Let's suppose we are given two fractions:
[tex]\frac{a}{b},\frac{c}{d}[/tex]In order to multiply them we simply multiply the numerators and denominators, like this:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]For example, let's say we are given the following fractions:
[tex]\frac{1}{2},\frac{3}{5}[/tex]We can multiply them following the previous rule:
[tex]\frac{1}{2}\times\frac{3}{5}=\frac{1\times3}{2\times5}=\frac{3}{10}[/tex]| 5-6x | -12 = 0Solve the absolute. equation for 2 values of x
Given
[tex]|5-6x|-12=0[/tex]To solve this equation for both possible values of x, you have to separate it into two calculations.
1) One will be for the case that the values inside the absolute term are multiplied by "+1":
[tex]\begin{gathered} 1\cdot(5-6x)-12=0 \\ 5-6x-12=0 \\ -6x+5-12=0 \\ -6x-7=0 \\ -6x=7 \\ -\frac{6x}{-6}=\frac{7}{-6} \\ x=-\frac{7}{6} \end{gathered}[/tex]The first value of x is -7/6
2) The second will be the case that the absolute values are negative, that is as if they are multiplied by -1
[tex]\begin{gathered} (-1)(5-6x)-12=0 \\ -5+6x-12=0 \\ 6x-5-12=0 \\ 6x-17=0 \\ 6x=17 \\ \frac{6x}{6}=\frac{17}{6} \\ x=\frac{17}{6} \end{gathered}[/tex]The second value of x is 17/6
So for this absolute equation, the possible values of x are -7/6 and 17/6
Collinear points are two or more points that lie on the sameA. planeB. angleC. lineD. space
Collinear points are two or more points that lie on the same line.
For Example:
Point A, B and C
Select the similarity transformation(s) that make ABC similar to EDC.
Given the triangles ABC and EDC
We will find the transformation that makes the triangles are similar
As shown: the triangles are reflected over the y-axis
the rule of the reflection over the y-axis will be as follows:
[tex](x,y)\rightarrow(-x,y)[/tex]And as shown, the length of the side AB = 3 units
And the length of the side ED = 1 units
So,
[tex]ED=\frac{1}{3}AB[/tex]So, the answer will be:
D) (x,y) ⇒ (-x, y)
E) (x,y) ⇒ (1/3 x, 1/3 y)
Amtrak's annual passenger revenue for the years 1985 - 1995 is modeled approximately by the formulaR = -60|x- 11| +962where R is the annual revenue in millions of dollars and x is the number of years after 1980. In what year was the passenger revenue $722 million?In the years ____ and ___, the passenger revenue was $722 million.
ANSWER
1987 and 1995
EXPLANATION
The revenue is modeled by:
[tex]R=-60|x-11|+962[/tex]To find the years that the revenue was $722 million, we have to solve for x when R is 722.
That is:
[tex]\begin{gathered} 722=-60|x-11|+962 \\ \Rightarrow722-962=-60|x-11| \\ -240=-60|x-11| \\ \Rightarrow|x-11|=\frac{-240}{-60} \\ |x-11|=4 \end{gathered}[/tex]We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.
That is:
[tex]\begin{gathered} x-11=4 \\ x-11=-4 \end{gathered}[/tex]Solve for x in both:
[tex]\begin{gathered} x=11+4 \\ \Rightarrow x=15 \\ x=11-4 \\ \Rightarrow x=7 \end{gathered}[/tex]That is to say 7 and 15 years after 1980.
Therefore, in the years 1987 and 1995, the revenue was $722 million.
SSS
L
J
++
A) LJ=HF
LK=LG
C)
K
H
G
F
B) LJ LF or
D) ZL=LH
Answer:
A. LJ≅HF
Step-by-step explanation:
Same as last time
In the diagram below of rhombus ABCD,angle C is 100,what is angle DBC
Okay, here we have this:
Considering the provided information, that in a rhombus opposite angles are equal, and that the sum of the angles of a triangle is 360 °, we obtain:
360°=100°+100°+4(m∠DBC)
Now, let's clear "m∠DBC":
360°=200°+4(m∠DBC)
4(m∠DBC)=360°-200°
4(m∠DBC)=160°
m∠DBC=160°/4
m∠DBC=40°
Finally we obtain that the correct answer is the option A.
Melissa works as a tutor for S12 an hour and as a waitress for S11 an hour. This month, she worked a combined total of 105 hoursat her two jobs.Lett be the number of hours Melissa worked as a tutor this month. Write an expression for the combined total dollar amount sheearned this month.
From the question
Melissa earns $12 an hour as a tutor
And $11 an hour as a waitress
Also,
This month, she worked a combined total of 105 hours
at her two jobs.
Let t be the number of hours Melissa worked as a tutor this month
Let w be the number of hours Melissa worked as a waitress this month
This implies
[tex]t+w=105[/tex]Since Melissa worked t hours as a tutor this month then
Total money earned as a tutor = $12t
Also,
Since Melissa worked w hours as a waitress this month then
Total money earned as a waitress this month = $11w
Therefore, the total combined earnings for the month is
[tex]\text{ \$12t }+\text{ \$11w}[/tex]Find the perimeter and area for each figure.
10.
6 in.
P =
A =
3 in.
6 in.
2 in.
5 in.
11.
7 in.
P =
A =
6 in.
(each side is 6 in.)
The perimeter and the area of a rectangle of dimensions 15 cm and 8 cm is given as follows:
Perimeter: 46 cm.Area: 120 cm².What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given, respectively, by these following equations:
Area: A = lw.Perimeter: = 2(l + w).In the context of this problem, the dimensions are given/supposed as follows:
l = 15 cm, w = 8 cm.
Applying the rule, the area, in cm², as the variables are multiplied, is given as follows:
A = 15 x 8 = 120 cm².
The perimeter, in cm, as the measures are added, is given as follows:
P = 2 x (15 + 8) = 2 x 23 = 46 cm.
Missing informationThis problem is incomplete and could not be found on any search engine, hence we suppose that it is a rectangle of dimensions 15 cm and 8 cm.
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Use any strategy to determine a combination of apples
and pineapples that will balance the scale.
Explain how you know it will balance.
1 Pine- apple equal to 9 Apples.
What is Ratio proportion?The divisional comparison of two quantities yields a ratio, and the equality of two ratios yields a proportion.
A ratio is commonly written as "x: y," though it can also be read as "x is to y" or "x/y."
In terms of comparison, a proportional equation says that two ratios are equal.
When x: y: z: w is used to represent a ratio, it is understood to mean that x is to y as z is to w.
In this case, w and Y are not equal to 0, therefore x/y Equals z/w.
6 Apples = 4 Pomegranates
6 Pomegranates = 1 Pine- apple
1 Pine- apple = 9 Apples.
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gus bought 2/3 pound of turkey and 1/4 pound of ham.The tukey cost 9 dollars per pound, and the ham cost 7 dollars per pound.In all,how much did Gus spend?
From the information given,
gus bought 2/3 pound of turkey. If tukey costs 9 dollars per pound, it means that the cost of 2/3 pound of turkey is
2/3 x 9 = 6
gus bought 1/4 pound of ham. If ham costs 7 dollars per pound, it means that the cost of 1/4 pound of ham is
1/4 x 7 = 7/4 = 1.75
Total amount spent = amount spent on turkey + amount spent on ham
Total amount = 6 + 1.75
Total amount = $7.75
The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(16Correct,5Correct) b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it. 0.2Incorrectc. Find the minimum number for the upper quarter of the time to pass a kidney stone. 0.8Incorrect days.
Answer:
• (a)X ~ N(16, 5)
,• (b)0.4207
,• (c)19.37 days
Explanation:
(a)
• The mean amount of time = 16 days
,• The standard deviation = 5 days.
Therefore, the distribution of X is:
[tex]X\sim N(16,5)[/tex](b)P(X>17)
To find the required probabability, recall the z-score formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]When X=17
[tex]z=\frac{17-16}{5}=\frac{1}{5}=0.2[/tex]Next, find the probability, P(x>0.2) from the z-score table:
[tex]P(x>0.2)=0.4207[/tex]The probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it is 0.4207.
(c)The upper quarter is the value under which 75% of data points are found.
The z-score associated with the 75th percentile = 0.674.
We want to find the value of X when z=0.674.
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ 0.674=\frac{X-16}{5} \\ \text{ Cross multiply} \\ X-16=5\times0.674 \\ X=16+(5\times0.674) \\ X=19.37 \end{gathered}[/tex]The minimum number for the upper quarter of the time to pass a kidney stone is 19.37 days.
what is the surface area of the rectangular prism? 1.8 ft 2/5 ft 1/2 ft
Each face of a rectangular prism has a rectangle shape. To calculate the surface area we need to calculate the area of all the faces. Each face appears twice on the prism, on opposite sides so we only need to make three calculations. These are done using the formulas below:
[tex]\begin{gathered} A_1=height\cdot width_{} \\ A_2=length\cdot width_{} \\ A_3=length\cdot height_{} \end{gathered}[/tex]Using the data from the problem we can calculate these areas.
[tex]\begin{gathered} A_1=\text{ 1.8}\cdot\frac{2}{5}=0.72\text{ square ft} \\ A_2=\frac{1}{2}\cdot\frac{2}{5}=0.2\text{ square ft} \\ A_3=1.8\cdot\frac{1}{2}=0.9\text{ square ft} \end{gathered}[/tex]The surface area of the prism is the sum of the areas above multiplied by two.
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(A_1+A_2+A_3) \\ A_{\text{surface}}=2\cdot(0.72+0.2+0.9)=2\cdot1.82=3.64\text{ square ft} \end{gathered}[/tex]O DESCRIPTIVE STATISTICInterpreting relative frequency-histogramsStudents at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have tocommute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in theschool newspaper, contains the following histogram summarizing the commute distances for a sample of 100 students at the university:Relative frequencyCommute distance (in miles)Based on the histogram, find the proportion of commute distances in the sample that are at least 16 miles. Write your answer as a decimal, and do not roundyour answer
Since the graph gives us the relative frequency we just have to add those who are more or equal to 16; in this case we have to add 0.11 and 0.06, therefore the proportion in this case is 0.17
a 14-member board used for admitted
Using the Borda's method, when one person is ranked as 1st, he/she gets 3 points, if he/she is ranked 2nd, get 2 points, also, if he/she is ranked as 3rd get 1 point, and finally, 0 points if she/he is ranked as 4th
so, let's detemine how many points got each one
Cardona: Was selected 1st by 6 people, 2nd by 2 people, 3rd by 4 people and 4th by 2 people
[tex]C=3*6+2*2+1*4=26[/tex]So, that's a total of 26 points
Pitts-Jones: Was selected as: #1 by 4 people, #2 by 3 people, #3 by 6 people and 4th by 1 person
[tex]P=3*4+2*3+1*6=24[/tex]So, that's 24 points for Pitts-Jones,
De Plata: Was ranked #1 by 2 people, #2 by 8 people, #3 by 1 person and #4 by 3 people
[tex]D=3*2+2*8+1*1=23[/tex]That's 23 points for De Plata
Vincent: Was ranked as #1 by 2 people, #2 by 1 person, #3 by 3 people and #4 by 8 people
[tex]V=3*2+2*1+1*3=11[/tex]that's 11 points for Vincent,
Answer: From the above, we can conclude that the winner using Borda's method is Cardona
38. A right rectangular prism has a volume of 5 cubic meters. The length ofthe rectangular prism is 8 meters, and the width of the rectangular prismis a meter.What is the height, in meters, of the prism?Niu4© 30 10
It's important to know that the volume formula for a rectangular prism is
[tex]V=l\cdot w\cdot h[/tex]Where V = 5, l = 8, and w = 1. Let's use these values and find h
[tex]\begin{gathered} 5m^3=8m\cdot1m\cdot h \\ h=\frac{5m^3}{8m^2} \\ h=0.625m \end{gathered}[/tex]Hence, the height of the prism is 0.625 meters.Two Way Tables, URGENT
Step-by-step explanation:
a) modal number is 3
b) mean is x = ∑fx/n
= ((5•1)+ (2•10)+(3•15)+(7•4)+(3•5))/(5+10+15+7+3)
= 113/40
= (Decimal: 2.825)
If the time to climb the mountain took an hour more than the time to hike down how long was entire hike?
4.8 mi
Explanation
[tex]\text{time}=\text{ }\frac{\text{distance}}{\text{rate}}[/tex]
Step 1
Set the equations
a) uphill
let
rate1= 1.5 miles per hour
time= unknow= t1
distance = x
b) down hille
rate=4 miles per hour
time=time2=one hour less than the time to climb = t1-1
distance = x
so
replacing
[tex]\begin{gathered} t_1=\frac{x}{1.5\frac{mi}{\text{hour}}}\rightarrow t_1=\frac{x}{1.5}\rightarrow equation(1) \\ t_2=\frac{x}{4\frac{mi}{\text{hour}}} \\ \text{replace t}_2=t_1-1 \\ t_1-1=\frac{x}{4} \\ \text{add 1 in both sides} \\ t_1-1+1=\frac{x}{4}+1 \\ t_1=\frac{x}{4}+1\rightarrow equation(2) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} t_1=\frac{x}{1.5}\rightarrow equation(1) \\ t_1=\frac{x}{4}+1\rightarrow equation(2) \end{gathered}[/tex]set t1= t1
[tex]\begin{gathered} t_1=t_1 \\ \frac{x}{1.5}=\frac{x}{4}+1 \\ \frac{x}{1.5}=\frac{x+4}{4} \\ 4x=(x+4)1.5 \\ 4x=1.5x+6 \\ subtract\text{ 1.5 x in both sides} \\ 4x-1.5x=1.5x+6-1.5x \\ 2.5x=6 \\ \text{divide both sides by 2.5} \\ \frac{2.5x}{2.5}=\frac{6}{2.5} \\ x=2.4 \end{gathered}[/tex]it means the distance to the top of the mountain is 2.4 miles, so the entire hike is twice that amount
total distance=2.4 mi*2
total distance=4.8 miles
Step 3
now, the times
[tex]\begin{gathered} t_1=\frac{x}{1.5} \\ t_1=\frac{2.4}{1.5} \\ t_1=1.6\text{ hours} \\ t_2=t_1-1 \\ t_2=1.6-1=\text{ 0.6 hours} \end{gathered}[/tex]table
I hope this helps you
Forty percent of 90 is what number
90 represents the 100%
Let's call x to the number that represents the 40%
To find the 40%, we can use the next proportion:
[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]36 is 40% of 90
Identify the leading coefficient, degree and end behavior. write the number of the LC and degree
Given
[tex]P(x)=-4x^4-3x^3+x^2+4[/tex]Solution
The LC is -4
End behavior is determined by the degree of the polynomial and the leading coefficient (LC).
TThe degree of this polynomial is the greatest exponent is
[tex]\begin{gathered} x\rightarrow\infty\text{ then P\lparen x\rparen} \\ p(\infty)=-4(\infty)^4-3(\infty)^3+\infty^2+4 \\ p(\infty)=-4\infty^4-3\infty^3+\infty^2+4 \\ P(\infty)=-\infty \\ \end{gathered}[/tex][tex]\begin{gathered} x\rightarrow-\infty \\ p(-\infty)=-4(-\infty)^4-3(-\infty)^3+(-\infty)^2+4 \\ P(-\infty)=-4\infty^4+3\infty^3+\infty^2+4 \\ P(-\infty)=-\infty \end{gathered}[/tex]The degree is even and the leading coefficient is negative.
The final answer
1
Pratap Puri rowed 26 miles down a river in 2 hours, but the return trip took him 6; hours. Find the rate Pratap can row
in still water and find the rate of the current. Let x=rate Pratap can row in still water and y = rate of the current.
What is the rate that Pratap rows in still water?
Pratap can row at a rate of
(Type an integer or a decimal.)
in still water.
The speed of current will be "4.5 mph" and the rate Pratap can row in still water will be "8.5 mph".
What does "speed" mean in mathematics?
Speed is what it means. the speed of a change in an object's location in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Speed is a scalar quantity because it just has a direction and no magnitude.Given:
Distance "26 miles" in time "2 hours".
Let,
Speed of water = y
Pratap speed when rowing in still water = x
As we know,
Speed = distance/time
then,
x + y = 26/2
x + y = 13
x = 13 - y
In return trip took him time "6.5 hours",
x - y = 26/6.5
x - y = 4
By substituting the value of "x", we get
13 - y - y = 4
13 - 2y = 4
2y = 13 - 4
2y = 9
y = 9/4 = 4.5 mph (Rate of the current)
By substituting the value of "y", we get
x = 13 - a
x = 13 - 4. 5 = 8.5 mph (Pratap can row in still water)
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Please help me ASAP I’ll mark brainly
1. The scholar made a mistake in the last step
where he said x=3.5
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14
AS A RESULTS GOT WRONG ANSWER . x is supposed to be 14.
Select all statements that are true about equilateral triangle ABC.
To determine statements that are correct, we proceed as follows:
Step 1: We recall the definition of an "equilateral" triangle
An equilateral triangle is one which"
- has all its sides equal to each other
- has all its internal angles equal to 60 degrees each
From the above definition, it can be concluded that
(A) Angles B and C are 60 degrees is a true statement
Step 2: We solve the triangle for x, as follows:
Now, consider the left right-triangle:
Now, we apply the sine trigonometric ratio to obtain the value of x,
[tex]undefined[/tex]Nicholas and Jack volunteer to fill gift boxes for soldiers serving overseas. Both work at a constant rate. They work together for 6 hours and fill 126 boxes. Nicholas fills 9 boxes every hour. How many boxes does Jack fill every hour?
Firstly, we need to know the number of boxes they both filled per hour.
From the question, we are told that 126 boxes were filled in six hours; thus in an hour, the number of boxes filled will be 126/26 = 21 boxes
Now in an hour, Nicholas filled 9 boxes; the number of boxes that will be filled is clearly the remainder of the 21 boxes.
The number of boxes filled by Jack is thus; 21 - 9 = 12 boxes
Jack fills 12 boxes in an hour
f (x+2) - 3o vertical shiftvertical stretchhorizontal reflectionhorizontal shiftvertical compressionhorizontal stretchhorizontal compressionvertical reflection
ANSWER:
[tex]\begin{gathered} (5x+3)\cdot(x+4) \\ x=-\frac{3}{5}\text{ and }x=-4 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]5x^2+23x+12[/tex]we factor and calculate the roots like this:
[tex]\begin{gathered} (5x+3)\cdot(x+4) \\ (5x+3)=0\rightarrow x=-\frac{3}{5} \\ (x+4)=0\rightarrow x=-4 \end{gathered}[/tex]Therefore the factored form would be
[tex](5x+3)\cdot(x+4)[/tex]And the roots of the functions are - 3/5 and -4
Unit 6 lesson3 plsss help
From the triangles ∠ABC ≅ ∠MNP.
Given we have two triangles ABC and PNM
Both triangles have same shape but different angles.
we need to find ∠ABC ≅ ?
we can notice that :
∠A ≅ ∠M
∠B ≅ ∠N
∠C ≅ ∠P
hence these angles are similar to each other.
So, ∠ABC ≅ ∠MNP.
Hence we get the answer as ∠ABC ≅ ∠MNP.
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dog brought a new jet ski for $299 down in 14 monthly payments are $57 how much did Doug pay for the jet ski total
If he paid $57 monthly for 14 months, the total amount paid is:
[tex]57\times14=798[/tex]He paid $798 in total
Explain if the triangles are similar using SAS-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)
We have two triangles GBL and XYL.
From the picture we notice that the GL=39 and BL=34. We also notice that XL=30 and YL=27.
The SAS theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
This means that we need that:
[tex]\frac{GL}{XL}=\frac{BL}{YL}[/tex]and that the angle between them is the same.
It is clear that the angle L is the same for both triangles, hence we only need to proof tha the sides are congruent, but in this case:
[tex]\frac{39}{30}\ne\frac{34}{27}[/tex]since the sides are not proportional, we conclude that triangles are not congruent.
u(x) = 4x - 2 w(x) = - 5x + 3The functions u and w are defined as follows.Find the value of u(w(- 3)) .
Solution
- We are given the two functions below:
[tex]\begin{gathered} u(x)=4x-2 \\ \\ w(x)=-5x+3 \end{gathered}[/tex]- We are asked to find u(w(-3)).
- In order to find u(w(-3)), we need to first find u(w(x)) and then we can substitute x = -3.
- Since we have been given u(x), then, it means that we can find u(w) as follows:
[tex]\begin{gathered} u(x)=4x-2 \\ u(w),\text{ can be gotten by substituting w for x} \\ \\ u(w)=4w-2 \end{gathered}[/tex]- But we have an expression for w in terms of x. This means that we can say:
[tex]\begin{gathered} u(w)=4w-2 \\ \\ w(x)=-5x+3 \\ \\ \therefore u(w(x))=4(-5x+3)-2 \\ \\ u(w(x))=-20x+12-2 \\ \\ \therefore u(w(x))=-20x+10 \end{gathered}[/tex]- Now that we have an expression for u(w(x)), we can proceed to find u(w(-3)) as follows:
[tex]\begin{gathered} u(w(x))=-20x+10 \\ put\text{ }x=-3 \\ \\ u(w(-3))=-20(-3)+10 \\ \\ u(w(-3))=60+10=70 \end{gathered}[/tex]Final Answer
The answer is
[tex]u(w(-3))=70[/tex]Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).
Using the first point given in the statement you can find a, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 0 and y = 18} \\ 18=ab^0 \\ 18=a\cdot1 \\ 18=a \end{gathered}[/tex]Now, since you already have the value of a, you can find the value of b using the second point, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 3 and y = 6174} \\ 6174=18\cdot b^3 \\ \text{ Divide by 18 into both sides of the equation} \\ \frac{6174}{18}=\frac{18\cdot b^3}{18} \\ 343=b^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{343}=\sqrt[3]{b^3} \\ 7=b \end{gathered}[/tex]Therefore, the exponential function that passes through the points (0,18) and (3,6174) is
[tex]y=18\cdot7^x[/tex]find x..in a right triangle ️ with a height of 10 and hypotenuse of 19
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (the longest side) = 19
a & b = the other 2 legs of the triangle
Replacing:
19^2 = 10^2 + x^2
Solve for x
361 = 100 + x^2
361 - 100 = x^2
261 = x^2
√261 =x
x= 16.16
