Answer:
x=14
Step-by-step explanation:
2x-7<21
+7=0
2×<21+7=28
2×/2=0
2/28
=14
Answer:
91
Step-by-step explanation:
Trust me, it's an Aops question, and I got mastery on it, or blue if you want.
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).
the sum of 45% of a number and 55% of the same number is 200. what is the number?
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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Which composition of similarity transformations would
map polygon ABDC to polygon A'B'D'O'?
a dilation with a scale factor greater than 1 and then
a translation
a dilation with a scale factor greater than 1 and then
a rotation
a dilation with a scale factor less than 1 and then a
reflection
a dilation with a scale factor less than 1 and then a
transation
Answer:
A dilation with a scale factor greater than 1 and then a translation.
Answer:
A
Step-by-step explanation:
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
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 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
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!
5 x 680 using distributive property
I believe it would be (5 x 600)+(5x80) = 3400
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.
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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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.
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.
Here's another, Thanks. (3/5)
You are correct. The scale factor is 1/5 = 0.2
Nice work.
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!
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
!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
A 10ounce container of milk contains 200 claories how many calories does each ounce of milk have
Each ounce of milk contains 20 calories, because 200/10 = 20.
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
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]
Use transformation (-2pie,2pie) with Y=2cos(x)-1
Answer:
See attachment
Step-by-step explanation:
We want to graph
[tex]y = 2 \cos(x) - 1[/tex]
on the interval (-2π, 2π)
First we graph
[tex]y = \cos(x)[/tex]
Then we stretch vertically by a factor of 2 and shift down 1 unit.
Since the amplitude is 2 and the graph is shifted down 1 unit, the range of the transformed graph is
[tex] - 3 \leqslant y \leqslant 1[/tex]
The graph is shown in the attachment
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
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.
Jerry collected 45000. Kramer collected 5 times more than jerry. Elaine collected 9 times less than jerry. Newman collects the same as jerry. Kramer and Elaine collected together. How much have the collectors each collected
Kramer collected = 225000
Elaine collected = 5000
Newman collected = 45000
Solution:
Given Jerry collected 45000.
Kramer collected = 5 times more than Jerry collected
= 45000 × 5
= 225000
Kramer collected = 225000
Elaine collected = 9 times less than Jerry collected
= 45000 ÷ 9
= 5000
Elaine collected = 5000
Newman collected = same as Jerry collected
= 45000
Newman collected = 45000
Hence, Kramer collected = 225000
Elaine collected = 5000
Newman collected = 45000
Answer:
2025000 kramers collected
Step-by-step explanation:
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.
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 ;)
Drag numbers to show which are closest to ‐3/4 and ‐1/2 on the number line. -0.65 -1/3 -7/8 -3/5
Answer:
for -3/4 it is -0.65 and for -1/2 it is -3/5
Step-by-step explanation:
Final answer:
The numbers closest to -3/4 (-0.75) and -1/2 (-0.5) on the number line are -0.65 and -0.6 (or -3/5), respectively.
Explanation:
The question involves identifying which numbers on a list are closest to -3/4 and -1/2 on the number line. To do this, we should consider converting all the fractions and decimals to a common format (decimals) to easily compare their distances to -3/4 (which is -0.75 as a decimal) and -1/2 (which is -0.5 as a decimal).
The numbers provided are:
-0.65
-1/3 (which is approximately -0.333 as a decimal)
-7/8 (which is -0.875 as a decimal)
-3/5 (which is -0.6 as a decimal)
Now, to determine which numbers are closest to -3/4 and -1/2:
For -3/4 (-0.75), the closest number is -0.65.
For -1/2 (-0.5), the closest number is -0.6 (or -3/5).
3/4 times what equals 9/8?
Answer:
I believe the answer to this question is: 3/2 simplified to 1 1/2.
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
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.