The value of "x" in the algebraic equation
3(-3x - 8) = 3(-6x + 3) which makes it true is equal to 11/3 and option C is correct.
What is an algebraic equation?An algebraic equation is a mathematical statement that contains two equated algebraic expressions.
We shall evaluate for the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) as follows:
-9x - 24 = -18x + 9 {expand the bracket}
18x - 9x = 24 + 9 {collect like terms}
9x = 33
x = 33/9 {divide through by 9}
x = 11/3
Therefore, 11/3 is the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) that makes it true.
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Find x if QT is an angle bisector. Round to the nearest tenth.
18
S
T
32
21
X
R
Rounding to the nearest tenth: x = 7.6
What is an angle bisector?
An angle bisector is a line or segment that divides an angle into two congruent angles. It is called an angle bisector because it bisects, or cuts in half, the measure of the angle. An angle bisector can also divide the angle into two angles of different measures if the angle is not congruent.
In order to find x, we can use the Angle Bisector Theorem which states that the ratio of the length of the segment from the vertex of the angle bisector to the sides of the angle is equal to the ratio of the length of the other two segments formed by the angle bisector.
In this case, we know that QT is an angle bisector of angle X, so we can set up the following proportion:
(ST/x) = (TR/XT)
We are given that ST = 21, TR = 32 and XT = 18
Solving for x:
x = (21*18) / (32+18) = 378 / 50 = 7.56
Hence, Rounding to the nearest tenth: x = 7.6
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Determine the type of dilation shown and the scale factor used.
The type of dilation that is used here as well as the factor used is given as: enlargement with scale of 2.5. Option 2
What is dilation in mathematics?Reducing the object's size by dilation is a change. The items are enlarged or shrunk by dilation. An picture that retains the original shape is created by this alteration. The size of the form does differ, though.
The smaller image is resized into a bigger image from what we can see in the images that we have before us.
We would have to divide all sides of the big square with the corresponding sides of the smaller square
20 / 8 = 2.5
15 / 6 = 2.5
Hence we would see that the scale factor that is used here is 2.5. Therefore the dilation that is used is the enlargement with scale factor 2.5. Option 2 is correct
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 5 If there were 4255 no votes, what was the total number of votes?
The total number of votes is given as 10212
How to solve for the number of votesThe total number of votes that would be in the city is given as 7400.
How to find the total number of votes
The ratio of votes is in terms of yes to no
This is 7 : 5
Given that the number of no votes is 4255, we can use this number in order to find the yes votes.
7 + 5 = 12
there were 4255 no votes.
we would have:
(5 / 12 )x= 4255
5x = 12 * 4255
5x = 51060
x = 10212
The total number of votes is given as 10212
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What is the table of 4?
The multiplication table for 4's underlying pattern: To begin with, let your child know that 4 is an even number. Therefore, no matter what number you multiply by 4 .
what is sequence ?A list of items in a sequence is one that is ordered (or events).The number of elements in an ordered sequence determines its length (potentially infinite). Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary types of sequences that you need to be familiar with. Number sequences are collections of numbers connected by some kind of rule. If you understand the rule, you can determine the numbers that will come after that in the sequence. Each number differs from the other in this case by 6. In this case, the rule for this sequence is to add 6 each time.
given
The multiplication table for 4's underlying pattern: To begin with, let your child know that 4 is an even number.
Therefore, no matter what number you multiply by 4, the result will always have either 0, 2, 4, 6 or 8 at the end.
With the aid of this method, kids will be able to distinguish multiples of 4, which will make learning the table of four much simpler.
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Lisa's father is 42 years old. His age is two more than five times Lisa's age. How old is Lisa?
Answer:
Lisa is 8 years old.
Step-by-step explanation:
If Lisa's father is 42, then we can easily find out what Lisa's age is from the problem. We simply just have to create an equation and then solve it.
The equation:
5x + 2 = 42
Solving said equation:
5x = 42 - 2
5x/5 = 40/5
x = 8
What you do to one side, must be done to the other.
Hope this helps!
maya wants to be able to take a series of four triangles and place them in a mobile design where all four triangles are attached at one point and are balanced so that they stay horizontal. Which statement best describes where she should attach each triangle?
A) Where the medians intersect
B) where the altitudes intersect
C) where perpendicular bisectors intersect
D) at any vortex
The correct statement is (D) at every vertex.
What is a vertex?The vertex of a triangle is the intersection of two sides. Vertices is the term used to describe objects with several vertices.
The ability to write an equation for a line given two points is a prerequisite. The intersection of two lines will then need to be solved, which will give you the intersection's coordinates.
One of the triangle's vertices is at this intersection of two lines.
So, we know that 4 triangles are joined to make them horizontal.
This can be done when the vertex is attached to all 4 triangles.
Then, statement (D) will be a correct statement.
Therefore, the correct statement is (D) at every vertex.
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PLS HELP!! 15 points!
The origin's coordinates are as follows: (0, 0). A pair of ordered numbers contains one point's coordinates in the coordinate system.
What do you meant by ordered pair ?To accomplish this, convert the total number of liters of fuel you purchased into gallons (multiply by 0.219). the initial mileage is subtracted from the total. Then, multiply the distance traveled by the number of gallons of fuel used. Miles per gallon are provided. The concept of proportionality refers to a graphed proportional relationship in which the independent variable is represented by x and the dependent variable by y.
Independent variables describe the input values in a relationship and are typically represented by the x coordinate in the ordered pairs (x, y). When two or more parameters are directly or indirectly proportional to one another, the relationship is denoted by the symbols a=kb or a = k/b, where k denotes the direction of the relationship between the two variables.
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It is given that y is directly proportional to x.
1
2345
y
-4
-8
-12
-16
-20
What is the constant of variation?
When it is assumed that y is directly proportional to x, the variational constant is -4.
what is variation ?A variation is a relationship between a set of values for one variable and another set of values. direct change. If m is a nonzero constant and b = 0, the function y = mx (commonly written y = kx) that results from the equation y = mx + b is known as a direct variation. Variation Theory is a broad theory of learning that is mostly applied in mathematics teaching and pedagogy. It highlights a concept's key components by concentrating on what remains the same and what changes, which creates the possibility for meaningful connections.
given
If y and x are directly proportionate, we would write:
If we include the proportionality constant, or variation, k, we get: y = kx
Any ordered pair from the table can be used to determine the value of y when x=1. y = -4 = k (1) k = -4
When it is assumed that y is directly proportional to x, the variational constant is -4.
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The graph below shows the percentages of ingredients in a salad mix.
A pie chart titled Percentages in salad mix. 40 percent is iceberg, 27 percent is romaine, 15 percent is spinach, 12 percent is arugula, 6 percent is carrots.
Alyssa buys a 38-ounce container of salad mix. About how many ounces of iceberg lettuce does the container have?
8 ounces
16 ounces
27 ounces
38 ounces
Using percentage to determine the ounce of iceberg lettuce in the salad from the pie chart, we have 15.2 ounces
What is Pie ChartA pie chart is a circular chart that is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents. Pie charts are very useful for displaying data and are most commonly used to show percentages or proportional values of different categories relative to the whole.
We can use the concept of percentage to determine the number of ounces of iceberg lettuce present.
In the pie chart, the percentage of ice berg lettuce is 40% and the quantity of salad bought is 38 ounce
40 / 100 = x / 38
0.4 = x / 38
x = 38 * 0.4
x = 15.2 ounces
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Planes X and Y and points C, D, E, and F are shown.
Vertical plane X intersects horizontal plane Y. Point D is on the left half of plane Y. Point F is on the bottom half of plane X. Point E is on the right half of plane Y. Point C is above and to the right of the planes.
Which statement is true about the points and planes?
The line that can be drawn through points C and D is contained in plane Y.
The line that can be drawn through points D and E is contained in plane Y.
The only point that can lie in plane X is point F.
The only points that can lie in plane Y are points D and E.
The correct option is (B) The line that can be drawn through points D and E is contained in plane Y.
What are planes and points?A point is a location in space. It has neither shape nor size. A line is a connected set of points that extends infinitely in two directions. A plane can be defined by three noncollinear points, two parallel lines, or two intersecting lines.
The planes X and Y and points C, D, E and F are shown in the given figure.
We are to select the TRUE statement about the points and the planes.
We know that, if two points lie in a plane, then the line drawn through the points will contain in the same plane.
The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contain in plane Y.
So, option (A) is NOT correct.
The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contain in plane Y.
So, option (B) is CORRECT.
Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.
So, option (C) is NOT correct.
Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.
So, option (D) is NOT correct.
Thus, the correct option is, The line that can be drawn through points D and E is contained in plane Y.
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In the coordinate plane point a has coordinates of A (-5,8). Which is further from a point B or point C given that they have coordinates of B(1,0) and C(-10,16)
The point that is further from point A is point B
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points A (-5, 8) and B(1, 0) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 1)² + (8 - 0)²}
d =√{36 + 64}
d = √100
d = 10 units
distance between points A (-5, 8) and C(-10, 16) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 + 10)² + (8 - 16)²}
d =√{25 + 64}
d = √89
d = 9.43 units
comparing both points shows that point B shows further away
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Sofia earned a score of 460 on Exam A that had a mean of 400 and a standard
deviation of 20. She is about to take Exam B that has a mean of 100 and a
standard deviation of 25. How well must Sofia score on Exam B in order to do
equivalently well as she did on Exam A? Assume that scores on each exam are
normally distributed.
X2 = 175 Sofia needed a certain grade on Exam B to perform at the same level as she did on Exam A.
What is standard deviation ?Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high. The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range. The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second, though, is unmistakably wider.
given
X1
u1 = 400 u2 = 100
20 25
X2
Z1 score = Z2 score
X1 - u1 / 20 = X2 - u2 / 25
460 - 400 / 20 = X2 -100 / 25
3 = X2 - 100 /25
X2 = 175 score on exam b
X2 = 175 Sofia needed a certain grade on Exam B to perform at the same level as she did on Exam A.
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Construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in non filtered and filtered cigarettes. Do the cigarette filters appear to be effective? ( Hint: the filters reduce the amount of tar ingested by the smoker)
The table including relative frequencies based on the frequency distributions is as follows:
Tar(mg) Relative frequency Relative frequency
(Nonfiltered) (Filtered)
3-8 0% 4%
9-14 0% 12%
15-20 4% 24%
21-26 0% 60%
27-32 56% 0%
33-38 28% 0%
39-44 12% 0%
Yes, the cigarette filters appear to be effective.
What are relative frequencies?
The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.
Tar(mg) Frequency Relative Frequency Relative
frequency frequency
(Nonfiltered) (Filtered)
3-8 0 0% 1 4%
9-14 0 0% 3 12%
15-20 1 4% 6 24%
21-26 0 0% 15 60%
27-32 14 56% 0 0%
33-38 7 28% 0 0%
39-44 3 12% 0 0%
Hence, the cigarette filters appear to be effective because the relative frequency of the higher tar classes is greater for non filtered cigarettes.
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what is 270 divided by 4.25
Answer:
1080 / 17
Step-by-step explanation:
270 divided by 4.25 = 27000 ÷ 425
= [tex]\frac{27000}{425}[/tex] = [tex]\frac{1080}{17}[/tex]
A milk truck delivers 459 dozen gallons of milk to stores in 1 day. Write and solve an equation to find g, the number of gallons of milk the milk truck delivers in 1 day I don't get it help!
If a milk truck delivers 459 dozen gallons of milk to stores in 1 day. the equation to show the quantity of milk delivered in one day is
459xand the amount of milk delivered in one day is
5508 gallons of milkHow to solve for the amount of milk truck delivered in one dayThe information necessary to find the quantity of milk delivered in one day is that 1 dozen is equal to 12 pieces
The total number of gallons of milk delivered
the equation is 459x
where x represents number in a dozen
amount delivered
= 12 * 459
= 5508 gallons of milks
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What scale factor was used in the dilation?
The scale factor used in the dilation of the triangle ABC is 3.
What is the dilation of a triangle?Dilation is a method for generating analogous figures decreasing or increasing their dimensions by some scaling factors.
By dividing distances by the scale factor, each point is stretched outward from the central point D if the scaling factor is more than 1 or inwards if the scale factor is less than 1.
Considering the triangle ABC:
The length of the side AB is 2 units
Compared with triangle DEF, the length of the similar side DE is 6 units
The scaling factor = length of side DE /length of the side AB
The scaling factor = 6 / 2
The scaling factor = 3
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For $2.75 you can buy 20 small bags of jelly beans. How much is 1 bag of jelly beans?
Answer:
The answer is $ 0.13
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Can the sides of a triangle have lengths 5'7 and 13?
The sum of the lengths of any two sides of a triangle must exceed the length of the third side; therefore, 5+7 > x, which cannot happen if x = 13.
Which Cannot be sides of a triangle?Assume that a triangle has sides that measure 5, 7, and 11. Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle. The triangle is therefore not acute. Thirteen plus seven equals twenty, and twenty is more than nine. The Triangle Inequality Theorem is satisfied by this set of side lengths. A triangle is formed by these lengths. No, not in the traditional sense of the word (Euclidean geometry). A "degenerate triangle" is possible, but it isn't exactly a triangle in the sense that we often think of triangles 8 + 7 = 15 the length of any two sides added together.To learn more about sides of a triangle refer to:
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After school Andy spends 15 minutes on science homework 20 minutes on math homework 15 minutes on literature homework what was the ratio of the number of minutes she spends on on math homework to the total she spends on homework each night
The ratio of the number of minutes she spends on on math homework to the total she spends on homework each night is 2:5.
What is ratio?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Here Andy spends 15 minutes on science homework 20 minutes on math homework 15 minutes on literature homework then,
Total time is ,
Science home work time+ Math home work time+ Literature home work time
=> 15+20+15 = 50 mins.
Now the ratio to the number of minutes she spends on on math homework to the total she spends on homework each night then
=> 20 : 50
=> 2 : 5.
Hence the ratio of the number of minutes she spends on on math homework to the total she spends on homework each night is 2:5.
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Solve the following equation for z
Answer: for one what equation and two what is your profile pic god dam you go a big nose
Step-by-step explanation:
what is the length of AB
Answer:
AB ≈ 5.2
Step-by-step explanation:
given ∠ CAD = ∠ BAD = Θ
then AD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is
[tex]\frac{BD}{CD}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )
[tex]\frac{4.1}{4.3}[/tex] = [tex]\frac{AB}{5.5}[/tex] ( cross- multiply )
4.,3 AB = 4.1 × 5.5 = 22.55 ( divide both sides by 4.3 )
AB ≈ 5.2 ( to one decimal place )
Write the standard equation of the circle given a center (-14,7) and a radius of 2
Answers-
A. (x-14)^2 + (y+7)^2 =1
B. (x+14)^2 + (y-7)^2 =8
C. (x-14)^2 + (y+7)^2 =4
D. (x+14)^2 + (y-7)^2 =4
The standard equation of the circle given a center (-14,7) and a radius of 2 is (x+14)^2 + (y-7)^2 =4.
What is standard equation?The standard equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. This equation can be used to graph any line, provided the values of m and b are known. It can also be used to calculate the slope and y-intercept of any given line.
This equation describes a circle that has a center at the point (-14,7) and a radius of 2 units.
The equation (x+14)^2 + (y-7)^2 =4 can be used to determine the coordinates of points on the circle, as well as the length of its circumference.
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subtract 11 hrs from 6 hrs 51 min
Answer:
(A) -5 hr 51 mins (B) 7:51 am/pm
Step-by-step explanation:
(A):
6 hr 51 mins
-
11 hr 0 mins
___________
-5 hr 51 mins
(B):
6 hr 51 mins - 11 hr 0 mins = 18 hr 51 mins - 11 hr 0 mins = 7 hr 51 mins am/pm or 7:51 am/pm.
Hope this helps!
P.S. Feel free to suggest any edits.
i need the answer please
Answer:
(1.5 , -5.5)
Step-by-step explanation:
Finding the midpoint when endpoints are given:(9 , -8) ; x₁ = 9 & y₁ = -8
(-6 , -3) ; x₂= -6 & y₂ = -3
[tex]\sf \boxed{\bf Midpoint= \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]
[tex]\sf = \left(\dfrac{9-6}{2},\dfrac{-8-3}{2}\right)\\\\\\=\left(\dfrac{3}{2},\dfrac{-11}{2}\right)\\\\\\=(1.5, -5.5)[/tex]
The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
The graphical representation that would be most appropriate for the data, given the number of different breakfast cereals sold, is B. Histogram, because there is a large set of data.
Why are histograms used for large sets of data ?Histograms are used for large sets of data because they provide a visual representation of the distribution of the data. They are particularly useful for understanding the distribution of continuous variables, such as measurements or time series data.
One of the main advantages of histograms is that they allow for easy comparison of large sets of data. The use of bars to represent the data makes it easy to see the overall shape of the distribution and identify patterns or outliers. Additionally, histograms can be used to compare multiple sets of data at once, allowing for easy comparison of different groups or changes over time.
Another advantage of histograms is that they can be used to identify the underlying probability distribution of a dataset, which is useful for statistical analysis and modeling.
This is why, given the fact that the data contains information from 1, 000 different cereals, a histogram is best to show this as the data is large.
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Answer: B Histogram
Step-by-step explanation:
Divide (36z^2y^6-12z^6y^6) divided by (4z^5y^2)
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
What is algebraic in mathematics?Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we use numbers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we use variables such as x, y, and z in addition to numbers.
Here,
Given:
=> (36z²y⁶ - 12z⁶y⁶) / 4z⁵y²
=> 9y⁴ /z³ - 3zy⁴
thus , we get the solution for the given algebraic expression.
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
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What are the 3 coordinate systems you use for AutoCAD drawings?
The 3 coordinate systems you use for Auto CAD drawings are the Absolute coordinate system, Relative Rectangular coordinate system, and Relative Polar coordinate system.
Absolute Coordinates use the Cartesian System to specify a position in the X, Y, and Z axes to locate a point from the 0 and X, 0 and Y, and 0 and Z (0,0,0) points.
The relative coordinate started with the symbol telling Auto CAD it was a relative coordinate. Using relative coordinate points entered by typing x,y.
Polar coordinates are used when you need to draw the next points at a specific angle. The polar coordinates system in Auto CAD specifies the distance length at which angle. Using polar coordinate points entered by typing distance<angle.
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A rock climber descends 31 feet into a small canyon. Then she climbs up 5 feet. Which integer represents her final position in feet, relative to where she started?
Answer:
-15ft
Step-by-step explanation:
Answer: - 26
-31 + 5 = -26
Solve the quadratic equation numerically (using tables of x- and y- values). X squared + 7 x + 12 = 0.
The quadratic equation numerically for [tex]x^{2} + 7x +12 = 0[/tex] is when
x = -4 and x =-3
The equation is [tex]x^{2} + 7x +12 = 0[/tex]
To solve this equation using the table, we change the equation into a function
So, the function is F(x) = y = [tex]x^{2} + 7x + 12[/tex]
We have to find the value of x which we can substitute to the equation to get the y value to become 0. Since it is a quadratic equation, x will have 2 values, on [tex]x^{2}[/tex] & 7x
X [tex]x^{2} + 7x + 12[/tex] = Y
-4 = [tex]-4^{2}[/tex] +7(-4) + 12 = 0
-3 = [tex]-3^{2}[/tex] +7(-3) + 12 = 0
-2 = [tex]-2^{2}[/tex] +7(-2) + 12 = 2
-1 = [tex]-1^{2}[/tex] +7(-1) + 12 = 6
0 = [tex]0^{2}[/tex] +7(0) + 12 = 12
1 = [tex]1^{2}[/tex] +7(1) + 12 = 20
2 = [tex]2^{2}[/tex] +7(2) + 12 = 30
Based on table above we can see Y = 0, when X = -4 and X = -3
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work out 4 1/2×1 2/5 give your answer in its simplest form