Answer:
17.5 inches
Step-by-step explanation:
Let the length of the shorter piece be x
Shorter piece + Longer piece = Whole string
x + (x + 7) = 42
x + x + 7 = 42
Both sides minus 7 to remove the 7 from the left side of the equation.
2x + 7 - 7 = 42 - 7
2x = 35
x = 17.5 inches
Hope this helped! ^^
Rory’s garden is square in shape. The length of one side of her garden is 5^2 feet. What is the area of her garden in square feet? Express your answer using exponents
If the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
Given that Rory' garden is square in shape and the length of one side of the garden is [tex]5^{2}[/tex] feet.
We are required to find the area of the garden.
Area is basically the quantity that expresses the extent of a region on the plane or on a curved surface.
Area of square=Side*Side
Area=[tex]5^{2}[/tex]*[tex]5^{2}[/tex]
=[tex]5^{4}[/tex]
=625 [tex]feet^{2}[/tex]
Hence if the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
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A doctor administers a drug to a 34-kg patient, using a dosage formula of 55mg/kg/day. Assume that the drug is available in a 200 mg per 5 mL suspension or in 300 mg tablets. a. How many tablets should a 34-kg patient take every four hours? b. The suspension with a drop factor of 10 gtt/mL delivers the drug intravenously to the patient over a twelve-hour period, i.e the patient receives the daily dose over a 12 hour period. What infusion rate should be used in units of gtt/hr?
The patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.
Given that, a doctor administers a drug to a 34-kg patient, using a dosage formula of 55mg/kg/day.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of tablets should a 34-kg patient takes every four hours to be x.
Now, 55 × 34 = 1870 mg/day
For every four hours:
1870 × 1 /24 × 4 = 311.666
≈312 mg per 4 hours
So, x=312/4 × 1/300 = 78 × 0.0033
=0.26 tablet
Liquid suspension is for every 12 hours:
So, 312/12 × 1/200 = 26 × 0.005 = 0.13 mL
Hence, the patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.
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On a website selling gifts, the total cost is given by the formula:
Total cost (£) = number of items × 12 + 5
Work out the total cost for 4 items.
Answer:
4x12 equals 48 therefore 48+5= 53......
guys!! please help me, I’ll give out brainliest just please help it’s my final question and it’s currently 4 in the morning .
(geometry)
what is the perimeter of the rectangle ABCD?
Answer:
Please disregard
Step-by-step explanation:
(2 x 10³) x (4 x 106)
Answer: 848000
Step-by-step explanation:
(2 x 10³) x (4 x 106)
⇒2000 * 424
⇒ 848000
Determine whether the following argument is inductive or deductive:
"The last mayor was honest. The current mayor is honest. All mayors are honest."
Answer:
Inductive
Step-by-step explanation:
The given argument presented is an example of inductive reasoning.
What is inductive reasoning?Inductive reasoning entails drawing broad generalizations based on a small number of observations, and the conclusion is not necessarily guaranteed to be correct, but simply likely based on the data.
The argument presented is an example of inductive reasoning, because it is based on a specific observation and a generalization that goes beyond the available evidence.
While the previous and current mayors may be honest, based on this limited evidence, it is not necessarily true that all mayors are honest.
The argument makes the assumption that the honesty of these two persons is indicative of all mayors, which is a conclusion based on little evidence.
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please refer to the image, thank you!
The values of the piecewise function is g(1) = 3, g(2) = 1 / 2, g(3) = 1 / 4.
How to evaluate a piecewise function
Piecewise functions are functions consisting in two or more expression constrained by intervals. In this case, we find a piecewise function formed by three equations. In this exercise we need to evaluate the function, whose expression depends on the x-value to be used. There are three values to be evaluated:
x = 1
g(1) = (1 + 1)² - 1
g(1) = 2² - 1
g(1) = 4 - 1
g(1) = 3
x = 2
g(2) = - (1 / 4) · 2 + 1
g(2) = - (1 / 2) + 1
g(2) = 1 / 2
x = 3
g(3) = - (1 / 4) · (3) + 1
g(3) = - (3 / 4) + 1
g(3) = 1 / 4
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How is subtracting integers related to adding integers
Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.
Are there any consistent rules for adding and subtracting integers?
