From a perfect square trinomial
[tex]a^2+2ab+b^2[/tex]We know that:
[tex]2ab=2\cdot\sqrt[]{a^2}\cdot\sqrt[]{b^2}[/tex]Now, let's use this for the trinomial given:
[tex]x^2-8x+b^2[/tex]We know that:
[tex]-8x=2\cdot x\cdot b^2[/tex]Solving for b,
[tex]\begin{gathered} -8x=2xb \\ \rightarrow b=-\frac{8x}{2x}\Rightarrow b=-4 \end{gathered}[/tex]This way, the complete perfect square trinomial is:
[tex]x^2-8x-16[/tex]Ans: Option A
Simplify the expression: 4(5x-3)20x-128x17x8
Answer:
20x-12
Explanation:
Given the expression:
[tex]4\mleft(5x-3\mright)[/tex]To simplify, we first distribute.
[tex]=4(5x)-4(3)[/tex]Next, we open the bracket to obtain:
[tex]=20x-12[/tex]The correct choice is the first one.
A rectangle's base is 2 in shorter than five times its height. The rectangle's area is 115 in². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
Answer:
The rectangle's height is 5 in,The rectangle's base is 23 in.Step-by-step explanation:
Let the dimensions are b and h.
The area of rectangle is the product of two dimensions.
We have:
b = 5h - 2,bh = 115 in².Solve the equation by substitution:
h(5h - 2) = 1155h² - 2h = 1155h² - 2h - 115 = 05h² - 25h + 23h - 115 = 05h(h - 5) + 23(h - 5) = 0(h - 5)(5h + 23) = 0h - 5 = 0 and 5h + 23 = 0h = 5 and h = - 23/5The second root is discarded as negative.
The height is 5 in,The base is: 5*5 - 2 = 23 inAnswer:
Height = 5 in
Base = 23 in
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectangle} = \sf Base \times Height}[/tex]
Let x be the height of the rectangle.
Given values:
Height = x inBase = (5x - 2) inArea = 115 in²Substitute the values into the formula for area and solve for x:
[tex]\begin{aligned}\sf Area & = \sf Base \times Height\\\\115&=x(5x-2)\\115&=5x^2-2x\\5x^2-2x-115&=0\\5x^2-25x+23x-115&=0\\5x(x-5)+23(x-5)&=0\\(5x+23)(x-5)&=0\\\\\implies 5x+23&=0 \implies x=-\dfrac{23}{5}\\\implies x-5&=0 \implies x=5\end{aligned}[/tex]
As length is positive, x = 5.
To find the rectangle's dimensions, substitute the found value of x into the expressions for the height and base:
[tex]\implies \sf Height=5\;in[/tex]
[tex]\begin{aligned}\implies \sf Base&=\sf 5(5)-2\\&=\sf 25-2\\&=\sf 23\;in\end{aligned}[/tex]
In the metric system, 1 gran is the mass of 1 milliliter of water. So, a 2-liter bottle of water has a mass of 2 kilograms. A gallon of water weighs about 8 pounds. What is the mass of a gallon of water to the nearest tenth of a kilogram?Parts A-D
We know that:
[tex]1\text{ lb }\to0.45\text{ kg}[/tex]A)
Using the conversion law, we can calculate the conversion factor as a fraction:
[tex]\frac{0.45\text{ kg}}{1\text{ lb}}=\frac{9\text{ kg}}{20\text{ lb}}[/tex]B)
Now, we multiplicate 8 pounds by the conversion factor:
[tex]\frac{9\text{ kg}}{20\text{ lb}}\cdot8\text{ lb }\approx3.6\text{ kg}[/tex]C)
The pound units cancel, resulting in an answer given in kilograms.
D)
When you choose a conversion factor, the unit you are converting to is the first quantity in the rate.
Solve for
x: 5/6x+7=1
Answer:
x=2/3
Step-by-step explanation:
5/(6x+1) * 6x+1 = 1 * (6x+1)
5=6x+1
5-1=6x+1-1
6x=4
6x/6=4/6
x=2/3
help me please
thank you
Answer:
(-7, 3)
Step-by-step explanation:
what Since the endpoints of the interval are not included, use parentheses.
