The value of the c is 1 which makes the perfect square trinomial.
According to the statement
We have to find that the value of the c.
So, For this purpose, we know that the
An expression obtained from the square of the binomial equation is a perfect square trinomial.
From the given information:
The Given statement is:
x² - 2x + c
is a perfect square of the form
(x - a)² = x² - 2ax + a²
Now,compare with x² - 2x + c, then
- 2a = - 2 ⇒ a = 1,
thus
a² = 1² = 1 = c
(x - 1)² = x² - 2x + 1 ← perfect square trinomial
It means the value of c is 1.
So, The value of the c is 1 which makes the perfect square trinomial.
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A motorboat can maintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 33 minutes; the return trip takes 19 minutes. What is the speed of the current?
Answer:
7 mph
Step-by-step explanation:
A boat whose speed in still water is 26 mph makes a trip upstream in 33 minutes and returns in 19 minutes. You want to know the speed of the current.
SetupThe travel time is inversely proportional to the speed, so we can write the proportion (using c for the current speed in mph) ...
time upstream / time downstream = speed downstream / speed upstream
33/19 = (26 +c)/(26 -c)
SolutionMultiplying by 19(26 -c) gives ...
33(26 -c) = 19(26 +c)
(33 -19)(26) = (33 +19)c . . . . add 33c -19(26)
14(26)/(52) = c = 7
The speed of the current is 7 miles per hour.
evaluate the expression 3 to the third power multiplied by 12-2 divided by 2 iready
Simplify the expression using order of operations. 14+18÷2×4−7
Answer:
Hi
Your answer is 43.
Solve(Using PEMDAS order of operations):
[tex]18\div \:2\times \:4\\18\div \:2=9\\=9\times \:4\\=36\\=14+36-7\\14+36=50\\=50-7\\=43[/tex]
Graph the linear equation.
x = 6
Use the graphing tool to graph the linear equation.
The graph of the linear equation, x = 6, is shown in the image attached below.
How to Graph the Equation of a Vertical Line?The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.
Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.
Thus, the graph of the linear equation, x = 6, is shown in the image attached below.
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A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof.
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
How to prove the angles in a Parallelogram?
From the given image of the parallelogram, we are given that;
Angle 1 and angle 3 are complementary.
Now, complementary angles sum up to 90°. Thus;
∠1 + ∠3 = 90°
Now, according to definition of parallelogram, we know that alternate interior angles of a parallelogram are congruent(equal). Thus;
∠1 = ∠2
Since ∠1 = ∠2, then by substitution property into the first equation, we have; ∠2 + ∠3 = 90°
Since the sum of ∠2 and ∠3 is equal to 90°, then we can say that they are both complementary angles.
Thus, we conclude that;
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
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Suppose you just won the state lottery, and you have a choice between receiving $4,500,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes
A 1.03% rate of return is built into the annuity.
First optionTo receive a single payment today of $4,500,000Second optionTo receive an annual payment of $250,000.Term is equal to 20 years.Let the rate of return be x%.A series of payments paid at regular intervals is known as an annuity. Regular savings account deposits, mortgage payments, insurance premiums, and pension payments are all examples of annuities. The periodicity of payment dates allows for the classification of annuities.At this rate, the present value of the annuity is $4,500,000.The present value of the first option equals the present value of the second option. $4,500,000 = $250,000[1/x + 1/x² + … + 1/x^20]Upon solving, we get approximately x is 1.03%.To learn more about annuity, visit :
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Find the least common denominator (LCD) of 1/2 and 11/12
Answer:
LCD = 12
Step-by-step explanation:
Solve the problem please.
