The slope is defined as rise/run - in other words, for every step you take horizontally, how many steps you should take vertically to get to a point on the same line.
In our case, the ladder rises 20 feet for every horizontal change of 4 feet; therefore, the slope is
[tex]\frac{\text{rise}}{\text{run}}=\frac{20ft}{4ft}[/tex]dividing 30 ft by 4 ft gives 5; therefore,
[tex]\frac{\text{rise}}{\text{run}}=5.[/tex]Hence, the correct answer to choose is A. 5.
You are cycling around Europe with your friends.You want to frame a photo from your trip to send home. Select a frame that is suitable for a photo with a perimeter of 70 cm. Is this frame suitable?YesNoIs this frame suitable?YesNoIs this frame suitable?YesNo
The perimeter of frame is given 70 cm.
There are two frames given.
For first frame , calculating the perimeter .
[tex]P=2(15+20)=2\times35=70\operatorname{cm}[/tex]For second frame, calculating the perimeter.
[tex]P=2(30+40)=2\times70=140\operatorname{cm}[/tex]Hence the first frame is suitable for for a photo with a perimeter of 70 cm.
This is the frame which is suitable.
Could you help me with these problems ? I don't really know how to put the equation together and the steps I should take to solve it, it would be amazing if you could show me how, and I'd be very thankful if you could also add a picture showing the steps if possible. Thank you so much.
Since it is a right triangle, you can use the trigonometric ratio sin(θ) to solve the exercise:
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} \theta=54\text{\degree} \\ \text{ Opposite side }=72 \\ \text{ Hypotenuse }=x \\ \sin (54\text{\degree})=\frac{72}{x} \\ \text{ Multiply by x from both sides of the equation} \\ \sin (54\text{\degree})\cdot x=\frac{72}{x}\cdot x \\ \sin (54\text{\degree})\cdot x=72 \\ \text{ Divide by }\sin (54\text{\degree})\text{ from both sides of the equation} \\ \frac{\sin(54\text{\degree})\cdot x}{\sin(54\text{\degree})}=\frac{72}{\sin(54\text{\degree})} \\ x=\frac{72}{\sin(54\text{\degree})} \\ x=\frac{72}{0.8090} \\ x=88.99 \\ \text{ Rounding to the nearest tenth} \\ x=89.0 \end{gathered}[/tex]Therefore, the measure of the missing side is 89.
David watches Maria and Alma race electric trains around a track. Maria's train goes around the track in 10 seconds. Alma's train goes around the track in 12 seconds.
How long will it take for both trains to cross the finish line together the first time?
Answer:
60 seconds
Step-by-step explanation:
The LCM of 10 and 12 is
10 = 2 × 5
12 = 2² × 3
LCM = 2² × 3 × 5 = 60
Answer: 60 seconds
the anwser is 60 seconds
A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution on the right shows the resultsUse the table to answer the following question. What is the probability that the next person surveyed is very prepared?
The probability the next person surveyed is very prepared is 0.119.
What actually does probability mean?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number ranging from zero and 1, where, roughly, 0 denotes the event's impossibility and 1 represents certainty.Formula of total frequency is,
Total = f₁ + f₂ + f₃ + f₄ +...............n∑fi
The total frequency is,
total = n∑i=2 fi ⇒ 262 + 992 + 587 + 313 + 52
The total number of people prepared for a long-term power outage, natural disaster, or terrorist attack is obtained by taking the sum of the all frequencies.
probability = N(E)/N(S)
the information given, there are 262 people are very prepared.
That is, N(A) = 262
The required probability is,
P(A) = 262/2206
= 0.119
The probability the next person surveyed is very prepared is 0.119.
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I need help with this question part a and b
Answer:
• (a)f[g(x)]=(3x-84)/4
,• (b)7.5
Explanation:
A function that converts shoe sizes in France to those in England is:
[tex]g(x)=\frac{3x-94}{4}[/tex]A function that converts shoe sizes in England to those in the United States is:
[tex]f(x)=x+\frac{5}{2}[/tex]Part A
To find a function that converts shoe sizes in France to those in the United States, we evaluate the composition, g(f(x)).
