8x² + 16x = 42
x² + 16/8x = 42/8 dividing by 8 at both sides
x² + 2x = 5.25
x² + 2x - 5.25 = 0
If we compute (x + 1)², we get:
(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1
Then,
x² + 2x - 5.25 + 1 - 1 = 0
(x² + 2x + 1) + (-5.25 - 1) = 0
(x + 1)² - 6.25 = 0
(x + 1)² = 6.25
x + 1 = √6.25
This has 2 solutions,
x + 1 = 2.5 or x + 1 = -2.5
x = 2.5 - 1 x = -2.5 - 1
x = 1.5 x = -3.5
How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60
Given:
The given numbers are 5,6,7,8,9.
Required:
Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.
Explanation:
Let n is the total number then the way to write m digits number is given by the formula:
[tex]A(n,m)=\frac{n!}{(n-m)!}[/tex]So the way to write 3 digits numbers are:
[tex]\begin{gathered} A(5,3)=\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =5\times4\times3 \\ =60 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
What is an equation of the points given? And is parallel to the line 4x-5y=5?
We know that two lines are parallel if they have the same slope. So we first find the slope of the given line. One way to do this is to rewrite the equation in its slope-intercept form, solving for y:
[tex]\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=5 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=5-4x \\ -5y=5-4x \\ \text{ Divide by -5 from both sides} \\ \frac{-5y}{-5}=\frac{5-4x}{-5} \\ y=\frac{5}{-5}-\frac{4x}{-5} \\ y=-1+\frac{4x}{5} \\ y=\frac{4x}{5}-1 \\ y=\frac{4}{5}x-1 \end{gathered}[/tex]Now, we have the slope and a point through which the line passes:
[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex]Then, we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{4}{5}(x-(-5)_{}) \\ y-2=\frac{4}{5}(x+5_{}) \end{gathered}[/tex]The above equation is the equation of the line in its point-slope form. However, we can also rewrite the equation of the line in its standard form by solving for the constant:
[tex]ax+by=c\Rightarrow\text{ Standard form}[/tex][tex]\begin{gathered} y-2=\frac{4}{5}(x+5_{}) \\ \text{ Multiply by 5 from both sides of the equation} \\ 5(y-2)=5\cdot\frac{4}{5}(x+5_{}) \\ 5(y-2)=4(x+5_{}) \\ \text{ Apply the distributive property} \\ 5\cdot y-5\cdot2=4\cdot x+4\cdot5 \\ 5y-10=4x+20 \\ \text{ Subtract 5y from both sides} \\ 5y-10-5y=4x+20-5y \\ -10=4x+20-5y \\ \text{Subtract 20 from both sides } \\ -10-20=4x+20-5y-20 \\ -30=4x-5y \end{gathered}[/tex]Therefore, an equation of the line that passes through the point (-5,2) and is parallel to the line 4x - 5y = 5 is
[tex]\boldsymbol{4x-5y=-30}[/tex]1. Find all real solutions to each equation. (a) x(2x − 5) = 1
Use the distributive property to expand the parenthesis:
[tex]x(2x-5)=2x^2-5x[/tex]Then:
[tex]undefined[/tex]12. A high school principal wants to determine if students' mathematical reasoning ability has any impact on their membership in academic clubs at the school. Twenty students were selected and given a mathematical reasoning test, with scores ranging from o to 50 (higher scores indicate more mathematical reasoning ability). Students were motivated to do well on the test with a reward system. These same students' membership in academic clubs was verified. Identify the response variable. A. Mathematical reasoning ability B. The high school C. Mathematical reasoning test D. Membership in academic clubs
Response variable: The response variable is the subject of an experiment.
In this question:
The experiment is about the mathematical reasoning ability of the students whom are members of academic clubs. So, we are focusing on mathematical reasoning ability, which is the response variable.
The answer is option A
can you please help me? I'm having trouble with algebra 2 doing online school
Brianna, this is the solutiuon:
Part 2: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x - 1)² = (x - 1) * (x - 1)
x² - x - x + 1
x² - 2x + 1
Thus, b = -2. The correct answer is A.
Part 3: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x + 25)² = (x + 25) * (x + 25)
x² + 25x + 25x + 625
x² + 50x + 625
Therefore, c = 625. The correct answer is D.
Factoring the polynomial 12g + 20h
A sole trader operates his business from
a warehouse, which has been damaged
by a fire, which occurred at the end of
the financial year. After the fire, the
remaining inventory that is undamaged
amounts to GHC 2,000 (cost). The
accountant establishes the following
information: I Inventory at the
beginning of the year was GHC 16,000 II
Purchases during the year were GHC
115,000 III Sales during the year were
GHC 140,000 IV The trader sells his
goods at a mark-up of 25% of cost What
is the value of the inventory lost in fire?
Beginning inventory = 16,000 Purchase = 115,000 Sales = 140,000 Mark up = 25% on cost Undamanged inventory = 2,000
The value of the inventory lost in fire is 2,000
How do you take inventory loss due to fire into account?
The cost of products available for sale is then subtracted from the cost of goods sold. The quantity will reflect how much inventory the fire has actually destroyed. As an illustration, $275,000 minus $80,000 = $195,000, which represents the amount of inventory destroyed in the fire.
Calculate the quantity of inventory destroyed by deducting the cost of sold goods from the cost of goods that are still in stock. In this scenario, the amount of merchandise lost in the fire was $275,000 less $70,000, or $205,000.
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Find an equivalent fraction with the given denominator 7/8 = ?/72
To find the missing numerator si that both fractions are equivalent, you have to multiply both sides of the equal sign by 72:
[tex]\begin{gathered} 72\cdot\frac{7}{8}=72\cdot\frac{?}{72} \\ 63=\text{?} \end{gathered}[/tex]The missing numerator is 63
The equivalent fractions are:
[tex]\frac{7}{8}=\frac{63}{72}[/tex]can I please get answer quickly I just need to confirm I got it right
SOLUTION
We want to find the magnitude of the vector (-3, 4)
Magnitude of a vector is given as
[tex]\begin{gathered} |v|=\sqrt{x^2+y^2} \\ (x,y)=(-3,4) \\ we\text{ have } \\ =\sqrt{(-3)^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}[/tex]Hence the answer is 5 units, the last option
shows four types of polygons which type of polygon shown has no pairs of parallel sides
Accoring to the given figures, the pentagon is the one without parallel sides.
Hence, the answer is Pentagon.Inequality-x less than or equal to 18
Answer: x[tex]\leq[/tex]18
find the unit price of a six pack of water for $6.90 fill in the amount per bottle of water
Given:
six pack of water = $6.90
To find:
Unit(one) price of water bottle(Price of one water bottle).
[tex]\frac{6.90}{6}=1.15[/tex]Therefore,
The price of one water bottle is $1.15.
I'm not sure if you can exactly give me the answers, but I need help solving these types of questions, I will attach them below. they are about tangent lines.
Question 1
Explanation
To solve these types of questions, we will use the Tangent radius theorem
Tangent to a Circle Theorem
The tangent theorem states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
The figure below helps give a pictorial view
The principle to be used here for question 1 will be
[tex]x^2+8^2=17^2[/tex]Simplifying further
[tex]\begin{gathered} x^2+64=289 \\ x^2=289-64 \\ x^2=225 \\ x=\sqrt{225} \\ x=15 \end{gathered}[/tex]Thus, the value of x is 15 units
ill take a pic of it
The line passes through the points given.
Select any two points from the table, (-4,2) and (-3,5).
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Hence the slope is:
[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]The slope is 3.
A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%
We can write a system of equations that describe our problem.
Since we don't know how the original $100,000 was divided, we call the two parts X and Y
So we know that X + Y = 100000
Then we know the Combined Interest coming from the accounts.
We use the Interest formula for return on investment:
I = P * r * t
were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)
Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:
I1 = X * 0.03 * 1 = 0.03 X
Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:
I2 = Y * 0.01 * 1 = 0.01 Y
Then, the addition of these two interest is our total return of $1800:
0.03 X + 0.01 Y = 1800
Then our system of equations is:
X + Y = 100000
0.03 X + 0.01 Y = 1800
which we solve by substituting for example for Y in the first equation:
Y = 100000 - X
and replacing the Y by this expression in our second equation:
0.03 X + 0.01 (100000 - X) = 1800
use distributive property to eliminate parenthesis:
0.03 X + 1000 - 0.01 X = 1800
combine like terms
0.02 X + 1000 = 1800
subtract 1000 from both sides
0.02 X = 800
divide both sides by 0.02 to completely isolate X:
X = 800 / 0.02
X = $40000
This is the amount deposited on the 3% account
Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:
Y = $100000 - $40000 = $60000
Then, the amount deposited in the 1% account was $60000
and the amount deposited in the 3% account was $40000.
Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|.
h(x)=?
an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4
What is vertical stretch/vertical compression ?
• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.
• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
The function g(x) is defined as |x|.
To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.
g(x) = f(x)/3
f(x) is equal to (|x|)/4.
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I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees
GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]4Select the correct equations.Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than  times the number of shells Mary has. Nancy has 1 more than  times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.
Given data:
Gracie has 5 more than times mary have G=5+a(x).
Nancy has 1 ore than ties mary have N=1+b(x)
Given that G=N
5+ax=1+bx
4=x(b-a)
Question 17. 4 pts
In 98 years of football, Loudon has averaged 296 points per season and the standard deviation is 14. What percent of the years has Loudon scored between 254 and 338 points per season?
Answer:
Over 98 years, London scored 75.14% per season between 254 and 338 points.
Step-by-step explanation:
Hector is thirsty and opens up the refrigerator and finds a half full gallon of milk. Hector drinks 2/5 of the milk Later kevin opens up the refrigerator and finds some milk left in the gallon. He drinks 1/3 of what is left. Draw a picture of the situation above. Include the amount of milk before hector drank any, after hector drank some, and then after kevin drank some. What fraction is the entire gallon did kevin drink What fraction of the entire gallon is left after both hector and kevin drink some milk?
When Hector opens up the refrigerator he finds the next :
He drinks 2/5 of the milk he found, then he drank:
[tex]\frac{1}{2}\times\frac{2}{5}=\frac{1\times2}{2\times5}=\frac{2}{10}=\frac{1}{5}gallon[/tex]And he left in the bottle of milk:
[tex]\frac{1}{2}-\frac{1}{5}=\frac{5-2}{2\times5}=\frac{3}{10}gallons\text{ of milk}[/tex]And after that Kevin open up the refrigerator and finds the next:
Kevin drinks 1/3 of what is left, then he drinks:
[tex]\frac{3}{10}\times\frac{1}{3}=\frac{3\times1}{10\times3}=\frac{3}{30}=\frac{1}{10}\text{gallon of milk}[/tex]And then he left:
[tex]\frac{3}{10}-\frac{1}{10}=\frac{3-1}{10}=\frac{2}{10}=\frac{1}{5}[/tex]And the milk he left in the bottle is:
Find the measure of Zx in the figure.
The measure of Zx isº.
57°
X
90°
...
Please help me with this
Consider right triangle PQR what is the value of tan(R)
6/8
8/10
8/6
10/6
The value of tan(R) in the right triangle PQR where Perpendicular=QP, Base=RQ, Tan R=P/B. The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,⟂, can be used to graphically represent the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
What is base?The base of a right angle triangle is the side on which it is positioned. The calculation can also be done using any of the two sides other than the hypotenuse as the base. It is the side of the right-angled triangle that is perpendicular to its base.
here,
Perpendicular=QP
Base=RQ
Tan R=P/B
=QP/RQ
Tan R=6/8
The perpendicular QP, base RQ, and tan's (R) values in the right triangle PQR. Tan's (R) = P/B. The tangent of the angle formed by the line with the positive x-axis is what determines a line's slope.
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Finish the other half of the graph if it was even and odd.
To solve this problem, first, let's remember the definitions of even and odd functions.
• A function f is ,even, if the graph of f is ,symmetric about the y-axis,.
,• A function f is ,odd, if the graph of f is ,symmetric about the origin.
a) To make the function even, we must complete the graph such the graph result is symmetric about the y-axis (the vertical axis). Doing that we get:
b) To make the function odd, we must complete the graph such the graph result is symmetric about the origin (the horizontal axis). Doing that we get:
[tex] \sqrt{18} (523 \div 8)[/tex]help I need help
Solution
Given question
11.85 = 2.1n + 4.5
Requirement
To isolate n
Step 1
Using the subtraction property of equality to isolate the variable
11.85 - 4.5 = 2.1n + 4.5 -4.5
7.35 = 2.1n
Step 2
use the division property of equality to isolate the variable
7.35/2.1= 2.1n/2.1
n = 3.5
Answers are 1 first, then 2 next, those are the 2 steps
Hello! By the way when answering the question just don’t mind my work shown or my answer I know for a fact I am wrong.
We have to calculate the height of the stack of hay bales.
We can start by calculating the volume as the number of bales times the volume of one hay:
[tex]\begin{gathered} V=n*V_0=8*(10+\frac{2}{3}) \\ V=8*10+8*\frac{2}{3} \\ V=80+\frac{16}{3} \\ V=80+\frac{15}{3}+\frac{1}{3} \\ V=80+5+\frac{1}{3} \\ V=85+\frac{1}{3} \end{gathered}[/tex]Now, we know that this volume will be the area of the base times the height.
The area of the base can be calculated as the product of the length and the width:
[tex]\begin{gathered} A_b=L*W \\ A_b=4*(1+\frac{1}{3}) \\ A_b=4+\frac{4}{3} \\ A_b=\frac{4*3+4}{3} \\ A_b=\frac{12+4}{3} \\ A_b=\frac{16}{3} \end{gathered}[/tex]We then can calculate the height as the volume divided by the base area:
[tex]\begin{gathered} h=\frac{V}{A} \\ h=\frac{85+\frac{1}{3}}{\frac{16}{3}} \\ h=\frac{85*3+1}{3}*\frac{3}{16} \\ h=\frac{256}{3}*\frac{3}{16} \\ h=\frac{256}{16} \\ h=16 \end{gathered}[/tex]Answer the height is 16 feet.
Need to graph and then mark length of stay (in days) on the bottom of the graph. Need 4 points on graph and 4 number on bottom of graph
given the data
13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,12,8,8
sort data
s= 2, 2, 2, 3, 3, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13
then we have
2 ---- 3
3 ----- 2
5----- 1
6 ---- 1
7 -----1
8------2
9 ------1
10-----3
11-------2
12------4
13-------1
Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.
The triangle formed is shown in the diagram below
The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
opposite side = 150
adjacent side = 40
Tan x = 150/40 = 3.75
x = Tan^-1(3.75)
x = 75.069
To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees
8 Solve: 2 3= 4x + 2 - O- O 1 2 AP 4 ( ) 1 4. O 1 2
We will have the following:
[tex]3=4x+2\Rightarrow1=4x[/tex][tex]\Rightarrow x=\frac{1}{4}[/tex][Third option]
Find all the powers of four in the range of 4 and 1000
compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2x²+3x+5=0
Given a quadratic equation in standard form
[tex]y=ax^2+bx+c[/tex]The discriminant D
[tex]D=b^2-4ac[/tex]tells the types of roots the equation has.
In this case, we have
[tex]\begin{gathered} -2x^2+3x+5=0 \\ a=-2 \\ b=3 \\ c=5 \end{gathered}[/tex]Then, the discriminant of this quadratic equation will be
[tex]\begin{gathered} D=b^2-4ac \\ D=(3)^2-4(-2)(5) \\ D=9+40 \\ \mathbf{D=49} \end{gathered}[/tex]Finally, the value of discriminat is 49 and as he discriminant is greater than zero then this quadratic equation has 2 different real solutions.