Option D √128 unit is the precise distance between the two points (-4, -2) and (4, 6).
Given,
The points;
(x₁, y₁) = (-4, -2)
(x₂, y₂) = (4, 6)
We have to find the exact distance from the points;
Here,
Distance between two points (x₁, y₁) and (x₂, y₂);
D = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2} -y_{1})^{2} }[/tex]
Here,
(x₁, y₁) = (-4, -2)
(x₂, y₂) = (4, 6)
Then,
Distance, D = [tex]\sqrt{(4 - -4)^{2} +(6--2)^{2} }[/tex]
Distance, D = [tex]\sqrt{8^{2}+8^{2} }[/tex]
Distance, D = [tex]\sqrt{64+64}[/tex]
Distance, D = √128
That is,
The exact distance between two points (-4, -2) and (4, 6) is option D √128 unit
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Type the correct answer in each box. Use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). The amount of time it takes a water pump to empty a tank varies directly as the capacity of the tank. If it takes a water pump 2. 5 hours to empty a tank containing 60,000 gallons of water, how long does it take the same pump to empty a tank containing 108,000 gallons of water? it will take hours to empty the second tank.
An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
What is an equation?When two equal expressions are added together with the aid of the equal sign "=," an equation is created.
Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,
V ∝ T
V = kT
Substituting the volume and time in the equation,
60,000 gallons = 2.5 hours × k
Solving the equation for k,
k = 60,000 gallons / 2.5 hours
k = 24,000 gallons per hour
Now, the equation for the relationship can be written as,
V = 24,000 gallons per hour × T
Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,
V = 24,000 gallons per hour × T
108,000 gallons = 24,000 gallons per hour × T
108,000 gallons / 24,000 gallons per hour = T
T = 4.5 hours
Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
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and D are noncoplanar. △ABC,△ABC,△ACD, and △ABD are equilateral. X and Y are midpoints of AC¯¯¯¯¯¯¯¯ and and AD.Z is a point on AB¯¯¯¯¯¯¯¯. What kind of triangle is △XYZ? Explain.
ΔXYZ will also be an equilateral triangle.
What is equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.
As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic
Hence XYZ will also be an equilateral triangle
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Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos cos($) -ISXS*, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.) n = 3: upper sum ll lower sum n = 4: upper sum II lower sum n = 6: upper sum IO lower sum
In this Trigonometric Functions F(x) = 1 + cos(1/X): n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
F(x) = 1 + cos(1/X)
for n=3
Upper sum = 12.01
Lower sum = 8.10
Δx = (b-a)/n = 2π / 3
for n=4
Upper sum = 11.65
Lower sum = 8.50
Δx = (b-a)/n = π / 2
for n=6
Upper sum = 11.24
Lower sum = 9.12
Δx = (b-a)/n = π / 3
Hence, n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value.
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In parallelogram TUVW, the diagonals tv and uw intersect at point z. If tz =5y -1, uz =2x, vt =78, and wz =3y +6, what is the sum of x+y
The sum of x and y i.e (x+y) is equal to 23
What is parallelogram law?When two diagonals of a parallelogram bisect each other. Each diagonal bisects the parallelogram into two congruent triangles. The Sum of the square of all the sides of a parallelogram is equal to the sum of the square of its diagonals.
This implies that line uz = wz, and vz= tz
therefore 3y+6= 2x equation 1
since vt = 78
5y-1= 78-(5y-1) equation 2
5y-1= 78-5y+1
collecting like terms,
5y+5y= 78+1+1
10y= 80
divide both sides by 10
y= 80/10
y= 8
substituting 8 for y in equation 1
3×8+6= 2x
24+6= 2x
30= 2x
divide both sides by 2
x= 30/2= 15
therefore the sum of x and y = 15+8= 23
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Pls help quick from hegarty maths
The mean lifetime of a bulb is 149.37 hours.
What is the meaning of mean?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).
