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Explanation:
A triangle is only possible if you can add two sides and have that sum be larger than the third side. This is the triangle inequality theorem.
Choice A is ruled out because the second and third sides add to 7+7 = 14, but that's not larger than the first side 15.
Choice B is a similar story: 6+8 = 14 is not larger than 14 (the first side)
Choice C as well: 6+7 = 13 is not larger than 14
------
Choice D is the answer because
15+7 > 9
15+9 > 7
7+9 > 15
These three inequalities show that picking any two sides of this triangle, then adding them up, leads to a sum larger than the third side.
Evaluate the expression 1/3 (4+18) 4
Answer:
29 1/3
Step-by-step explanation:
1/3 (4 + 18) 4
1/3 (22) 4
7 1/3 x 4
29 1/3
Twenty nine and one third is your answer.
Final answer:
The expression 1/3 (4+18) 4 evaluates to approximately 29.333 following the order of operations; first the addition inside the parentheses, then multiplication by 1/3, and lastly by 4.
Explanation:
When evaluating the expression 1/3 (4+18) 4, it's essential to follow the orders of operation, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right)). Let's break down the problem step by step:
First, handle the operations inside the parentheses: 4 + 18 = 22.Multiply by the fraction outside, which is 1/3 of 22: (1/3) * 22 = 22/3.Finally, multiply by the last number, which is 4: (22/3) * 4.Now, perform the multiplication: 22 * 4 = 88. Since we are multiplying by a division by 3 (22/3), it is the same as dividing 88 by 3, which gives us the final answer: 88 divided by 3 equals 29 with a remainder of 1, or as a decimal, approximately 29.333.
The correct answer to the expression 1/3 (4+18) 4 is therefore approximately 29.333. It is crucial to always follow the order of operations in any math problem to get the correct result.
X^2 + Y^2 +4y =3 complete the square on the x and y terms to find the radius and center of a circle
Answer:
Center = (0, -4)
Radius = [tex]\sqrt{7}[/tex] units
Step-by-step explanation:
We are given;
The equation of a circle;
[tex]x^2+y^2+4y=3[/tex]
We are required to determine the radius and the center of the circle;
To do this we are going to use completing square method;
[tex]x^2+y^2+4y=3[/tex]
Since we don't have the x term then;
[tex]x^2+ox+y^2+4y=3[/tex]
We add the square of half the coefficients of x and y on both sides of the equation;
That is;
[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=3+0+(2^2)[/tex]
We get;
[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=7[/tex]
Taking the squares;
[tex](x+0)^2+(y+4)^2=7[/tex]
But we know when the equation of a circle is written in the form of;
[tex](x-a)^2+(y-b)^2=r^2[/tex], where (a,b) is the center and r is the radius of the circle.
Thus, in this case;
[tex](x+0)^2+(y+4)^2=7[/tex]
Center = (0, -4)
Radius = [tex]\sqrt{7}[/tex] units
2 fields are 1,200 meters from each other. On a map the 2 fields are 8 centimeters apart. What scale is the map using.
Answer:
The scale 150 metres : 1 centimeters is the map using.
Step-by-step explanation:
Given:
2 fields are 1,200 meters from each other.
On a map the 2 fields are 8 centimeters apart.
Now, to find the scale map is using.
Actual distance between the 2 fields = 1200 meters.
Distance in the map between the 2 fields = 8 centimeters.
So, to get the scale map is using we find the ratio:
[tex]Actual\ distance\ between\ the\ 2 fields/ Distance\ in\ the\ map\ between\ the\ 2 fields[/tex].
[tex]=\frac{1200}{8}[/tex]
[tex]=\frac{150}{1}[/tex]
[tex]=150\ meters:1\ centimeters[/tex]
Therefore, the scale 150 metres : 1 centimeters is the map using.