[tex]\begin{gathered} f(x)=x+\frac{5}{2} \\ f[g(x)]=g(x)+\frac{5}{2}=\frac{3x-94}{4}+\frac{5}{2}\frac{=3x-94+10}{4} \\ \implies f[g(x)]=\frac{3x-84}{4} \end{gathered}[/tex]A function that converts shoe sizes in France to those in the U.S is:
[tex]f[g(x)]=\frac{3x-84}{4}[/tex]Part B
Given a size 38 shoe in France:
[tex]f[g(38)]=\frac{3(38)-84}{4}=\frac{114-84}{4}=\frac{30}{4}=7.5[/tex]A size 38 shoe in France is of size 7.5 in the United States.
Simplify using order of
operations.
3 • 10 (9 + 1)²
Answer:
3000
Step-by-step explanation:
Parentheses - (9 + 1) = 10
Exponents - 10 x 10 = 100
Multiplication - 10 x 100 = 1000 then 1000 x 3 = 3000
D
A
S
Lesson 4: Proportional Relationships a 2. A recip Equations the qu a. Let's write equations describing proportional relationships. b. 4.1: Number Talk: Division Find each quotient mentally. C. 645 - 100 645:50 48.6 - 30 48.6 + x
Move the decimal point of 645 two units left ( You are dividing by 100)
---------------------------
[tex]\frac{645}{50}=\frac{129}{10}=12.9[/tex]Simplify 645/50 as 129/10, now move the decimal point of 129 one unit left (You are dividing by 10).
-----------------------
[tex]\frac{48.6}{30}=\frac{243}{\frac{5}{30}}=\frac{243}{150}=\frac{81}{50}[/tex]Express 48.6 as 243/5, then use division of fractions to get 243/150, then simplify 243/150 as 81/50
-----------------------
[tex]\frac{48.6}{x}=\frac{\frac{243}{5}}{x}=\frac{243}{5x}[/tex]Express 48.6 as 243/5, then use division of fractions to get 243/5x
Steve Conway wants his team to win more than 57 games this year. His team has already won 2 games this season and there are 5 more months to play. Based on his goal, how many games must his team win per month?
Using a linear function, it is found that:
The inequality is: 5m + 2 > 57.The solution is: m > 11.They team needs to win more than 11 games per month.Linear functionThe linear function that models this situation is defined as follows:
y = mx + b.
In which the parameters are as follows:
m is the slope, which is the number of games that he wants to win per month.b = 2 is the intercept, which is the number of games that he has already won.They want to win more than 57 games, and there are 5 months to play, hence the inequality is given as follows:
5m + 2 > 57.
It is solved similarly to an equality, isolating the variable m and finding the range of values, as follows:
5m > 55
m > 55/5
m > 11.
Hence the team needs to win more than 11 games a month, and the solutions is illustrated by the image given at the end of the answer.
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At a school concert the total value of tickets sold was $3990. Student tickets sold for $8 and adult tickets sold for $11. The number of adult tickets sold was 6 less than 4 times the number of student tickets. Find the number of student tickets sold.
The number of student tickets sold is 78.
Given,
The number of student tickets sold = x
The number of adult tickets sold = 4x - 6
Total value of tickets sold = $3990
Value of one student ticket = $8
Value of one adult ticket = $11
Now, we have to find the number of student tickets sold:
Here,
The expression :8x + 11(4x - 6) = 3990
Solve the expression:
8x + 44x - 66 = 3990
52x - 66 = 3990
Add 66 to both sides
52x - 66 + 66 = 3990 + 66
We get,
52x = 4056
Divide 52 on both sides
52x / 52 = 4056/52
That is,
x = 78
Therefore,
The number of student tickets sold is 78.
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The two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. Allowance No Allowance Do Chores 13 3 Do Not Do Chores 5 4 a. How many total students do chores? b. What is the relative frequency of students that do chores and get an allowance to the number of students that do chores? Round to the nearest hundredth if necessary.
Given the table showing the number of students who do or do not perform chores, and who do or do not receive an allowance, we can add the numbers along the rows and columns, as shown in the diagram below:
Now, that we have summed the numbers along the vertical and horizontal directions, we can now proceed to answer the questions asked.
a.) The total number of students who do chores is equal to the horizontal sum of the numbers in the 'DO CHORES' row. This value is 16
Thus, 16 students do chores
b) The relative frequency of the students that do chores and get an allowance to the number of students that do chores is simply the ratio of the value in the cell that represents an intersection of the first 'DO CHORES' row, and the first 'ALLOWANCE' column, to the value that represents the sum of all the students that do chores ( i.e, the value at the end of the first row).
Thus, this is equal to = 13/16
Therefore, 13/16 is the relative frequency of the students that do chores and get an allowance to the number of students that do chores
c) The relative frequency of the students that do not do chores nor get an allowance to the total number of students, is simply the ratio of the value in the cell that represents an intersection of the second 'DO NOT DO CHORES' row, and the second 'NO ALLOWANCE' column, to the sum of the values in the last row or the last column.
Thus, this is equal to = 4/( 18 + 7) OR 4/(16 + 9) both of which is still 4/25
Therefore, 4/25 is the relative frequency of the students that do not do chores nor get an allowance to the total number of students.
d) The students who do not do chores are a total of 9
Of this 9, the number of students that do receive their allowance fall under the 'ALLOWANCE' column, and is equal to 5.
Therefore, expressed as a percentage of those who do not do their chores, the students who do not get an allowance are = (5/9) * 100 = 55% ( to the nearest whole number)
Thus 55% of students who do not do chores do not get an allowance
Find the equation of the line with Slope = −3-3 and passing through (2,−13)(2,-13) . Write your equation in the form y=mx+by=mx+b .
Given that the slope of the line is:
[tex]m=-3[/tex]And knowing that the line passes through this point:
[tex]\mleft(2,-13\mright)[/tex]You need to remember that the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
In order to find the value of "b", you can substitute the slope and the coordinates of the point on the line, into the equation:
[tex]-13=(-3)(2)+b[/tex]Now you can solve for "b":
[tex]\begin{gathered} -13=-6+b \\ -13+6=b \\ b=-7 \end{gathered}[/tex]Knowing "m" and "b", you can write the following equation of the line in Slope-Intercept Form:
[tex]y=-3x-7[/tex]Hence, the answer is:
[tex]y=-3x-7[/tex]Joshua earned $646 for 40 hours. Find the unit rate.
To find the unit rate (amount per hour) you divide the given amount into the given number of hours:
[tex]\frac{646}{40h}=16.15/h[/tex]Then, the unit rate is $16.15/hour
Which expression can be used to find the difference of the polynomials?
[10m + (-7m)] is the formula that can be used to find the difference between the polynomials (10m - 6) and (7m - 4). + [(-6) + 4].
[10m + (-7m)] + [(-6) + 4]
With more calculation
= 10m - 7m - 6 + 4
so we do
= 3m - 2 …. (2)
As (1) and (2) are equivalent
The polynomial's differences can be calculated using the equation [10m + (-7m)] + [(-6) + 4].
In order to find the difference between the polynomials, one can utilize the formula [10m + (-7m)] + [(-6) + 4].
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Iman is playing a game. On one turn she earns 2 points and on the next turn she loses 5 points.
Graph her points on the number line.
Iman will be on - 3 on the number line after the game.
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
When laying a game, Iman earns 2 points on one turn and losses 5 points on the next turn.
Now, let's say Iman started from zero on the number line,
Then, on the first turn, she earns 2 points.
So, the number of points Iman has will be:
x = 0 + 2 = 2
After the next turn she losses 5 points.
x = 2 - 5 = - 3
Then Iman will be on - 3 on the number line.
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The graph of a function f is shown below.Find f(3). f(3)=
when x is 3, y is 1
look 3 units to the right, and then see where the line crosses
5 Jamila sells honey. She posts this sign for her customers.Then she makes a graph that shows the price of each size jar.Is Jamila's price the same per ounce for any size jar? Explain.HONE201612Price ($)4Х004 81216Jar Capacity (oz)
it is given that, the relation between the price of honey and jar capacity is in the given graph.
so, we have three points on the graph,
A(4,5), B(10,12.5) and C (15,19)
so, price of 4 oz = 5 $
price of 1 oz = 5/4 = 1.25 $
price of 10 oz = 12.5
price of 1 oz = 1.25 $
price of 15 oz is 19 $
price of 1 oz is 19/15 = 1.26 $
so, the approx price for 1 oz of honey is 1.25 that is approx same per ounce for any size of the jar.
thus, yes Jamila's price is the same per ounce for any size jar
convert 3.2 yards to feet
1 yard is equivalent to 3 feet. Then to convert 3.2 yards to feet we can use the next proportion,
[tex]\frac{1\text{ yard}}{3.2\text{ yard}}=\frac{3\text{ ft}}{x\text{ ft}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=3\cdot3.2 \\ x=9.6 \end{gathered}[/tex]3.2 yards is equivalent to 9.6 feet
f(x) = 4
this line is
vertical
O horizontal
O diagonal
O impossible to graph
f(x) = 4
this line is
O vertical
O horizontal
O diagonal
O impossible to graph
A cyclist rides his bike at a speed of 24miles per hour what is this speed in miles per minute how many miles will the cyclist travel in 5minutes ?