Integer addition and subtraction formulas: 1) Subtract the two numbers and indicate the sign of the larger number if the two numbers have different signs, such as positive and negative. 2) Add the two numbers and give the common sign if the two numbers have the same sign, that is, either positive or negative signs.What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Learn more about integer
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One-seventh of a number, increased by twelve?
Answer:
x/7+12
Step-by-step explanation:
One seventh refers to 1/7.
Since we do not know what "a number" is it, it is written as "x."
Whenever you see the word "increased" think addition.
So in this case,
x / 7 + 12
NO LINKS!! Please help me with these problems. Part 13a1
Answer's:
27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)
28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)
29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)
To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.
where:
(h, k) is the vertex27.
g(x) = x² + 8x + 11
completing square:
g(x) = (x² + 8x) + 11
g(x) = (x + 4)² + 11 - (4)²
g(x) = (x + 4)² - 5
g(x) = (x - (-4))² - 5
To find x-intercept: set y = 0
[tex]\sf (x + 4)^2 - 5 = 0[/tex]
[tex]\sf (x + 4)^2 = 5[/tex]
[tex]\sf x + 4 = \pm \sqrt{5}[/tex]
[tex]\sf x= \sqrt{5}-4, \ - \sqrt{5}-4[/tex]
Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).
28.
f(x) = x² + 10x + 14
completing square:
f(x) = (x² + 10x) + 14
f(x) = (x + 5)² + 14 - (5)²
f(x) = (x + 5)² - 11
Find x intercept, so y = 0:
[tex]\sf (x + 5)^2 - 11 = 0[/tex]
[tex]\sf (x + 5)^2 = 11[/tex]
[tex]\sf x + 5 = \pm\sqrt{11}[/tex]
[tex]\sf x = \sqrt{11} -5, \ -\sqrt{11} -5[/tex]
Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).
29.
f(x) = -(x² - 2x - 15)
f(x) = -((x² - 2x)) + 15
f(x) = -(x - 1)² + 15 + (-1)²
f(x) = -(x - 1)² + 16
Find the x-intercept's:
[tex]\sf -(x - 1)^2 + 16 = 0[/tex]
[tex]\sf -(x - 1)^2 = -16[/tex]
[tex]\sf (x - 1)^2 = 16[/tex]
[tex]\sf x - 1 = \pm\sqrt{16}[/tex]
[tex]\sf x - 1 = \pm4[/tex]
[tex]\sf x = -3, \ 5[/tex]
Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).
Answer:
[tex]\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}[/tex]
[tex]\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}[/tex]
[tex]\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.[tex]a[/tex] is some constant.Question 27Given function:
[tex]g(x)=x^2+8x+11[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies g(x)=x^2+8x+11 +16-16[/tex]
[tex]\implies g(x)=x^2+8x+16+11-16[/tex]
[tex]\implies g(x)=x^2+8x+16-5[/tex]
Factor the perfect trinomial:
[tex]\implies g(x)=(x+4)^2-5[/tex]
Therefore, the vertex is (-4, -5).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}[/tex]
---------------------------------------------------------------------
Question 28Given function:
[tex]f(x)=x^2+10x+14[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+10x+14+25-25[/tex]
[tex]\implies f(x)=x^2+10x+25+14-25[/tex]
[tex]\implies f(x)=x^2+10x+25-11[/tex]
Factor the perfect trinomial:
[tex]\implies f(x)=(x+5)^2-11[/tex]
Therefore, the vertex is (-5, -11).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}[/tex]
---------------------------------------------------------------------
Question 29Given function:
[tex]f(x)=-(x^2-2x-15)[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)[/tex]
[tex]f(x)=-\left(x^2-2x-15+1-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-15-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-16\right)[/tex]
Factor the perfect trinomial:
[tex]f(x)=-\left((x-1)^2-16\right)[/tex]
Simplify:
[tex]f(x)=-(x-1)^2+16[/tex]
Therefore, the vertex is (1, 16).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = 5, \quad x=-3[/tex]
Jane bought a watch for $30 that she is going
to re-sell with a 15% markup price. How much
is Jane selling the watch for?
Step 1:
Step 2:
Step 3:
a² + 6b when a = -3 and b = 2
Answer:
21
Step-by-step explanation:
Just substitute -3 in for a and 2 in for b
[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]
When you square a negative number, the answer is positive. Good luck, and have a great day!
Also, Jesus loves you!!!!
if √x = 7 then x must be ____.