Find the Discriminant and describe the number and type of solutions of the equations. 1) 4x^2 + 8x + 4 =0
Given:
[tex]4x^2+8x+4=0[/tex]To find the discriminant, use the formula:
[tex]\Delta=b^2-4ac[/tex]Where a = 4, b = 8, c = 4
Thus, we have:
[tex]\begin{gathered} \Delta=8^2-4(4)(4) \\ \\ \Delta=64-64\text{ =0} \end{gathered}[/tex]The discriminant is = 0
To find the number of solutions, since the disriminant is zero, we have two real and identical roots.
ANSWER:
Discriminant = 0
Number of roots = 2 real and identical roots
Judy has 15 books in her library. She bought several books at a thrift storeon Saturday. She now has 84 books in her library. How many books did shebuy at the thrift store? Write an equation to solve the problem use b forthe variable.
Let b the number of books Judy has bought.
The given data can be expressed as,
[tex]15+b=84[/tex]Answer:
69 books
15+ b= 84
Step-by-step explanation:
On a coordinate plane, a parabola with a solid boundary line opens up. It goes through (negative 1, 0), has a vertex at (4, negative 125), and goes through (9, 0). Which inequality in standard form represents the shaded region? y greater-than-or-equal-to x squared + 8 x + 9 y greater-than-or-equal-to x squared minus 8 x minus 9 y greater-than-or-equal-to 5 x squared minus 40 x minus 45 y greater-than-or-equal-to 5 x squared + 40 x + 45
The inequality represented by the parabola is given as follows:
y ≥ 5x² - 40x -45.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:
y = a(x - h)² + k
In which the parameters are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.In the context of this problem, the vertex is given by:
(4, -125).
Hence:
y = a(x - 4)² - 125
When x = -1, y = 0, hence the leading coefficient is found as follows:
0 = 25a - 125
25a = 125
a = 125/25
a = 5.
Hence the equation is given as follows:
y = 5(x - 4)² - 125
y = 5(x² - 8x + 16) - 125
y = 5x² - 40x -45.
The inequality has a solid boundary line, hence it contains the equal sign, and the values above the parabola are plotted, hence it is given by:
y ≥ 5x² - 40x -45.
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Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown?
May I please get help with this place. I have tried multiple times but still could not get the correct
(a) Which figures are parallelograms.
A parallelogram is a quadrilateral whose opposite sides are parallel, and therefore opposite angles are equal.
Figure B, and C are parallelogram since all of the opposite angles are equal.
Figure A is also a parallelogram since the all of the opposite sides are congruent.
FIGURE A,B, and C are parallelograms.
(b) Which figures are rectangles.
A rectangle is a parallelogram where all of the angles are 90°. A square is also a type of rectangle where all the sides are congruent.
FIGURE B and C are rectangles.
(c) Which figures are squares.
As mentioned earlier, as square is a rectangle where all the interior angles is 90°, and has all of the sides congruent.
FIGURE C is a square.
2. Write an equation of the ellipse with foci at (0, +2) and co-vertices at （+1, 0）.དུ དུའི - 1།14︽ 》སོ – །
Given,
The foci of the ellipse is (0, +2)(0.-2)
The co vertices of the ellipse is (1, 0)(-1, 0)
The genral equation of ellipse is,
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The equation of the foci is,
[tex]\begin{gathered} (0,\text{ }\pm c)=(0,\text{ }\pm2) \\ \text{The value of c is 2.} \end{gathered}[/tex]The equation of co vertices is,
[tex]\begin{gathered} (\pm a,\text{ 0)=(}\pm1,\text{ 0)} \\ \text{The value of a is 1.} \end{gathered}[/tex]we know that,
[tex]\begin{gathered} b^2=a^2+c^2 \\ b=\sqrt[]{5} \end{gathered}[/tex]Substituting the value then,
[tex]\begin{gathered} \frac{x^2}{1^2}+\frac{y^2}{\sqrt[]{5}^2}=1 \\ x^2+\frac{y^2}{5}=1 \end{gathered}[/tex]Hence, option d is correct.
Simplify.
(4.17x−1.32)+(−7.6x+3.54)
Responses
−3.43x+2.22
negatvie 3.43 x plus 2.22
7.71x−8.92
7.71 x minus 8.92
11.77x + 4.86
11.77, x, + 4.86
2.85x−4.06
The value of the expression (4.17x−1.32)+(−7.6x+3.54) is A. −3.43x+2.22 or negatvie 3.43 x plus 2.22
What are expressions?Expressions are used in Mathematics to illustrate the relationship between the variables.
The expression is given as:
(4.17x−1.32)+(−7.6x+3.54)
Open the parentheses and collect like terms
4.17x - 7.6x - 1.32 + 3.54
-3.43x + 2.22
Therefore, the correct option is A.
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what is the answer to 8/8^12
Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80
The dimension of the rectangle after the scale will be 5 cm wide and 6.25 cm long.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
Tyler wants to sketch out his bedroom to scale. His bedroom is a rectangle that is 5 meters long and 4 meters wide. He chooses based on a scale of 1 to 80.
Then the dimension of the rectangle after the scale.
Width = (1/80) x 4
Width = 5 cm
Length = (1/80) x 5
Length = 6.25 cm
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After entering the table values in his calculator, Cory used the LinReg button to get the results shown. Identify the correlation coefficient and the type of correlation.
The value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
From the data given in the table,
The value of the correlation coefficient can be found using the formula:
r = -0.2984713607
After rounding off:
r = -0.2985
As the value of r is not near the -1 so the relation between x and y is weak negative:
Thus, the value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
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Suppose you deposited $13000 in a saving account in which interest is compounded continuously. It takes 14 years to double your money in this account.(1) What is the annual rate of interest? (Round your answer to one decimal place.) % Tries 0/99(2) How much will you have in this account after 26 years? (Round your answer to two decimal places.) dollars Tries 0/99
Remember that
The formula to calculate continuously compounded interest is equal to
[tex]A=P\left(e\right)^{\left\{rt\right\}}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the Number of Time Periods
e is the mathematical constant number
In this problem, we have that
Part 1
P=$13,000
A=$26,000
t=14 years
substitute given values
[tex]\begin{gathered} 26,000=13,000\left(e\right)^{\left\{14r\right\}} \\ solve\text{ for r} \\ 2=e^{14r} \\ apply\text{ ln on both sides} \\ ln(2)=lne^{14r} \\ ln(2)=14r \\ r=\frac{ln(2)}{14} \\ \\ r=0.0495 \\ r=4.95\% \\ r=5\% \end{gathered}[/tex]Part 2
we have
P=$13,000
r=5%=0.05
t=26 years
substitute in the formula
[tex]\begin{gathered} A=13,000(e)^{\operatorname{\{}0.05*26\operatorname{\}}} \\ A=\$47,700.86 \end{gathered}[/tex]Determine the smallest possible co-terminal
angle for a) 410. b)-45
The smallest possible co-terminal are:
a)50
b) -495
Define co terminal angles.Angles that share the terminal side with an angle occupying the standard position are said to be co terminal angles. In the conventional position, the vertex is at the origin and one side of the angle is fixed along the positive x-axis.
In other words, two angles are co terminal when their vertices and sides are the same but their angles themselves differ.
Additionally, you can recall the concept of co terminal angles as angles that differ by an exact number of full circles.
Given Data
The smallest co terminal angle for:
a) 410
Divide the first number by the second, rounding down (towards the floor).
[tex]\frac{360}{410}[/tex]
= 1
after that, multiply the divisor by the result (called the quotient),
360(1)
= 360
Take this amount out of your starting amount.
410-360
= 50
b) -45
- 45 [tex]\frac{pie}{4}[/tex]
= -495
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name three fractions that are equivalent to 2/5
I'll send a better pic I just need help doing the work and understanding what it's about
The formula to calculate the rate of change is given to be:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]In the question, time will be the x-variable while distance will be the y-variable.
QUESTION A: Between 0 and 1.
Between 0 and 1, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=0 \\ x_2=1 \\ y_1=6 \\ y_2=4 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{4-6}{1-0}=\frac{-2}{1} \\ r=-2 \end{gathered}[/tex]The rate is -2.
QUESTION B: Between 1 and 3.
Between 1 and 3, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=4 \\ y_2=2 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{2-4}{3-1}=\frac{-2}{2} \\ r=-1 \end{gathered}[/tex]The rate is -1.
QUESTION C: Between 3 and 6.
Between 3 and 6, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=3 \\ x_2=6 \\ y_1=2 \\ y_2=3 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{3-2}{6-3} \\ r=\frac{1}{3} \end{gathered}[/tex]The rate is 1/3.
What is the graph of the equation y = 2x + 4?
The y-intercept is which means the line crosses the y-axis at the
). Plot this point.
point
The slope of the line is positive, so it goes
Start at the y-intercept. Move up
0
0 and then move right
). Plot this point.
You are now at the point (
0
Draw a line to connect the two points.
from left to right.
