The distance on the map is 14 cm
Explanation:Parameters:
Map scale: 5 cm = 2 km
Given actual distance = 5.6km
Let x be the distance on map, then
x = 5.6 km
2x = 5 * 5.6
2x = 28
x = 28/2
= 14 cm
What is the solution to the equation below? 3x = x + 10 O A. x = 10 B. x = 0 C. X = 5 D. No Solutions
Hence, the correct option is C: x=5
What value of x would make lines land m parallel?5050°t55°75xº55m105
If l and m are parallel, then ∠1 must measure 55°.
The addition of the angles of a triangle is equal to 180°, in consequence,
Help on question on math precalculus Question states-Which interval(s) is the function decreasing?Group of answer choicesBetween 1.5 and 4.5Between -3 and -1.5Between 7 and 9Between -1.5 and 4.5
We have a function of which we only know the graph.
We have to find in which intervals the function is decreasing.
We know that a function is decreasing in some interval when, for any xb > xa in the interval, we have f(xa) < f(xb).
This means that when x increases, f(x) decreases.
We can see this intervals in the graph as:
We assume each division represents one unit of x. Between divisions, we can only approximate the values.
Then, we identify all the segments in the graph where f(x) has a negative slope, meaning it is decreasing.
We have the segments: [-3, -1.5), (1,5, 4.5) and (7,9].
Answer:
The right options are:
Between 1.5 and 4.5
Between -3 and -1.5
Between 7 and 9
Graph each equation rewrite in slope intercept form first if necessary -8+6x=4y
slope intercept form of the required graph:
-8 + 6x = 4y
y = 3/2x - 2
0.350 km as meters and please show work
Step 1
Given
[tex]0.350\operatorname{km}[/tex]Required; To convert it to meter
Step 2
1 kilometer is equivalent to 1000 meters
Therefore using ratio we will have
[tex]\frac{1\operatorname{km}}{0.350\operatorname{km}}=\frac{1000m}{xm}[/tex]Step 3
Get the conversion to meter
[tex]\begin{gathered} 1\operatorname{km}\text{ }\times\text{ xm = 0.350km }\times\text{ 1000m} \\ \frac{xm\times1\operatorname{km}}{1\operatorname{km}}\text{ = }\frac{\text{ 0.350km }\times\text{ 1000m}}{1\operatorname{km}} \\ xm\text{ = 350 m} \end{gathered}[/tex]Hence, 0.350km as meters = 350m
I need help to:Determine what the 3 sets of numbers have in common.1. 2/5 and 8/202. 12/28 and 21/493. 10/18 and 15/27
Notice that:
(1)
[tex]\frac{8}{20}=\frac{2\cdot4}{5\cdot4}=\frac{2}{5}\text{.}[/tex]Therefore:
[tex]\frac{8}{20}=\frac{2}{5}\text{.}[/tex](2)
[tex]\begin{gathered} \frac{12}{28}=\frac{3\cdot4}{7\cdot4}=\frac{3}{7}, \\ \frac{21}{49}=\frac{3\cdot7}{7\cdot7}=\frac{3}{7}\text{.} \end{gathered}[/tex]Therefore:
[tex]\frac{12}{28}=\frac{21}{49}\text{.}[/tex](3)
[tex]\begin{gathered} \frac{10}{18}=\frac{5\cdot2}{9\cdot2}=\frac{5}{9}, \\ \frac{15}{27}=\frac{5\cdot3}{9\cdot3}=\frac{5}{9}\text{.} \end{gathered}[/tex]Therefore:
[tex]\frac{10}{18}=\frac{15}{27}\text{.}[/tex]Answer: The 3 sets have in common that in each case both fractions represent the same number.
6. An odometer shows that a car has traveled 56,000 miles by January 1, 2020. The car travels 14,000 miles each year. Write an equation that represents the number y of miles on the car's odometer x years after 2020.
Answer:
y=14000x
Step-by-step explanation:
x represents years after 2020 and y is the number of miles
The required equation for the distance travelled versus number of years after 2020 is given as y = 14000x + 56000.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given problem can be solved as follows,
Suppose the year 2020 represents x = 0.
The distance travelled per year can be taken as the slope of the linear equation.
This implies that slope = 14000.
And, the distance travelled by January 1, 2020 is 56000.
It implies that for x = 0, y = 56000.
The slope-point form of a linear equation is given as y = mx + c.
Substitute the corresponding values in the above equation to obtain,
y = 14000x + c
At x = 0, y = 56000
=> 56000 = 14000 × 0 + c
=> c = 56000
Now, the equation can be written as,
y = 14000x + 56000
Hence, the required equation for number of miles and years for the car is given as y = 14000x + 56000.
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The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a random sample of 35 football players is taken, what is the probability that that the random sample will have a mean more than 210 pounds?
We know that
• The mean is 200 pounds.
,• The standard deviation is 25 pounds.
,• The random sample is 35.
First, let's find the Z value using the following formula
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Let's replace the mean, the standard deviation, and x = 210.
[tex]Z=\frac{210-200}{25}=\frac{10}{25}=0.4[/tex]Then, using a p-value table associated with z-scores, we find the probability
[tex]P(x>210)=P(Z>0.4)=0.1554[/tex]Therefore, the probability is 0.1554.The table used is shown below
(Score for Question 3: of 6 points)3. Felipe is ordering new carpet for his bedroom floor. (The floor is represented in the picture below asrectangle JKLM). He knows the base edge, ML, measures 18 ft. And the distance of diagonal KMmeasures 25 ft. What is the area of Felipe's bedroom floor? Show all work and round your answer tothe nearest tenth.JKM
Solution:
Given:
[tex]\begin{gathered} The\text{ length of the room floor is 18 ft} \\ The\text{ width of the room floor is }x \end{gathered}[/tex]
Considering the right triangle KLM,
To get the width (x), we use the Pythagoras theorem.
[tex]\begin{gathered} 18^2+x^2=25^2 \\ x^2=25^2-18^2 \\ x^2=625-324 \\ x^2=301 \\ x=\sqrt{301} \\ x=17.35ft \\ \\ Hence,\text{ the width is 17.35ft} \end{gathered}[/tex]
The area of the bedroom floor is;
[tex]\begin{gathered} A=l\times w \\ A=18\times17.35 \\ A=312.3ft^2 \end{gathered}[/tex]
Therefore, the area of Felipe's bedroom floor to the nearest tenth is 312.3 square feet.
-3.9-3.99-3.999-4-4.001-4.01-4.10.420.4020.4002-41.5039991.53991.89try valueclear tableDNEundefinedlim f(2)=lim f(2)=2-)-4+lim f (30)f(-4)-4
In order to determine the limit of f(x) when x tends to -4 from the right (4^+), we need to look in the table the value that f(x) is approaching when x goes from -3.9 to -3.99 to -3.999.
From the table we can see that this value is 0.4.
Then, to determine the limit of f(x) when x tends to -4 from the left (4^-), we need to look in the table the value that f(x) is approaching when x goes from -4.1 to -4.01 to -4.001.
From the table we can see that this value is 1.5.
Since the limit from the left is different from the limit from the right, the limit when x tends to -4 is undefined.
Finally, the value of f(-4) is the value of f(x) when x = -4. From the table, we can see that this value is -4.
the item to the trashcan. Click the trashcan to clear all your answers.
Factor completely, then place the factors in The proper location on the grid.3y2 +7y+4
We are asked to factor in the following expression:
[tex]3y^2+7y+4[/tex]To do that we will multiply by 3/3:
[tex]3y^2+7y+4=\frac{3(3y^2+7y+4)}{3}[/tex]Now, we use the distributive property on the numerator:
[tex]\frac{3(3y^2+7y+4)}{3}=\frac{9y^2+7(3y)+12}{3}[/tex]Now we factor in the numerator on the right side in the following form:
[tex]\frac{9y^2+7(3y)+12}{3}=\frac{(3y+\cdot)(3y+\cdot)}{3}[/tex]Now, in the spaces, we need to find 2 numbers whose product is 12 and their algebraic sum is 7. Those numbers are 4 and 3, since:
[tex]\begin{gathered} 4\times3=12 \\ 4+3=7 \end{gathered}[/tex]Substituting the numbers we get:
[tex]\frac{(3y+4)(3y+3)}{3}[/tex]Now we take 3 as a common factor on the parenthesis on the right:
[tex]\frac{(3y+4)(3y+3)}{3}=\frac{(3y+4)3(y+1)}{3}[/tex]Now we cancel out the 3:
[tex]\frac{(3y+4)3(y+1)}{3}=(3y+4)(y+1)[/tex]Therefore, the factored form of the expression is (3y + 4)(y + 1).
When broken open Austins jawbreaker will make a hemisphere, what is it surface area if the diameter is 16.4 inches?
When broken open Austen's jawbreaker will make a hemisphere.
Recall that the total surface area of a hemisphere is given by
[tex]TSA=3\pi r^2[/tex]Where r is the radius of the hemisphere.
We are given the diameter of the hemisphere that is 16.4 inches.
The radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{16.4}{2}=8.2\: in[/tex]So, the radius is 8.2 inches
Substitute the radius into the above formula of total surface area
[tex]TSA=3\pi r^2=3\pi(8.2)^2=3\pi(67.24)=633.72\: in^2[/tex]Therefore, the total surface area of the hemisphere is 633.72 square inches.
Please note that if you want to find out only the curved surface area then use the following formula
[tex]CSA=2\pi r^2=2\pi(8.2)^2=453.96\: in^2[/tex]For the given case, the curved surface area is 453.96 square inches.
2. The length of Sally's garden is 4 meters greater than 3 times the width. Theperimeter of her garden is 72 meters. Find the dimensions of Sally's garden.The garden has a width of 8 and a length of 28.
L = length
W = width
L = 4 + 3*W
The perimeter of a rectangle is the sum of its sides: 2L + 2W. Since it's 72, we have:
2L + 2W = 72
Now, to solve for L and W, the dimensions of the garden, we can use the first equation (L = 4 + 3*W) into the second one (2L + 2W = 72):
2L + 2W = 72
2 * (4 + 3*W) + 2W = 72
2 * 4 + 2 * 3W + 2W = 72
8 + 6W + 2W = 72
8W = 72 - 8
8W = 64
W = 64/8 = 8
Then we can use this result to find L:
L = 4 + 3W = 4 + 3 * 8 = 4 + 24 = 28
Therefore, the garden has a width of 8 and a length of 28.
If 6 times a certain number is added to 8, the result is 32.Which of the following equations could be used to solve the problem?O6(x+8)=326 x=8+326 x+8 = 326 x= 32
Answer: 6x + 8 = 32
Explanation:
Let x represent the number
6 times the number = 6 * x = 6x
If we add 6x to 8, it becomes
6x + 8
Given that the result is 32, the equation could be used to solve the problem is
6x + 8 = 32
19.657 < 19.67 is this true or false
The given expression is
[tex]19.657<19.67[/tex]Notice that the hundredth 7 is greater than 5, this means 19.67 is greater than 19.657.
Therefore, the given expression is false.For each system through the best description of a solution if applicable give the solution
System A
[tex]\begin{gathered} -x+5y-5=0 \\ x-5y=5 \end{gathered}[/tex]solve the second equation for x
[tex]x=5+5y[/tex]replace in the first equation
[tex]\begin{gathered} -(5+5y)+5y-5=0 \\ -5-5y+5y-5=0 \\ -10=0;\text{FALSE} \end{gathered}[/tex]The system has no solution.
System B
[tex]\begin{gathered} -X+2Y=8 \\ X-2Y=-8 \end{gathered}[/tex]solve the second equation for x
[tex]x=-8+2y[/tex]replace in the first equation
[tex]\begin{gathered} -(-8+2y)+2y=8 \\ 8-2y+2y=8 \\ 8=8 \end{gathered}[/tex]The system has infinitely many solutions, they must satisfy the following equation:
[tex]\begin{gathered} -x+2y=8 \\ 2y=8+x \\ y=\frac{8}{2}+\frac{x}{2} \\ y=\frac{x}{2}+4 \end{gathered}[/tex]Emma went to bed at 7:28 p.m. and got up at 6:08 a.m. How many hours and minutes did she sleep?
We will have the following:
First, calcuate the difference in hours:
From 7pm to 6am there are 11 hours.
Then we add the number of minutes, those would be 40 minutes.
So, she slept 11 hours and 40 minutes.
Solve the equation algebraically. x2 +6x+9=25
We must solve for x the following equation:
[tex]x^2+6x+9=25.[/tex]1) We pass the +25 on the right to left as -25:
[tex]\begin{gathered} x^2+6x+9-25=0, \\ x^2+6x-16=0. \end{gathered}[/tex]2) Now, we can rewrite the equation in the following form:
[tex]x\cdot x+8\cdot x-2\cdot x-2\cdot8=0.[/tex]3) Factoring the last expression, we have:
[tex]x\cdot(x+8)-2\cdot(x+8)=0.[/tex]Factoring the (x+8) in each term:
[tex](x-2)\cdot(x+8)=0.[/tex]4) By replacing x = 2 or x = -8 in the last expression, we see that the equation is satisfied. So the solutions of the equation are:
[tex]\begin{gathered} x=2, \\ x=-8. \end{gathered}[/tex]Answer
The solutions are:
• x = 2
,• x = -8
question 15:A new webpage received 5,000 page views on the first day. The number of page views decreased by 10% every day. How many total page views did the webpage have after seven days? Round to the nearest whole number.
Explanation
This question wants us to compute the depreciation formula and also get the value of the total page views did the webpage have after seven days.
The general formula is given by
[tex]A=P(1-\frac{r}{100})^n[/tex]In our case
[tex]\begin{gathered} A=? \\ P=5000 \\ r=10 \\ n=n \end{gathered}[/tex]Thus, we will have
[tex]A=5000(1-\frac{10}{100})^n[/tex]We will now have to write the first three terms of the expression to get the required equation
[tex]\begin{gathered} when\text{ n=1} \\ A_1=5000(0.9)^1=4500 \end{gathered}[/tex][tex]\begin{gathered} when\text{ n=2} \\ A_2=5000(0.9)^2=4050 \end{gathered}[/tex]Now, we can list the first three terms as
[tex]5000,4500,4050[/tex]With the above, we can now compute the total web pages after 7 days using the sum of the geometric sequence:
We will get the common ratio
[tex]ratio=r=\frac{4500}{5000}=0.9[/tex][tex]\begin{gathered} S=\frac{a(1-r^n)}{1-r} \\ \\ a=5000 \\ r=0.9 \\ n=7 \end{gathered}[/tex][tex]S=\frac{5000(1-0.9^7)}{1-0.9}=26085[/tex]
Thus, we can see that the answer is option C
[tex]\frac{5000(1-0.9^7)}{1-0.9}=26,085[/tex]13.Find the missing side. Round to the nearest tenth.25912XA.5.6B. 7.1С8.1D. 25.7
We were provided with a right-angled triangle. For a right-angled triangle, we can use the trigonometric ratios to solve for unknown sides or angles.
First, let's label the triangle to determine the trigonometric ratios to use:
From the diagram above, we are given:
adjacent = 12
angle = 25 degrees
x = oppossite
We are going to use the tangent ratio, which is:
[tex]\tan \text{ }\phi\text{ = }\frac{opposite}{adjacent}[/tex]When, we substitute the given data, we have:
[tex]\begin{gathered} \tan 25^0\text{ = }\frac{x}{12} \\ x=tan25^0\text{ }\times\text{ 12} \\ =\text{ 5.6 (nearest tenth)} \end{gathered}[/tex]Answer: x = 5.6 (option A)
The graph below shows the relationship between the amount of time a ferris wheel has been moving and the height above ground of a seat on the ferris wheel. based on the graph. Which statement best describes why height is a function of time in the relationship?
ANSWER
b. Each value of time has exactly 1 value for height associated with it.
EXPLANATION
A function is a relationship where each value of the function has only one value of the variable associated with that value. In this problem, the function is height and the variable is time, therefore the answer is option b.
mr Smith is flying his single engine plane at an altitude of 2400 feet. he sees a cornfield at an angle of depression of 30 degrees. what is his horizontal distance to the corn field?
Let the horizontal distance be represented with x
By Trigonometric Ratio,
[tex]\begin{gathered} \tan 30=\frac{2400}{x} \\ \text{cross multiply, we get,} \\ x=\text{ }\frac{2400}{\tan30}=\text{ 4156.922}\approx\text{ 4156.9 fe}et \end{gathered}[/tex]Study 8 22,29,36 Which expression could be used to find the missing number in the pattern? A. (8 +36) - 2 C. (29-22) + 8 B. (8 x 22) - 2 D. (22 - 7) + 8
8,22,29,36
between 22 - 8 = 14
divide by 2 ,14/2= 7
now add 8+7 = 15
Then anwer is
Option C) (29-22) + 8 = 7 + 8
If m 2 DFC = 40° and m= 55°, then mCDBG2580135
Here we are given a geometrical shape with the following inner and an arc angle as follows:
[tex]The property to note here is from geometric properties of a circle.Property: The inner angle is always the mean of corresponding verticaly opposite arc angles.
We can express the above property in lieu to the geometry question at hand. We see that the two arc angles:
[tex]\text{Arc CD = 55 degrees , Arc BG = ?}[/tex]Ther inner vertically opposite angle are:
[tex]<\text{ DFC < }BFG\text{= 40 degrees }[/tex]The property can be expressed mathematically as follows:
[tex]<\text{ DFC = }\frac{1}{2}\cdot\text{ ( Arc CD + Arc BG )}[/tex]Next plug in the respective values of angles and evaluate for the arc angle BG as follows:
[tex]\begin{gathered} 40\text{ = }\frac{1}{2}\cdot\text{ ( 55 + Arc BG )} \\ 80\text{ = 55 + Arc BG } \\ \text{\textcolor{#FF7968}{Arc BG = 25 degrees}} \end{gathered}[/tex]Therefore the correct option is:
[tex]\textcolor{#FF7968}{25}\text{\textcolor{#FF7968}{ degrees}}[/tex]Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?
Given the rates:
[tex]\begin{gathered} \frac{1}{t}=Sarah^{\prime}s\text{ }Rate \\ \\ \frac{1}{t+3}=Heidi^{\prime}s\text{ }Rate \\ \\ \frac{1}{2}=Rate\text{ }working\text{ }together \end{gathered}[/tex]Add their rates of cleaning to get rate working together:
[tex]\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}[/tex]Solving for t:
[tex]\begin{gathered} \frac{2(t+3)+2t-t(t+3)}{2t(t+3)}=0 \\ \\ \frac{2t+6+2t-t^2-3t}{2t(t+3)}=0 \\ \\ \frac{t+6-t^2}{2t(t+3)}=0 \\ \\ -t^2+t+6=0 \\ \\ (t+2)(t-3)=0 \end{gathered}[/tex]Hence:
t = -2
t = 3
Time can't be negative; then:
Heidi's time: t + 3
3 + 3 = 9
ANSWER
It will take Heidi 9 hrs to clean garage working alone
2) The ratio of trucks to cars on the freeway is 5 to 8. If thereare 440 cars on the freeway, how many trucks are there?
If the ratio of trucks to trucks is 5 to 8,
then we can use proportions to solve for the number of truck (unknown "x"):
5 / 8 = x / 440
we solve for x by multiplying: by 440 both sides
x = 440 * 5 / 8
x = 275
There are 275 trucks on the freeway.
Find the values of the variables so that the figure is aparallelogram.
Given the following question:
[tex]\begin{gathered} \text{ The property of a }parallelogram \\ A\text{ + B = 180} \\ B\text{ + C = 180} \\ 64\text{ + }116\text{ = 180} \\ 116+64=180 \\ y=116 \\ x=64 \end{gathered}[/tex]y = 116
x = 64
Evaluate. 3/4 - 1/2 × 7/8 Write your answer in simplest form.
we have the expression
3/4 - 1/2 × 7/8
so
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
First Multiplication
so
[tex]\frac{1}{2}\cdot\frac{7}{8}=\frac{7}{16}[/tex]substitute
[tex]\frac{3}{4}-\frac{7}{16}[/tex]Remember that
3/4 is equivalent to 12/16 (multiply by 4 both numerator and denominator)
substitute
[tex]\frac{12}{16}-\frac{7}{16}=\frac{5}{16}[/tex]therefore
the answer is 5/16Solve the inequality. Graph the solution.Z/4 is less than or equal to 12.
You have the following inequality:
z/4 ≤ 12
To solve the previous inequality you proceed as follow:
z/4 ≤ 12 multiply both sides by 4
z ≤ 48
Hence, the solution is z ≤ 48
when you want to graph a solution of the form "z lower or equal than", you draw a black point, that means the solution are all number lower than 48, including 48.
Last weekend, 26, 675 tickets were sold at County Stadium. This weekend 24,567 tickets were sold at County Stadium. If you estimate the number of tickets County Stadium sold over the two weekends by rounding each number to the nearest thousand, then you will find there were about ____ tickets sold.
We have the tickets sold each weekend:
• Last weekend: 26,675
,• This weekend: 24,567
We have to find how many tickets where sold in both weekends by rounding each number to the nearest thousand units. This will let us do the math without a calculator.
Then, we can approximate 26,675 to 27,000 and 24,567 to 25,000.
NOTE: we round the numbers up because the next number is 5 or greater. Then 675 is and 567 are approximated as 1,000.
We then can add them as: 27,000+25,000 = 52,000.
Answer: the solution is about 52,000 tickets sold.
NOTE: the exact solution would have been 51,242