The height is a function of the time, given by the following equation:
h(t) = 16(8+t)(5-t)
The object hits the ground when h(t) = 0. So
16(8 + t)(5 - t) = 0
This means that:
8 + t = 0 or 5 - t = 0
8 + t = 0
t = -8
We cannot have negative values for t.
5 - t = 0
-t = -5 *(-1)
t = 5
The object hits the ground when t = 5, which was easy to find since the equation was already factored by it's roots.
A line has a slope of 8 and passes through the point (1,4). What is its equation in slope-intercept form? Show work
The equation of the line in slope intercept form is:
y = 8x - 4
Given, we have slope = 8
Point = (1,4)
Equation in slope intercept form is:
y = mx+c
let the point (1,4) ne (x₁,y₁)
and slope (m) = 8
y - y₁ = m(x-x₁)
y - 4 = 8(x - 1)
y - 4 = 8x - 8
y = 8x - 8 + 4
y = 8x - 4
Hence the equation in slope intercept form is y = 8x-4
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Which is greater, 1/2 or 2/7?
If we have two fractions a/b and c/d:
[tex]\frac{a}{b}(\text{ })\frac{c}{d}[/tex]To determine which one of them is greater we make the cross product:
[tex]ad(\text{ })bc[/tex]We have 3 cases:
- If ad is greater than bc, then a/b is greater than c/d
- If bc is greater than ad, then c/d is greater than a/b
- If ad is equal to bc, then a/b is equal to c/d
For 1/2 and 2/7:
[tex]\begin{gathered} \frac{1}{2}(\text{ })\frac{2}{7} \\ 7\cdot1(_{\square})2\cdot2 \\ 7>4 \\ \Rightarrow\frac{1}{2}>\frac{2}{7} \end{gathered}[/tex]lonny and mia each take out a 250,000 loan for a new house. each has to repay the loan in 25 years. lonny will pay an interest rate of 3.4% per year. his monthly payments will be $1250. because mia has a lower credit score she will have to pay an interest rate of 4.1% per year. her monthly payments will be $1360. how much more will a 250,000 loan cost mia than lonny?
Lonny takes a loan of 250000 and repays $1250 /month
in a year he pays 1250 x 12 =$15000
in 25 years he pays 15000 x 25 =$375000
mia pays 1360/ month. In a year she pays 1360 x 12 =$16320
in 25 years she pays 16320 x 25= $408000
difference in cost = 408000 -37500 = $33000
it will cost mia $33000 more for the loan.
I need help please!!
Ok, well, I think I need to the see previous problem. But from the information given, I think the right choices are:
a) tenth
b) 31.8
c) 32
The points (2,11) and (6,33) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope (m) of the line using the given coordinates is 11/2 and the equation of the slope is plotted on the graph.
What do we mean by slope?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on a straight line, a slope can be determined using a variety of approaches.A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).So, the slope formula is:
m = y₂ - y₁/x₂ - x₁Now, put the values and calculate as follows:
m = 33 - 11/6 - 2m = 22/4m = 11/2So, the slope equation will be:
y = mx + by = 11/2x + bNow, plot the graph of the equation, taking b = 1.
(Refer to the graph attached below)Therefore, the slope (m) of the line using the given coordinates is 11/2 and the equation of the slope is plotted on the graph.
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Find the volume of this cone.Use 3 for TT.V = Tigh3Hint: The radius (1) is1/2 of the diameter.6 ft6 ft-3V ~ [?]ft
ANSWER
[tex]54ft^3[/tex]EXPLANATION
The volume of a cone is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]where r = radius
h = height
The height of the given cone is 6 ft and its diameter is 6 ft. The radius of a cone is half its diameter, hence its radius is:
[tex]\begin{gathered} r=\frac{6}{2} \\ r=3ft \end{gathered}[/tex]Hence, the volume of the cone is:
[tex]\begin{gathered} V=\frac{3\cdot3^2\cdot6}{3} \\ V=54ft^3 \end{gathered}[/tex]That is the answer.
If the ratio of m to nis 7 to 6which of the following could be true?
m = 7/3, n = 2 could be true if the m/n ratio is 7:6. Option-E is correct.
Given that,
Which of the following could be true if the m/n ratio is 7:6.
Option are
A. m = 8, n = 7
B. m = 12,n= 14
C. m=14, n=0
D. m = 42, n = 42
E. m = 7/3, n = 2
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
Consider each of the m and n values that are provided.
Option-A
m:n = 8:7 ≠ 7 : 6
Option-B
m:n = 12:14 = 6:7 ≠ 7 : 6
Option-C
m:n = 14:0 ≠ 7 : 6
Option-D
m:n = 42:42 = 1:1 ≠ 7 : 6
Option-E
m:n = 7/3 : 2 = 7 : 6
Thus E is the only true ratio
Therefore, m = 7/3, n = 2 could be true if the m/n ratio is 7:6.
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what is the slope of a passing line through the points(2, 5) and ( o, -4)?
The slope of the line is 9/2 passing line through the points(2, 5) and ( o, -4)
What is slope ?A line's slope is how steep it is moving from LEFT to RIGHT. The slope of a line is the ratio of its climb, or vertical change, to its run, or horizontal change. The slope remains consistent regardless of where you choose for the line's starting and finishing locations (it never changes).
CalculationWe know that the formula to find the slope of a line is
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the points
The points given are (2, 5) and (0, -4)
Substituting it in the formula
m = (-4 - 5)/ (0 - 2)
So we get
m = -9/ -2
m = 9/2
Therefore, the slope of the line is 9/2.
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I need help question
The domain is all values of x except 1
the range is all values of y < -1
domain (-∞,1)U(1,∞)
range (-∞,-1)
Which is equivalent to StartFraction x Superscript 3 Baseline over StartRoot x EndRoot EndFraction?
We need to re-write x into one exponent:
[tex]\begin{gathered} \sqrt{x}\text{ = x}^{\frac{1}{2}} \\ \frac{x^3}{\sqrt{x}}=\text{ }\frac{x^3}{x^{\frac{1}{2}}} \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} The\text{ operation between the exponent is division} \\ To\text{ combine the exponents, we will subtract the 1/2 from 3} \\ \frac{x^3}{x^{\frac{1}{2}}}\text{ = x}^{3-\frac{1}{2}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ x}^{\frac{6-1}{2}} \\ =\text{ x}^{\frac{5}{2}}\text{ \lparen option C\rparen} \end{gathered}[/tex]14 Select all that apple Which of these fractions are equivalent to ?
the initial fraction es 1/4, so if we multiply the fraction by 2/2 it become:
[tex]\frac{2}{2}\cdot\frac{1}{4}=\frac{2}{8}[/tex]and if we multiply by 6/6
[tex]\frac{6}{6}\cdot\frac{1}{4}=\frac{6}{24}[/tex]So the solution is fraction 2/8 and fraction 6/24
what do you do in the following problem... "Michael is leaning a 12 foot ladder is leaning against the side of a building. The top of the ladder reaches 10 feet up the side of the building. Approximately how far, to the nearest hundredth, is the bottom of the ladder from the base of the building?"
The distance between the bottom of the ladder to the base of the building = 6.63 feet
Explanations:The height of the ladder, l = 12 feet
Height of the wall covered by the ladder, h = 10 feet
Distance between the base of the building and the bottom of the ladder = x
Using the pythagoras theorem:
[tex]\begin{gathered} (\text{Hypotenuse)}^2=(opposite)^2+(Adjacent)^2 \\ l^2=h^2+x^2 \\ 12^2=10^2+x^2 \\ 144=100+x^2 \\ 144-100=x^2 \\ 44=x^2 \\ \sqrt[]{44}=\text{ x} \\ x\text{ = }6.63 \end{gathered}[/tex]The distance between the bottom of the ladder to the base of the building = 6.63 feet
For the function, determine whether y varies directly with x. If so, find the constant of variation and write the function rule.Select the correct choice below and, if necessary, fill in the answer box within your choice.O A. Yes, y varies directly with x. The constant of variation is k = and the function rule is(Simplify your answers. Use integers or fractions for any numbers in the expression)No, y does not vary directly with x.
Answer: No, y does not vary directly with x
Explanation:
y varies directly with x when y divided by x is always the same constant. In this case, we get:
x y y/x
2 6 6/2 = 3
4 14 14/4 = 3.5
5 17 17/5 = 3.4
Since 3, 3.5, and 3.4 are distinct, the answer is No, y does not vary directly with x.
An aquarium is 0.5 feet wide, 1.5 feet tall, and 2 feet long.The bottom is covered with gravel to a height of 3 inches.The tank will be filled with water to 3 inches below the top.How many gallons of water are needed to fill the aquarium?(Use 1 gallon = 0.134 ft.) Ignore any water that might seepinto the layer of gravel. Round to the nearest tenth.
Step 1: Find the base area of the tank.
The base of the tank is a rectangle of length 2 ft and width 0.5 ft.
Hence,
[tex]\text{ the base area of the tank }=2ft\times0.5ft=1ft^2[/tex]Step 2: Find the height of the water in the tank.
The height of the tank = 1.5ft
the height of the gravel = 3in = 3/12 ft = 1/4 ft
The water is 3 inches (= 1/4 ft) below the top of the tank.
Hence, we must have that
[tex]\begin{gathered} x+\frac{1}{4}+\frac{1}{4}=1.5 \\ x+0.25+0.25=1.5 \\ x+0.5=1.5 \\ x=1.5-0.5=1\text{ ft} \end{gathered}[/tex]Therefore, the height of the water in the tank is 1 ft.
Step 3: Find the volume of the water in the tank
[tex]\begin{gathered} \text{ the volume of the water is given by} \\ V=\text{ base area of the tank }\times\text{ height of the water} \\ \text{ Where V is the volume of the water} \end{gathered}[/tex]Therefore,
[tex]V=1ft^2\times1ft=1ft^3[/tex]Since 1 gallon is equivalengt to 0.134 ft³ then
[tex]V=\frac{1}{0.134}\text{gallons }=7.5\text{ gallons}[/tex]Hence, the number of gallons of water are needed to fill the aquarium is 7.5 gallons.
Distributive property to solve-4(s-4)
The distributive property can be applied in the following form:
[tex]a(b-c)=a\times b-a\times c[/tex]Now, the given values are: a=-4, b=s and c=4.
Let's replace them in the equation and solve:
[tex]\begin{gathered} -4(s-4)=(-4)\cdot(s)-(-4)\cdot(4) \\ By\text{ the law of signs -}\cdot-=+and-\cdot+=-\text{ thus:} \\ -4(s-4)=-4s+16 \end{gathered}[/tex]Then, the answer is -4s+16
This is homework the answers are (1/2) (2) (0) (4)
Given:
Given a line.
To determine the slope, we use the formula:
Next, we select the points based on the give line:
We plug in what we know:
Therefore, the slope is 2.
The segments in each figure are tangent to the circle. Solve for x.4x -9AB15DС
CIRCLE THEOREM: Two tangents drawn from an external point to a circle are equal.
Thus, AB is a tangent to the circle and also BC is another tangent to the circle, both drawn from point B.
AB = BC;
[tex]\begin{gathered} 4x-19=15 \\ 4x=15+19 \\ 4x=34 \\ x=\frac{34}{4} \\ x=8.5 \end{gathered}[/tex]The value of x is 8.5
2y = 14xDirect variationk =Not direct variation
2y = 14x
divide both sides by 2
so,
y = 7x
direct variation and k = 7
the Santa Ana College theartre department sold 177 tickets to the spring play student tickets were sold for $7 each and general admission ticket were $9 if the total tickets sales were 1365 how many of each type of tickets were sold?
Let
x -----> number of play student tickets sold
y ----> number of general admission tickets sold
we have that
x+y=177 ------> x=177-y -----> equation A
7x+9y=1365 -----> equation B
solve the system
substitute equation A in equation B
7(177-y)+9y=1365
solve for y
1239-7y+9y=1365
2y=1365-1239
2y=126
y=63
Find the value of x
x=177-63
x=114
therefore
student tickets sold was 114general admission ticket sold was 63determine if the rate 8 cups with 56 Forks in 4 cups with 28 Forks are equivalent
Divde the number of cups by the number of forks
8 cups to 56 forks = 8 /56 = 0.14
4 cupts to 28 forks = 4 /28= 0.14
Both are rates are equivalent
What is the equation of the circle whose diameter has endpoints (10,1) and (-8,1)
Since the endpoints of the diameter are (10, 1) and (-8, 1)
Then the center of the circle is the midpoint of these 2 points
We will use the rule of the midpoint to find the center
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex][tex]\begin{gathered} M=(\frac{10+-8}{2},\frac{1+1}{2}) \\ \\ M=(\frac{2}{2},\frac{2}{2}) \\ \\ M=(1,1) \end{gathered}[/tex]The center of the circle is (1, 1)
The length of the diameter is the difference between the x-coordinate
[tex]y {}^{2} + 5y - 24[/tex]Help to do this problem by Factoring triinomials by Box Method. please
Factor the trinomial
[tex]y^2+5y-24[/tex]by the box method.
The multiplication gives -24y^2. Now we need to find two factor that gives 5x. It should be creal that this factor are 8y and -3y. Then:
Now we find the common factor for each column and row:
Therefore:
[tex]y^2+5y-24=(y-3)(y+8)[/tex]A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine theamount of money saved, s, in dollars, when purchasing this desk on sale?A s= 0.2(380)BS = (380 = 0.8) - 380Cs= (380 = 0.5) – 380D8 = (380 = 0.8)
Since the desk was 20% off, the price of $380 represents 80% of the original price.
Step 1. Define an expression to find the original price.
To find this original price, we divide the discounted price of 380 by the percentage it represents: 0.8 (we represent 80% in decimal form as 0.8)
[tex]380\div0.8[/tex]That expression represents the original price.
Step 2. To find the amount saved, we subtract the sale price to the original price:
[tex]s=(380\div0.8)-380[/tex]This expression will give as a result the amount saved s.
Answer:
[tex]s=(380\div0.8)-380[/tex]Hello, can you help me find the solutions to this problem?
Given,
The expression is,
[tex]\begin{gathered} x^3=216 \\ x^3-216=0 \end{gathered}[/tex]The rational theorem tells that if the polynomial has the rational 0 then it must be a fraction p/q, where p is a factor of constant term and q is the factor of leading coefficient.
The constant term 216 with factors:
[tex]1,2,3,4,6,8,9,12,18,24,27,36,54,72,108\text{ }and\text{ }216.[/tex]The leading coefficient is 1, with a single factor of 1.
[tex]\begin{gathered} \frac{p}{q}=\frac{factor\text{ of 216}}{factor\text{ of 1}}=\pm\frac{1}{1},\operatorname{\pm}\frac{2}{1},\operatorname{\pm}\frac{3}{1},\operatorname{\pm}\frac{4}{1},\operatorname{\pm}\frac{6}{1},\operatorname{\pm}\frac{8}{1},\operatorname{\pm}\frac{9}{1},\operatorname{\pm}\frac{12}{1}, \\ \operatorname{\pm}\frac{18}{1},\operatorname{\pm}\frac{24}{1},\operatorname{\pm}\frac{27}{1},\operatorname{\pm}\frac{36}{1},\operatorname{\pm}\frac{54}{1},\operatorname{\pm}\frac{72}{1},\operatorname{\pm}\frac{108}{1},\operatorname{\pm}\frac{216}{1} \end{gathered}[/tex]Substitute the possible roots one by one into the polynomial to find the actual roots. Start first with the whole numbers.
p(6)=0 so x=6 is a root of a polynomial p(x).
Using factor theorem to find the remaining roots,
[tex]\begin{gathered} \frac{x^3-216}{x-6}=x^2+6x+36 \\ By\text{ formula method,} \\ x=\frac{-6\pm\sqrt{36-144}}{2} \\ x=\frac{-6\pm\sqrt{108}}{2} \\ x=\frac{-6\pm6\sqrt{-3}}{2} \\ x=-3\pm3\sqrt{3i} \end{gathered}[/tex]Hence, the roots are 6, -3-3sqrt(3)i, and -3+3sqrt(3)i. So, option A is correct.
Evaluate the piecewise defined function for the given values of x.F(x)= -x -1 for x<-1, -3 for -1≤x<2, √x-2 for x≥2A. f(-3)B. f(-1)C. f(2)D. f(6)
Answer:
[tex]\begin{gathered} f(-3)=2 \\ f(-1)=-3 \\ f(2)=0 \\ f(6)=2 \end{gathered}[/tex]Explanation:
Given the piecewise defined function;
[tex]f(x)=\mleft\{\begin{aligned}-x-1for\rightarrow x<-1_{} \\ -3\text{for} \\ \sqrt[]{x-2}\text{ for}\rightarrow x\ge2\end{aligned}\mright.\rightarrow-1\leq x<2[/tex]a) f(-3)
we want to find the value of f(x) at x=-3.
-3 is less than -1, so it falls within the interval x<-1.
[tex]\begin{gathered} f(x)=-x-1 \\ f(-3)=-(-3)-1 \\ f(-3)=3-1 \\ f(-3)=2 \end{gathered}[/tex]b) f(-1)
-1 falls with the second interval
[tex]-1\leq x\leq2[/tex]For this interval, f(x) is always equal to -3.
[tex]\begin{gathered} f(x)=-3 \\ f(-1)=-3 \end{gathered}[/tex]c) f(2)
2 falls within the last interval.
[tex]\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(2)=\sqrt[]{2-2} \\ f(2)=0 \end{gathered}[/tex]d) f(6)
6 falls within the last interval.
[tex]\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(6)=\sqrt[]{6-2} \\ f(6)=\sqrt[]{4} \\ f(6)=2 \end{gathered}[/tex]How can you write the expression with a rationalized denominator?See image
Okay, here we have this:
Considering the provided expression, we are going to rationalize the denominator, so we obtain the following:
[tex]\begin{gathered} \frac{\sqrt[3]{3}}{\sqrt[3]{4}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{4^2}}{\sqrt[3]{4}\cdot\sqrt[3]{4^2}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{2^4}}{4^{\frac{1}{3}+\frac{2}{3}}} \\ =\frac{\sqrt[3]{3}\cdot2^{\frac{4}{3}}}{2^2} \\ =\frac{\sqrt[3]{3}\sqrt[3]{2}}{2} \\ =\frac{\sqrt[3]{6}}{2} \end{gathered}[/tex]Finally we obtain that the correct answer is the second option.
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
The measure of angle Y from triangle XYZ is 99°. Therefore, option C is the correct answer.
Given that, in ΔXYZ, m∠X = 38°, m∠Y = (5x - 11)°, and m∠Z = (4x - 45)°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Using angle sum property of triangle, we get
m∠X+m∠Y+m∠Z=180°
⇒ 38°+(5x - 11)°+(4x - 45)°=180°
⇒ 9x+38-11-45=180
⇒ 9x-18=180
⇒ 9x=180+18
⇒ 9x=198
⇒ x=22°
So, m∠Y = (5×22 - 11)°
=110-11
= 99°
The measure of angle Y from triangle XYZ is 99°. Therefore, option C is the correct answer.
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Please help me with this quickly, the questions says to show work or explain but I want explanation, thank you!
Solution
- Experimental probability is the probability gotten from conducting experiments and it is different from theoretical probability which is derived from hypothetical situations.
- In this question, the hypothetical situation that leads to the theoretical probabilities of getting a red, an orange, and so on, is the fact that the question already said the smallest section of the circle is 1/16 and every other portion is a multiple of this.
- The experimental probabilities are gotten from the table and the formula for calculating this probability is given below:
[tex]\begin{gathered} Given\text{ Event \lparen E\rparen,} \\ P(E)=\frac{Number\text{ of times an event occurs}}{Total\text{ number of trials}} \end{gathered}[/tex]- Thus, we can proceed to find the experimental probabilities of finding any of these colors as follows:
Orange:
[tex]\begin{gathered} E=\text{ Event of spinning an Orange} \\ P(orange)=\frac{3}{30}=\frac{1}{10} \end{gathered}[/tex]Green:
[tex]P(green)=\frac{6}{30}=\frac{1}{5}[/tex]Blue:
[tex]P(blue)=\frac{5}{30}=\frac{1}{6}[/tex]I have the answers to the question but I’m not sure how they got them?
Hello there. To solve this question, we'll have to use the data from the graph (dot plot) and determine the answers for each letter.
a) How many babies begin walking before 13 months of age?
For this, we have to add all the number of babies walking from the dot plot that are less than 13.
In this case, we add the values of babies walking with 9, 10, 11 and 12 months:
1 + 1 + 3 + 5 = 10
Therefore 10 babies have begun walking before 13 months of age.
b) What percent of babies begin walking at 12 months?
For this, we add the entire number of babies walking by age and calculate the ratio between the number of babies walking at 12 months and this result.
We have 25 babies at total and 5 of them began walking at 12 months of age, so now we take the ratio:
[tex]\frac{5}{25}=\frac{1}{5}=20\%[/tex]c) Which three ages combined account for less than 16% of the babies?
For this, we find how many is 16% of 25, that is, the total of babies:
[tex]0.16\cdot25=4[/tex]So we have to find which three ages combined gives us less than 4 babies.
Notice we cannot choose the ages 12, 13, 14 because their number of babies, alone, are already bigger than 4.
We cannot also choose 11, because it is equal to 3 and all the other options are bigger than or equal to 1, so adding it with something else already would be equal to 4.
The same happens to 15 and 16, because their assigned value is 2, so adding both together gives us 4 and since all the others are greater than or equal to 1, we could not add other two together with them.
That's why the final answer is 9, 10 and 17, because they are the only numbers left that add up to 3 and this is a number less than 4, that is, less than 16% of the babies.
Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times
that the coin shows heads. You have previously shown that all conditions have been met and that this scenario
describes a binomial setting.
Determine the value of n and p and calculate the mean and standard deviation of X. Round the standard deviation to
three decimal places.
■ n=
■
■
p=
Hx=
0x =
h
Done
The given solutions are:
n = 3
p = 0.5
mean Hx= 1.5
standard deviation 0x = 0.866
How to solve the probabilityThe value of n = 3
The fair coin is said to have been flipped 3 times
P = 0.5
The coin has two faces, the probability of either face would be 1 / 2
= 0.5
Next we have to solve for the mean of x
μ[tex]_{x}[/tex] = n * p
= number * probability
= 0.5 * 3
= 1.5
The standard deviation
σ[tex]_{x}[/tex] = [tex]\sqrt{np(1-p)}[/tex]
= √1.5(1-0.5)
= √1.5*0.5
= √0.75
= 0.866
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