Answer: 8
Step-by-step explanation: x2 + 4 is 4 x 2
:D
What is 4 notes that are important to the concept of. Absolute Value and the Additive
This problem is about absolute value.
Four important notes to remember are:
• Absolute value is the modulus of a number, that is, includes only the number without any signs.
• The absolute value of a number can be positive, when the number is positive, that is
[tex]|x|=x[/tex]• The absolute value can be negative if the number is negative
[tex]|x|=-x[/tex]• The absolute value of zero is zero.
[tex]|0|=0[/tex]There you have it, those are 4 important notes to keep in mind about absolute value.
On the other hand, "the additive" would refer to a wide variety of subjects, so, there's a word missing to complete the question.
help me please
thank you
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Do the points on the linehave a constant ratio of they-coordinate to the x-co-ordinate for any point onthe line except the y-inter-cept? Explain your answer.
This table shows the amount of gas Sharla's car uses to travel different distances on a highway.Number of Gallons Number of Miles41446216324912432Based on the data in the table, how many miles per gallon does Sharla's car get on a highway?O A. 18 mpgO B. 28 mpgOC. 36 mpgO D. 72 mpg
We'll calculate the miles per gallon using the following formula and the data on the table:
[tex]\text{mpg}=\frac{miles\text{ traveled}}{\text{gallons used}}[/tex]From the first set of data:
[tex]\text{mpg}_1=\frac{144}{4}=36[/tex]From the second:
[tex]\text{mpg}_2=\text{ }\frac{216}{6}=36[/tex]From the third
[tex]\text{mpg}_3=\frac{324}{9}=36[/tex]and from the fourth
[tex]\text{mpg}_4=\frac{432}{12}=36[/tex]Since all the data on the table showed us that the car gets 36 miles per gallon, we can conclude that it indeed gets 36 miles per gallon.
jewel brought home four gallons of milk how many quarts is four gallon
Here, we want to know the number of quarts that are in 4 gallons
Mathematically;
1 quart = 0.25 gallons
This means that ;
4 quarts = 1 gallon
Hence, 4 gallons = 4 * 4 quarts
= 16 quarts
There are 16 quarts in 4 gallons
hi Ms or Mr i need help with this problem would mind helping me out step by step? because i don't understand this
Looking at the given diagram,
HI + JI = JH
Given the HI = 3x - 5
JI = x - 1
HJ = 7x - 27
Therefore,
3x - 5 + x - 1 = 7x - 27
3x + x - 7x = - 27 + 5 + 1
- 3x = - 21
Diving bith sides - 3, it becomes
- 3x/3 = - 21/- 3
The negative signs nullify each other
x = 7
A rectangle has vertices at (-2, 11), (-2,4), (6, 11), and (6, 4). Pablo says the area of the rectangle is 49 square units and his work is shown below. Steps Step 1 Pablo's Work Base: 1- 21+61= 8 Step 2 Step 3 Height: 11-4-7 Area: 8x7=49 square units Where, if at all, did Pablo first make a mistake finding the area of the rectangle? Step 1 Step 2 Step 3
The result of the calculation of the base is good because the distance between -2 and 6 is 8. The result of the calculation of the height is good because the distance between 4 and 11 is 7. The mistake is seen in the part of the multiplication, because 8x7 is equal to 56 , not 49.
So, the mistake was made when doing the Step 3.
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
The diameter d is 35 ft.
Therefore, the radius r is given by:
[tex]r=\frac{35}{2}=17.5\text{ ft}[/tex]Therefore, the area of the slice is given by:
[tex]\frac{37^{\circ}}{360^{\circ}}\times\pi\times17.5^2\approx98.88[/tex]Therefore, the required area is approximately 98.88 ft².
Therefore, the closest correct answer is choice 98.83 ft².
Find if -3w - 6(u + 2v) if u = -3j, v = i + 2], and w =combination of unit vectors.-;. Express your answer as a linear
we have the expressiob
-3w - 6(u + 2v)
where
u=-3j
v=i+2j
w=-(1/3)i-(7/3)j
substitute the given values in the expression
so
-3(-(1/3)i-(7/3)j)-6(-3j+2(i+2j))
(i+7j)-6(-3j+2i+4j)
(i+7j)-6(2i+j)
(i+7j)-12i-6j
answer is
-11i+jTim likes to play video games. If he cancomplete a level in of an hour, howmany levels can he complete in 4hours?
Given:
Number of levels he can complete in 1 hour = 1 level
To find the number of levels he can complete in 4 hours, we have:
4 * 1 = 4