The given table represents a continuous data.
The table attached in below. To get mean lifetime of a bulb, find the mean of the given table.
The formula for mean is = Σ fm/N
Where f is frequency and m is midpoint of the class.
N is total number of observation.
From the table, Σ fm = 53175
Total number of bulb is 356.
The mean lifetime is 53175/ 356 = 149.37 hours
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Will give Brainlest!
What is the direct variation of the table below?
The direct variation of the table is y = 5x + 10.
What is direct variation?The definition of direct variation is the relationship between two variables when one is a fixed multiple of the other.
Let the direct variation of the table is,
y =kx +c (1)
To find the direct variation,
Substitute x=1 and y = 15 in equation (1)
15 = k + c (2)
Substitute x=4 and y = 30 in equation (1)
30 = 4k +c (3)
By solving equation (2) and (3)
k = 5 and c = 10
Substitute values of k and c in equation (1),
y = 5x + 10
The direct variation of the table is y = 5x + 10.
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Which expression is equivalent to13k+7+5(k+6)?
Answer:
18k +37
Step-by-step explanation:
13k + 7 + 5(k + 6)
13k + 7 + 5k + 30
13k + 5k + 7 + 30
18k +37
An animal shelter has cats and dogs available for adoption in a ratio of 3:5. If there are 25 dogs available for adoption, how many cats are available? Use a tape diagram to help organize your thinking. (1 point)
cats
Answer:
15 cats
Step-by-step explanation:
c:d
3:5
5=25
25/5=5
5*3=15
15 cats
======================================================
Explanation:
The tape diagram is shown below.
"C" represents a sub-group of cats, and "D" represents a sub-group of dogs. Each sub-group has the same number of animals.
There are 3 copies of "C" and 5 copies of "D" to represent the ratio 3:5 of cats to dogs. For every 3 cats, there are 5 dogs.
We are told there are 25 dogs available for adoption. This consists of all five blocks of "D" combined. If each "D" is the same number of dogs, then there must be 25/5 = 5 dogs per "D" block. By extension, there are 5 cats per "C" block.
In short, each block has 5 animals.
3 blocks of C = 3*5 = 15 cats are available.
-----------------
Another approach:
C = number of cats available = unknown
D = number of dogs available = 25
C/D = 3/5
C/25 = 3/5
5C = 25*3 ... cross multiply
5C = 75
C = 75/5
C = 15 cats are available
-----------------
A third approach:
The ratio 3:5 scales up to 15:25 after multiplying both parts by 5. This is so the "5" in "3:5" becomes "25".
The ratio of cats to dogs of 15:25 reduces to 3:5 when you divide both parts by the GCF 5.
So this is another way to see how 15 cats are available.
Not sure if I did this right, I'm given a line to plot it on
zeroes are 2,-2,
vertical asymptotes are -1,3
plotted on the number line
---------|---------|---------|---------|---------|---------|
-2 -1 0 1 2 3
What is vertical asymptote?
A vertical asymptote is a line that appears to correspond with a function's graph but never really touches the curve. When graphing a function, the vertical asymptote of the function is crucial.
The curve is neither touched or crossed by a vertical asymptote, which is a vertical line along which the function becomes unbounded (either y tends to or -). K is NOT present in the domain of the function if x = k is the vertical asymptote of a function y = f(x). Any quantity of vertical asymptotes is possible for a function. i.e., it may have 0 vertical asymptote, 1, 2,..., or a limitless amount. If the y-axis represents the vertical asymptote, we often do not portray it by a dotted line. Instead, we represent a vertical asymptote by a vertical dotted line.
1)
zeros means that the value were g(x) is zero
that means (x-2) and (x+2) = 0
x = 2 ,-2
2)
for vertical asymptote (x+1)and (x-3) = 0
x = -1,3
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S = k/t where k is a constant, which two statements are correct?
Answer:
B) S is inversely proportional to T.
Step-by-step explanation:
Since S is inversely proportional to T, then S = k/T, where k is a constant.
The solution is Option B , Option C.
The value of S is inversely proportional to the value of T or the value of S is directly proportional to 1/T
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
S = k/T be equation (1)
The equation is of the form y = kx where k is the proportionality constant
The equation is true when it is directly proportional to the value
So , S ∝ 1 / T
where k is the proportionality constant
On simplifying the equation , we get
S = k ( 1 / T )
From the equation , we can see than S is inversely proportional to T
And ,
From the equation , we can see that S is directly proportional to ( 1 / T )
Hence , the proportion is S ∝ 1 / T and k is the proportionality constant
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Units help please due today 50 points
Answer:
12.8
Step-by-step explanation:
You can see that triangle DAF and BED are equal.
So lineAF is lineDE.
6.4*2=12.8.
T/F alyssa is learning how to drive and is intently focused on the car she is operating, the traffic on the road, and the road signs and traffic signals. this concentration is an aspect of her
True, Alyssa is learning to drive and is paying close attention to the road conditions, other vehicles on the road, and traffic signs and signals. This focus is a quality of hers.
What is Focus during the Drive?
It means to concentrate only on driving during the time of driving to avoid accidents etc. Yeah when she is driving the car she must focus intently on car and on nothing else because she is a beginner. When people get experience in driving cars they use mobile phones etc kind of things easily during driving but beginners have to be careful a lot regarding this. Its very very good if she is also focusing road signs like zebra crossing and where traffic signals are there it would help her in great way
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Bob bought three pizza. Each pizza wa cut into 8 lice. He eat three lice of pizza and then decide to package the remaining pizza into bag with one erving in each bag. If one erving of pizza i 1/4 of the pizza, how many erving doe Bob have left?
If one serving is 1/4 of the pizza, then the number of servings left is 10.5 servings
Total number of pizza = 3
Each pizza was cut into 8 slice.
Total number of slices = 3 × 8
= 24 slices
He ate 3 slice of pizza
Remaining slices = 24 - 3
= 21 slices
The fraction pizza that left = 21/24
If one serving of pizza is 1/4 of the pizza, that is the 1/12 of three pizza
Number serving left = The fraction pizza that left ÷ one serving of pizza
= 21/24 ÷ 1/12
= 21/24 × 12
= 10.5 servings
Hence, there will 10.5 servings left
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What is the area of this triangle?
3 cm height
8 cm base
Answer: 12cm^2
Step-by-step explanation: We use the equation 1/2(bh) to get the area. If you put the number in the equation you will get the answer 12.
Explain what the phrases no more than and no less than mean when writing inequalities that model real-world situations.
For no more than, the inequality used is → ≤ and for no less than, the inequality used is → ≥.
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following statements in inequalities -
no more than and no less than
For no more than, the inequality used is → ≤
For no less than, the inequality used is → ≥
Therefore, for no more than, the inequality used is → ≤ and for no less than, the inequality used is → ≥.
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ANSWER FOR BRAINLY!! AND 20 POINTS please
(x+1)(2x-4)=0
rewrite the equation as a compound statement and find 2 solutions to the equation.
x=0
Step-by-step explanation:
4(x+1)=2x+4
Distribute
4x+4 = 2x+4
Subtract 4 from each side
4x+4-4 = 2x+4-4
4x= 2x
Subtract 2x from each side
4x-2x = 2x-2x
2x=0
Divide by 2
x =0
Which expression is equivalent to x6 – 9?
(x3)2 – 33
(x3)2 – 32
(x3)3 – 32
The expression equivalent to x⁶ - 9 is : (x³)² - 3²
What is expression?A statement is considered to be an expression if it contains at least two numbers or variables and one mathematical action.
What is power?Power is the factor that is multiplied by itself, and exponent is the number of times the same base number has been multiplied.
Calculation:
we have given ,
x⁶ - 9
now we know that,
(xᵃ)ᵇ - yᵇ
similarly,
(x³)² - 3² = x⁶- 9.
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y is directly proportional to the square root of t.
y = 15 when t = 9
t is inversely proportional to the cube of x.
t = 8 when x = 2
Find a formula for y in terms of x.
Give your answer in its simplest form.
The formula for y in terms of x in its simplest form is y=5120/27x⁴.
What is proportional?In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Form an equation for y and t first.
y∝ t² y=15 t=9
y=kt²
15=k(9²)
15=k(81)
15=81k
Divide both side by 81
5/27 =k
Equation y=5/27t²
Form an equation for t and x
t∝1/x² t=8 x=2
t=k/x²
8=k/2²
8=k/4
Multiply both side by 4
32=k
Equation: t=32/x²
Replace t with 32/x² in other equation .
y= 5/27 (32/x²)²
y=5120/27x⁴
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Which of the following points lie on the line y = 2x - 3? (2, 3) (-2, -1) (4, 1) (0, -3)
Answer:(0,-3)
Step-by-step explanation:
Answer:
(0,-3)
Step-by-step explanation:
just fill in the coordinates to see if it’s true
3=2(2)-3
3=4-3
3-1
Not true
-1=2(-2)-3
-1=-4-3
-1=-7
Not true
1=2(4)-3
1=8-3
1=5
Not true
-3=2(0)-3
-3=0-3
-3=-3
True
Hopes this helps please mark brainliest
please help.................
Answer:
ratio of amount of skills to time is 1:4
Step-by-step explanation:
1 skill is 4 seconds. so for 5 skills it would be 20 seconds
1. A painting crew bought 45 gallons of paint for a job. The crew members used 5 gallons of paint per hour until they used all the paint. Sketch a graph to represent the start to the end of the job, assuming all paint was used. Be sure to title your graph, label your axes, and label your intercepts. This must be graphed by hand or by using the tools in Word. You may not use a web-based graphing program.
The graph that shows the equation, y = -5x + 45, that represents the scenario given is shown in the attachment.
How to Graph a Linear Equation?Determine the slope (m) and the y-intercept (b), then input the values in the equation, y = mx + b, to write the equation of the line that would be graphed.
Given the information above, we have the following:
Let x = hours, and y = quantity of gallons of paint left
Slope (m) = -5
Y-intercept (b) = 45
Write the equation of the graph by substituting m = 5 and b = 45 into y = mx + b:
y = -5x + 45
The graph shown below for y = 5x + 45 would be labelled as follows:
x-axis = hours
y-axis = quantity of paint (in gallons)
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Lines l and m are parallel and intersect transversal p as shown in the diagram below
What is the value of n?
Answer: a
Step-by-step explanation:
The value of n from the given parallel lines is 6. Therefore, the option A is the correct answer.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Given that, the angles from the parallel lines are (3n+16)° and (5n+4)°.
Here, (3n+16)°=(5n+4)° (Interior alternate angles are equal)
5n-3n=16-4
2n=12
n=6
Therefore, the option A is the correct answer.
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$20 +$25.75x = $15.50 +$26.50x
Please help due tomorrow and it is from a sheet that’s half if my grade help please!!
Answer:x=6
Step-by-step explanation:
20+25.75x=26.5x+15.5
20+(25.75x-26.5x)=15.5
-0.75x=15.5-20
-0.75=-4.5
x=6
Answer:
x = 6
Step-by-step explanation:
First, determine which variable to solve for: x.
Use the Identity Property to gather x on one side of the equation:
$25.75x - $26.50x = $15.50 - $20
Simplify:
-$0.75x = -$4.50
To solve for x, divide both sides by x:
-x = -6
Multiply by -1 to remove the negative:
x = 6
label the vertices then use the pythagorean theorem to find x
Answer:
5cm. 8cm
Step-by-step explanation:
Label all the vertices then use Pythagorean theorem
c² = a² + b²
What is the slope of the x-axis? Explain. _
Answer:
zero
The x‐axis or any line parallel to the x‐axis has a slope of zero.
Step-by-step explanation:
The Y corodinate on X -axis is constant (zero). So the slope of X-axis is 0. Therefore the answer is zero
The function f(w) = w³ + 2w² - 11w - 12 has zeros at
u = -4,-1, and 3 as shown below.
If the function is divided by (w - 3) what would be the
remainder?
If a function f(w) = w³ + 2w² - 11w - 12 is divided by (w - 3) then the remainder would be 0.
What is a polynomial long division?
Polynomial long division is an algorithm in algebra for dividing a polynomial by another polynomial of the same or lower degree, which is a generalized version of the well-known arithmetic technique known as long division. It is simple to do by hand because it divides an otherwise complex division problem into smaller ones.
The given polynomial function is [tex]f(w)=w^3+2w^2-11w-12[/tex].
And we have to divide the above function by (w - 3).
[tex]=\frac{w^3+2w^2-11w-12}{w-3}\\\\=w^2+\frac{5w^2-11w-12}{w-3}\\\\=w^2+5w+\frac{4w-12}{w-3}\\\\=w^2+5w+4(\frac{w-3}{w-3})\\\\=w^2+5w+4[/tex]
Hence, after taking division, the remainder would be 0.
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use the image to answer the question what does the absolute vaule of the point labeled in the image if the number line represents temperature change.
Please help!!!
Answer:i don't know I just need the points
Step-by-step explanation:
Somebody please help me
a) k = 1/2 then v = 1 cubic unit
b) k = 0.6 then v = 1.728 cubic units
c) k = 1 then v = 8 cubic units
d) k = 1.5 then v = 27 cubic units
The value of scale factor k, which is used to obtain a solid with volume v cubic units by 8 cubic unit is, ∛v / 2.
The volume of the solid is 8 cubic units.The scale factor of dilation is kThe volume of new solid obtained is v.Here the new volume of the solid is find out by the volume of 8 units and the scale factor k. Thus the scale factor k should be equal to the ratio of the volume of these two solid.
The volume of the solid is represents in cubic units. Thus, k = ∛(v/2)
k = (∛v) / 2
a) k = 1/2
(1/2)³ * 2³ = v
v = 1 cubic units
b) k = 0.6
(0.6)³ * 8 = v
0.216 * 8 = v
v = 1.728 cubic units
c) k = 1
1³ * 8 = v
v = 8 cubic units
d) k = 1.5
(1.5)³ * 8 = v
3.375 * 8 =v
v = 27 cubic units
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It has long been thought that the length of one's femur is positively correlated to the length of one's tibia. The following are data for a classroom of students who measured each (approximately) in inches. Femur Length Tibia Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3 15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8 Regression Statistics Multiple R 0.9305 R Square 0.8659 Adjusted R Square 0.8510 Standard Error 0.5963 Observations ANOVA SS MS F Significance F Regression 1 20.6611 20.6611 58.0968 3.25116E-05 Residual 9 3.2007 0.3556 Total 10 23.8618 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.5850 1.4137 2.5359 0.0319 0.3871 6.7830 Femur Length 0.5899 0.0774 7.6221 0.0000 0.4148 0.7650 A strong linear correlation was found between the two variables. Find the standard error of estimate. Round answer to 4 decimal places.
The linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
Given, data for a classroom of students who measured each (approximately) in inches.
Femur Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3
Tibia Length 15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8
we have to find a linear correlation between the two variables,
linear correlation be,
(y - 15.8)/(x - 18.7) = (15.8 - 21.0)/(18.7 - 14.2)
(y - 15.8)/(x - 18.7) = (- 5.2)/4.5
4.5y - 71.1 = -5.2x + 97.24
4.5y + 5.2x = 168.34
So, the linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
Hence, the linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