∑ Hey, shadowwolf9764 ⊃
Answer:
x = - 7.5
Step-by-step explanation:
Given:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}\left(x+5\right)[/tex]
Solution~:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}\left(x+5\right)[/tex]
Distribute:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}x+\frac{5}{2}[/tex]
Subtract 1/4 from both sides:
[tex]\frac{1}{5}x+\frac{1}{4}-\frac{1}{4}=\frac{1}{2}x+\frac{5}{2}-\frac{1}{4}[/tex]
[tex]\frac{1}{5}x=\frac{9}{4}+\frac{1}{2}x[/tex]
Subtract 1/2x from both sides:
[tex]\frac{1}{5}x-\frac{1}{2}x=\frac{9}{4}+\frac{1}{2}x-\frac{1}{2}x[/tex]
[tex]-\frac{3}{10}x=\frac{9}{4}[/tex]
Multiply both sides by 10:
[tex]10\left(-\frac{3}{10}x\right)=\frac{9\cdot \:10}{4}[/tex]
[tex]-3x=\frac{45}{2}[/tex]
Divide both sides by -3:
[tex]\frac{-3x}{-3}=\frac{\frac{45}{2}}{-3}[/tex]
x = -15/2
x = -7.5
xcookiex12
9/4/2022
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A rectangle the width of m-5 inches and height of 2m+1 inches. Find the simplified area of the rectangle
Answer:
6m - 8
Step-by-step explanation:
Add all of the sides
2m+1+2m+1+m-5+m-5
Then combine everything
6m - 8
▶ Use the part of the nutrition label on the right. If protein contains approximately 4 calories per gram, find the percent of calories from protein from one serving of this food. (Round to the nearest tenth of a percent.) ww. The percent of calories from protein from one serving of this food is %. Nutritional information per serving Calories 277 Protein Carbohydrate Fat 11g 45g 6g
The percent of calories from protein from one serving of the food is found as 15.88%.
What is defined as the term percentage?A relative value representing the hundredth part of any quantity One percent (denoted 1%) is one hundredth part; thereby the, 100 percent describes the entire amount and 200 % identifies twice the given amount.
For the given information;
The total calories is 277.
Nutrients information in food.
Protein - 11g
Carbohydrate - 45g
Fat - 6g
The protein contains 4 calories per gram.
Thus, 11 grams of protein contains 4×11 = 44 calories per grams.
Find the % content of protein out of 277 calories;
p% of 277 = 44
p% = (44×100)/277
p% = 15.88%.
Therefore, the percentage of protein contained in the serving food is 15.88%.
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Please help find the range
Answer:
Any Nber between 0-58 or 1-59
Step-by-step explanation:
Well you are already given the range which is 58. The question is asking for two number that are in the range. The range 58 means it can't be greater than 59. The range is how far apart the great y vaule is from the lowest y vaule.
Hope this helps!
Have any questions? Feel free to ask
A bank charged $10 to open an account. Shelly opened an account then deposited
$125 into the account. She then wrote checks for $15 and $35, made a deposit of
$50, then got $40 quick cash from an ATM which charged her a fee of $2.50. What is
her balance?
Answer:
$72.50
Step-by-step explanation:
-$10
+$125
-$50
+$50
-$42.50
Use the method of completing the square to solve the quadratic equation
t2+5t−1=0.
The solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4
Completing the square methodGiven the quadratic equation expressed as;
t^2+5t−1=0
Add 1 to both sides
t^2+5t−1 + 1 = 0+1
t^2 + 5t = 1
Take the square of half of the coefficient of t to have:
t^2 + 5t + (5/2)^2 = 1 + (5/2)^2
(t+5/2)^2 = 1+25/4
(t+5/2)^2 = 29/4
t + 5/2 = ±√29/4
t = -5/2 ±√29/4
Hence the solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4
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Divide:
35x³-25x4y³/5x²y²
Answer:
35x³-25x4y³/5x²y² = −5x6y5+35x3
What is the value of the underlined digit: 498,217 *
Answer:
B.) 90.000
Step-by-step explanation:
Your pre-selected answer choice is correct. The 9 is in the Ten Thousands place.
Measure the length and width of a rectangular room in your house/apartment in feet. Determine the area of the room in square feet. Convert the area to both square inches and square yards. Explain how you made these conversions. When would you want to have the area in square feet? Square inches? Square yards?
Then measure the height of the room in feet. Calculate the volume of the room in cubic feet. Convert the volume to both cubic inches and cubic yards. Explain how you made these conversions. When would you want to have the area in cubic feet? Cubic inches? Cubic yards?
1) The area of the room in square feet, square inches, and square yards is as follows:
Area = 120 ft²
Area = 1,440 in²
Area = 40 yards²
2) The volume of the room in cubic feet, cubic inches, and cubic yards is as follows:
Volume = 1,440 ft³
Voluem = 17,280 in²
Volume = 480 yards²
What are the conversion rates?The conversion rates are:
1 foot equals 12 inches 3 feet are equivalent to 1 yard.The mathematical operations of multiplication and division are used.
Data and Calculations:Let the length = 12 feet
Let the width = 10 feet
Let the height = 12 feet
1 foot = 12 inches
3 feet = 1 yard
Area = 120 ft² (12 x 10)
Area = 1,440 in² (120 x 12)
Area = 40 yards² (120/3)
Volume = 1,440 ft³ (12 x 10 x 12)
Voluem = 17,280 in² (1,440 x 12)
Volume = 480 yards² (1,440/3)
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Use the number line to complete the sentence.
<————————-> (its on (point A, 1) and (point B, 6) what is
The distance from point A to point Bis [blank] units.
Enter your answer as the number that correctly fills in the blank in the previous sentence
Answer:
5
Step-by-step explanation:
Hop the spaces from 1 until you reach to 6 and you get 5 hops
A bowl weighs 11/40 pound express this weight as a decimal
Answer:
0.275 lb
Step-by-step explanation:
Use a calculator to divide 11 by 40.
11/40 = 0.275
Answer:
0.275 pounds
Step-by-step explanation:
divide 11 (numerator) by 40 (denominator).
Use the diagram to find the measures of the lengths of the
sides. The perimeter of the trapezoid on the right is 67
inches.
The length of all four sides of the Isoclesles Trapezium is 67 inches.
What is an area of a Trapezium?Area of a Trapezium is (1/2)(a+b)h.Where and b are the parallel sides of the trapezium and h is the distance between the two parallel side
We know that for a plane 2D figure perimeter is the sum of the lengths of all the sides.
Given an isosceles Trapezium with a perimeter of 67 inches,
As the sides are given in variables we can equate the sum of all the sides with the given perimeter and obtain the value of x.
∴ (x + 1.5x + 2.5x - 5 + x) = 67.
6x = 67 + 5.
6x = 72.
x = 12.
So, the measure of lengths of four sides are [ 12 + 1.5(12) + 2.5(12) - 5 + 12) which is ( 12 + 18 + 30 - 5 + 12 ) = 67 inches.
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what is the area of the rectangle?
Width;
4x-1 ,
Top length;
2x+17
Bottom Length;
6x+9 .
Please help
==============================================================
Explanation:
Recall that the opposite sides of any rectangle are the same length.
This means the top and bottom sides are the same length
top = bottom
2x+17 = 6x+9
2x-6x = 9-17
-4x = -8
x = -8/(-4)
x = 2
Then we can find each side:
width = 4x-1 = 4*2-1 = 8-1 = 7top = 2x+17 = 2*2+17 = 4+17 = 21bottom = 6x+9 = 6*2+9 = 12+9 = 21We get the same length for top and bottom (21), which confirms the correct x value.
This is a 7 by 21 rectangle with area = length*width = 7*21 = 147 square units.
If the sum of a number and two is tripled, the result is five less than twice the number . Find the number
If the sum of a number and two is tripled, the result is five less than twice the number, the number is - 11
Let the given number be x,
the number, x is added with 2 and then it is tripled which means (x + 2)*3 is equal to five less than two times of that number which is 2x - 5
3(x + 2) = 2x - 5
3x + 6 = 2x - 5
3x - 2x = - 5 + (-6)
x = - 11
Therefore, If the sum of a number and two is tripled, the result is five less than twice the number, the number is - 11
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Estimate the quotient of
68)6080
Express any remainder beginning with an R.
Missing value of principal when rate is 12% and time is 5 years will simple interest is $87
The principal is $145 .
Simple interest is the interest amount for a particular principal amount of money at rate of interest. The interest is calculated by multiplying the principal with the time and rate. The total amount after a certain time is given by the sum of the principal and the interest for that time.
The formula for calculating the Interest on a Principal(P) , time(t) and rate(R).
Interest=P×R×t
Now let us consider the principal to be P.
Time(t)=5 years
Simple Interest(I)=$87
Rate(R)=12%=0.12
Now let us find the principle for the this interest using the above formula.
I=P×R×t
Substituting the given values we calculate the Principal(P).
