Question 1. Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C.
(a) Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)
(b) Show that PQ is parallel to BC. (2 marks)
a) The coordinates of the midpoints P and Q are given as follows:
P(-0.5, 1.5).Q(-1.5, -4).b) The two segments are parallel because they have the same slope.
How to calculate the midpoints?The midpoints between two points is given by the mean of the coordinates of these two points.
Hence the midpoint P of AB has the coordinates given as follows:
x - coordinate: (2 - 3)/2 = -0.5.y - coordinate: (-1 + 4)/2 = 1.5.The midpoint Q of AC has the coordinates given as follows:
x - coordinate: (2 - 5)/2 = -1.5.y - coordinate: (-1 - 7)/2 = -4.What are parallel segments?Parallel segments are segments that have the same slope, that is, the same result of the division of the change in y by the change of x of two points in the segment.
The slopes of PQ and BC are given as follows:
PQ: m = (-4 - 1.5)/(-1.5 - (-0.5)) = 5.5BC: m = (-7 - 4)/(-5 - (-3)) = 5.5.More can be learned about midpoints at https://brainly.com/question/5566419
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3. What is the best description of the function in Item 2?
Answer:
Could you give a little more context. I can help.
Draw the image of triangle ABC under a dilation whose center is A and scale factor is 4.
The image of triangle ABC under a dilation whose center is A and scale factor is 4 is as follows.
What is dilation?
Dilation involves changing the size of a shape.
Main body:
Assume point P is the center of origin, then we have the following coordinates of ABC
A= (1,0)
B= (-2,0)
C= (0,2)
The scale factor (k) is given as:
K = 4
So, the dilation rule is represented as:
(x, y) = 4 *(x,y)
Using the above dilation rule, the following coordinates represent the image of triangle ABC
A' =(4,0)
B' =(-8,0)
C' =(0,8)
See attachment for the image of the dilation.
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Find how long it takes$ 2500 to double if it is invested at 6 % interest compounded semiannually. Use the formula A=P(1+r/n ) to solve the compound interest problem.
It will take approximately ___years.
It takes 11.55 years for money to double if invested at 6% compound interest.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.Compound interest is commonly abbreviated C.I. in mathematics.Calculating the answer exactly: P⁰°⁰⁶ⁿ=A .
We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.
P⁰°⁰⁶ⁿ = 2P
We divide both sides by P
e⁰°⁰⁶ⁿ = 2
Using natural logarithm:
0.06 n = ln(2)
n = ln(2)/0.06
n = 11.55 years
Hence, It takes 11.55 years for money to double if invested at 6% compound interest.
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Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
A number line going from negative 110 to positive 10. A closed circle is at negative 50. Everything to the right of the circle is shaded.
She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.
What is an inequality ?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
From given question :
-5x-3.5>6.5
-5x > 10
X > -50
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
- 5x - 3.5 + 3.5 > 6.5 + 3.5
- 5x > 10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
- 5x / -5 < - 50 / -5
we get
x < 10
so,
She should divide both sides by -5 while she multiplied by -5 on other side
and she also did not change the > symbol to a < symbol
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A total of 627 tickets were sold for the school play. They were either adult tickets or student tickets. There were 73 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350
Step-by-step explanation:
Let "a" represent the number of adult tickets sold and "s" represent the number of student tickets sold. We can set up the following equation to represent the information given:
a + s = 627
s = a - 73
Substituting the second equation into the first equation gives us:
a + (a - 73) = 627
2a - 73 = 627
2a = 700
a = 350
Thus, there were 350 adult tickets sold.
Why do you think taxes have become more complicated since 1913?
Answer:
Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.
Step-by-step explanation:
What was the tax rate in 1913?
The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.
Evaluate the expression (x+3)(3x^2-4x-5) ?
