1.
a+6=6
Solving for a:
a = 0
a-5= -8
Solving for a:
a = -13
a x -10= 100
Solving for a:
a = -10
(5+2a) ÷ 17 = 3
Solving for a:
a = -4
2.
a) The dimensions of the field are 7m by 7m.
b) The perimeter of the field is 28m.
c) To find the area of the field, you could use the equation: length x width = area. In this case, the length and width are both 7m, so the equation would be 7m x 7m = 49m^23
3.
a) T | V
1 | 3
2 | 5
3 | 7
4 | 9
5 | 11
b) The pattern rule is that the value (V) is 2 greater than the previous value.
a test has 75 questions worth 216 points total. the test consists of multiple-choice questions worth 2 points each and short answer questions worth 4 points each. how many of the total points on the test are from short-answer questions? do your figuring here.
There are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.
What is algebra ?
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division.
We know that the test has 75 questions and it is worth 216 points total.
We know that multiple-choice questions worth 2 points each and short answer questions worth 4 points each.
To calculate the number of points from short-answer questions, we need to find out how many questions are short-answer and multiply that by 4 (points per question).
Let x be the number of short-answer questions.
We know that x + 75 - x = 75, which is the total number of questions on the test.
Also, we know that x * 4 + (75-x) * 2 = 216, which is the total number of points on the test.
Solving for x, we get:
x * 4 + 150 - 2x = 216
2x = 66
x = 33
So there are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.
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Which of the following is a solution of the equation 2x+y =10 ?
A.x=2, y =3
B.y =0
C.x=7, y=-2
D.x= 3, y =3
The solution of the equation 2x + y = 10 is B. x = 5, y = 0.
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x, y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given, A linear equation 2x + y = 10.
To find the solution we can put the solutions given in the options.
Let, x = 2, y = 3.
So, 2x + y = 10.
4 + 3 ≠ 10.
Let,
x = 7, y = - 2.
14 - 2 ≠ 10.
let,
x = 3, y = 3.
6 + 3 ≠ 10.
Let, x = 5, y = 0.
10 + 0 = 10 (satisfied).
Q.Which of the following is a solution of the equation 2x+y =10 ?
A.x=2, y =3
B.x = 5, y =0
C.x=7, y=-2
D.x= 3, y =3
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When the two segments are equal then the two segments are both?
When two line segments are of equal length then both the line segments are congruent to each other.
As given in the question,
Let us consider two line segments are AB and PQ.Length of the line segment AB is equal to 5 cm.And the length of the line segment PQ is equal to 2( 2.5 )cm.After simply the length of the line segment PQ is equal to 5 cm.Length of the line segment AB is equal to the length of the line segment PQ.When the length of two line segments are of equal length they are known as congruent line segments.Therefore, the two line segments with equal lengths they both are congruent to each other.
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suppose that 70% of college women have been on a diet within the past 12 months. a sample survey interviews an srs of 267 college women. what is the probability that 75% or more of the women in the sample have been on a diet?
The probability that 75% or more of the women in the sample have been on a diet is 0.944.
The probability that 75% or more of the women in the sample have been on a diet can be calculated by using the binomial formula. The formula is P(X>=x) = 1 - P(X<x). The parameters in this case are as follows: n = 267, p = 0.7, and x = 201.5 (which is 75% of 267). Therefore, the probability that 75% or more of the women in the sample have been on a diet is 1 - P(X<201.5). Solving for this probability, P(X>=201.5) is 0.944. Therefore, the probability that 75% or more of the women in the sample have been on a diet is 0.944.
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Explain how to solve 5x − 2 = 8 using the change of base formula . include the solution for x in your answer. round your answer to the nearest thousandth.
x = 2 is the solution to the equation 5x - 2 = 8.
What is the logarithm?
A logarithm is a power to which a number must be raised in order to get some other number. For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.
The change of base formula for logarithms allows us to change the base of a logarithm without changing the value of the logarithm.
The formula is: logb(x) = (logc(x)) / (logc(b))
To solve 5x - 2 = 8 using the change of base formula, we will first bring the equation to one side and get 2 = 5x - 8.
Then we will add 8 to both sides of the equation to get 2 + 8 = 5x, which gives us 10 = 5x.
Finally, we will divide both sides of the equation by 5 to get x = 2.
x = 2
Therefore, x = 2 is the solution to the equation 5x - 2 = 8.
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The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) and its respective focus at (0, 14). Which equation represents the comet's orbit
The equation of comet's orbit is [tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1
what is hyperbola?A hyperbola is a geometric shape made up of two branches that are symmetric about a center point and asymptotic to two lines called the asymptotes. It is defined by the equation (x^2/a^2) - (y^2/b^2) = 1. It is a type of conic section, similar to a parabola and an ellipse.
If the vertices and foci's of hyperbola have specified coordinates are of the form (0,10) and (0,14)
then
The y-axis serves as the transverse axis.
so
The formula for the equation is:
(y-k)^2/a^2-(x-h)^2/b^2=1
In this issue
The value of the center (h,k) is (0,4)
It follows that (0,a-k)) = (0,10)
a=10-4=6
(0,c-k) equals (0,14)
c=14-4=10
Identify b's value.
b^2=c^2-a^2
b^2=10^2-6^2
b^2=64
therefore
The formula reads as follows:
[tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1
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I really need helppp
Answer:
b = 8,3
Step-by-step explanation:
b + (-8,3) = 0
b - 8,3 = 0
b = 8,3
In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE?
The triangles are similar because all the pairs of corresponding angles are congruent. Therefore, the answer is D.
How to find similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
In a simpler term, similar triangle have the same shape but the sizes might varies.
Therefore, Let's check if ΔACB is similar to ΔDCE.
If two triangles have two of their angles equal, the triangles are similar.
Hence,
m∠A = 55 degrees
m∠E = 35 degrees
Therefore, using sum of angles of a triangle is 180 degrees,
∠ACE = ∠DCE = 90 degrees
m∠B = 35 degrees
Therefore,
m∠B = m∠E
∠ACE = ∠DCE = 90 degrees
Finally, the triangles are similar because al pairs of corresponding angles are congruent.
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a rectangular prism measures 2 yd by 10 yd by 5 yd. if the dimensions of the box were all doubled, how would the surface area of the box change?
If the dimensions of the box were all doubled, then the surface area of the box be 640 square units.
Use the concept of prism defined as:
A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat sides, and identical bases.
Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.
Given that,
The dimension of the rectangular prism = 2yd x 10yd x 5yd
Since we know that,
Dimension of prism = length x breadth x height
length x breadth x height = 2yd x 10yd x 5yd
Therefore,
Length = 2 yd
Breadth = 10 yd
Height = 5 yd
Now if dimension doubled the,
The dimension of the new prism = 4yd x 20yd x 10yd
Then,
Length 'l' = 4 yd
Breadth 'b'= 20 yd
Height 'h' = 10 yd
Since we know that,
The surface area of a rectangular prism is,
A=2(bl+hl+hb)
Substitute the values,
A = 2(20x4 +10x4 + 10x20)
A = 640 square units.
Hence the surface area is 640 square units.
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convert 1.75 m to km
Answer is :
0.00175 km
Someone please help me as fast as you can!!
I would really appreciate it!
Solve for X, Leave in simplest radical form
Therefore , the value of the given problem of trigonometry comes out to be x = 2 √3.
What is a trigonometry?Trigonometry is the branch of mathematics that studies the relationship between triangle side length The field was first developed in the Classical era, most likely in the third century BC, as a product of the fusion of geometry and astronomy research. Certain geometric equations and potential applications to calculations are covered in precise methods to mathematics. In trigonometry, there are six typical trigonometric operations. Sine, quadrature, tangent, secant, etc. are some of the names and acronyms that they go by (csc). Trigonometry is the study of triangle properties, particularly those of right triangles. However, understanding about the properties of all polygons is a necessary part of mastering geometry.
Here,
Given : Let x be the given
2 is the base
Using trigonometric ratio comes out to be :
=> Tan 30 = 2/x
=> 1/√3 = 2/x
=> x = 2 √3
Therefore , the value of the given problem of trigonometric comes out to be x = 2 √3.
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ummmm im confused thanks if you help
Answer:
480ft.it does not matter how much east or west they are.it asks how much"they are apart"
so it should be 480.
Determine the principal stresses and the absolute maximum shear stress.
The principal stresses are the maximum normal stresses in the x, y, and z directions.
These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.
The principal stresses are determined using Mohr's circle and the absolute maximum shear stress is equal to one-half the difference between the two principal stresses.
The principal stresses are the maximum normal stresses in the x, y, and z directions.
These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.
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Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not yellow) when choosing one marble from the bag.
A. 8%
B. 24%
C. 40%
D. 60%
Answer:
D. 60
Step-by-step explanation:
Not yellow marbles are 15/25 = 60/100
pls help
giving 100 points
The value of the expression [tex]\frac{999999999\times 999999999}{1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1}[/tex] , which involves the division of a large number is obtained by making use of a scientific calculator is; 12345678987654321
How calculators can be used to divide large numbers?Depending on the processor of the calculator, and the number of digits the calculator can handle, the exact value following the operations with very large numbers can be obtained. Graphing calculators can also be made to increase the number of digits of precession, up to 9999 digits.
The expression in the question can be presented as follows;
999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1)
The value can be computed using a calculator;
999999999 × 999999999 = 999999998000000001
(1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 81
999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 999999998000000001 ÷ 81 = 12345678987654321
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Solve the following system of equations graphically on the set of axes below.
y=-,t-4
2
y= ,r+2
3
Plot two lines by clicking the graph.
Click a line to delete it.
HELP ASAP
The given system of equations intersect in quadrant II at (-6,2)
What is linear equation ?
linear equation can be defined as the equation in which highest power is one.
Given system of equations,
y = (-1/3) x -4
y = (2/3) x + 2
In the first equation ,
y = (-1/3)x- 4
the 1st line slopes up with y intercept = -4
y = (2/3) x + 2
the 2nd line slopes down with y intercept = 2
By equating the equations , we get
(-1/3) x -4 = (2/3) x + 2
-4-2 = (2/3) x + (1/3) x
-6 = x
x = -6
By putting x = -6 in y = (-1/3) x -4
we get ,
y= (-1/3 ) -6 - 4
y = 2-4
y = -2
Hence, The given system of equations intersect in quadrant II at (-6,2).
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help me solve this answer asap please help
Answer:
11. Slope = 1, y-int = (0, -3)
Step-by-step explanation:
Move the numbers so that they math the formula y=mx+b, m being the slope, and b being the y intercept. If for example its 2y, divide the entire equation by 2. Basically you separate "y" on one side, and whatever is next to the x is your slope.
Two examples below:
Select all situations that could be represented by a graph with a Y -intercept of 10 .
The situations that could be represented by a graph with an y-intercept of 10 is given as follows:
A. Sign up fee of $10.
B. Lilly starts with $10 in her savings account.
E. Tank begins with 10 gallons of water.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Hence options A, B and E are the correct options as they have an initial amount of $10.
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Consider the diagram. Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R S is 3 x 2. Line segment S Q is 5 x minus 8. What is QS
A triangle is a three-edged polygon with three vertices. The length of QS is equal to 17 units.
How do triangles work?
A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. A triangle's total angles are always equal to 180 degrees.
Given that the line segment RQ is bisected at point T by the perpendicular bisector Line l. As a result, RT = QT is the length of the two lines.
Now, in ΔRST and ΔQST,
RT ≅ QT
ST ≅ ST {Common side}
Now, since the two triangles are the right-angled triangle, therefore, the two triangles are congruent. Thus, we can write,
RS = SQ
Given that the Line segment, RS is 3x+2. Line segment SQ is 5x-8.
RS = SQ
3x + 2 = 5x - 8
2 + 8 = 5x - 3x
10 = 2x
x = 5
QS = 5x - 8
= 5(5) - 8
= 25 - 8
= 17 units
Hence, the length of QS is equal to 17 units.
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The following variances were calculated for two traits in a herd of hogs.Trait VP VG VABack fat 28.9 13.7 7.98Body length 49.1 27.2 12.4Part ACalculate broad-sense (H2 ) heritability for back fat in this herd.Enter your answer to three decimal places (example: 0.123).Part BCalculate broad-sense (H2 ) heritability for body length in this herd.Enter your answer to three decimal places (example: 0.123).Part CCalculate narrow-sense (h2 ) heritability for back fat in this herd.Enter your answer to three decimal places (example: 0.123).Part DCalculate narrow-sense (h2 ) heritability for body length in this herd.Enter your answer to three decimal places (example: 0.123).Part EWhich of the two traits will respond best to selection by a breeder?back fatbody length
Heritability is typically divided into two categories, namely broad sense and narrow sense heritability.
The following formulas are used to calculate heritability in the broad sense:
H² = Vg / Vp
Where,
H² = Heredity
Vg = Genotypic Variance
Vp = Phenotypic Variance
FOR BACK FAT:
Vg = 13.7
Vp = 28.9
H² = Vg / Vp
H² = 13.7 / 28.9
H² = 0.474
FOR BODY LENGTH:
Vg = 27.2
Vp = 49.1
H² = Vg / Vp
H² = 27.2 / 49.1
H² = 0.553
These formulas are used to calculate narrow sense heredity:
H² = Vg / Vp
Where,
H² = Heredity
Vg = Genotypic Variance
Va = Additive Genetic Difference
FOR BACK FAT:
Vp = 28.9
Va = 7.98
H² = Va / Vp
H² = 7.98 / 28.9
H² = 0.276
FOR BODY LENGTH:
Vp = 49.1
Va = 12.4
H² = Va / Vp
H² = 12.4 / 49.1
H² = 0.252
Because back fat has a high narrow sense of heredity and a low broad sense of heritability, it is the best pick. Additionally, heritability in the restricted sense has good breeding value.
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What is the equation of the line that passes through the point (−6,4) and has a slope of 0?
Answer:
Below
Step-by-step explanation:
A line with a slope of 0 is a HORIZONTAL line
to include the point (-6,4) the equation would just be
y = 4
What is a zero solution?
A zero solution, also known as the trivial solution, refers to a solution of a system of equations in which all variables are equal to zero.
This type of solution occurs when the coefficients in the system of equations are set up in such a way that the only solution to the system is for all the variables to be equal to zero.
A zero solution is the answer to a system of equations where all the variables are equal to zero. This happens when the coefficients in the equations are set up such that the only solution is for all the variables to be equal to zero. This type of solution is also known as the trivial solution. A trivial solution can be thought of as a “placeholder” for when there is no other meaningful solution to a system of equations.
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A pole is being decorated with 13-meter ribbons that are strung from the top of the 6-meter pole to a point on the ground. Which is the measure of the angle formed by the ribbon and the pole? a. 24.8 b. 65.2 c. 27.5 d. 62.5
the tangent of the angle, which we can then use to calculate the angle in degrees. Therefore, angle = tan-1(6/13) = 65.2 degrees.
b. 65.2
To find the measure of the angle, we need to use the inverse tangent (tan-1) function.
angle = tan-1(6/13)
angle = 65.2
We need to use the inverse tangent (tan-1) function to calculate the measure of the angle. To do this, we need to divide the height of the pole (6 meters) by the length of the ribbon (13 meters). This will give us the tangent of the angle, which we can then use to calculate the angle in degrees. Therefore, angle = tan-1(6/13) = 65.2 degrees.
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if two numbers are randomly chosen without replacement from $\{1, 2, 3, 4, 5\}$, what is the probability their sum is greater than their product? express your answer as a common fraction.
What is the likelihood that for at least a single two numbers is 1 if they are randomly selected from the range of 1, 2, 3, 4, 5, and 6? To remove one from the chance that no choices for 1 are made:
How do probability and an example work?
The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of tossing a coin & obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail).
We denote this with P(heads)
12 P(at least 1 one) = 1 - P. (no ones)
P(no ones) equals (5/6)*(5/6)
25/36 P(at least 1 one) equals (1 - 25/36)
11/36 P(sum higher than product) equals P(at least 1 one) = 11/36
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The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
1
1
a.
b.
c.
d.
y = f(x+3)
y = f(x-3)
y + 3 = f(x)
y-3 = f(x)
Answer:
the black graph is the graph of
y = f(x). Choose the equation for the
red graph.
1
1
a.
b.
c.
d.
y = f(x+3)
y = f(x-3)
y + 3 = f(x)
y-3=f(x)
AB = AC and D i the mid-point of BC. (i) State the three pair of equal part in
∆ADB and ∆ADC
It is proved that 1) AB = AC, 2) angle B = angle C fo the given triangles.
What is triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Accprding to question:Here in Delta ADB and Delta ADC.
i) Three pair of equal parts are:
AD = AD ( common side )
BD = CD ( as d is the mid point of BC)
AB = AC (given in the question)
ii) Now,
by SSS Concurrency rule,
Delta ADB\cong \Delta ADC
iii) As both triangles are congruent to each other we can compare them and say
angle B = angle C.
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Complete question:
In figure AB=AC and D is the mid point of BC state the 3 pairs of equal parts in
Triangle ADB and triangle ADC
is ADB= ADC? give reason
is <B = <C? why?
PLEASE ANSWERRR ASAP
PLEASE HELP ASAP!!!!!! WORTH 100 POINTS
The expression shows the differences of cubes is (5x⁷)³-(4y)³. Therefore, option C is the correct answer.
What is a perfect cube?A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y³.
A) 27x¹⁵-9y³
= 3³x¹⁵-3²y³
= (3x⁵)³-3²y³
B) 3x⁹-64y³
= 3x⁹-4³y³
= 3x⁹-(4y)³
C) 125x²¹-64y³
= 5³x²¹-4³y³
= (5x⁷)³-(4y)³
D) x⁶+27y⁹
= (x²)³+(3y)³
Therefore, option C is the correct answer.
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What is a line that divides a line segment into two exact half called?
Answer: the midpoint
Step-by-step explanation:
suppose we pick 2 distinct integers in the range from 1 to 100. how many ways are there to pick these 2 integers such that their product is a multiple of 11?
Therefore , the solution of the given problem of combination comes out to be 945 ways to pick an distinct integer.
What is combination?Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.
Here,
Given:
We have 10 options for each if we take any figure between 1 and 100 , call it x. From there, we may select any number among x+1 and x+10.
For instance, if you select 91, you can choose from 9 other numbers
Similarly, 93 offers us 8 options, 94 offers us 7, and so on until 99 offers us just one.
In light of this,
=>(90*10)+9+8+7++1=945 =10C2 - 9C2
Therefore , the solution of the given problem of combination comes out to be 945 ways to pick an distinct integer.
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