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A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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Related Questions
Evaluate 4w - 3y if w = 7 and y = 6
Answers
Answer:
10
Explanation:
Given the expression:
[tex]4w-3y[/tex]If w=7 and y=6
[tex]\begin{gathered} 4w-3y=4(7)-3(6) \\ =28-18 \\ =10 \end{gathered}[/tex]The value of the expression is 10.
Write the equation below in standard form and then answer the following questions. If a value is a non-integer type your answer as a decimal rounded to the hundredths place. 4x^2+24x+25y^2+200y+336=0The center of the ellipse is (h,k). h= Answer and k= AnswerThe value for a is Answer . The value for b is Answer .The foci with the positive x value is the point ( Answer, Answer)The foci with the negative x value is the point ( Answer, Answer)
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Given:
[tex]4x^2+24x+25y^2+200y+336=0[/tex]Aim:
We need to convert the given equation into the standard form of the ellipse equation.
Explanation:
Consider the standard form of the ellipse equation.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Consider the given equation.
[tex]4x^2+24x+25y^2+200y+336=0[/tex][tex]Use\text{ }336=36+400-100.[/tex][tex]4x^2+24x+25y^2+200y+36+400-100=0[/tex][tex]4x^2+24x+36+25y^2+200y+400-100=0[/tex]Take out the common terms.
[tex]4(x^2+6x+9)+25(y^2+8y+16)-100=0[/tex]Add 100 on both sides of the equation.
[tex]4(x^2+6x+9)+25(y^2+8y+16)-100+100=0+100[/tex][tex]4(x^2+6x+9)+25(y^2+8y+16)=100[/tex][tex]4(x^2+2\times3x+3^2)+25(y^2+2\times4y+4^2)=100[/tex][tex]\text{Use (a+b)}^2=a^2+2ab+b^2.[/tex][tex]4(x+3)^2+25(y+4)^2=100[/tex]Divide both sides by 100.
[tex]\frac{4\mleft(x+3\mright)^2}{100}+\frac{25\mleft(y+4\mright)^2}{100}=\frac{100}{100}[/tex][tex]\frac{\mleft(x+3\mright)^2}{25}+\frac{\mleft(y+4\mright)^2}{4}=1[/tex][tex]\frac{\mleft(x+3\mright)^2}{5^2}+\frac{\mleft(y+4\mright)^2}{2^2}=1[/tex][tex]\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1[/tex]The standard form of the given equation is
[tex]\frac{\mleft(x-(-3)\mright)^2}{5^2}+\frac{\mleft(y-(-4)\mright)^2}{2^2}=1[/tex]Compare with the general form of the ellipse equation.
We get h=-3, k=-4, a=5 and b=2.
The centre of the ellipse is h= -3 and k = -4.
The value of a is 5.
The value of b is 2.
We need to find the eccentricity of the ellipse.
[tex]e=\sqrt[]{1-\frac{b^2}{a^2}}[/tex]Substitute b=2 and a =5 in the formula.
[tex]e=\sqrt[]{1-\frac{2^2}{5^2}}=\sqrt[]{1-\frac{4}{25}}=\sqrt[]{\frac{25-4}{25}}=\sqrt[]{\frac{21}{25}}=0.9165[/tex][tex]e=0.9165[/tex]The foci of the ellipse are
[tex]((h\pm a)e,0)[/tex]Substitute h =-3, a=5 and e =0.9165 in the formula.
[tex]((-3\pm5)0.9165,0)[/tex]The foci with a positive x value are the point
[tex]((-3+5)0.9165,0)\text{ =}(1.83,0)[/tex]
[tex](1.83,0)[/tex]
The foci with a negative x value are the point
[tex]((-3-5)0.9165,0)\text{ =}(-7.33,0)[/tex][tex](-7.33,0)[/tex]Please help me asap with both I’ll mark you brainly
Answers
1. The scholar made a mistake in the last step
where he said x=3.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS
[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]
Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n
[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]
FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.
I HOPE THIS HELPS.
An inspector found 18 defective radios during an inspection. If this is 0.024% of the total number of radios inspected, how many radios were inspected?
Answers
Total number of defected radios is 18
Let the total number of defective radios be taken as y
If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y
[tex]\frac{0.024}{100}y=18[/tex]Solve for y, by cross multiplying
[tex]\begin{gathered} \frac{0.024}{100}y=18 \\ 0.024y=18\times100 \\ \text{Divide both sides by 0.024} \\ \frac{0.024y}{0.024}=\frac{1800}{0.024} \\ y=75000 \end{gathered}[/tex]Hence, the number of radios inspected, y, is 75000
Shandar rents a pickup truck for her house move. She has to pay $96 for the first day, $88 for each additional day she keeps the truck, and 45 cents for each mile she drives. She will also be able to use a $25 coupon. Write an expression that represents the total cost when Shandar keeps the truck for h days and travels a total of p miles.Simplify the expression completely.List the terms in your expression.For each term, identify the coefficient and variable.
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96 first day
88 for each additional day (h)
0.45 for each mile driven (p)
$25 coupon
Expression
Total cost = 96 + 88h + 0.45p - 25
Simplify:
Combine like terms:
TC = 96 - 25 + 88h + 0.45p
TC = 71 + 88h + 0.45p
Terms:
71 = constant
88h = coefficient 88 , variable h
0.45p= coeficcient 0.45 , variable p
Please help me solve this using six grade math (easy formulas)
Answers
We will break the surface area of the tent up into its sides, the front and the back and the bottom.
Area of the sides: 2(5*7) = 70
Area of the front and the back: 2( 1/2 (6*4)) = 24
Area of the bottom: 7*6 = 42
Least amount of fabric required = 136ft
Fifty people in a room are wearing clothes either in red orwhite or a combination of the two colors. Thirty are wearingonly red and 16 are wearing a combination of both red andwhite. How many are wearing clothes that have white in them?
Answers
SOLUTION
We will solve the question using a Venn diagram
Let R represents people wearing clothes that have red
Let W represents people wearing clothes that have white
We have the Venn diagram as follow
So from the Venn diagram small letter w represent those wearing clothes that have only white. So we have that
[tex]\begin{gathered} 30+16+w=50 \\ 46+w=50 \\ w=50-46 \\ w=4 \end{gathered}[/tex]So those for "only" white is 4.
But those wearing clothes that have white in them will be only white plus those wearing combination of red and white. We have
[tex]16+4=20[/tex]Hence the answer is 20
Find the equation of the linear function represented by the table below inslope-intercept form.xy1-3 -723-114-15
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To find the linear equation, we use two points from the table (1, -3) and (3, -11). First, we have to find the slope with the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=-3 \\ y_2=-11 \end{gathered}[/tex]Let's those coordinates to find the slope.
[tex]\begin{gathered} m=\frac{-11-(-3)_{}}{3-1}=\frac{-11+3}{2}=\frac{-8}{2}=-4\to m=-4 \\ \end{gathered}[/tex]The slope is -4.
Now, we use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-1) \\ y+3=-4x+4 \end{gathered}[/tex]Now, we solve for y to express it in slope-intercept form.
[tex]\begin{gathered} y+3=-4x+4 \\ y=-4x+4-3 \\ y=-4x+1 \end{gathered}[/tex]Therefore, the equation in slope-intercept form is y = -4x+1.Riley read 1 book in 2 months. If she reads at a constant rate, how many books did she read in one month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
To find out the unit rate
Divide the total books by the total months
so
1/2=0.5 books per month
the answer is 0.5 books per monthIn the double number line
we have
books 0 0.5 1
months 0 1 2
A firm incurs $70,000 in interest expenses each year. If the tax rate of the firm is 30%, what is the effective after-tax interest rate expense for the firm?
Answers
Answer:
After tax interest expenses = Interest expenses x (100 - Tax Rate)
= 70000 x (100 - 30)%
= 70000 x 70%
= $49,000.00
Step-by-step explanation:
How much did he invest in Fund B, if both guns together returned a 8% profit.
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Taylor has $430 in her savings account. The annual simple interest at the bank is 2%. How much intreast will she earn on her savings in 9 months?
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we have the following equation
[tex]m(t)=430+430\cdot0.02\cdot t[/tex]where t is the time in years, as we have 9 months, we have to change to years
[tex]t=\frac{9}{12}=\frac{3}{4}=0.75[/tex]so after 9 months we get
[tex]430+430\cdot0.02\cdot0.75=430+6.45[/tex]So she will earn $6.45 in 9 month
Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The sum of a number and -41 is equal to the quotient of the number and 11. Step 2 of 3: Translate "the quotient of the number and 11". Answer
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An algebraic expression which represents the translation of "The sum of a number and -41 is equal to the quotient of the number and 11" is z - 1 = z/11.
How to translate an English phrase into an algebraic expression?In order to translate a word problem into an algebraic expression, we would have to assign a variable to the unknown number:
Let z represent the unknown number.
The sum of a number and -41 is given by:
z + (-1) = z - 1 ....equation 1.
The quotient of the number and 11 is given by:
z/11 .....equation 2.
Next, we would equate equation 1 and equation 2 as follows:
Translation; z - 1 = z/11
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What is the center of the circle simplify any fractions
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Answer:
[tex](x,y)\rightarrow(0,4)[/tex]Explanation: We have to find the center of the circle, the equation of the circle is as follows:
[tex]x^2+y^2-8y-48=0\rightarrow(0)[/tex]Ploting the equation (0) gives the following result:
Therefore the center of the circle has the coordinates (0,4).
If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.
Answers
Effective Rate in Compound Interest
Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:
[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.
Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):
[tex]R=(1+\frac{0.048}{2})^2-1[/tex]Calculating:
[tex]R=(1.024)^2-1=0.048576[/tex]The effective rate is 4.86%
Mrs. Brown is putting different colored sand into cups for her 4 daughters to make sand art bottles. The total amount of each color she has is shown in the table. Sand Color Weight (lb) Blue 1516 Pink 34 Purple 12 Turquoise 78 If each color is divided equally among the daughters, how much more pink sand will be available for each girl than purple sand? Write in simplest fraction form
Answers
Answer:
11/2 lb
Step-by-step explanation:
If 34 lb of pink sand and 12 lb of purple sand are equally divided among 4 daughters, you want to know how much more pink sand each girl receives.
DifferenceThe difference in amounts seen by each daughter will be ...
difference in amounts / number of daughters = (34 lb -12 lb)/(4 daughters)
= 22/4 lb/daughter = 11/2 lb/daughter
Each girl will have 11/2 more pounds of pink sand than purple sand.
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The amounts of money three students earn at their jobs over time are given in the tablesStudent ETime (hr) Amount Earned2$15.005$37.508$60.00Student FTime (hr) Amount Earned3$27.006$54.0010$90.00Student GTime (hr) Amount Earned1$8.504$34.007S59.50According to the tables, which statement is true?Student E cams the most amount of money per hourStudent E cars more money per hour than studentStudent Goarns the least amount of money per hourStudent G earns less money per hour than student F
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the answer is:
Student G earns less money per hour than student F
The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?
Answers
Answer:
300 in²
Step-by-step explanation:
Hello!
Because the diagonal forms right triangles, we can use the Pythagorean Theorem to find the missing length of the rectangle.
a² + b² = c²
a = legb = legc = hypotenuseIn this case, 25 is c, and 15 is a. We can solve for b using the formula.
Solve for ba² + b² = c²15² + b² = 25²225 + b² = 625b² = 400b = 20So the missing length of the rectangle is 20. We can find the area by multiplying 15 and 20
15 * 20 = A300 = AThe area is 300 in².
In the national park, the ratio of black bear bears to grizzly bears is 3:1. If the park had 12 grizzly bears, how many black bears would it have?
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The number of black bears in the national park is 36
Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has
Let the number of black bears be x
what this mean is that the total number of bears in the park is (x + 12)
The total ratio of the two is 3 + 1 = 4
Matematically;
[tex]\begin{gathered} \frac{3}{4}\text{ }\times\text{ (x + 12) = x} \\ \\ 3(x\text{ + 12) = 4 }\times\text{ x} \\ \\ 3x\text{ + 36 = 4x} \\ 4x-3x\text{ = 36} \\ \\ x\text{ = 36} \end{gathered}[/tex]Find the mzEFH, given that mzEFG = 50°. F E G . I
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By theorem, we will have that m
m
=> m
=>2m
Then, we replace values and solve:
2m m
So, we have that m
how do you work the problem 3k+16=5k?
Answers
We have the following:
[tex]3k+16=5k[/tex]solving for k
[tex]\begin{gathered} 5k-3k=16 \\ k=\frac{16}{2} \\ k=8 \end{gathered}[/tex]The value of k is 8
Jan is looking at a mapof Roaring River. The map wascreated using the scale 1 inch :25 miles. If the river is 5.5inches long on the map, then itis actuallymiles long.
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The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;
[tex]\begin{gathered} \text{Scale; 1 inch=25 miles} \\ 5.5\text{ inches=25 x 5.5 miles} \\ 5.5\text{ inches=137.5miles} \end{gathered}[/tex]The river is "actually" 137.5 miles long
What’s negative 5 + 1 fourth equal
Answers
Answer:
-4 3/4
Step-by-step explanation:
-5 x 4/4 + 1/4
-19/4 = -4 3/4
18 area = in. 114, 134, Jordan's game started at 6:05 pm. The game finished at 7:10 pm, and it took 20 minutor to got home what time did
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Notice that the first term is 114 and the third term is 134, then, between the first and the third, there are 20 units of difference.
Then, the common difference between each term must be 10, thus, the complete sequence is:
[tex]114,124,134,144,154[/tex]A ladder that is 55 meters in length is resting on a branch of a tree, and the base of the ladder is 33 meters from the tree on the level ground. How high up is the branch on which the ladder is resting?
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the diagram of situation is given as follows
so by using the right-angle property.
[tex]x^2+33^2=55^2[/tex][tex]\begin{gathered} x^2=3025-1089=1936 \\ x=\sqrt[]{1936} \end{gathered}[/tex][tex]x=44[/tex]so the height of the tree is 44
Sara’s dogsMorning: 39, 21, 12, 27, 23, 19, 31, 36, 25Afternoon: 15, 51, 8, 16, 43, 34, 27, 11, 8, 39Comparing the morning and afternoon groups Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds.
Answers
Answer;
Medain for morning is 25
Median for evening is 21.5
Explanation;
Here, we want to create frequency tables for each of the given groups
We start with the morning group
The frequency table for it is as follows;
Now, we proceed to the afternoon group
We have this as follows;
Lastly, we will want to get the median value of both groups
To do this, we need to re-arrange the values in the data set in ascending or descending order
For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value
For the morning group, we have;
12, 19,21, 23,25,27,31,36,39
Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right
Thus, we have the median value as 25
The afternoon set, we have it as;
8,8,11,15,16,27,34,39,43,51
We proceed to choose the mid 5th values comig from both ends
We have this as;
We have these values as; 16 and 27
We add these and divide by 2
We have this as;
[tex]\frac{16+27}{2}\text{ = 21.5}[/tex]
A body is moving in simple harmonic motion with position function
s(t) =2 + 2 cos t
where s is in meters and t is in seconds. Find the at time t.
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The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
A type of self-sustaining periodic motion known as simple harmonic motion.
It is observed by the formula:
y = y' + Δy · cos ωt ....1.
Where,
y' = Initial position
Δy = Amplitude
ω = Angular frequency.
t = Time
To find the equation for the velocity of the body in simple harmonic motion differentiating equation w.r.t time (1),
then we get
v = - ω · Δy · sin ωt ....2.
If we know that ω = 1, t = t and Δt = 2, then the velocity of the body is:
v = - 1 · 2 · sin t
v = -2sint
The velocity is equal to -2sint
The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
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Pat bought a washer/dryer for $900 and made 24 payments of $46.23. Howmuch did she pay in interest?a. $1,109.52b. $900c. $92.40d. $209.52
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Given that:
Cost of the washer/dryer = $900
Number of payments made = 24
Amount paid in each payment = $46.23
Total amount she paid
[tex]\begin{gathered} =\text{Amount paid in each payment}\cdot Number\text{ of payments} \\ =46.23\cdot24 \\ =1109.52 \end{gathered}[/tex]Interest paid = Total amount paid - Cost of the washer/dryer
[tex]\begin{gathered} =1109.52-900 \\ =209.52 \end{gathered}[/tex]Option d is correct.
an airliner travels 30 miles in 4 minutes. what is its speed in miles per hour?
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We need to convert minutes to hours. We know that 1 hour is 60 minutes so we can use the conversion factor of 1 hour = 60 minutes. We make sure the minutes cancel in the top and bottom leaving
30 miles 60 minutes
------------- * --------------
4 minutes 1 hour
30 miles * 60
--------------------
1 hour
180 miles
--------------
hour
what is the slope for the following points?(-1,1) and(3,3)
Answers
To find the slope for a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Use:
(x1,y1) = (-1,1)
(x2,y2) = (3,3)
replace the values of the previous parameters in the formula for m:
[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]Hence, the slope is 1/2