3x³ + 5x² - 17x - 15
Step-by-step explanation:Here are the steps for solving your problem:1. Distribute
(x + 3)(3x² - 4x - 5)
x(3x² - 4x - 5) + 3(3x² - 4x - 5)
2. Distribute
x(3x² - 4x - 5) + 3 (3x² - 4x - 5)
3x³ - 4x² - 5x + 3 (3x² -4x - 5)
3. Distribute
3x³ - 4x² - 5x + 3 (3x² -4x - 5)
3x³ - 4x² -5x + 9x² - 12x - 15
4. Combine like terms
3x³ - 4x² -5x + 9x² - 12x - 15
3x³ + 5x² - 5x - 12x - 15
5. Combine like terms
3x³ + 5x² - 5x - 12x - 15
3x³ + 5x² - 17x - 15
Solution:
3x³ + 5x² - 17x - 15
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
What is the domain of the inverse of the function graphed below?
Write your answer as a compound inequality.
The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.
What is compound inequality?A mathematical statement that expresses the inequality between two inequalities combinedly.
from the graph, we have two inequalities, x>5 and x<6
it can be written as 5<x<6
What is inverse of a function?A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.
The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}
The graph also refers the inequalities of x>5 And x<6
compound inequalities of domain 5<x<6
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Find the mean and standard deviation for each uniform continuous model. (Round "Mean" answers to 1 decimal place and "Standard deviation" answers to 4 decimal places.) Mean a. U(0, 15) b. U(90, 230) c. U(4, 92)
The mean and the standard deviation of the distributions are
Mean = 7.5, Standard deviation = 4.3301Mean = 160. Standard deviation = 40.4145Mean = 48, Standard deviation = 25.4034How to determine the mean and the standard deviation?The distribution is given as:
A uniform continuous model
The mean and the standard deviation of this type of model are
Mean = (a + b)/2
Standard deviation = (b−a)/√12
Using the above formulas, we have
a. U(0, 15)
Mean = (0 + 15)/2 = 7.5
Standard deviation = (15−0)/√12 = 4.3301
b. U(90, 230)
Mean = (90 + 230)/2 = 160
Standard deviation = (230 − 90)/√12 = 40.4145
c. U(4, 92)
Mean = (4 + 92)/2 = 48
Standard deviation = (92 - 4)/√12 = 25.4034
Hence, the standard deviation of U(4, 92) is 25.4034
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write 500;000 in expanded form in tow different ways
Answer:
500,000 can be written in expanded form in two different ways:
500,000 = 500,000
500,000 = 5 x 100,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 0 x 1
In both cases, the expanded form shows the value of each digit in the number. The first way simply lists the number itself, while the second way breaks down the number into its component parts and shows the value of each digit in relation to the place value it holds in the number.
to create a pivottable layout, you can drag fields from the field list to an area box in the pivottable fields pane
a. true
b. false
Yes , we can drag fields from the field list to an area box in the pivot table fields pane in order to create a pivot table. Hence , true.
The four sections of the pivot table
Report FilterColumn LabelsRow LabelsValuesare located at the bottom of the PivotTable Field List window.
The fields will appear in the corresponding region of the worksheet's pivot table layout when you drag them into these locations.
Only the fields included in the PivotTable Field List can be moved in Excel 2007. If you try to drag the Promo field onto the pivot table in the screen photo below, the cursor displays an X. The drag-and-drop function is broken.
You can alter a setting in the pivot table options if you'd like to drag the pivot fields onto the worksheet layout.
To access the PivotTable Options menu, right-click a cell in the pivot table.Put a checkmark next to Classic PivotTable Layout on the Display tab.PivotDrag02To close the PivotTable Options dialogue box, click OK.To learn more about pivot table
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Which of the following is the equation of the line that is perpendicular to y = - 4x - 5 and goes through the point (-2, 3)?
O y = - 4x-5
Oy = 4x + 11
O y = x + 1/
O y = -x + 1/
Answer:
[tex]y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=-4x-5[/tex]
If two lines are perpendicular to each other, their slopes are negative reciprocals.
The slope of the given equation is -4.
Therefore, the slope of the perpendicular line is ¹/₄.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-2, 3) into the point-slope formula to create the equation of the perpendicular line.
[tex]\implies y-3=\dfrac{1}{4}(x-(-2))[/tex]
[tex]\implies y-3=\dfrac{1}{4}(x+2)[/tex]
[tex]\implies y-3=\dfrac{1}{4}x+\dfrac{1}{2}[/tex]
[tex]\implies y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]
Need a Detailed explanation
Answer:
The dividend in the synthetic division below is x+2:
4 | -6 -5 4 -7
- --------------
- -1 -1 1 -5
0 | -5 -4 3 -2
- --------------
2 | x+2
In synthetic division, the numbers in the top row represent the coefficients of the polynomial being divided, and the number in the bottom row represents the value of the dividend. In this case, the dividend is x+2 because it is the only number in the bottom row that is not a result of the division operation
How is a system of two linear inequalities in two variables different from a system of two linear equations in two variables?
Answer:
A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.
There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:
Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).
The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.
The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.
The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.
Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.
Liam spent $5.76 on 12 pounds of potatoes. How much did he spend per pound?
Answer:
$0.48/pound
Step-by-step explanation:
$5.76 divided by 12
Select all the equations that are equivalent to y-4 =2/3(x-1)
The equivalent equations of y - 4 = 2/3(x - 1) are y - 4 = 2/3x - 2/3 and y = 2/3x + 10/3
How to determine the equivalent equation?From the question, we have the following parameters that can be used in our computation:
y - 4 = 2/3(x - 1)
We start by expanding the bracket
So, we have the following representation
y - 4 = 2/3x - 2/3
Next, we add 4 to both sides of the equation
This gives
y - 4 + 4 = 2/3x - 2/3 + 4
Evaluate the like terms
So, we have the following representation
y = 2/3x + 10/3
Hence, the equivalent equation is y = 2/3x + 10/3
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Kristin spends 30% of her savings on a watch and 60% of the
remainder on a dress. What percentage of her savings is left?
Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
Given that,
Kristin spends thirty percent of her savings on a watch and sixty percent on a dress.
We have to find what portion of her savings is still available.
We know that,
Kristin spends thirty percent of her savings on a watch.
Sixty percent on a dress.
The money she has a 100% in that if she spend 30% on watch she get 70% then if she spend 60% on dress she will have 10%
Therefore, Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
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43. What system of inequalities is represented by the graph? (1 point)
-2 -1
2
- C
0
-1
0 1
2
Oy≤3x-2 and y2-4x+2
Oy23x-2 and y≤-4x+2
Oy≤-2x+3 and y 22x-4
Oy2-3x-2 and y ≤4x+2
3 4 question is in the photo. Please help if you can and thank you in advance.
The graph's representation of the inequality system is
y≤3x-2 and y≥-4x+2. So, option a is correct.
What is meant by inequality?One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:
A less than sign, such as a, denotes that an is greater than b.
Therefore, The system of inequalities that is represented by the graph is
y≤3x-2 and y≥-4x+2. So, option a is correct.
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URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
identify the conic section represented by the equation (x+1)^2+(y-2)^2=8
Step-by-step explanation:
A circle with a center of (-1,2) and a radius
of
[tex]2 \sqrt{2} [/tex]
What is the value of x in the figure
shown?
37°
y
(3x + 1)
Answer:
x=4
Step-by-step explanation:
x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123
The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.
The angle is formed by two rays and a common point.
To calculate the value of x using the diagram attached below:
∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°
On substituting the values from the figure,
∠AOC=3x-7
∠COD=55
∠BOD=x+20
∠AOC+∠COD+∠BOD =3x-7+55+x+20
3x-7+55+x+20=180
4x+68=180
4x=112
x=28
Thus, the value of x is 28 for the figure attached below.
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(3x-2)(2x2+5x-1) what is not equivalent to the product
The only option that is not an equivalent of the product of both polynomials is; C: 6x³ + 11x² − 13x + 2
What kinds of equations are there?Equations can be classified as either identities or conditioned equations. For each quantity of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equals sign ("="), which separates two expressions, is a symbol for an equation.
Here,
We are given the expression;
(3x - 2)(2x² + 5x - 1)
The result of expanding the polynomial is;
6x³ + 11x² − 13x + 2
Looking at the given options as seen online, the only one that is not an equivalent of the given product is;
Option C) : 6x³ + 11x² − 13x + 2 is correct
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or
Rewrite the following equation in standard form.
y = 9x + 6
Answer:
9x-y=10
Step-by-step explanation:
The formula for standard form is Ax + By =C
So, y=9x-10
-1(-9x+y=-10)
9x-y= 10
Dos lados de un triángulo miden 10 y 14m y el ángulo comprendido entre ellos mide 37º. Calcula el área de dicha región triangular.
From the given parameters, the area of the triangle is 288m².
How to calculate the area of a triangle?
A triangle is a polygon with three angles, three vertices and three sides whose sum of angles is 180⁰
Let the vertices of the triangle be labelled ABC
/AB/=16m
/BC/=45m
<ABC=127⁰
The given information formed an obtuse angled triangle.
Area of the triangle (A) = [tex]\frac{1}{2}[/tex]ACsinB
Substituting the various values in the formula we have;
A=[tex]\frac{1}{2} *16*45*sin127^{0}[/tex]
simplifying the equation to get;
A=8*45*0.7986
A=287.5088
A=288m²
Therefore, the area of the triangle to the nearest whole number is 288m²
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Reflect (8,
-6) across the x-axis.
Then reflect the result across the y-axis.
What are the coordinates of the final point?l
Answer:
(-8.6)
Step-by-step explanation: If you look at a graph and pinpoint the location of (8,-6) by going up 8 and then going to the left 6. so the point of (8.-6) is in the top left box and if we are reflecting over the x-axis and the y-axis the point will be at the lower right box therefore the answer is (-8.6).
Compare the triangles and determine whether they can be proven congruent, if possible by SSS, SAS, ASA, AAS, HL, or N/A (not congruent or not enough information). Select your answer.... Take your time this is a grade!O N/AO SASO SSSO AASO HL
The triangles can be proven congruent using the ASA congruence postulate.
∠ABK is congruent to ∠CBK.BK is congruent to BK (common side )∠AKB is congruent to ∠CKB.Thus, we can say that triangles ABK and CBK are congruent.
Triangles are congruent, according to the Angle Side Angle Postulate (ASA), if any two angles and their included side are equivalent in the triangle. The side between two angles is considered an included side.
Additionally, you can confirm that your two triangles are congruent by employing the Side Angle Side Postulate (SAS). In this case, we choose a side and its equivalent side on two triangles rather than two angles.
Triangles are said to be congruent according to the SAS Postulate if any pair of corresponding sides and their included angle are also congruent.
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Which of the following graphs represents the equation x-5y=27
The graph that shows the straight line → x - 5y = 27 is plotted and attached.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
[m] is slope of the line.
[c] is the y - intercept of the line.
Given is the equation of the line as -
x - 5y = 27
The given equation of the line is -
x - 5y = 27
Rearranging the equation, we get -
5y = x - 27
y = (1/5)x - (27/5)
y = 0.2x - 5.4
Now, refer to the graph attached. The slope [m] of the equation will be -
m = 0.2 and the [y] - intercept will be y = - 5.4.
Therefore, the graph that shows the linear relation → y = 0.2x - 5.4 is plotted and attached.
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A wood state casket labeled 6/6XX would measure in length 6 feet 6 inches and in width
Answer: 28 inches
Hope this helps!!! :)
What is the quotient of 14 divided by 3/4
Answer:
18.6
Step-by-step explanation:
Answer this! You'll get brainliest!
Answer:
See below
Step-by-step explanation: