
What is the degree of the polynomial 2x² 5x³ 7 *?
The degree of the polynomial 2x² 5x³ 7 is 5.
The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of the variable is 5, which appears in the term 5x³. The degree of a polynomial is a whole number that tells us how many times the variable is multiplied by itself. The degree of the polynomial is 5.
It's worth noting that polynomials can be constant or non-constant, meaning they don't have to have a variable in them, in that case the degree is 0. And also a polynomial with only one term, the degree of that polynomial is the exponent of that term.
In this case, we only have one term with variable x in it, 5x³, and the degree is the exponent of that term which is 5.
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How do you write an equation for a parabola with the vertex and Y intercept?
To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Consider an example where vertex is (2,1) and y-intercept is (0,-3).
The equation of parabola needs to be deduced using these points.
The equation of a parabola in vertex form is -
y=a(x-h)^2+k
Here, a is a constant and (h ,k) are the coordinates of the vertex.
So, (h,k)=(2,1)
⇒y=a(x−2)^2+1
To obtain the value of a, substitute (0,−3) into the equation -
-3=4a+1
4a=-4
a=-1
⇒y=-1(x−2)^2+1
Now, distribute and simplify -
y=-1(x−2)^2+1
y=-(x^2-4x+4)+1
y=-x^2+4x-4+1
y=-x^2+4x-3
On, graphing this equation a parabola is obtained.
Therefore, to write an equation of parabola vertex form is used.
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Use 10% to find 40% of 40
A. What must the side length of each square represent for the rectangle to correctly represent (0. 3). (0. 5)?
The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.
A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.
Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).
Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).
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Which is the complete factorization of this expression?
-20x - 5y
A)5(4x+y)
B) 4(5x - y)
C) -5(4x + y)
D)-5(4x - y)
Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.
What is meant by factorization ?When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).
GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.
Therefore the correct answer is option A)5(4x+y)
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A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Identify and interpret the ordered pair in the solution region.
The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.
How to calculate the ordered pair for shipment?The total volume of the trailer = 3800 cubic feet
The volume of each recliner = 40 cubic feet
The volume of each sofa = 80 cubic feet
The number of recliner needed = 30
The number of sofas needed = 25
The volume that the sofa will cover = 25 × 80 = 2000
The volume that the recliner will cover= 30 × 40 = 1200
Therefore the total volume both will take = 3200 cubic feet.
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Pls answer question number 1 pls it’s for my math that is due tomorrow
Answer:
Total cost =3over8 x 48 x0. 55=9.9
Answer:
$9.90
Step-by-step explanation:
First, we need to find the number of vanilla cupcakes.
The question tell us that 3/8 of the 48 cupcakes are Vanilla flavored, so we can start by dividing 48 by 8 to find what 1/8 of 48 is:
48/8 = 6
1/8 of 48 = 6
Now to find 3/8, we just need to multiply that number by 3:
6 x 3 = 18
3/8 of 48 = 18
So now we know that she bought 18 vanilla cupcakes.
Finally to find the price, we just need to multiply the price per cupcake by the number of cupcakes:
$0.55 per cupcake x 18 cupcakes = 0.55 x 18 = $9.90
The total cost of the vanilla cupcakes was $9.90
Hope this helped!
Kelsey rolls a fair die 390 times. The table below shows the outcomes.
Side
Times
Rolled
Kelsey rolls the die 24 more times. What is the most likely number of times she rolls a 4 or a 5?
Ο Α. 8
OB. 12
O c. 2
OD. 4
Answer:
12
Step-by-step explanation:
i have help with this q
The slope of the graph is equivalent to 6 units.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the graph showing the amount of water in the tank after the several minutes of it being turned off.
We can write the slope of the graph as -
m = (16 - 10)/(2 - 1)
m = 6
Therefore, the slope of the graph is equivalent to 6 units.
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PLEASE HELP DUE IN 1 HOUR, AND PLEASE DON'T PUT THOSE LINKS OR ELSE I WILL REPORT YOU.
Answer:
Step-by-step explanation:
m≥150
draw a solid dot (since it is greater than or equal to) starting at 150 and continue to the end of the number line.
Answer:
B. m is greater than or equal to 150
Step-by-step explanation:
if he has to drive at least 150, then he must drive 150 miles or more
Ratio, proportion and percent unit 4 homework 3 wages hours 1 wage is $9.50 2 $19.00 3 $28.50 4 $38.00
Answer:
(a) The complete table
[tex]\begin{array}{cccccc}Hours & {1} & {2} & {3} & {4} &{5}\ \\ {Amount} & {\$9.50} & {\$19.00} & {\$28.50} & {\$38.00} & {\$47.50} \ \end{array}[/tex]
(b) $38.00
(c) 3 hours
Step-by-step explanation:
Given
[tex]Earnings = \$9.50[/tex] per hour
See attachment for complete question;
Solving (a): Complete the table
To complete the table, we simply multiply the earnings by the number of hours.
So, we have:
[tex]Hours = 2 \to Earnings = \$9.50 * 2 = \$19.00[/tex]
[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]
[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]
[tex]Hours = 5 \to Earnings = \$9.50 * 5 = \$47.50[/tex]
Solving (b): Earnings, if Megan works for 4 hours
In (a) above, we have:
[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]
This implies that Megan will earn $38.00
Solving (c): Hours to earn $28.50
In (a) above, we have:
[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]
This implies that Megan will work for 3 hours to earn $28.50