ABC has vertices at A(5,-1), B(9, -9), and C(4,-1). Write the equation of the line in slope-intercept form that is perpendicular to AB and passes through point C
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
step 1
Find the slope of AB
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
A(5,-1), B(9, -9)
substitute the values
[tex]m=\frac{-9+1}{9-5}[/tex]
[tex]m=\frac{-8}{4}[/tex]
[tex]m=-2[/tex]
step 2
Find the slope of the line that is perpendicular to AB
we know that
If two lines are perpendicular, their their slopes are opposite reciprocal (the product of their slopes is equal to -1)
we have
[tex]m_A_B=-2[/tex]
therefore
The slope of the perpendicular line is
[tex]m=\frac{1}{2}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{2}[/tex]
[tex]C(4,-1)[/tex]
substitute
[tex]y+1=\frac{1}{2}(x-4)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{1}{2}x-2\\\\y=\frac{1}{2}x-2-1\\\\y=\frac{1}{2}x-3[/tex]
if The price tag on a trumpet says 104 how much did the store pay for it
Without the markup percentage or discount percentage, it is impossible to calculate the actual cost price the store paid for the trumpet. One needs this additional information to provide a precise answer.
The question "if the price tag on a trumpet says $104, how much did the store pay for it" cannot be answered with the information provided. To calculate how much the store paid for the trumpet, we need additional details such as the markup percentage or the discount percentage. Retail stores typically apply a markup to the cost of the goods they purchase from suppliers to cover their operating expenses and make a profit.
Let's assume the markup percentage is known. For example, if a store generally marks up items by 50%, and the selling price of the trumpet is $104, we can calculate the store's cost using the formula: Cost Price = Selling Price / (1 + Markup Percentage). So the cost would be $104 / (1 + 0.50), which is $69.33.
Without the markup or discount information, it is impossible to determine the exact cost price that the store paid for the trumpet.
if everything costs $25.30 and there is an 8% meals tax, how much does the meal cost ?
Answer:
Total cost of the meal is $ 27.32.
Step-by-step explanation:
Given:
Cost of the meal = $25.30
Tax levied on it = 8%
We have to find the total cost.
Total cost of the meal = Summation of cost of the meal and levied tax.
So,
We have to calculate the tax.
⇒ [tex]8\%\ of\ \$25.30[/tex]
⇒ [tex]\frac{8}{100}\times \$25.30[/tex]
⇒ [tex]0.08\times \$25.30[/tex]
⇒ [tex]\$2.024[/tex]
Tax imposed = [tex]\$2.024[/tex]
Now,
Total cost of the meal =Tax + Meal cost
⇒ [tex]\$(2.024+25.30)[/tex]
⇒ [tex]\$27.324[/tex]
Total cost of the meal is $ 27.32.
Lamont works for an electric utility and is installing a 40 foot utility pole as shown. Lamont drills the anchor of a support cable into the ground 15 feet from the base of the pole. What is the minimum length of cable Lamont needs?
Answer:
Approximately 43 feet of minimum cable is needed.
Step-by-step explanation:
This problem can be solved using Trigonometry and Pythagorean theorem. Pythagorean theorem applies on right-triangles (which are known to have one 90° angle). The theorem states that the square of the Hypotenuse is obtained by the squared sum of the other two sides of the triangle (i.e the two sides forming the 90° angle - with the hypotenuse side being across it as:
[tex]h^2=a^2+b^2[/tex] Eqn. (1)
where
[tex]h[/tex] is the hypotenuse
[tex]a[/tex] is a side
[tex]b[/tex] is a side
Now in this case, the utility pole must be perpendicular to the ground and the anchor being parallel to the ground, and a 90° angle formed between them. Conclusively the cable length will be represented by the hypotenuse in a right triangle. So here we have [tex]a=40ft[/tex] and [tex]b=15ft[/tex]. Plugging in Eqn.(1) and solving for [tex]h[/tex] we have:
[tex]h^2=40^2+15^2\\h=\sqrt{40^2+15^2} \\h=\sqrt{1600+225}\\ h=\sqrt{1825}\\ h=5\sqrt{73}\\ h=42.72ft[/tex]
So we conclude that the minimum length of cable needed by Lamont is
≈43 feet (rounded up).
Anyone knows what the slope of this is?
Answer:
The slope is 0
Step-by-step explanation:
This is a horizontal line, and all horizontal lines have a slope of 0.
(to see why, just pick any two points, and work out the change in x over the change in y. i.e. rise/run. Since the y coordinates are all equal to 2, the numerator will be 2 -2, meaning the fraction is 0).
The slope is 0. This is because the line is horizontal. Any horizontal line has a slope of 0. Please tell me if you understand! I hope this helps!
Do you have to simplify 1/8 as a fraction
Answer:no
Step-by-step explanation:
Because it can not get any smaller
HELP PLEASE
The sum of the roots of 5 - 2m - 3m^2 = 0 is:
A) -2/3
B) 1
C) 5/3
Answer:
A) -2/3
Step-by-step explanation:
We are given the equation;
5 - 2m - 3m² = 0
We are required to get the sum of the roots of the equation;
We will solve the equation to get the two roots,Using factor method;Rearranging the equation;
3m² + 2m - 5 = 0
product = -15 m²
sum = 2 m
Terms = 5m and -3m
Therefore;
3m² + 5m - 3m - 5 = 0
Factorizing by pairing
m(3m + 5) - 1 (3m + 5) = 0
Thus;
(m - 1) (3m + 5) = 0
This means;
m - 1 = 0 or 3m + 5 =0
Hence; the roots of the equation are;
m = 1 or m = -5/3
Thus, the sum of the roots is;
= 1 + -5/3
= -2/3
Hence, the sum of the roots of the equation is -2/3
What is the equation of a line that contains the following two points?
20 points
(3,-1) , (4,4)
A) y = -5x + 8
B) y = 3x + 5
C) y = 5x -16
D) y = -3x + 6
Answer:
the equation that contains the following 2 points is y=5x-16 which is C.
What is 2 3/4 * 2 1/2
Answer:
6.875
Step-by-step explanation:
Used a calculator to solve this one, it might be incorrect, i suggest doing some extra research on how to solve to see if you get this answer ;)
Show that x+2 is a factor of f(x)=x^4+2x^3−27x−54 . Then factor f(x) completely.
f(x)=
Answer:
Step-by-step explanation:
The polynomial f(x)=x^4+2x^3−27x−54 has x+2 as a factor. The complete factorization of f(x) after polynomial division and analysis is (x + 2)(x^2 - 3x + 9)(x + 3).
Explanation:To show that x+2 is a factor of f(x)=x^4+2x^3−27x−54, we need to use the Factor theorem which states that if a polynomial f(x) has a factor of the form x - k, then f(k) = 0.
So, if x + 2 is a factor of the function, then f(-2) should equal 0. Let's apply this to our function:
f(-2) = (-2)^4 + 2(-2)^3 - 27(-2) -54 = 16 -16+54 -54 = 0. So x+2 is indeed a factor.
To factor f(x) completely, we will perform polynomial division of f(x) by the factor (x+2) which will give us g(x) = x^3 - 27. This can be further factored to x^3 - 3^3 which is a difference of cubes. Consequently, the complete factorization of f(x) would be:
f(x) = (x + 2)(x^2 - 3x + 9)(x + 3).
Learn more about Factorization here:https://brainly.com/question/34290719
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Find altitude of a triangle whose area is 22.86m square and base is 2.4m
Answer:
H = 21.7
Step-by-step explanation:
A = 1/2 x b x h
26 = 1/2 x2.4xh
26= 1.2h
divide both sides by 1.2
26/1.2 = 1.2/1.2 h
h = 21.7
What is three tenths of six thousand
Answer:
1,800
Step-by-step explanation:
Danielle and her friends put their money together to buy a book of tickets for the fair that contains 50
tickets. She and her two friends each paid $5.00. What is the price per ticket?!
Step-by-step explanation:
There are 3 people in total, Danielle and w of her friends. Since they paid $5 each they paid $15 in total for the 50 tickets. To find the price per ticket simply divide the total paid by the amount of tickets.
Price per ticket = 15.0÷50 = $0.30
Answer: Each ticket cost 0,3$
Step-by-step:
You have to divide 15 by 50 (15/50)
In this way you get the answer really quickly.
Hope I helped you!
what is 5x to the third times 6
Answer:
The answer is that 5x to the third times 6 is 30x³
Step-by-step explanation:
Let's answer the question, this way:
5x to the third = 5x³
5x³ times 6 = 5x³ * 6 = 30x³
The answer is that 5x to the third times 6 is 30x³
Which segments are congruent?
PLEASE MARK BRAINLIEST!
Answer:
The two congruent segments are EF and GF, and EH and GH.
Step-by-step explanation:
That being said, your answer is A because EF and GF are in fact congruent segments.
