Express
(
x
+
3
)
2
(x+3)
2
as a trinomial in standard form
Answers
The trinomial in standard form that represents (x + 3)^2 is x^2 + 6x + 9.
To express the expression (x + 3)^2 as a trinomial in standard form, we need to expand the expression. The process of expanding involves multiplying the terms in the expression using the distributive property.
(x + 3)^2 can be expanded as follows:
(x + 3)(x + 3)
Using the distributive property, we multiply the terms inside the parentheses:
x(x) + x(3) + 3(x) + 3(3)
Simplifying each term, we get:
x^2 + 3x + 3x + 9
Combining like terms, we have:
x^2 + 6x + 9
Consequently, x2 + 6x + 9 is the trinomial in standard form that represents (x + 3)2.
In general, to expand a binomial squared, we multiply each term in the first binomial by each term in the second binomial, and then combine like terms. The result is a trinomial in standard form, which consists of three terms with the highest degree term appearing first, followed by the middle degree term, and finally the constant term.
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Related Questions
A researcher is studying the effect of a stress-reduction program on people's levels of cortisol (a stress hormone). She tests the cortisol levels of 50 people before starting the program, and then tests the participants' cortisol levels again after completing the program. She wants to test the claim that the stress-reduction program reduces cortisol levels. Which of the following describes the researcher's null and alternative hypotheses? (Opts) null hypothesis: 4-4 = 0; alternative hypothesis: 1-4 <0 X (O pts) null hypothesis: 1-4 <0; alternative hypothesis: -4 > 0 (1 pt) null hypothesis: Hp = 0; alternative hypothesis: Hp <0 (0 pts) null hypothesis: Hp <0; alternative hypothesis: 4p = 0
Answers
The null and alternative hypotheses for the researcher's study on the effect of a stress-reduction program on people's levels of cortisol. None of the options you provided match these hypotheses.
The null hypothesis (H0) is that the stress-reduction program has no effect on cortisol levels, while the alternative hypothesis (H1) is that the program reduces cortisol levels. In this case, the null and alternative hypotheses can be represented as follows:
Null hypothesis (H0): Δcortisol = 0 (no difference in cortisol levels before and after the program)
Alternative hypothesis (H1): Δcortisol < 0 (cortisol levels are lower after the program)
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PLZ help it is due today
Answers
Answer:
45 gallons
Step-by-step explanation:
60/4=15 so each quarter is 15 gallons. He already has 15 gallons so he needs 45 more.
Answer:
45 gallons
Step-by-step explanation:
60*1/4=15
15*3= 45
help me with this please
Answers
Answer:
Here is the sample space:
(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),
(3, 2), (3, 3)
what is-12x + 16 – 4x = -112
Answers
Answer:
\(x=8\)
Step-by-step explanation:
First, I wanna point out a minor mistake, are we supposed to figure out x?
If we are, let's start.
\(-12x+16-4x=-112.\)
We don't need the \(16.\)
We subtract the 16 from both sides.
SImplify, =\(16x=128\)
Also, group like terms, and add similar elements.
Answer:
x = 8
Step-by-step explanation:
-12x + 16 - 4x = -112
Combine like terms on the left side.
-16x + 16 = -112
Subtract 16 from both sides.
-16x = -128
Divide both sides by 16.
x = 8
Check:
-12x + 16 - 4x =
= -12(8) + 16 - 4(8)
= -96 + 16 - 32
= -80 - 32
= -112
-112 = -112
x = 8 is correct.
Answer: x = 8
if you take an intelligence test three times within a week and get scores of 100, 75, and 125, the iq test is probably not:
Answers
If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not reliable. So the option 4 is correct.
A set of standardized tests or subtests created to measure human intellect result in a total score known as an intelligence quotient (IQ). When an intelligence test was given, a person's mental age score was calculated. This score was then divided by their chronological age, which was also expressed in years and months. The resulting fraction (quotient), which yielded the IQ score, was multiplied by 100.
Test results that measure intelligence are estimates of intelligence.
A vast range of item material can be found on the many distinct IQ test types. There are both verbal and visual test items. Test questions can range from being grounded on abstract reasoning issues to focusing on math, language, or general knowledge.
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If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not:
1. powerful.
2. accurate.
3. valid.
4. reliable.
sin(90°– x)= - square root 3 over 2 the value of x is
Answers
Answer:
x=30
Step-by-step explanation:
Sin 60 = ((√3)/2), so x=90-60. x=30.