If the speed of the cyclist is 24 miles/hour
In miles per minutes, 60 minutes = 1 hour
To convert into miles per minutes,
[tex]\text{Speed in miles per mins=}\frac{24}{60}=0.4\text{ miles/min}[/tex]Speed in miles/min is 0.4 miles/min
If the cyclist travels for 5 minutes, distance travelled in miles will be,
[tex]\begin{gathered} dis\tan ce=\text{speed}\times\text{time} \\ \text{Where sp}eed=0.4\text{ miles/min} \\ \text{time}=5\min \\ \text{distance}=0.4\text{ miles/min}\times5\min =2\text{ miles} \end{gathered}[/tex]Distance travelled in miles is 2 miles
HELP!!!
In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.
54°
58°
122°
126°
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.
What is a triangle?
A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
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Find the perimeter.A rectangle measuring 4 1/3 mm by 4 1/2 mm
Answer:
[tex]17\text{ }\frac{2}{3}\text{ mm}[/tex]Explanation:
Here, we want to find the perimeter of the rectangle
Mathematically, the formula for the perimeter of a rectangle is:
[tex]P\text{ = 2\lparen L + B\rparen}[/tex]Substituting the values, we have it that:
[tex]\begin{gathered} P\text{ = 2\lparen4}\frac{1}{3}\text{ + 4}\frac{1}{2}) \\ \\ P\text{ = 2\lparen}\frac{13}{3}+\text{ }\frac{9}{2}) \\ \\ P\text{ = 2\lparen}\frac{26\text{ + 27}}{6}) \\ \\ P\text{ = }\frac{53}{3}\text{ = 17 }\frac{2}{3}\text{ mm} \end{gathered}[/tex]Write an expression that is the product of two factors and is equivalent to - 3x - 15.Which expression is the product of two factors and is equivalent to - 3x - 15?A. - 3x-2-13B.-3(x - 5)C. (7x-2)-(10x - 13)D. -3(x+5)
Amon the choices given, letter D is equivalent to - 3x - 15.
-3 ( x + 5 )
if we distribute -3 , we will have
-3 (x ) = -3x , and
-3 ( +5) = -15
-3 ( x + 5) = -3x - 15
Answer: D. -3 (X + 5)
Hey, I’m really having trouble with this question and could use some help.
From the given graph, we have 2 points with coordinates:
[tex]\begin{gathered} (x_1,y_1)=(1,2) \\ \text{and} \\ (x_2,y_2)=(4,1) \end{gathered}[/tex]The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]With the given points, we can find the slope m as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{then} \\ m=\frac{1-2}{4-1} \end{gathered}[/tex]which gives
[tex]m=\frac{-1}{3}=-\frac{1}{3}[/tex]Then, our line equation has the form
[tex]y=-\frac{1}{3}x+b[/tex]Now, we can find the y-intercept b by substituting one of the two given points. For instance, if we substitute point (1,2) into the last result, we get
[tex]2=-\frac{1}{3}(1)+b[/tex]which gives
[tex]\begin{gathered} 2=-\frac{1}{3}+b \\ \text{then} \\ 2+\frac{1}{3}=b \\ \frac{7}{3}=b \end{gathered}[/tex]then, the line equations is
[tex]y=-\frac{1}{3}x+\frac{7}{3}[/tex]a) The linear function is
[tex]f(x)=-\frac{1}{3}x+\frac{7}{3}[/tex]b) What is f(6)?