I hope this helps!
- sincerelynini
Which of the following is the solution to the equation 2/3 over 3x = 12?
x=4
x=8
x=18
x=24
Answer:
x = 54 and none of the alternatives given is correct
Step-by-step explanation:
Let's solve for x in the equation given, this way:
2/3 ÷ 3x = 12
2/3 * x/3 = 12
2x/9 = 12
2x = 108
x = 108/2 = 54
Proof of x = 54
2/3 * 54/3 = 108/9 = 12
x = 54 and none of the alternatives given is correct
the sum of 45% of a number and 55% of the same number is 200. what is the number?
Convert 2671(in base 9), to base 3 without first converting to base 10.
Since 9 is 3², each digit in base nine takes two digits in base 3.
2₉ = 02₃
6₉ = 20₃
7₉ = 21₃
1₉ = 01₃
Putting it together
2671₉ = 2202101₃
A customer/member owes $11.02 and pays $100.00 in cash. The change due is $88.98. Provide the amount owed using the smallest number of bills and coins possible.
Answer: subtract
Step-by-step explanation: you’ll see
The smallest number of bills and coins to make up $88.98 is: 4 $20, 1 $5, 3 $1, 3 quarters, 2 dimes, 3 pennies.
Explanation:The change due back to the customer is $88.98. The smallest number of bills and coins that equals this amount can be broken down as follows:
Four $20 bills, giving us $80.00,One $5 bill, adding $5.00, making the total now $85.00,Three $1 bills, adding $3.00, making the total now $88.00,Three quarters (25 cents), adding $0.75, making the total $88.75,Two dimes (10 cents), adding $0.20, puts the total at $88.95,Lastly, three pennies (1 cent), adding $0.03, gives the final total of $88.98.So, the smallest amount of bills and coins possible to make up $88.98 is: 4 $20, 1 $5, 3 $1, 3 quarters, 2 dimes, 3 pennies.
Learn more about Change Calculation here:https://brainly.com/question/31055625
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g(5x + 9) = g(9x + 2)
Answer:
x = 7/4 or x = 1.75 or x = 1 and 3/4
they all mean the same thing but there just in different forms (decimal form, fraction form, and mixed number form)
what’s the slope of -1,-10 and -1,-2
Answer:
slope = undefined
Step-by-step explanation:
for two points (x1,y1) (x2, y2)
slope, m = (y2 - y1)/(x2 - x1)
so, for (-1,-10) (-1,-2)
slope = (-2 - (-10))/(-1 -(-1)) = 8/0
slope = undefined
Ninety-eight percent of the mules who were surveyed said that stubbornness was a good character trait. If 343 mules gave this response, how many were surveyed in total?
Answer:
350 people
Step-by-step explanation:
you would cross multiply
98/100 times 343/x
98x = 34300
34300/98= 350
So the answer is 350 people
Find the value of the polynomial 3xy+7x2−3x2y+3y2x−2x2−2xy+4x2y−2y2x, when x=1 and y=−2
9514 1404 393
Answer:
5
Step-by-step explanation:
The evaluation can be easier if terms are collected first.
3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x
= x^2y(-3+4) +xy^2(3-2) +x^2(7-2) +xy(3-2)
= x^2y +xy^2 +5x^2 +xy
= x(xy +y^2 +5x +y)
Filling in the numbers, we have ...
= (1)(1(-2) +(-2)^2 +5(1) +(-2))
= -2 +4 +5 -2
= 5
The value of the polynomial is 5.
!HELP!
Look at the figure below:
*look at image attached*
Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ACB.
(please show in a two-column proof)
I hope this help you with what you need
Here's another, Thanks. (3/5)
You are correct. The scale factor is 1/5 = 0.2
Nice work.
3/4 times what equals 9/8?
Answer:
I believe the answer to this question is: 3/2 simplified to 1 1/2.
what is the side of equilateral triangle is altitude is 10
Answer:
11.55
Step-by-step explanation:
An equilateral triangle is one which all it sides are equal.
10cm altitude means the height is 10cm.
Using Pythagoras theorem,
x² = 10² + (x/2)²
Assume that the side of the triangle is xcm
x² - x²/4 = 100
3x²/4 = 100
x = √(400/3)
x = 11.55cm