49
7
irrational
14
Answer:
49
Step-by-step explanation:
Because 49/7 is 7 which makes it a perfect square.And it saids the square root of x is 49
Hope that helped!
Have any questions? Feel free to ask questions
In the pyramid of Khafre, AC = 108 m and angle A = 53°. Find the height of the pyramid (BC) to the nearest whole meter
The length of BC to the nearest while meters is 143m
SOH CAH TOAGiven the following parameters
AC = 108 m
<A = 53°
Using the SOH CAH TOA identity
tan 53 = opp/hyp
tan53 = BC/108
Determine the measure of BC
BC = 108tan53
BC = 143.32m
Hence the length of BC to the nearest while meters is 143m
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Can someone tell me the answer to the domain and range please
Answer:
1)
D) -4<x≤-1
R) 4>y≥2
2)
D) 3≤x<5
R) 0≥y>-3
Step-by-step explanation:
(only in 7th so might be wrong)
1)
D) -4<x≤-1
R) 4>y≥2
2)
D) 3≤x<5
R) 0≥y>-3
Just find the range of how far the function goes (both how high; y, and how far; x)
Consider Line 2, which has the equation: y = = - 1/3x + 14, Give the equation of the line parallel to Line 2 which passes through: (-7,4).
Answer:
x + y = -3.
Step-by-step explanation:
x + y = 2y = -x + 2 - the slope of this line is -1 . The line parallel to it will also have a slope of -1.It also passes through (-7,4) so we havey - 4 = -1(x - -7)y - 4 = -1(x + 7)y - 4 = -x - 7x + y = -3 is the required equation.
HELP ME AGINS SNDJJEJEJE
Answer: 0
Step-by-step explanation:
-2+-1 = -3
-3+0 = -3
-3+1 = -2
-2+2 = 0
Haaaaaaallllllllllllllllllppppppppp
Name 3-Dimensional Rectangular Items that are something you can hold. And then name those items' Length, Width, Height, Area, or Volume.
Cube: Rubrics Cube or Dice
Rectangular Prism: Notebook or Gift box
Sphere: Globe or Beach ball
Cone: Carrot or Cone
Cylinder: Barrel or Bucket
Volume Formulas:
Cube = a^3
Rectangular Prism = L x B x H
Sphere = 4/3 pi(r^2)
Cone = 1/3 pi(r^2)h
Cylinder = pi(r^2)h
(pi = 3.14)
Hope this helps.
Question 3 (1 point)
Solve the following equation for x
X=
Blank 1:
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4 (x5)-8 (8 + x) = -64 Pls answer quick
Answer: -72 I think
Step-by-step explanation:
Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1
(Use 1 for the leading coefficient.)
The polynomial function with degree 5 is formed as:
f (x) = x (x + 2)³ (x - 2).
What are termed as the polynomial functions?Polynomials are algebraic representations that contain indeterminates and constants.A polynomial is an algebraic expression in which all of the variable exponents have become whole numbers.Any polynomial's variable exponents must be non-negative integers.A polynomial's degree is the highest and greatest exponent of a variable in such a polynomial.The degree is used to approximate the optimal number of solutions to a polynomial function using Descartes' Rule of Signs.(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.
0 is derived from the factor x.
2 is derived from of the factor (x - 2).
The factored polynomial function is:
f (x) = x (x + 2)³ (x - 2)
Thus, the polynomial function with degree 5 is composed.
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Lucy’s chocolate bar is 54% cocoa. If the weight of the chocolate bar is 54 grams, how many grams of cocoa does it contain? Round the answer to the nearest tenth
Answer:
29.16 grams
Step-by-step explanation:
To solve this, you have to use the weight of cocoa formula. So the weight of cocoa = 54% percent of chocolate bar's weight which is 54 gram. So weight of cocoa = 54/100*54. This will give you 29.16 grams.
the patter is 1, 8, 27, 64, 125 if this patter was produced in a normal spreadsheet what is the number in cell A14?
The number in cell A14 is 2744
How to determine the number in cell A14?The pattern is given as
1, 8, 27, 64, 125
When the above number in the pattern is represented as exponents, we have
1^3, 2^3, 3^3, 4^3, 5^3
So, the nth term is
Tn = n^3
In cell A14, the value of n is 14
So, we have
T14 = 14^3
Evaluate
T14 = 2744
Hence, the number in cell A14 is 2744
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A game show airs on television five days per week. Each day, a prize is randomly placed behind one of two doors. The contestant wins the prize by selecting the correct door.
