The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation
[tex]\frac{45}{x}=\frac{9}{4}[/tex]Solving for x, we have
[tex]\begin{gathered} \frac{45}{x}=\frac{9}{4} \\ \frac{x}{45}=\frac{4}{9} \\ x=\frac{4}{9}\cdot45 \\ x=\frac{4\cdot45}{9} \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is
[tex]45+20=65[/tex]65 problems.
Find the explicit formula for the geometric sequence. Then find a8. 4, 8, 16, 64, ...
The given sequence is : 4,8, 16,64
The geometric series is exoress as :
[tex]\text{ Geometric series=a, ar, ar}^2\ldots.ar^n[/tex]where r i the common ratio
In the given sequence the ratio is
[tex]\begin{gathered} r=\frac{\sec ond\text{ term}}{first\text{ term}} \\ r=\frac{8}{4} \\ r=2 \end{gathered}[/tex]So, the series will express as :
[tex]\begin{gathered} \text{Explict formula = 4(2)}^{n-1} \\ \text{Explict form = }4(2)^{n-1} \end{gathered}[/tex]Now for the 8 term
n=8
[tex]\begin{gathered} a_n=4\cdot2^{n-1} \\ a_8=4\cdot2^{8-1} \\ a_8=4\cdot2^7 \\ a_8=512 \end{gathered}[/tex]Answer : C) an=4.2^n-1, 512
For the function f(x) = x2 + 2x - 15 solve the following.f(x) = 0
Given:
[tex]f\mleft(x\mright)=x^2+2x-15[/tex]To find: The value of x when
[tex]f(x)=0[/tex]Explanation:
Since,
[tex]f(x)=0[/tex]We can write it as,
[tex]\begin{gathered} x^2+2x-15=0 \\ x^2+5x-3x-15=0 \\ x(x^{}+5)-3(x-5)=0 \\ (x+5)(x-3)=0 \\ x=-5,3 \end{gathered}[/tex]Hence, the solution is x = -5, and 3.
Final answer: The solution is,
[tex]\mleft\lbrace-5,3\mright\rbrace[/tex]PLEASE HELP ME!!!!!
Subtract the linear expressions.
(-3 + 4x - 9x) - (9 - 11x + 7)
6x + 19 is the difference between both the linear expression.
What is linear equation ?In a linear equation, the variable's greatest power always equals 1. It is also referred to as a one-degree equation. The usual form of a linear equation with one variable is written as Ax + B = 0. In this case, x is a variable, A is a coefficient, and B is a constant.
Calculation-3 + 4x -9x - 9 + 11x - 7
= -19+6x
= 6x + 19
learn more about linear equation here :
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Answer:
Between the two linear expressions, there is a difference of 6x + 19.
How do linear equations work?
In a linear model, the largest power of the variable is always equal to 1. Another name for it is a one-degree equation. Ax + B = 0 is how a statistical model with one term is typically written. In this scenario, the variables x and A are coefficients, while B is a standard.
Calculation -3+4x-9x-09+11x-7-9
= -19+6x
= 6x + 19
Step-by-step explanation:
I'm also in k12 hope this helps! :3
We want to factor the following expression: x^3 - 25 which pattern can we use to factor the expression? U and V are either constant integers or single variable expression.
The pattern that is used to factor the expression x³ - 25 is given as follows:
B. (U - V)(U + V).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares, as the multiplication of the square roots of the two terms subtracted by the square of the two terms subtracted, as follows.
a² - b² = (a - b)(a + b).
In the context of this problem, the expression is presented as follows:
x³ - 25.
The square root of x³ is obtained as follows:
sqrt(x³) = (x³)^(0.5) = x^(3 x 0.5) = x^1.5 = [tex]\sqrt{x^3}[/tex]
The square root of 25 is obtained as follows:
5.
Because 5² = 25.
Then, applying the subtraction of perfect squares notable product, the factored expression is given as follows:
[tex]x^3 - 25 = (\sqrt{x^3} - 5)(\sqrt{x^3} + 5)[/tex]
Which is the pattern given by option B.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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evaluate each using the values given y+y-(y-x); use x = 1, and y = 4Options12154
The given expression is
y + y - (y - x)
We would substitute x = 1 and y = 4 into the expression. it becomes
4 + 4 - (4 - 1)
8 - 3
= 5
the correct answer is 5
A board game uses a spinner like one below, where 0, 1, 2, and 3 are all equally likely.Each turn, a player spins twice and subtracts the results of the spins. The game only looks at non-negativedifferences. For example, if a player spins a 1 and a 3, the difference is 2.Let X represent the difference in given turn.Which tables represents the theoretical probability distribution of X?Choose 1 answer:
The possible outcomes are:
0: 1-1, 2-2, 3-3, 4-4 => 4
1: |2-1|, |3-2|, |4-3|, |1-2|, |2-3|, |3-4| => 6
2: |3-1|, |4-2|, |1-3|, |2-4| => 4
3: |4-1|, |1-4| => 2
The total number of outcomes is 4+6+4+2 = 16. Then, the table that represents the theoretical distribution is:
Answer:
It should be B, the one that has 0,1,2,3 on the top.
Step-by-step explanation:
right on khan
What is the image of (8,−4) after a dilation by a scale factor of 1/4 centered at the origin?
Answer:
[tex](2, -1)[/tex]
Step-by-step explanation:
When dilating with a scale factor of [tex]k[/tex] about the origin, [tex](x,y) \longrightarrow (kx, ky)[/tex].
Find two numbers whose sum is 256, but whose product is a maximum?
ANSWER
The two numbers are 128 and 128
EXPLANATION
Let the two numbers be x and y.
We have that:
[tex]\begin{gathered} x+y=256 \\ x\cdot y=A \end{gathered}[/tex]where A is a maximum.
From the first equation:
[tex]x=256-y[/tex]Substitute that into the second equation:
[tex]\begin{gathered} (256-y)\cdot y=A \\ \Rightarrow256y-y^2=A \\ \Rightarrow y^2-256y+A=0 \end{gathered}[/tex]The equation above is a quadratic equation in the general form:
[tex]ax^2+bx+c=0[/tex]The parabola is downward facing and so, its vertex will be the maximum.
We can find the vertex (x, y) of the parabola by using:
[tex]x=\frac{-b}{2a}[/tex]In the case given, the vertex can be found by using:
[tex]\begin{gathered} y=\frac{-(-256)}{2(1)}=\frac{256}{2} \\ y=128 \end{gathered}[/tex]Recall that:
[tex]x=256-y[/tex]Therefore, we have that:
[tex]\begin{gathered} x=256-128 \\ x=128 \end{gathered}[/tex]Hence, the two numbers are 128 and 128.
Two ships were 700 miles apart at midnight and were headed directly towards each other if they collided at 10 a:m find the speeds of both ships if one was traveling 30 miles faster than the other
Given:
Two ships were 700 miles apart at midnight .
Let x be the speed of first ship and (x+30) be speed of second ship (faster ship).
The equation is,
[tex]\begin{gathered} Dis\tan ce=rate\times time \\ 10x+10(x+30)=700 \\ 10x+10x+300=700 \\ 20x=700-300 \\ 20x=400 \\ x=\frac{400}{20} \\ x=20 \end{gathered}[/tex]Answer: the speed of first ship ( slower) is 20 miles and the speed of second ship ( faster) is 20+30=50 miles.
in DEF, DE =29 feet, EF = 26 feet, and DF = 32 feet. Which correctly gives the order of the angle measure from largest to smallest?
Answer:
Choice A.
Explanation:
The sketch of the triangle is given below
The angle opposite the longest side is the widest.
The longest side is DF; therefore, the angle opposite to it (angle E) is the widest.
The second-longest side is DE; therefore, the angle opposite to it (angle F) is the second widest.
Lastly, the third-longest side is EF; therefore, the angle opposite to it (angle D) is the third widest (or the smallest angle).
Hence, the angle measures when ordered from greatest to smallest are
∠E, ∠F, ∠D
which is given by choice A.
Find the value of x, if m<3 is 13x-13 and m<4 is 8x+67.2 points43Your answer
Answer
x = 6
Explanation:
m<3 and m<4 are supplementary angles
supplementarrh angles is 180 degrees
m<3 + m<4 = 180
13x - 13 + 8x + 67 = 180
collect the like terms
13x + 8x - 13 + 67 = 180
21x + 54= 180
Isolate 21x
21x = 180 - 54
21x = 126
divide both sides by 21
21x/21 = 126/21
x = 6.
Therefore, x = 6
You might need: Calculator h(r) = 72 +11r - 26 1) What are the zeros of the function? Write the smaller r first, and the larger r second.
1) Notice that:
[tex]r^2+11r-26=r^2+13r-2r-2(13).[/tex]Grouping like terms we get:
[tex]\begin{gathered} r^2+13r-2r-2(13)=r(r+13)-2(r+13) \\ =(r-2)(r+13). \end{gathered}[/tex]Therefore:
[tex]h(r)=(r-2)(r+13).[/tex]Then the zeros of h(r) are:
[tex]r=2\text{ and }r=-13.[/tex]2) Notice that:
[tex]\begin{gathered} h(r)=r^2+11r-26=r^2+11r+(\frac{11}{2})^2-(\frac{11}{2})^2-26 \\ =(r+\frac{11}{2})^2-\frac{121}{4}-26=(r+\frac{11}{2})^2-\frac{225}{4}. \end{gathered}[/tex]Therefore the vertex of the given parabola is:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]Answer:
1)
[tex]\begin{gathered} smaller\text{ r=-13,} \\ larger\text{ r=2.} \end{gathered}[/tex]2) Vertex:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]
Find the intersection if possibleExpress your answer in interval notation
Solution:
The first set given as;
[tex][-9,-1)[/tex]Then in list form, the set is;
[tex]\lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace[/tex][tex]\lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace[/tex]Also, the second set given as;
[tex](-3,4)[/tex]Then, in list form, the set is;
[tex]\lbrace-2,-1,0,1,2,3\rbrace[/tex]The intersection of the two sets is;
[tex]\begin{gathered} \lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace\cap\lbrace-2,-1,0,1,2,3\rbrace=\lbrace-2\rbrace \\ \\ \text{ Note that there are some real numbers on the number line} \end{gathered}[/tex]Thus, the solution in interval notation is;
[tex](-3,-1)[/tex]ANSWER: (-3,-1)
(6,3) and (2, -9)equation in slope intercept form
Let:
(x1,y1)=(6,3)
(x2,y2)=(2,-9)
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{-9-3}{2-6}=\frac{-12}{-4}=3[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=3(x-6) \\ \text{Solve for y:} \\ y=3x-15 \end{gathered}[/tex]unit 4: solving quadratic equations
Homework 9: quadratic equations applications
Help please !
Answer:
what is the Question
Step-by-step explanation:
math is ezy :3
Solve each equation by completing the square. X^2+10x=17
Completing squares
Before attempting to complete squares, let's recall the following identity
[tex](a+b)^2=a^2+2ab+b^2[/tex]the expression at the right side can be converted to the square of a binomial, provided we have the terms completed as shown
We have the equation:
[tex]x^2+10x=17[/tex]note the left side has TWO of the terms required for the square of a binomial. we only need the final number. but what number should we add?
the first term is the square of a, in this case, it's x
the second term has 10x and it should be 2ab, if we already know a=x, then
2ab=10x, then
b=10x/(2x)=5
now we know a=x and b=5, we only need to have b^2=25
that is exactly the number to add on both sides of the equation
[tex]x^2+10x+25=17+25=42[/tex]now we factor the left side:
[tex](x+5)^2=42[/tex]taking the square root, recall the square root can
I need help on this problem, it’s from my act prep guide
Answer:
Recall that:
[tex]\begin{gathered} \log _bx+\log _by=\log _b(xy), \\ \log _bx-\log _by=\log _b(\frac{x}{y})\text{.} \end{gathered}[/tex]Therefore, Arjun used the properties incorrectly, he should´ve written:
[tex]\log _7x+\log _7y-\log _7z=\log _7(xy)-\log _7z=\log _y(\frac{xy}{z})\text{.}[/tex]5. A ball is thrown from a platform. The equation h = -4.9t2 + 18t + 14 gives the ball's height, h, in meters in terms of time, t, in seconds. Part A: What was the initial velocity of the ball? Part B: From what height was the ball thrown? Part C: If we measure the height in feet, how would the function change? What would be the gravity coefficient?
We have the following:
[tex]h=-4.9t^2+18t+14[/tex]now,
This equation is divided as follows:
The quadratic part (-4.9t ^ 2) that represents the acceleration (gravity coefficient), the linear part (18t) that represents the velocity and the constant part (14) that is the initial height, therefore
Part A:
The initial velocity is 18 meters per seconds, the number that accompanies the linear term
Part B:
The initial height corresponds to 14 meters
Part C:
the equivalence between meters and feet is as follows
1 meter = 3.28 feet
Therefore the change of the function would be
[tex]\begin{gathered} h=3.28\cdot(-4.9t^2+18t+14) \\ h=-16.072t^2+59.04+45.92 \end{gathered}[/tex]The gravity coefficiente is -16.072 feet per square seconds
If trapezoid ABCD was dilated by a scale factor of 2\3 to form trapezoid A'B'C'D,what is the area of trapezoid ABCD?The area of trapezoid A'B'C'D is 12 units^2
As a general rule, we know that the area of a dilated figure is the area of the original figure multiplied by the square of the scale factor. We can see this in the following formula:
[tex]A=A^{\prime}\cdot k^2[/tex]where A is the area of the original figure, A' is the area of the dilated figure and k is the scale factor.
In this case, we have that the area of the dilated figure (trapezoid A'B'C') is 12 square units, and the scale factor is k = 2/3. Then, using the equation we get the following:
[tex]\begin{gathered} A^{\prime}=12 \\ k=\frac{2}{3} \\ \Rightarrow A=12\cdot(\frac{2}{3})^2=12\cdot(\frac{4}{9})=\frac{12\cdot4}{9}=\frac{48}{9}=5\frac{1}{3} \\ A=5\frac{1}{3}u^2 \end{gathered}[/tex]therefore, the area of trapezoid ABCD is 5 1/3 square units
An expression is shown. 14.1-(2.24*5); what is the value of the expression?
Given the expression:
[tex]14.1-(2.24\ast5)[/tex]Let's find the value of the expression.
To find the value of the expression, first evaluate the values in the parentheses:
[tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]undefined[/tex]i need the x and y intercept
so, the x intercept is when the line touches the x-axis, we can see from the graph, the line touches x-axis on 3, so the point is
[tex](3,0)[/tex]the y intercept is when the lone touches the y-axis, we can see from the graph, the line touches y-axis on -9, so the point is
[tex](0,-9)[/tex]solve the equation 3.75x+3.7=1.7+1.75xA 10 B -1 C 1D .1
The question is given to be:
[tex]3.75x+3.7=1.7+1.75x[/tex]Step 1
Multiply every number by 100:
[tex]\begin{gathered} 3.75x\cdot100+3.7\cdot100=1.7\cdot100+1.75x\cdot100 \\ 375x+370=170+175x \end{gathered}[/tex]Step 2
Subtract 370 from both sides:
[tex]\begin{gathered} 375x+370-370=170+175x-370 \\ 375x=175x-200 \end{gathered}[/tex]Step 3
Subtract 175x from both sides:
[tex]\begin{gathered} 375x-175x=175x-200-175x \\ 200x=-200 \end{gathered}[/tex]Step 4
Divide both sides by 200:
[tex]\begin{gathered} \frac{200x}{200}=-\frac{200}{200} \\ x=-1 \end{gathered}[/tex]ANSWER
The correct option is OPTION B, the SECOND OPTION.
The probability distribution of a random variable x is given in the table below.X10-505101520Probability.2015.05.1.25.1.15Find the probability that x ⩾ 5
Answer:
0.6
Explanation:
From the given data:
[tex]\begin{gathered} P\left(x=-10\right)=0.20 \\ P\left(x=-5\right)=0.15 \\ P\left(x=0\right)=0.05 \\ P\left(x=5\right)=0.1 \\ P\left(x=10\right)=0.25 \\ P\left(x=15\right)=0.1 \\ P\left(x=20\right)=0.15 \end{gathered}[/tex]The probability that x is greater than or equal to 5 is:
[tex]\begin{gathered} P(x\geq5)=P\left(x=5\right)+P\left(x=10\right)+P\left(x=15\right)+P\left(x=20\right) \\ =0.1+0.25+0.1+0.15 \\ =0.6 \end{gathered}[/tex]1) Write an equation of the line perpendicular to: y = 3x - 9 with a y-intercept of 4.
The given equation is
[tex]y=3x-9[/tex]The new line is perpendicular to the given equation, which means we have to use the following formula.
[tex]m\cdot m_1=-1[/tex]Where the slope of the given line is 3 (the coefficient of x).
[tex]m\cdot3=-1[/tex]We solve for m.
[tex]m=-\frac{1}{3}[/tex]So, the slope of the new perpendicular line is -1/3.
According to the problem, the y-intercept of the new perpendicular line is 4. Now, we use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]Therefore, the equation of the new line is[tex]y=-\frac{1}{3}x+4[/tex]Morgan wants to order at least $45 worth of merchandise, so she will get free shipping. If Morgan has picked out a key chain for $8 and a bag for $19, which inequality represents the amount of money, m, she needs to spend to get free shipping?
Morgan wants to order at least $45 worth of merchandise.
She spent $8 and $19. m represents the amount of money she needs to spend to get free shipping. The inequality is:
8 + 19 + m ≥ 45
m ≥ 45 - 8 - 19
m ≥ 18
that the triangles below are congruent select all options that would provide enough information to prove the triangles are congruent
The correct options are options C and D;
1) Angle C is congruent to E
2) BA and FD are congruent
Here, we want to select the options that would prove that the triangles are congruent
We can get that from the markings on the diagram
As we can see from the question, we already have two sides being equal as we can see from the markings
Hence, we need an extra information to see through that the two triangles are indeed congruent
If the sides BA and FD are equal, it will simply mean that the three sides of the triangle are equal. In that case, the two triangles are congruent by SSS (side-side-side)
Also, if the angles C and E are congruent, we will have that the two triangles are similar by the SAS (side-angle-side)
So, the correct options are C and D
An archaeologist found a fossil that has a length of 459.89 in.Use the table of facts to find the length of the fossil in feet.Round your answer to the nearest tenth.Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)-0 1ftХ??
Answer: 38.3ft
We need to convert 459.89 inches into feet. Given that 12 inches is equal to 1 foot, we can solve this by dividing the length by 12
[tex]459.89in\times\frac{1ft}{12in}[/tex]*Cancel the inches sign leaving us with ft
[tex]459.89\times\frac{1ft}{12}=\frac{459.89}{12}ft=38.32\approx38.3[/tex]Therefore 459.89 inches is equal to 38.3 feet.
Jonathan finds some nickels and quarters in his change purse. How many coins does he have if he has 12 nickels and 4 quarters? How many coins does he have if he has xx nickels and yy quarters?Total coins, 12 nickels and 4 quarters: Total coins, xx nickels and yy quarters:
Each nickel is worth 5 cents, and each quarter is worth 25 cents.
So, if we have 12 nickels, we can multiply this value by 5 to get its value in cents:
[tex]12\cdot5=60[/tex]Similarly, if we have 4 quarters, we can multiply this value by 25 to get its value in cents:
[tex]4\cdot25=100[/tex]So, in total, we have:
[tex]60+100=160[/tex]So, for 12 nickels and 4 quarter, we have the value of 160 cents.
We can do this generally by setting the values of nickel and quarter to x and y.
If we have x nickels and each one is worth 5 cents, we have the value:
[tex]5x[/tex]And if we have y quarters and each is worth 25 cents, we have the value:
[tex]25y[/tex]So, in total, we have:
[tex]5x+25y[/tex]So, for x nickels and y quarter, we have the value of 5x + 25y cents.
2. Zero can be a negative number.OTrueFalse
In the real numbers system, any negative number x meets the following property:
[tex]x<0[/tex]The symbol "<" means that x is smaller than 0 but never equal to 0 so the definition of negative numbers excludes the zero. Then this statement is False.
Arithmetic and Geometric Sequences (Context)
The formula for compound interest
A = P( 1 + r/n) ^ (nt)
A is the amount in the account at the end
P is the principal balance or the amount initially invested
r is the annual interest rate in decimal form
n is the number of times it is coupounded per year
t is the number of years
A = 1800 ( 1+ .0375/1) ^ (1*6)
A = 1800 ( 1.0375)^6
A = 2244.92138
Rounding to the nearest cent
A = 2244.92