Answer:
x = 3, x = -5
Step-by-step explanation:
A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:
a^2 = x^2
a = x
Now, we can substitute x for a in the other expression to create the equation:
2ab = 2x
2(x)b=2x
b = 1
From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:
x^2 + 2x = 15
x^2 + 2x + 1 = 16
Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:
(x + 1)^2 = 16
Now, we take the square root of both sides:
x + 1 = ± 4
We can separate this into two equations and solve:
x + 1 = 4
x = 3
x + 1 = -4
x = -5
Answer:
Step-by-step explanation:
x^2 + 2x = 15
x^2 + 2x + [1/2(2)]^2 = 15 + [1/2(2)]^2
(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2
(x + 1)^2 = 15 + 1^2
(x + 1)^2 = 15 + 1
(x+1)^2 = 16 Take the square root of both sides.
sqrt( (x + 1)^2 ) = sqrt(16)
x + 1 = +/- 4
x + 1 = 4
x = 4 - 1 = 3
x + 1 = -4
x = -4 - 1
x = - 5
So the roots are 3 and - 5
To paint interior walls, a person charges 50¢ per square foot plus the cost of the paint. For a recent job, the paint cost $100 and the total bill was $475.
The person must have painted ____ ft^2.
Answer: [tex]750\ ft^2[/tex]
Step-by-step explanation:
Given
Rate of painting 50¢ per square foot
Cost of paint is $100
If the total bill is $475
We can write,
[tex]\Rightarrow 475=100+0.5\times x\quad [x=\text{area in square foot}]\\\Rightarrow 375=0.5x\\\Rightarrow x=750\ ft^2[/tex]
Thus, [tex]750\ ft^2[/tex] must be painted.
If f(x) is a linear function, f(−2)=4, and f(1)=−1, find an equation for f(x)
Answer:
[tex]y = -\frac{5}{3}x+\frac{2}{3}[/tex]
Step-by-step explanation:
Given
[tex]f(-2) = 4[/tex]
[tex]f(1) = -1[/tex]
Required
The equation of the function
The given parameters means that:
[tex](x_1,y_1) = (-2,4)[/tex]
[tex](x_2,y_2) = (1,-1)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{-1-4}{1--2}[/tex]
[tex]m = \frac{-5}{3}[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y =\frac{-5}{3}(x--2)+4[/tex]
[tex]y =\frac{-5}{3}(x+2)+4[/tex]
Open bracket
[tex]y = -\frac{5}{3}x-\frac{10}{3}+4[/tex]
Take LCM
[tex]y = -\frac{5}{3}x+\frac{-10+12}{3}[/tex]
[tex]y = -\frac{5}{3}x+\frac{2}{3}[/tex]
A triangle has side lengths of 24 centimeters and 35. The third side has a length of x centimeters. Complete the inequality to show all the possible values of x.
*2 answers*
Answer: [tex]11<x<59[/tex]
Step-by-step explanation:
Given
The side of the triangle are [tex]24\ \text{and }35[/tex]
Suppose the third side is [tex]x[/tex]
Also, the sum of the two sides of the triangle is always greater than the third
[tex]\therefore x<24+35\\\Rightarrow x<59\quad \ldots(i)[/tex]
Similarly,
[tex]\Rightarrow x+35>24\\\Rightarrow x>-11[/tex]
Also,
[tex]\Rightarrow x+24>35\\\Rightarrow x>11\quad \ldots(ii)[/tex]
From (i) and (ii) we get
[tex]\Rightarrow 11<x<59[/tex]
which is an irrational number
Answer:
The irrational number is [tex]\sqrt{\frac{5}{3}}[/tex].
__________________________________
Definition : In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
Answer:
Step-by-step explanation:
I'm not sure but I think it's A
I'm not sure!!
(pls do not vote ..)
Bye!
Find the lowest common multiple of 10 and 12
Can someone please help me?
Answer:
The Answer for your question is B
Answer:
78%
Step-by-step explanation:
They are asking for spotted animals and dogs so
Spotted animals=40%
Dogs=38%
So just add them to get 78%
(Don’t get confused by the 12% spotted dogs those are from the 38%)
Find tan 0, where is the angle shown. Give an exact value, not a decimal approximation. (PLZ HELP DUE SOON I GIVE BRAINLIST :D)
Answer:
[tex]\frac{24}{7}[/tex]
Step-by-step explanation:
Tanθ=Opposite/Adjacent
we have the adjacent side but need the oppsoite
We will use a²+b²=c²
25²=7²+b²
576=b²
b=24
Therefore the answer is
[tex]\frac{24}{7}[/tex]
. How much time, in minutes, did she spend studying Spanish?
The time Kathleen spent studying Spanish is
SEE IMAGE BELOW AND ONLY ANSWER IF YOU KNOW THE ANSWER
x-value of 0
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6
9514 1404 393
Answer:
0, 3, 3, -6, -3
Step-by-step explanation:
Maybe you want to find f(0) in each case. Put 0 where x is, and do the arithmetic.
f(0) = |0| = 0
f(0) = |0| +3 = 3
f(0) = |0 +3| = 3
f(0) = |0| -6 = -6
f(0) = |0 +3| -6 = -3
Are these triangles congruent?
Answer:
yes...
Step-by-step explanation:
its a congrate triangle
The vertices of a trapezoid are located at (1, 2), (3, 1), (3, 5), (1, 4). The trapezoid is translated 4 units to the right. What are the coordinates of the image of the trapezoid?
Answer:
Suppose that we have a given point (x, y)
If we translate this point N units to the right, then the new coordinates of the point are:
(x + N, y)
Ok, now if we know that the vertices of the trapezoid are:
(1, 2), (3, 1), (3, 5), (1, 4)
And we move the whole figure 4 units to the right, then all the vertices are moved 4 units to the right.
Then the new vertices of the figure will be:
(1 + 4, 2) = (5, 2)
(3 + 4, 1) = (7, 1)
(3 + 4, 5) = (7, 5)
(1 + 4, 4) = (5, 4)
Then the coordinates of the image of the trapezoid (of the new vertices) are:
(5, 2), (7, 1), (7, 5), (5, 4)
Find the area of the parallelogram below
Step-by-step explanation:
area of the parallelogram = 7 × 14
=98 cm²
The list price on slacks is $22, and the list price on jumpers is $37. If Petit’s Clothing Store orders 30 pairs of slacks and 40 jumpers at a discount rate of 11%, what is the trade discount on the purchase?
Step-by-step explanation:
Calculate the value of decimal equivalents of complements, net decimal equivalent and net price with the help of given data:
List price= $200
Trade discount series= 20/10
Calculate the decimal equivalents of complements using given formula:
Complements of successive discount = 
= 80% / 90%
Hence, decimal equivalent of complements are 80% / 90%.
Answer:
Trade discount = $235.40
Step-by-step explanation:
List price :
Slacks = 22
Jumpers = 37
Total amount before discount = (30 x 22) + ( 40 x 37)
= 660 + 1480
= 2140
Discount rate = 11%
So,
[tex]Discount \ price = 11 \% \ of \ 2140\\\\Discount \ price = \frac{11}{100} \times 2140 = 235.40[/tex]
A right cone has a surface area of 440 square inches and a radius of 7 inches. Find its slant height.
Answer:
13 inches
Step-by-step explanation:
Surface area of a right cone = pi*r(r+L)
i,e, 440 = 22/7*7(7+L)
440 = 22(7+L)
440 = 154 + 22L
440 - 154 = 22L
286 = 22L
286/22 = L
13 = L
Therefore the slant height is 13inches
Hope u understand
Thank You
Find the mean for the following data set: 5, 3, 6, 8, 1, 1 *
Answer:
add all the numbers
which will get you 24
then divide by how many numbers you got which will give you 6
the answer is six
Step-by-step explanation:
Hope this helps :D
Answer:
The mean is equal to 4.
Step-by-step explanation:
To find the mean of any set of numbers, you have to add all of those numbers and divide the result by however many numbers their are.
For example, the mean of 2,5,6, and 7 would be the following: 2+5+6+7/4
The mean of 5,3,6,8,1, and 1 is the following: 5+3+6+8+1+1/6=24/6=4
The mean is equal to 4.
f(x)=3x-3
g(x) 3x^3+5
Find F(-3) and g(-2)
Answer:
f(-3) = -12
g(-2) = -19
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 3x - 3
g(x) = 3x³ + 5
f(-3) is x = -3 for function f(x)
g(-2) is x = -2 for function g(x)
Step 2: Evaluate
f(-3)
Substitute in x [Function f(x)]: f(-3) = 3(-3) - 3Multiply: f(-3) = -9 - 3Subtract: f(-3) = -12g(-2)
Substitute in x [Function g(x)]: g(-2) = 3(-2)³ + 5Exponents: g(-2) = 3(-8) + 5Multiply: g(-2) = -24 + 5Add: g(-2) = -19Answer:
f(-3) = -12
g(-2) = -19
Step-by-step explanation:
1.
f(x) = 3x - 3
One is asked to find (f(-3)), substitute (-3) into the given function (f) in place of (-3), and solve to evaluate,
f(-3) = 3(-3) - 3
Simplify,
= -9 - 3
= -12
2.
g(x) = [tex]3x^3+5[/tex]
The problem asks one to find (g(-2)), subtitute (-2) into the function in place of (x) and solve to find tis value,
g(-2) = [tex]3(-2)^3+5\\[/tex]
Remember any number raised to an exponent is equal to the base (the number that is being raised to the exponent) times itself the number of times that the exponent indicates,
[tex]=3(-8)+5\\=-24+5\\=-19[/tex]
PLEASE HELP ME WILL MARK YPU IF YOU HELP ME
ok check image file in the image is answers with color code
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 7500 households, and the data collected today will be used to determine the proportion of households tuned to a particular sports program. Which type of observational study is described in the problem statement?
Answer:
Cross sectional study
Step-by-step explanation:
Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).
Jenny made 200 bracelets. She sold 64% of the bracelets at a craft fair.
a. How many bracelets did she sell?
b. How many bracelets were not sold?
Step-by-step explanation:
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Answer:
Jenny sold 128 braclets. 72 bracelets weren't sold.
Step-by-step explanation:
IMPORTANT FORMULA: TO CONVERT A NUMBER TO A PERCENT, YOU HAVE TO MULTIPLY BY 100. TO CONVERT A PERCENT TO A NUMBER, YOU HAVE TO DIVIDE BY 100.
a) How many bracelets did she sell?
Using the formula that is shown above, I can conclude that 64%=64/100=32/50=16/25
Jenny sold 64% of the 200 bracelets.
In mathematics, the word "of" means multiplication.
64% of 200 = 16/25 * 200 = 128
Jenny sold 128 braclets.
to answer part 2, 200 bracelets - 128 bracelets = 72 bracelets.
72 bracelets weren't sold.
Lydiagrace33
Image attached
A) 1 point Write an inequality for this graph . Use the shift key and the key or key to type the < or > symbol . *
B) Water boils when the temperature is at least 212 degrees F. Which inequality shows this situation ?
C) When the temperature drops below 50 degrees F , crickets usually stop chirping . Which inequality shows this situation ?
D) Explain the difference between the meaning of a closed
circle and an open circle on a graph of an inequality .
How many natural numbers are there between 8² and 9² ?
Answer:
19
Step-by-step explanation:
Answer:
i think the answer 17
81-64 =17the temperature of a cup of coffee obeys newton's law of cooling. The initial temperature of the coffee is 150F and 1 minute later it is 135F. The temperature of the room is 70F. If T(t) represents the temperature of the coffee at time T the correct differential equation for the temperature for this condition is
Answer:
Newton's law of cooling says that:
T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)
or:
[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]
in the differential form.
where:
T is the temperature as a function of time
Tₐ is the ambient temperature, in this case, 70F
T₀ is the initial temperature of the object, in this case, 150F
k is a constant, and we want to find the value of k.
Then our equation is:
T = 70F + (150F - 70F)*e^(k*t)
Now we also know that after a minute, or 60 seconds, the temperature was 135F
then:
135F = 70F + (150F - 70F)*e^(k*60s)
We can solve this for k:
135F = 70F + 80F*e^(k*60s)
135F - 70F = 80F*e^(k*60s)
65F = 80F*e^(k*60s)
(65/80) = e^(k*60s)
Now we can apply the Ln(x) function to both sides to get:
Ln(65/80) = Ln(e^(k*60s))
Ln(65/80) = k*60s
Ln(65/80)/60s = k = -0.0035 s^-1
Then the differential equation is:
[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]
At a basketball game, a vender sold a combined total of 101 sodas and hot dogs. The number of sodas sold was 37 more than the number of hot dogs sold. Find
the number of sodas sold and the number of hot dogs sold.
Answer:
101 - 37 = 64
I hope this is correct
Hello, I need help with this math question please
Option B:- x = -3/2 or x = 2
Help need help fast
Answer:
Answer is in bold form
Step-by-step explanation:
Given
radius = 3feet
Height = 6feet
Volume of the cylinder = πr²h
Volume of the cylinder = 3.14 * 3² * 6
Volume of the cylinder = 169.56ft³
volume of the cone = Volume of cylinder/3
volume of the cone = 169.56/3
volume of the cone = 56.52ft³
Volume of the sphere = 4/3πr³
Volume of the sphere = 4/3*3.14*(3)³
Volume of the sphere = 4 * 3.14* 9
Volume of the sphere = 113.04ft³
It is A (45). Hope this helps!
Choose the inequality that repersents the following graph
Answer:
B. x</=-3
Step-by-step explanation:
the arrow is pointed to the left which means less than and the end is shaded which means or equal to
HELP !!!! look at the picture
Answer:
Option C:
g(x) = -3^x
Step-by-step explanation:
Here we can see the graphs of f(x) and the graph of g(x).
By only looking at that, we can see that g(x) is a reflection across the x-axis of f(x).
Remember that for a general function f(x), the reflection across the x-axis is written as:
g(x) = -f(x).
Then, if f(x) = 3^x
and g(x) = -f(x)
replacing f(x) we get:
g(x) = -(3^x) = -3^x
The correct option is C.
What is the range of g(x) = -2 [X + 3] + 2?
Answer:
A.
Step-by-step explanation:
When x = -3 g(x) = + 2 and this is the maximum value of g(x).
All other values of x give a value of g(x) < 2.
The range is (-∞, 2]
Which expression represents the area in square centimeters of the new cup opening? Use A=2
Answer:
A = πx² - 2πx + π
Step-by-step explanation:
The area of the new cup opening :
We are given the area formula to use :
Area, A = πr²
r = Radius = x-1
Area = π(x - 1)²
A = π(x - 1)(x - 1)
A = π(x² - x - x + 1)
A =π(x² - 2x + 1)
A = πx² - 2πx + π