The required value of x for function sin(90°– x)= - √3/2 is x =150°.
A function is given as sin(90°– x)= - √3/2, Value of x for the function is to be determined.
What are trigonometric equations?The equation contains trigonometric operators such as sin, cos.. etc. In algebraic operation.
sin(90°– x)= - √3/2
sin(90°– x) = -sin60
90°-x = sin(-60°)
90°-x = -60°
-x = -60°-90°
x = 150°
Thus, the required value of x for function sin(90°– x)= - √3/2 is x =150°.
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you are making a blueprint of your bedroom and you plan to use a scale factor of 1/8. The actual width of your room is 14 fret and the actual length of your room is 16 feet. Determine the length and width of your room in the blueprint.
Answers
Answer:
1.75 feet in the blueprints for the width
2 feet in the blueprints for the length
Step-by-step explanation:
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what is the inverse of the function y=5x+30?
Answers
The inverse of the function is y = ( 1/5 )x - 6.
An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Consider the function,
y = 5x + 30
To find the inverse of the function we interchange x and y then find the equation for y.
Therefore, after interchanging x and y:
x = 5y + 30
Subtracting 30 from each side of the equation.
x - 30 = 5y + 30 - 30
x - 30 = 5y
Now, dividing the whole equation by 5
( x - 30 ) / 5 = 5y / 5
y = ( 1/5 )x - 30/ 5
y = ( 1/5 )x - 6
Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.
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is (, ) = 3 − 32 an harmonic function? if yes, then find a corresponding analytic function ()
Answers
No, f(x, y) = 3x - 3y^2 is not a harmonic function.
A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
∂²f/∂x² + ∂²f/∂y² = 0.
Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0
Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.
As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.
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On the grid below, which point is located in the quadrant where the x- and y-coordinates are both negative numbers?
Answers
Answer:
Point C
Step-by-step explanation:
Given
See attachment for grid
Required
Which point is x and y = negative
From the attached grid, we have the following points
\(A = (6,4)\)
\(B = (-4,2)\)
\(C =(-7,-2)\)
\(D = (5,-4)\)
From the above points, only point C has negative x and y
Another way to go about it is:
Quadrant 3 has negative x and y values and point C is located in quadrant C.
Please help me and explain thank u
Answers
The solution to this expression (√5 - 3√2)(√5 + 3√2) is equal to -13.
What is a difference of two (2) squares?In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b represent numerical values (numbers or numerals).
Based on the information provided, we have the following mathematical expression:
(√5 - 3√2)(√5 + 3√2);
By comparison, we have the following:
(√5 - 3√2)(√5 + 3√2) = (a + b)(a - b)
a² - b² = (√5)² - (3√2)²
a² - b² = 5 - 18
a² - b² = -13.
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the measures of the angles of a 9-gon are in ratio $3:1:4:1:5:9:2:6:5.$ what is the number of degrees in the measure of the largest angle?
Answers
The number of degrees in the measure of the largest angle is 315°
given that
In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon.
The name nonagon is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name enneagon comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct,though less common than "nonagon".
Although a regular nonagon is not constructible with compass and straightedge (as 9 = 32, which is not a product of distinct Fermat primes), there are very old methods of construction that produce very close approximations.
It can be also constructed using neusis, or by allowing the use of an angle trisector.
the angles of a 9-gon are in ratio 3:1:4:1:5:9:2:6:5
the sum of interior angles of an 9-gon = (9-2)* 180
= 7*180
=1260°
now, we need to find the largest angle
9/(3+1+4+1+5+9+2+6+5) *1260
=9/(36)*1260
=(1/4)*1260
=315°
The number of degrees in the measure of the largest angle is 315°
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Which expression is equivalent to
Answers
Answer:
option D is the correct answer
hope it helps you
make me brainliest if u are satisfied with this answer
Answer:
option D
hope it helps you
1/2(4x − 8) = 2(x+3)
Answers
Answer:
the equation is false
Step-by-step explanation:
1/2(4x − 8) = 2(x+3)
2x - 4 = 2x + 6
0 = 10
the equation is false
Topic: Probability
Only complete question 13.
Answers
Answer:
see below
Step-by-step explanation:
Assuming the comma means and
a) P(A , E) = P(A) * P(E) = .1 * .5 = .05
b) P( A, L, E) = P(A) * P(L) *P(E) = .1 *.4* .5 = .002
C This means that it snows in Abbostford, Lehtbridge and Estevan today is .002 or .2%
under what circumstances can a very small treatment effect still be significant? group of answer choices if the standard error of m (s m) is very large if the sample size (n) is very large all of the other factors are likely to produce a significant result. if the sample standard deviation (s) is very large
Answers
A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
What is the standard error, and sample size?The standard error calculates the discrepancy between a sample's estimate and the actual value for the population. Therefore, the standard error should be smaller the better. In fact, a standard error of zero or extremely close to it would indicate that the projected value and the actual value are identical.Sample size determination is the process of deciding how many observations or replicates to include in a statistical sample. The sample size is an important consideration in any empirical study that aims to infer information about a population from a sample.Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
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Lisa is assembling fruit baskets for a large corporate order. She starts with 66 pears and will put 5 pears in each fruit basket.
Write an equation that shows how the number of pears remaining, y, depends on the number of fruit baskets Lisa assembles, x.
Answers
Answer:
x = 61
Step-by-step explanation:
Based on the given conditions, formulate: x = 66 - 5
Calculate the sum or difference: x = 61
Get the result: x = 61
solving systems by elimination
3x-4y=7
2x+4y=8
Answers
Refer to the attachment!
What is the solution y 2 3x 3 x =- 2?
Answers
The solution of the equation y = (2/3)x + 3 is 5/3
The given equation is
y = (2/3)x + 3
The slope of the line is the change in y coordinates with respect to the change in x coordinates.
This is the linear equation in the the slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept
y is the y coordinates
x is the x coordinates
The value of x = -2
Substitute the value of x in the equation
y = (2/3) × -2 + 3
Do the arithmetic operations
= -4/3 + 3
Add the numbers
= 5/3
Therefore, the solution is 5/3
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the solution of the equation y = (2/3)x + 3x, when x = -2?
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Dora wants to put up a vegetable garden in their backyard. If the perimeter of the garden is 32 m and the area is 60 m2, what must be the length and the width of the vegetable garden?
Answers
Width=10
Or vice versa
Step-by-step explanation:
so, it is an ideal rectangular shape ? because that is what the problem description is "hiding".
if that assumption is true, then we have
l = length
w = width
perimeter = 32 = 2×l + 2×w
=> 16 = l + w
l = 16 - w
area = 60 = l×w
now we use the perimeter equation to substitute in the area equation
60 = (16 - w) × w = 16w - w²
so, we get the squared equation
-w² + 16w - 60 = 0
the solution for such an equation is
x (or w in our case) = (-b ± sqrt(b² - 4ac))/(2a)
a = -1
b = 16
c = -60
w = (-16 ± sqrt(256 - 4×-1×-60))/-2 =
= (-16 ± sqrt(256 - 240))/-2 =
= (-16 ± sqrt(16))/-2 = (-16 ± 4)/-2
w1 = (-16 + 4) / -2 = -12/-2 = 6 m
w2 = (-16 - 4) / -2 = -20/-2 = 10 m
l1 = 16 - 6 = 10 m
l2 = 16 - 10 = 6 m
so, one of length and width must be 6 meter and the other 10 meter long. it does not matter which, as a rectangle turned by 90 degrees is still the same rectangle.
Find g(x), where g(x) is the translation 2 units right of f(x)=x.
Write your answer in the form mx+b, where m and b are integers.
Answers
The image of the function f(x) = x , after the translation is g(x) = x -2 .
In the question
it is given that
the function f(x) = x ,
and f(x) has to be translated 2 units to the right means subtract 2 from the function .
which means g(x) = f(x) - 2
substituting f(x) = x , we get
g(x) = x - 2
the answer in the form of mx+b is g(x) = x - 2
(can refer to the graph given below)
Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .
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find the gradient of the curve y=x^2 + 5x-3 at the point x= 2.
please help.
Answers
Answer:
gradient = 9
Step-by-step explanation:
Note that \(\frac{dy}{dx}\) is a measure of the gradient.
Differentiate y using the power rule
\(\frac{d}{dx}\) (a\(x^{n}\)) = na\(x^{n-1}\)
Given
y = x² + 5x - 3, then
\(\frac{dy}{dx}\) = 2x + 5
x = 2 : \(\frac{dy}{dx}\) = 2(2) + 5 = 4 + 5 = 9 ← gradient
find ac if ab =9,ac=x+19,and bc=2x+18.
Answers
By solving a linear equation, we can see that the measures of the segments are:
ab = 9ac = 11bc = 2How to find the length of each segment?Here we have 3 collinear points, a, b, and c.
We know that the measures are:
ab = 9
ac = x + 19
bc = 2x + 18
If b is between a and c, then we should have that:
ac = ab + bc
Replacing the measures we get:
x + 19 = 9 + (2x + 18)
Now we can solve this linear equation to find the value of x.
x + 19 = 9 + 2x + 18
x + 19 = 27 + 2x
19 - 27 = 2x -x
-8 = x
Then the measures are:
ab = 9
ac = -8 + 19 = 11
bc = 2*(-8) + 18 = -16 + 18 = 2
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1. what is the distributive Property
2. what does it means to combine '' like terms''?
Answers
Answer:
the distributive property is to divide something or give a share or part of something to combine like terms means to add their coefficients or the number in front of their variable for example 2x the coefficient is 2
3/1 + 1/3
What is the answer to this?
Answers
Answer:
10/3, or 3 1/3.
Step-by-step explanation:
3/1 + 1/3
3 + 1/3
9+1/3
10/3, or 3 1/3.
I NEED IN THE NEXT 10 MIN PLS. GRAPH ATTACHED WILL GIVE BRAINLIEST Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis at five that ends at the open point 2, 5, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3 and continues to the right. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
Answers
Answer:
Step-by-step explanation:
You gave very clear instructions on how to draw this graph, so that's what I did. What you need to remember in particular with limits is that you do not care in the least what happens AT the x value of 2, only what happens as it is being approached. Because we are asked the limit as x is approaching from the left and the right, this is a one-sided limit question. In order for the limit to exist as x approaches 2 (NOT from the left or the right), the limit would have to agree from the left and the right, and this one doesn't. Having said that there is "a horizontal line crossing the y-axis at 5 that ends at the open point (2, 5)..." is a limit approaching x from the left. Therefore,
\(\lim_{x \to 2^-} f(x)=5\)
Having also said there is "...another horizontal line starting at the open point (2, -3) and continues to the right..." is a limit approaching x from the right. Therefore,
\(\lim_{x \to 2^+} f(x)= -3\)
The closed point at (2, 1) is where x IS, and remember that we don't care about what happens AT x. So disregard this point in limits.
The BP station sold gas for $2.49 per gallon. This week their gas prices are $2.61 a gallon. What was the percent increase in gas from last week to this week?
Answers
Answer:
.12%
Step-by-step explanation
2.61-2.49= 0.12
.12%
A basketball coach is ordering jerseys for members of the basketball team and can choose between small, medium, and large jerseys. The cost of a small jersey is x dollars. The cost of a medium jersey is 1 dollar more than the small jersey, and the cost of a large jersey is 2 dollars more than the medium jersey.
The coach orders 5 medium jerseys and 7 large jerseys for a total cost of $146. The equation below can be used to find the cost, in dollars, of one small jersey.
5(x+1)+7(x+3)=146
Enter the cost, in dollars, of one small jersey.
for my 8th grade math test
Answers
Answer: $10 dollars for a small jersey
Step-by-step explanation: distrubute 5 to (x+1) then distrubute 7 to (x+3) to get 5x+5+7x+21=146, add x values and non x values to get 12x+26=146, then subtract 26 from both sides to get 12x=120, divide 120 by 12 to get x=10
Write the steps in detail
On how to solve an angle bisector
problem, please use completé sentences.
Answers
A triangle's opposite side is split in half by an angle bisector into two segments that are proportional to the other two sides.
We can solve this problem by using the formula explained in the angle bisector theorem below.
Angle Bisector theorem :
In the below image, PS is the angle bisector of ∠P in ΔPQR.
As a result, we can state that by using the angle bisector theorem as
PQ/PR = QS/SR
or
a/b = x/y.
By this, we can solve the angle bisector theorem.
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A tourist exchanged BD$2000 into US dollars at the rate of
BD$1 = US$0.50. The bank charged commission of 1.5%.
How many US$ did the tourist receive?
Answers
US$ the tourist received finally is US$985.
How to find the amount he received?BD$2000 is there.
BD$1 = US$0.50
Bank charged a commission of 1.5%.
Solution:
For one BD i.e., BD$1 he gets US$0.50.
It is half the value of BD$.
By cross multiplication technique, you can find this.
Then for,
BD$2000 he will get US$ 1000.
Bank charges = 1.5%.
That is,
1.5/100*1000 = $15
US$ the tourist received finally = 1000-15
= $985
US$ the tourist received finally is US$985.
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