In this case, we have that x=6. Then, by replacing this value into our function, we get
[tex]f(6)=-\frac{1}{3}(6)+\frac{7}{3}[/tex]which gives
[tex]\begin{gathered} f(6)=-\frac{6}{3}+\frac{7}{3} \\ f(6)=\frac{-6+7}{3} \\ f(6)=\frac{1}{3} \end{gathered}[/tex]therefore, the answer for part b is
[tex]\frac{1}{3}[/tex]what is8.546 rounded to nearest tenth
If we round to the nearest tenth, it would be 8.5 because the hundredth digit is less than 5.
Hence, the answer is 8.5.VAn item costs $310 before tax, and the sales tax is $6.20.Find the sales tax rate. Write your answer as a percentage.0%X5?
Given:
The cost of the item is
[tex]\text{ \$}310.[/tex]The sales tax is
[tex]\text{ \$}6.20[/tex]Required:
We have to find the Sale tax rate and write the answer in percentage.
Explanation:
The formula for the sales tax rate is
[tex](\frac{\text{ sales tax}}{\text{ cost}}\times100)\%.[/tex]Therefore, The required sales tax rate is
[tex](\frac{6.20}{310}\times100)\%=(\frac{620}{310})\%=2\%.[/tex]Final answer:
Hence the final answer is
[tex]2\%.[/tex]community gym charges a $50 membership fee and a $60 monthly fee. Workout gym charges a $225 fee and a $5 monthly fee. After how many months will the total amount paid to both gyms be the same?
Step 1 : Let's review the information given to us to answer the problem correctly:
Community Gym = $50 (Membership fee) + $ 60 (Monthly fee)
Workout Gym = $ 225 (Membership fee) + $ 5 (Monthly fee)
Step 2: Let's write the equation to answer the question, as follows:
Let x to represent the number of months that the total amount paid to both gyms will be the same
Community Gym = Workout Gym
Therefore,
50 + 60x = 225 + 5x
Like terms:
60x - 5x = 225 - 50
55x = 175
Dividing by 55 at both sides:
55x/55 = 175/55
x = 3.18 months
0.18 * 30 = 5.4 days
Step 3: Interpretation of the answer
Approximately after 3 months and 5 days and a half the total amount paid to both gyms will be the same
Given g(k) = 2k² - 4, find g(-5).
Answer:
g(-5)=46
Step-by-step explanation:
given that function is,
g(k) = 2k² - 4,
and we find the value of g(-5)
so,
g(-5)=2(5)^2-4
simpley put -5 in place of k
g(-5)=2×25-4
g(-5)=46
Answer:
g(-5) = 46
Step-by-step explanation:
Given function:
[tex]g(k)=2k^2-4[/tex]
To find g(-5), substitute k = -5 into the given function:
[tex]\begin{aligned}\implies g(-5)&=2(-5)^2-4\\&=2(25)-4\\&=50-4\\&=46\end{aligned}[/tex]
Martin orders a pasta dish that is priced at $11.99. He also orders a drink. The total cost for the pasta and drink is $14.48. What is the cost of the drink?
Explanation
Let the cost of the drink be x.
Therefore;
[tex]\begin{gathered} cost\text{ of dish+cost of drinks =total cost} \\ 11.99+x=14.48 \\ x=14.48-11.99 \\ x=2.49 \end{gathered}[/tex]Answer: 2.49 dollars
If $360 is invested at an interest rate of 4% per year and is compounded quarterly, how much will the investment be worth in 18 years?Use the compound interest formula A = P(1 + r over n)nt.
Answer:
The formula for compound interest is given below as
[tex]\begin{gathered} A=P\left(1+\frac{r}{n}\right?^{nt} \\ P=money\text{ invested=\$360} \\ r=rate=4\% \\ n=number\text{ of times compounded=4} \\ t=time=18years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=P\left(1+\frac{r}{n}\right?^{nt} \\ A=360\left(1+\frac{4}{400}\right?^{4\times18} \\ A=360\left(1.01\right)^{72} \\ A=360\times2.0471 \\ A=736.96 \end{gathered}[/tex]Hence,
The total amount accrued, principal plus interest, with compound interest on a principal of $360.00 at a rate of 4% per year compounded 4 times per year over 18 years is $736.96.
Factor completely 12m^2-3
Answer:
3 ( 2m-1)(2m+1)
Step-by-step explanation:
12m^2-3
Factor out the 3
3( 4m^2 -1)
3 ( ( 2m)^2 - 1^2)
Using the difference of squares ( a^2 - b^2) = ( a-b) (a+b)
3 ( 2m-1)(2m+1)