The probability that exactly 2(two) out of the 5(five) contestants win a prize is 31.25%.
What is probability?
Probability is the(one) branch of mathematics concerning numerical descriptions of how probable a (one) event is to do, or how likely it's that a(one) proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.The more advanced the probability of an event, the more likely it's that the event will do. A simple illustration is the tossing of a fair( unprejudiced) coin. Since the coin is fair, the two issues(" heads" and" tails") are both inversely probable; the probability of" heads" equals the probability of" tails"; and since no other issues are possible, the probability of either" heads" or" tails" is 1/2( which could also be written as 0.5 or 50).The probability that exactly 2(two) out of the 5(five) contestants win a price is given by,
P(x = 2)(two) = 5/16
This is equivalent (equal) to 31.25%.
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Rewrite without parentheses.
3
-4bc²(7b²³-5b5c6 +8c6)
The answer is [tex]-28b^4c^2+20b^6c^8-32bc^8[/tex] without parentheses .
Parentheses, or "brackets", are the familiar ( ) symbols used in pairs to group things or indicate the order of operations in an equation. Example: 5 × (6 − 4) = 5 × 2 = 10 the parentheses group 6-4 and tell us to compute it first.The singular form of parentheses is called parentheses. Parentheses are used to indicate changes in the normal order of operations. Parentheses are also known as parentheses, curly braces, elliptical brackets, or simply parentheses. The "and" symbol is called parenthesis and is commonly used for grouping.
To write this expression without parentheses, each term inside the parentheses must be multiplied by the term outside the parentheses.
[tex]-4bc^2(7b^3-5b^5c^6 +8c^6)=(-4bc.7b^3)+(4bc^2.5b^5c^6)-(4bc^2.8c^6)\\-4bc^2(7b^3-5b^5c^6 +8c^6)=-28b^4c+20b^6c^8-32bc^8[/tex]
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Simon bought bags of potting soil to plant flowers on his patio. A large bag contains of soil, a medium bag contains of soil, and a small bag contains of soil. If he buys one large bag, one medium bag, and two small bags of soil, how many pots can Simon fill?
Answer:
12
Step-by-step explanation:
HELP PLEASE I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
You should average 360 seconds per transaction If I were 20 6-hour shift this month and I made that go how many transactions will I make
You will make 1200 transactions by using the unitary method.
What is the unitary method?
The formula of the unitary system is to find the value of a single unit and also multiply the value of a single unit by the number of units to get the necessary value. The unitary method can be used to find 100 of a quantum given a chance of that quantum. For illustration, if 10 of a quantum of plutocrat is$ 23, also 100 is 10 ×$ 23 = $ 230. 8 of a quantum of plutocrat is$ 6000. The order of terms in a(one) proportion is important. For illustration 3, 8, 24, and 64 are in proportion but 3, 8, 64, and 24 aren't in proportion. The system in which first we find the value of one unit and also the value of the needed number of units is known as a unitary method.Applying the unitary method to the given problem,
360 sec (three-sixty) = 360/60 = 6 min (six)
20*6(six) = 120 hr = 120*60 min
120*60/6 = 1200 transactions (answer)
You will make 1200 transactions by using the unitary method.
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What is the third common multiple of two numbers is 72
Answer:
x-2-10123
y0.1 0.3 0.9 2.7 8.1 24.3
Please answer quick!
Answer:
-67
Step-by-step explanation:
[tex]x=-20 \implies x<-12 \\ \\ \therefore f(-20)=3(-20)-7=-67[/tex]
Convert 10.6% to a fraction in the lowest terms.
10.6% is equivalent to 1/9.43 as a fraction in the lowest terms.
To convert 10.6% to a fraction in the lowest terms, we divide the percentage by 100 and simplify if necessary.
10.6% can be written as 10.6/100.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 10.6 in this case.
10.6/100
= (10.6 ÷ 10.6) / (100 ÷ 10.6)
= 1/9.43
Since 1 and 9.43 do not share any common factors other than 1, the fraction 1/9.43 is already in its lowest terms.
Therefore, 10.6% is equivalent to 1/9.43 as a fraction in the lowest terms.
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