Answer:
soln:
x+16=4x-5
16+5=4x-x
21/3=x
Therefore x=7
Draw a line representing the 'rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Rise and Run of line's ratio gives the Slope of the line.
What is rise of line and run of line?Rise of a line is the how many units you move up or down to reach from one point to another point. Run of a line is the how many units you move left or right to reach from one point to another.
>Slope of a line is the ratio of the rise to the run of the line.
Let us assume the graph of y = x.
Now in the graph we take three points
let point 1 be (3,3) = (x1,y1)
point 2 be (5,5)= (x2,y2)
point 3 be (5,3)= (x3,y3)
Now the rise is y2 - y1 which is 2
Now the run is x2 - x1 which is 2
Slope is [tex]\frac{rise}{run}[/tex] = [tex]\frac{2}{2} =1[/tex], we know that slope of line y=x is 1 and here we get the same so it is proved that slope of line is [tex]\frac{rise}{run}[/tex] .
Rise and Run of line's ratio gives the Slope of the line.
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In a series of transformations, which transformation would make two figures similar as opposed to congruent? answer choices.
a. translation
b. dilation.
c. reflection.
d. rotation.
An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 1300 meters, and Plane B was at an altitude of 1092 meters. Plane A is gaining altitude at 17 meters per second, and Plane B is gaining altitude at 21 meters per second. Let x be the number of seconds passed
(A) The expression for each plane are as follows;
Plane A; 1300 + 17x
Plane B; 1092 + 21x
B). The equation to show when the two planes would be at the same altitude is; 1300 + 17x = 1092 + 21x.
Which equation shows when the two planes would be at the same altitude?It follows from the task content that the initial altitudes of plane A and B are 1300 and 1092 respectively.
Since plane A gains altitude at 17 meters per second; The expression for the altitude after x seconds is;
1300 + 17x
Also, since plane B gains altitude at 21 meters per second; The expression for the altitude after x seconds is;
1092 + 21x
Ultimately, at the point when the two planes are at the same altitude; the equation which is true about the situation is;
1300 + 17x = 1092 + 21x.
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S= n(n+1)/2 despejar para n
Por propiedades algebraicas, la ecuación de la variable n es función de la variable S es igual a n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S).
¿Cómo despejar una variable en una ecuación?
En esta pregunta tenemos un ecuación donde la variable S en función de la variable n y debemos reescribir la expresión como una de la variable n en función de la variable S. Esto es posible mediante el uso de propiedades algebraicas. Primero, escriba la ecuación:
S = n · (n + 1) / 2
Segundo, utiliza la propiedad distributiva:
S = (n² + n) / 2
Tercero, aplica compatibilidad con la multiplicación, existencia del inverso multiplicativo y propiedad modulativa:
2 · S = n² + n
Tercero, construya una ecuación cuadrática:
n² + n - 2 · S = 0
Cuarto, utilice la fórmula cuadrática:
n = - 1 / 2 ± (1 / 2) · √[1² - 4 · (- 2 · S)]
n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S)
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A student uses a solution that contains 16 grams of water to conduct an evaporation experiment. At the end of one hour the amount of water in the solution has decreased by 3.5%
Answer:
Step-by-step explanation:
.035*16=.56 solution has decreased for this part
16 divided by 3.5⁶66677⁷54776367
Step-by-step explanation:
4_35665567
25. The manager of a coffee shop has Costa Rican coffee that sells for $7 per pound and Kenyan coffee that sells for $10
per pound. The manager wishes to mix 80 pounds of the Kenyan coffee with the Costa Rican coffee to get a mixture that
will sell for SS per pound. How many pounds of the Costa Rican coffee should be used?
The Costa Rican coffee should be used is 160 pound.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the cost of Costa Rican coffee that sells for $7 per pound and Kenyan coffee that sells for $10.
The cost of the mixture is $8.5 per pound.
Assume that the manager mixed 80 pounds of the Kenyan coffee with the x pound of the Costa Rican coffee to get a mixture.
The cost of 80 pound Kenyan coffee is $(80×10) = $800.
The cost of x pound Costa Rican coffee is 7x.
The cost of mixture coffee is (80 + x)8.5
According to the question:
800 + 7x = (80 + x)8
800 + 7x = 640 + 8.x
640 + 8x = 800 + 7x
x = 800 - 640
x = 160
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help me with this please
The evaluated value of the expression b² - 4ac when a = -2, b = -4 and c = 1 is 24.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
Therefore, let's evaluate b² - 4ac when a = -2, b = -4 and c = 1.
Hence,
b² - 4ac = (-4)² - 4(-2)(1) = 16 + 8 = 24
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What are the factors of 6x² 5x 6?
Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .Quadratics can be defined using an equation of a second-degree polynomial.
what is quadratic equation ?The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.
here
= 6x² - 5x- 6
= 6x² - 9x + 4x - 6
= 2 ( 2x - 3 ) + 3x ( 2x - 3 )
= (3x+2) ( 2x - 3 )
So , Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .
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How do you find the vertical and horizontal asymptotes of a function using limits?
To find the vertical asymptote, take the limit of the function as x approaches infinity or negative infinity. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain.
To find the vertical asymptote of a function, take the limit of the function as x approaches either infinity or negative infinity. This will give the value at which the output of the function approaches infinity or negative infinity, respectively. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain. If the limit of the function as x approaches the endpoint is finite, then the horizontal asymptote is the value of the limit. If the limit of the function as x approaches the endpoint is infinite, then the horizontal asymptote is undefined. If the limit of the function as x approaches the endpoint is undefined, then the horizontal asymptote is undefined.
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How do I do this question and I need answer please
Answer: x = 3/4
Step-by-step explanation:
1/3x + 3 = 4 - x
Subtract 3 from both sides
1/3x = 1 - x
Then times 3 from both sides
x = 3 - 3x
Add 3x on both sides
4x = 3
Divided by 4, both side
x = 3/4
Help me with this I will give brainliest
Answer:
1) x = 29; m∠3 = 6º
2a) scalene
2b) acute
Step-by-step explanation:
1) We can first solve for m∠3, as it is supplementary to 174º.
174º + m∠3 = 180º
m∠3 = (180 - 174)º
m∠3 = 6º
Then, we can solve for x by setting the sum of the measures of the interior angles of the triangle to 180º.
m∠1 + m∠2 + m∠3 = 180º
↓ substitute in given and solved values
(3x + 2)º + (5x - 60)º + 6º = 180º
↓ combine like terms
8xº - 52º = 180º
↓ add 52 to both sides
8xº = 232º
↓ divide both sides by 8º
x = 29
2a) We know that this triangle is not equilateral, as the measure of one of its interior angles (m∠3) is 6º. However, the triangle may be isosceles if m∠1 = m∠2. We can check for that by substituting x into each angle measure expression.
m∠1 ≟ m∠2
(3x + 2)º ≟ (5x - 60)º
↓ substitute in x-value
3(29)º + 2º ≟ 5(29)º - 60º
↓ simplify
(87 + 2)º ≟ (145 - 60)º
89º ≠ 85º
m∠1 ≠ m∠2; the triangle is not isosceles. Therefore, it must be scalene.
2b) All of the triangle's angles are less than 90º. Hence, it is an acute triangle.
D
.0
A
58d
B
A, B, C and D are points on a circle, centre O.
Angle ABC = 58°
Calculate the size of angle ADC.
(1 mark)
Diagram NOT
accurately drawn
Answer:
∠ ADC = 122°
Step-by-step explanation:
ABCD is a cyclic quadrilateral.
opposite angles in a cyclic quadrilateral sum to 180° , that is
∠ ADC + ∠ ABC = 180∠
∠ ADC + 58° = 180° ( subtract 58° from both sides )
∠ ADC = 122°
Determine the domain of the following graph:
Step-by-step explanation:
the domain of a function is the interval or set of all valid x (input) values.
the range of a function is the interval or set of all valid y (function result) values.
the graph shows us that the x values are continuously between -5 and +3.
and the end points are filled, so, they are to be included as valid points (via the <= or >= signs).
so, the domain is
-5 <= x <= 3
What is median class example?
The continuous data that is presented as a frequency distribution makes up the median of the grouped data.
The center number in the set of data, known as the median, is what divides the data set's upper and lower halves. Since the data is divided into class intervals, the middle value is unknown when calculating the median of grouped data.
Let us understand this with the help of a median class example.
Consider the data as 48, 20, 59, 69,73. We have to calculate the median.
Arranging in ascending order we get, 20, 48, 59, 69, 73.
Here the number of observations is n = 5.
To find the median of odd data we will use the formula:
[(n+1)/2] = (5+1)/2 = 3.
Therefore, median = 3rd observation.
Median = 59.
Hence we got the idea of the median with the example of class.
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How do you determine if a triangle is SSS SAS or ASA?
SSS Stands on Side - Side - Side
SAS Stands on Side - Angle - Side
ASA Stands for Angle - Side - Angle.
There are three theorems that may be used to determine whether two triangles are similar: Angle - Side - Angle (ASA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).
SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.
According to the ASA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent and one side is equal to the corresponding side of the other triangles.
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Please help I will give brainliest
Answer:
cos(x) = r/t
sin(x) = s/t
tan(x) = s/r
Step-by-step explanation:
Background info:
This question becomes simple when we remember SohCahToa.
Soh stands for Sine = Opposite/ Hypotenuse
Cah stands for Cosine = Adjacent/ Hypotenuse
Toa stands for Tangent = Opposite/ Adjacent
Solving:
1. Cosine of angle x (think Cah)
The adjacent side is r and the hypotenuse is t.
so the answer is r/t
2. sine of angle x (think Soh)
The opposite side is s and the hypotenuse is t.
so the answer is s/t
3. Tangent of angle x (think toa)
The opposite side is s and the adjacent side is r.
so so the answer is s/r
Emma had to finish her 249-page novel by Friday. She had already read 166 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p + 166 = 249; p = 83 pages
p − 166 = 249; p = 415 pages
p over 166 equals 2; p = 332 pages
83p = 166; p = 2 pages
Answer:
p + 166 = 249
p = 83 pages
Step-by-step explanation:
We know that she has to finish 249 pages novel and read 166.
So, let p represent the number of pages left to read; we have the equation
p + 166 = 249
Now let's solve by subtracting 166 from both sides
p = 83 pages
So, Emma had 83 pages left to read by friday
For what value of k (- 2 is a zero of the polynomial 3x² 4x 2k?
-2 is the zero of the polynomial 3x²+ 4x + 2k for the value of k equals to -2.
As given in the question,
Given polynomial is equal to :
3x²+ 4x + 2k
-2 is the zero of the given polynomial 3x²+ 4x + 2k
Compare with the standard quadratic equation ax² + bx + c
Let 'α' be the zero whose value is equal to -2.
And 'β' be the another zero.
Sum of the zeros of the polynomial = -b/ a
⇒ α + β = -4 / (3)
⇒α + β = -4/3 ___(1)
Product of the zeros = c/a
⇒αβ = 2k / 3
⇒(-2)β = 2k/3
⇒β = -k/3
Substitute the value of α and β in (1)
-2 + -k/3 = -4/3
⇒-k/3 = -4/3 + 2
⇒ -k/3 =2/3
⇒ k = -2
Therefore , the value of k for the given polynomial with the given condition is equal to -2.
The above question is incomplete , the complete question is :
For what value of k , - 2 is a zero of the polynomial 3x²+ 4x + 2k?
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Find [g ο f](-4) given f(x) = x + 4 and g(x) = -2x2
Answer:
Step-by-step explanation:
(
1
)
.
plugging the
4
into
g
(
x
)
and then putting what you get from that in to
f
(
x
)
(
2
)
.
plug
g
(
x
)
into
f
(
x
)
and then plug in the
4
Option 1:
Plug
4
into
g
(
x
)
:
g
(
x
)
=
−
2
(
4
)
−
6
=
−
8
−
6
=
−
14
Then plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
14
)
−
7
=
−
42
−
7
=
−
49
Option 2:
Plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
2
x
−
6
)
−
7
=
−
6
x
−
18
−
7
=
−
6
x
−
25
Finally plug
4
into our current
f
(
x
)
:
f
(
x
)
=
−
6
(
4
)
−
25
=
−
24
−
25
=
−
49
Which tool would you use to make chart?
The
tools
used to make a
chart
are Info-gram, tableau, Grafan, Chartist
What is a chart?
A
chart
can be defined as a
graphical
representation for
data
visualization, such that the data is represented with symbols as bars lines in line chart, or slices in a pie chart"
It is used to represent tabular numeric data and functions or other kinds of quality structure, providing different information.
The tools used in a chart includes;
Info-gram
tableau
Grafana
Chartist,
FusionCharts,
Datawrapper
ChartBlocks
Hence, a
chart
is a graphic representation of data.
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What is the domain and range of f/x )= x³?
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
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How do you find the degree and the number of turning points in a polynomial function?
To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.
To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.
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please help me with this problem
Answer:
40 orange marbles
Step-by-step explanation:
We know for every 12 marbles, we have 5 orange marbles and 7 green marbles
Now we have 56 green marbles. To get from 7 to 56, we take 7 times 8.
So, we do the same take 5 times 8 = 40 orange marbles
So, it contains 40 orange marbles!
Please help. In plus only answer if know the answer
Answer:x-int=4 1/4 y-int=-5 1/3
Step-by-step explanation:[tex]4x-3y=17\\ +3y =+3y\\ 4x=3y+17\\4x/4=3y/4 +17/4\\x=\frac{3}{4}x+ 4 \frac{1}{4} \\\\4x-3y=17\\-4x=-4x\\-3y=-4x+17\\-3y/-3=-4x/-3+17/-3\\y=\frac{4}{3}x -5\frac{1}{3}[/tex]
If 3x + 5y = 25, what is the value of 3x + 5y/5 =
Answer: 5
Step-by-step explanation: if you do something to one side of the equation, it has to be done to the other side.
in this case, they divided the left side (3x+5y) by 5
so so make both sides equal, you'd have to divide the right side (25) by 5 as well which would give you 5
2/9 x 1/3 =
Enter your answer as a mixed number in simplest form
Answer:
2 / 27
Step-by-step explanation:
2/9 * 1/3 = (2*1) / (9*3) = 2/27
The sum of 3 33 consecutive odd numbers is 69 6969. What is the third number in this sequence?.
The third number in this sequence is 23.
The sum of three consecutive odd numbers can be written as (2n-1) + (2n+1) + (2n+3) = 69, where n is a positive integer. Expanding the left side gives us 6n+1 = 69, which means n = 11. The third number in the sequence is (2n+1) = (2 × 11+1) = 23. Therefore, the third number in the sequence is 23.
In the given sequence, 1, –3, 9, –27, 81,..., each number is multiplied by -3 to get the next one in the sequence. Since the absolute values of the numbers in the sequence are increasing, the sequence is diverging to an infinite value, either positive or negative. Therefore, it can be concluded that the given sequence is a divergent sequence.
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If PS= RS = 31, PQ = 2v, and QR = v + 23, what is the value of v?
The value of the v is 11.5 units.
What is a Line Segment?
A line segment is a portion of a straight line that is defined by two points. It is a one-dimensional geometric figure with no width or area. Line segments can be drawn in many ways, including straight, curved, or jagged. The length of a line segment is the distance between the two points that define it. Line segments are commonly used to measure distances, form shapes, and construct geometric figures. Line segments can be used to define polygons, circles, and other shapes. Line segments are also used in mathematics to represent vectors and calculate angles. Line segments are a fundamental element of geometry and are used in a variety of applications, including navigation, construction, engineering, and computer graphics.
We have,
PS= RS = 31,
PQ = 2v,
and QR = v + 23,
v = ?
If PS= RS = 31,
then PQ = QR,
so, 2v = v + 23,
v = 23/2
v = 11.5 unit
Hence, the value of the v is 11.5 units.
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you are playing a game with your friend to see who can make the most baskets from the free throw line. each of you has 5 shots at the basket. how many ways are there for you to make exactly 4 shots?
The probability of making exactly 4 shots is 4/5, in where 4 is outcomes Favour to me and 5 is total possible outcomes.
what is probability?The probability is measured as the ratio of favorable outcomes of a particular event to the total possible outcomes of that event. The value of probability should be lies between 0 to 1.
what are favorable outcomes of an event?The term favorable outcome uses to determine the probability in mathematics. It is the possibility of happening expected incident of a particular event.
the ways in how i can make exactly 4 shots in the game = my favorable outcomes/total possible outcomes
=4/5
hence, the result is 4/5.
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Are there 2 answers to a quadratic equation?
The above quadratic equation has two solutions, as shown by the question Yes.
A quadratic equation is what?A second-order polynomial equation with a single variable, x, is known as a quadratic equation.
ax2 + bx + c = 0 is a quadratic equation in standard form.
x stands for an unknown (an variable)
With respect to known numbers, a, b, and c, where a 0
The polynomial's number of solutions is influenced by the equation's highest possible power given in the question.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation.
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