[tex]87=P\times0.012\times5\\or,P=87\div(0.012\times5)\\or,P=87\div0.6\\or,P=145[/tex]
Therefore the Principal for the simple interest of $87 for 5 years at rate of 12% is $145.
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Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x-2
s(x)=3x+6
Write the expressions for (r+s) (x) and (r-s)(x) and evaluate (r·s)(−1).
(r+s)(x) =
(r-s)(x) =
(r.s) (-1) =
Assume that the following definitions of the functions r and s apply to all real numbers x. r(x)=x-2s(x)=3x+6 Evaluate (rs)(1) and write the equations for (r+s)(x) and (r-s)(x). r+s(x) = r-s(x) = r.s(-1) =
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
The types of functions can be broadly classified into four types. Based on Element: One to one Function, many to one function, onto function, one to one and onto function, into function.
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what is the net decimal equivalent if all discounts were applied in the series?
40% 15% 30%
The net decimal equivalent of the series 40/15/30 is 0.357;
Here we assume let X be retail price.
So,
X - 0.40 × X = Y ⇒ first discounted price.
Y - 0.15 × Y = Z ⇒ second discounted price.
Z - 0.30 × Z = T ⇒ total discounted price.
Now
X - 0.40 × X = (1 - 0.40) × X = 0.60 × X = Y
Y - 0.15 × Y = (1 - 0.15) × Y = 0.85 × Y = Z
Z - 0.30 × Z = (1 - 0.30) × Z = 0.70 × Z = T
Also, Z = 0.85 × Y, then 0.70 × Z = 0.70 × 0.85 × Y
And, Y = 0.60 × X, then 0.70 × Z = 0.70 × 0.85 × 0.60 × X
So,
= 0.70 × 0.85 × 0.60 × X
= 0.357X;
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PLS HELP ASAP
(50 POINTS)
What is the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}?
A) {2,4}
B) {1, 2, 3, 4)
C) {2, 4, 6}
D) {1, 2, 3, 4, 6}
Answer:
a
Step-by-step explanation:
the answer is a
Answer:
C
Step-by-step explanation:
A carry on bag costs $24 less than a suitcase. Janice bought 3 suitcases and 2 carry ons for $547. How much does one suitcase cost?
f the gray suitcase weighs 11 lb more than the pink suitcase, the pink suitcase weighs 5 lb than the blue suitcase, and the total of 3 suitcases is 127 lb, then the blue suitcase weighs 35.3 lb
Let the gray suitcase be represented by g
Let the pink suitcase be represented by p
Let the blue suitcase be represented by b
The gray suitcase weighs 11 lb more than the pink suitcase
g = p + 11........(1)
The pink suitcase weighs 5 lb than the blue suitcase.
p = b + 5
b = p - 5...........(2)
Total of 3 suitcases = 127 lb
p + b + g = 127............(3)
Substitute equations (1) and (2) into equation (3)
p + p - 5 + p + 11 = 127
3p + 6 = 127
3p = 127 - 6
3p = 121
p = 121/3
p = 40.3 lb
Substitute p = 40.3 into equation (2)
b = p - 5
b = 40.3 - 5
b = 35.3
The blue suitcase weigh 35.3 lb
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What is the number of combinations on a lock. (for a 40-number lock, no successive repeating numbers)
(permutations or combinations).
The cube of the product of 4 and a number
hi
if you call the number "n" you have : ( 4n)³
The cube formed by the product of 4 and a number is (4 * n)^3.
What are cubes?A number's third power, or the outcome of multiplying three occurrences of the number n together, is known as the cube In mathematics and algebra. A superscript 3 represents the cube of a number or any other mathematical expression.The name comes from the fact that the volume of a geometric cube is equal to the cube of its side length.According to our question ,
Let n be any number on any integer.The cube of the product of and any number will be = (4 * n)^3.Hence we can say that the cube formed by the product of 4 and a number is (4 * n)^3.
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Simplify 7+5c+4d-8c+d
Step-by-step explanation:
if there is no typo the expression is :
7 + 5c + 4d - 8c + d
to simplify combine all terms with the same variable and exponent of that variable.
so, this is
7 + (5c - 8c) + (4d + d) = 7 - 3c + 5d
Answer:
-3c+5d+7
Step-by-step explanation: