Answer:
16
Step-by-step explanation:
the first thing is to rearrange terms
Kelly’s car travels 26 1/4 miles on 5/8 gallon of gas how much Can the car go per gallon
Answer:
42 miles per gallon
Step-by-step explanation:
First, Convert it into a decimal to make it easier, 26.25 miles on .625 gallon. Now we Divide the two numbers 26.25 ÷ .625 = 42.
Hope this helps :D
In ΔVWX, the measure of ∠X=90°, XW = 48, WV = 73, and VX = 55. What is the value of the sine of ∠W to the nearest hundredth?
Answer: sinW≈0.75
Step-by-step explanation:
[tex]m\angle X=90^0\ \ \ \ XV=48\ \ \ \ \ WV=73\ \ \ \ \ VX=55\ \ \ \ sinW=?[/tex]
The sine theorem: The sides of a triangle are proportional to the sines of the opposing angles
Hence,
[tex]\displaystyle\\\frac{WV}{sinX} =\frac{VX}{sinW} \\\\\frac{73}{sin90^0} =\frac{55}{sinW} \\\\\frac{73}{1} =\frac{55}{sinW} \\\\sinW=\frac{55}{73} \\\\sinW\approx0.75[/tex]
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=11 x-11 for x=-11
f(-11) = -132 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= 11 x-11
Put x = -11 ⇒ 11 * - 11 - 11
⇒ - 121 - 11
⇒ -132
Therefore f (-11) = -132
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Is it possible for an inconsistent linear system to contain two lines with the same y -intercept? Explain.
If they have the same slope and different intercepts then they are parallel and there is no solution to the system.
If the two lines have different slopes, the system has exactly one solution (whether the lines have the same intercept or different intercepts).
If they have the same slope and the same intercept they are the same line, so there are infinitely many solutions to the system.
If they have the same slope and different intercepts then they are parallel and there is no solution to the system.
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Geometry: fill in the blanks (ASAP!)
the elevator starts on floor 12 it goes down 8 floors then it goes up 14 floors what floor does it end on?
When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of Np-240, a radioactive isotope of Neptunium, initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
What is radioactive decay?The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.Alpha, beta, and gamma decay are three of the most prevalent types of decay, and they all entail the emission of one or more particles.The formula so used: A = [tex]\frac{-dN}{dt}[/tex]
=> N = A ([tex]e^{-kt}[/tex]), where:
N = amount left after the decay.A = initial amountk = constantt = time taken by the decayNow,
AS shown in the table (refer to the image attached), for k:
=> 322 = 1284[tex]e^{-2k}[/tex]
=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]
=> 0.25 = [tex]e^{-2k}[/tex]
Taking natural logarithm on both sides.
=> ln(0.25) = ln([tex]e^{-2k}[/tex])
=> ln(0.25) = (-2k) ln(e)
As ln (e) = 1,
=> ln (0.25) = -2k
=> -1.386 = -2k
=> k = 0.693
Now, for t = 1 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(1)}[/tex])
=> N = 1284 (0.5)
=> N = 642
For t = 3 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(3)}[/tex])
=> N = 1284 (0.125)
=> N = 160.6g
For t = 4 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(4)}[/tex])
=> N = 1284(0.0625)
=> N = 80.3g
Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
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what is the mean, median, and mode of the following data set? 27, 31, 33, 33, 35, 45
Answer: mean = 34
median = 33
mode = 33
Step-by-step explanation:
To figure out the mean you add every number and divide them by the number of values you added together so 27 + 31 + 33 + 33 + 35 + 45 = 204 then we would divide that by 6 = 34
To find the median you put all the numbers into order so which it already is meaning now you find the number in the middle which is 33 and 33 if there were two more values you would have to find the mean of them, but in this case its 33
The mode is the number which appears the most which is 33 as it appeared more than 2 times.
Find the percent of the given number. 92 % of 90
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 92% of 90 is 82.8.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 92% of 90
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
92% of 90 = 92/100 of 90
92/100 × 90 = 82.8
Therefore, the percent of the given number 92% of 90 is 82.8.
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Write an equation in slope-intercept form for each line.
(-5,-3) and (10,-6)
A slope-intercept equation for each line (-5,-3) and (10,-6)
y = (3/5)x + 3.
How do you calculate the intercept form?The slope-intercept form of the line's equation is y = MX + b, where the material has deposited the slope and b symbolizes the y-intercept. We can see from our equation, y = 7 x + 4, that the y-intercept of the line is 4.
According to the given data:To begin, are using the slope formula to figure out the average slope between two points here.
Let:
x1 = -5
y1 = -3
x2 = 10
y2 = -6
m = (y2-y1)/(x2-x1)
= (-6 - (-3))/ (-10-(-5))
= -3/(-5)
= 3/5
So the slope is 3/5.
We must now find the y-intercept. This will be performed by translating one of the points and the slope into to the point-slope form of a linear equation. y2-y1 = m(x2-x1).
Let’s plug in the point (10,-5).
So we get y-(-3) = (3/5)(x-(-5)) ⇒ y+3
= (3/5)x + 3 ⇒ y
= (3/5)x + 3.
So y = (3/5)x + 3.
a slope-intercept equation for each line (-5,-3) and (10,-6)
y = (3/5)x + 3.
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Use the Distance Formula to calculate the distance between points A (-4, 2) and B (0,-2), and round your answer to 1 decimal place.
The distance between the given 2 points using the distance formula is 4√2.
What is the Distance Formula?Distance is a numerical or qualitative measurement of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage.So, the Distance formula: [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
Substitute values in the distance formula as follows:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\d=\sqrt{\left(0-(-4)\right)^2+\left((-2)-2\right)^2}\\d=\sqrt{\left(4\right)^2+\left(-4\right)^2}\\\\d=\sqrt{16+16}\\d=\sqrt{32}\\\\d=\sqrt2*2*2*2*2\\d=2*2\sqrt2\\\\d=4\sqrt2[/tex]
Therefore, the distance between the 2 points is 4√2.
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Type the correct answer in the box. round your answer to the nearest whole number. dylan has two cubes of iron. the larger cube has twice the mass of the smaller cube. he measures the smaller cube. its mass is 20 grams, and its density is 7.87 g/cm3. what’s the larger cube’s volume? the larger cube’s volume is about cm3.
The larger cube's volume is 5.08 cm³.
As per the given information, expressing the relation between the mass of iron cubes -
Mass of large iron cube = 2×mass of small cube
Mass of large iron cube = 2×20
Performing multiplication to find the mass
Mass of large iron cube = 40 grams
Now calculating the volume of large iron -
Density = mass ÷ volume
Keep the values in formula to find the volume of cube -
Volume = mass ÷ density
Volume = 40 ÷ 7.87
Performing division to find the volume of cube -
Volume = 5.08 cm³
Hence, the volume of larger iron cube is 5.08 cm³.
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The midpoint of CD is M(–9, –8). One endpoint is D(–9, –7). Find the coordinates of the other endpoint C
Use the link below to answer your question:
https://www.omnicalculator.com/math/endpoint
Hope this helps!
T= {(-5, -3), (8, -6), (-5, 1), (0,8)}
Give the domain and range of T.
Write your answers using set notation.
Answer:
d: {-5, 0, 8}
r: {-6, -3, 1, 8}
Step-by-step explanation:
You want the domain and range of the relation T= {(-5, -3), (8, -6), (-5, 1), (0,8)}.
DomainThe domain is the set of first values. We usually like to see duplicates eliminated and the values written in increasing order:
{-5, 0, 8}
RangeThe range is the set of second values. Again, we like them in order:
{-6, -3, 1, 8}
__
Additional comment
If there are duplicates among the domain values (as here), the relation is not a function.
Find the distance between the points (-5, -4) and (7, -4).
Answer:
12
Step-by-step explanation:
the distance would be 12 because if you see the y values they are both -4 so they dont have any distance between them. Now if u look in the x values you will see different values -5 and 7 what u have to do now is do the equation 7 - - 5 which will be 12 because minus and minus will be plus so 7 plus 5 is 12, the distance between those points is 12.
Hope this answers ur question.
Express 5.5 recurring as mixed number
Answer:
5.5 = 5 5/10 = 5 1/2 (simplified)
Hope this helps in any way :)
PROOF Write a flow proof.
Given: MJ ≅ ML ; K is the midpoint of JL .
Prove: Δ M J K ≅ ΔM L K
Corresponding angles of congruent must be equal .
What exactly do you mean by congruent?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.Given , L is mid point of JL .
JL = LN Mid point
L is mid point of KM .
KL = LM Mid point
JM = NK Given
Δle JLM ≅ Δ le KLN ( SSS)
∠MJL ≅ ∠ KNL
Corresponding angles of congruent must be equal .
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Simone calculates the volume of a cube with side length 2.3 cm to be 6.9 cm3. Meiki says the volume is 12.167 cm3. Who is correct, and why?
Step-by-step explanation:
Philipp Heinrich Scheidemann was a German politician of the Social Democratic Party of Germany. In the first quarter of the 20th century he played a leading role in both his party and in the young Weimar Republic. Wikipedia
Born: July 26, 1865, Kassel, Germany
Died: November 29, 1939, Copenhagen, Denmark
Party: Social Democratic Party of Germany
Spouse: Johanna Dibbern (m. 1889–1926)
Previous offices: Mayor of Kassel (1919–1925), Chancellor of the German Reich (1919–1919), More
Books: The Making of New Germany: The Memoirs of Philipp Scheidemann
Nationality: German, Weimar
which of the following is an example of a rational number between 7 and 8?
The six rational number between 7 and 8 are 7.5 ,7.75, 7.875 , 7. 9375 ,7.9675 and 7.98375
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=4 x(7-2 x)
The given function
f(x) = y = 4x(7 - 2x) , is a Quadratic function
where its quadratic term is -8x².
Its linear term is 28x
Constant 0
What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:
f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.
4x (7 - 2x) we apply the distributive property
28x - 8x² is a quadratic function
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need working out pls
As shown in the above figure:
AB = 4m, AD = 8m, AC = 3m, DE = 12m
Problem A:Ratio of the length AB to the length AD
[tex] →\frac{AB}{AD} = \frac{4}{8} = \frac{1}{2} [/tex]
Ratio = 1:2
Problem B:The length AE
[tex] \frac{AB}{AD} = \frac{AC}{AE} → \frac{4}{8} = \frac{3}{AE} [/tex]
Cross multiply the above.
[tex]4AE = 24[/tex]
Divide both sides by 4
[tex]AE = 6m[/tex]
Problem C:The length BC
[tex] \frac{AB}{AD} = \frac{BC}{DE} → \frac{4}{8} = \frac{BC} {12} [/tex]
Cross multiply the above
[tex]8BC = 48[/tex]
Divide both sides by 8
[tex]BC = 6m[/tex]
Please mark my answer brainliest
What is the slope of the line passing through the following points? (2,4) and (4,2)
The slope of the line passing through the points (2,4) and (4,2) is -1
How do you determine a line's slope?
Determine the coordinates of two locations along the line that you choose. Find the difference between these two locations' y-coordinates (rise). Find the difference between these two locations' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Formula to determine the slope is - y₂ - y₁ / x₂ - x₁
Given are the points -
(2,4) and (4,2)
slope of the line = 2 - 4 / 4 - 2
= -2 / 2
= -1
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If you vertically compress the absolute value parent function, f(x) = Ixl, by a
factor of 3, what is the equation of the new function?
OA. g(x) = 1x - 31
OB. g(x)=x
O C. g(x) = 31x1
O D. g(x) = 13x|
Answer:
The equation for new function is
Step-by-step explanation:
We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.
If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.
We have below conditions for vertical stretch and compression.
a > 1 => vertically stretch
0 < a < 1 => vertically compression
Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3
Therefore, the equation for new function is
Step-by-step explanation:
g(x) = 1/3 |x| !
(3x + 4)(x + 2x + 3)
Answer:
9x^2 + 21x + 12
Step-by-step explanation:
(3x+4)(x+2x+3)
Combine x and 2x to get 3x.
(3x+4)(3x+3)
Apply the distributive property by multiplying each term of 3x+4 by each term of 3x+3.
9x^2 + 9x + 12x + 12
Combine 9x and 12x to get 21x.
9x^2 + 21x + 12
Rewrite (128 + 32) using factoring.
2(124 + 17)
4(32 + 8)
8(17 + 4)
12(14 + 3)
The expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)
How to rewrite the expression using factoring?The expression in the question s given as
(128 + 32)
Express the numbers 128 and 32 as the product of their factors
i.e. we factor out 4 from the expression
So, we have
(128 + 32) = (4 * 32 + 4 * 8)
Next, we factor out the common factor (i.e. 4) from the expression
So, we have
(128 + 32) = 4 * (32 + 8)
Rewrite the above expression as follows
(128 + 32) = 4(32 + 8)
Hence, the expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)
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The expressions c - e, where c
stands for the money collected and e
stands for the expenses, is used to find
the profit from a basketball concession.
If $500 was collected and expenses
were $150, find the profit for the
concession.
The profit of the concession is $350.
What specifically are expressions?A group of numbers or variables combined with the operations +, -, ×, or ÷ form an expression.While algebraic expressions include variables, numbers, and mathematical operators, arithmetic expressions only contain numbers and mathematical operators.Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.So, c - e:
Substitute the values in the expression:
c - e500 - 150$350Therefore, the profit of the concession is $350.
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d at ( − 6 , − 3 ) (−6,−3) on the coordinate plane. Point K K is reflected over the y y-axis
the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).
The reflection transformation can be with respect to x-axis and y-axis. When a point is reflected about the x-axis, the x-coordinates stay the same and y-coordinates are transformed and written with their opposite signs.
For example, the reflection of the point with coordinates (x, y) across x-axis is (x, -y).
When a point is reflected about the y-axis, the y-coordinates stay the same and the x-coordinates are transformed and written with their opposite signs.
For example, the reflection of the point (x, y) across y-axis is (-x, y).
As we can see that the point with coordinates ( -6, -3 ) lies in the third quadrant and thus the reflection of this point on y-axis lies in fourth quadrant. We know that in fourth quadrant the x coordinate is positive and y coordinate is negative.
By changing the signs according to the above rules, we get
from ( -6, -3 ) to ( 6, -3 ).
Therefore, we can conclude that the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).
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Can someone help me on this question and explain the process?
Solve for x. The triangles in each pair are similar.
Answer:
x = 10
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{TS}{TB}[/tex] = [tex]\frac{TR}{TC}[/tex] ( substitute values )
[tex]\frac{10x+17}{65}[/tex] = [tex]\frac{90}{50}[/tex] ( cross- multiply )
50(10x + 17) = 90 × 65 = 5850 ( divide both sides by 50 )
10x + 17 = 117 ( subtract 17 from both sides )
10x = 100 ( divide both sides by 10 )
x = 10
Which equation is parallel to 4x- 2y = 6 and passes through (0, 1)
The equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
How to determine the linear equation?The given parameters are
4x - 2y = 6
Divide through by 2
So, we have
2x - y = 3
Make y the subject of formula
So, we have
y = 2x + 3
A linear equation is represented as
y = mx + c
Where
Slope = m
This means that
m = 2
Parallel lines have equal slopes
So, the slope of the other line is
m = 2
The point on the line is given as (0, 1)
The equation is then calculated as
y = m(x- x1) + y1
So, we have
y = 2(x - 0) + 1
Evaluate
y = 2x + 1
Hence, the equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
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Which expressions are equivalent to -6(b+2)+8−6(b+2)+8minus, 6, left parenthesis, b, plus, 2, right parenthesis, plus, 8 ?
The equivalent expression of -6(b + 2) + 8 is -6b - 4
How to determine the equivalent expression?The expression is given as
-6(b + 2) + 8
Expand
-6b - 12 + 8
Evaluate the like terms
-6b - 4
Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4
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