The rule for translating △ABC to △A''B''C'' is (x, y) ⇒ (1, 3)
How to determine the translation rule?The translation of the triangles are given as
△ABC to △A'B'C' to △A''B''C'' .
Also, we have the vector transformation to be:
Vector (-3, 5)Vector (4, -2)When these vectors are combined, we have
(x, y) ⇒ (-3, 5) + (4, -2)
Combine the vectors
(x, y) ⇒ (-3 + 4, 5 - 2)
Evaluate the like terms
(x, y) ⇒ (1, 3)
Hence, the translation rule is (x, y) ⇒ (1, 3)
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Complete question
A translation maps △ABC to △A'B'C' using the vector (-3, 5). A second translation maps △A'B'C' to △A'B'C' using the vector (4, -2). Write a rule for translating △ABC to △A''B''C'' .
Find the coordinates of any points of intersection between the graphs of y = x^2 – 4x + 2 and y = -x^2 – 8x
Answer:
(-1, 7)
Step-by-step explanation:
First, set both equations equal to each other:
(y = x^2 – 4x + 2) = (y = -x^2 – 8x)
x^2 – 4x + 2 = -x^2 – 8x
x^2 + x^2 – 4x + 2 = -x^2 + x^2 – 8x
2x^2 - 4x + 2 = -8x
2x^2 - 4x +8x + 2 = -8x + 8x
2x^2 + 4x + 2 = 0
2(x^2 + 2x + 1) = 0
x^2 + 2x + 1 = 0
x^2 + x + x + 1 = 0
x(x+1) + 1(x+1) = 0
(x+1)(x+1) = 0
x+1=0
x=-1
y = -x^2 – 8x
y = -(-1)^2 – 8(-1) ==> plug in the x-value back into one of the equations
y = -1 – (-8)
y = -1 + 8
y=7
(-1, 7)
72 items to ship 6 in each case how many cases total
The unknown number of cases that to be shipped if there are 72 items to ship 6 in each case is 12.
How many number of cases in total will be shipped?To determine the total number of cases needed to ship 72 items, we need to divide the total number of items by the number of items in each case. In this case, we have 72 items to ship and each case can hold 6 items.
When we divide 72 by 6, we get 12. This means that there are 12 groups of 6 items that can be packed into cases. Each group represents one case.
Therefore, the total number of cases needed to ship 72 items is 12. Each case will contain 6 items, and there will be 12 cases in total.
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Carlos finished his English assignment in
1/3 hours Then he completed his chemistry assignment in 3/4
hours. How much more time did Carlos spend on his chemistry assignment?
Answer:
5/12
Step-by-step explanation:
we need to subtract these 2 fractions
3/4-1/3
to start we change so they can have common denominators and both of them can be 12
3x3/4x3-1x4/3x4
9/12-4/12
5/12
hopes this helps please mark brainliest
What is (-i)6?
O A. -i
OB. i
O C. 1
O D. -1
Answer: C. 1
Step-by-step explanation:
[tex](-i)^6 =(-1)^6 i^6 =(-1)(-1)=1[/tex]
Please help As soon as possible I don't quite get this and I need this handed in PLEASE!!
The polynomial 1 / 10 x² + 10 - 3x in standard form is 1 / 10 x² - 3x + 10.
How to represent polynomial in standard form?The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Standard form simply refers to the format of a polynomial expression where the terms are arranged by decreasing order of degree. Where the degree is determined by the exponent value of the variable of each term.
Therefore, let's rewrite the expression in standard form.
1 / 10 x² + 10 - 3x
Hence, in standard form,
1 / 10 x² - 3x + 10
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at castle rock school 575 students ride their bikes to school. If this number is 92% of the school enrollment then how many students are enrolled?
The number of students enrolled in castle rock school is 625
How to find the number of seats in the theatreinformation from the problem
At castle rock school 575 students ride their bikes to schoolin the theater
If this number is 92% of the school enrollment
how many students are enrolled = ?
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
92%
= 92 percent
= 92 / 100
= 0.92
The factor 0.92 of the total number gives 575 students
let the total number be x
0.92 * x = 575
0.92x = 575
x = 575 / 0.92
x = 625
The total number of students is 625
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When an integer is subtracted from 8 times the next consecutive even integer, the difference is 86. Find the value of the greater integer.
Step-by-step explanation:
x = the integer number
8×(x + 2) - x = 86
8x + 16 - x = 86
7x = 70
x = 10
x + 2 = 12
the larger integer is 12.
What are the property of multiplication?
The most commonly known properties of multiplication are commutative property, associative property and identity property of multiplication.
According to the question,
We have the following information:
We need to find the names of the properties of the multiplication.
There are most commonly three properties of multiplication which are used most often:
Commutative property of multiplication which states that the product of two integers will always remain same even if we change their order.
Associative property of multiplication states that the product of three integers will always be the same even if we change the bracket from the first two to last two.
Identity property states that the product of an integer and 1 is always that integer.
Hence, the most commonly known properties of multiplication are commutative property, associative property and identity property of multiplication.
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Which pair of triangles is congruent by the ASA postulate?
In the concept of geometry, the pair of triangles that are congruent by the ASA Congruent Theorem are the pairs that have two corresponding angles and an included side that are congruent to each other.
Congruent:
Congruent refers the identical in shape and size.
Given,
Here we need to find in which pair of triangles is congruent by the ASA postulate.
As per the Angle-Side-Angle Congruent Theorem (ASA) states that when two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.
So, this one included side is the side that is lie between the two congruent angles in each of the triangles.
Therefore, the triangle which form the pairs of angles given has two corresponding angles and an included side that are congruent to each other in each triangle.
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which are equivalent equations select two correct answers d1 2ad2 d1 d2 d2 d2 2ad1
the d1 = 2A/d2 and d2 = 2A/d1 are correct options.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
The given A=a equals Start Fraction one-half End d1, d2, 2d1d2 where d1 and d2 are the lengths of the diagonals.
So the correct options are
d1 = 2A/d2
d2 = 2A/d1
Hence the d1 = 2A/d2 and d2 = 2A/d1 are correct options.
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Jenna bought some apples for $1.25 per pound and some avocados for $4 per pound. Altogether, she spent $14. 25 for 7 pounds of apples and avocados. What is the total number of pounds of avocados Jenna bought?
A. 1
B. 2
C. 3
D. 4
E. 5
The total number of pounds of avocados Jenna bought is B. 2
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Assuming Jenna bought x pounds of apples and y pounds of avocados.
Altogether she bought 7 pounds of apples and avocados.
∴ x + y = 7...(i)
Altogether, she spent $14. 25.
∴ 1.25x + 4y = 14.25...(ii)
Now multiplying eqn(i) by 1.25 and subtracting from eqn(ii) to cancel out the variable x, we get
2.75y = 5.5.
y = 2 pounds of avocados and hence 5 pounds of apples.
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Slope = ½; (h, k) = (1, -2) find the slope-point
The linear equation with a slope of 1/2 and that passes through the point (1, -2) is written in point-slope form as:
y = (1/2)*(x - 1) - 2
How to find the equation of the line?For a linear equation with a slope m and a known point (h, k), the slope-point form is written as:
y = m*(x - h) + k
Where y and x are the two variables.
Here we know that the slope is 1/2, and the known point is (1, -2), then the values on the equation above are:
m = 1/2
h = 1
k = -2
Replacing that in the general formula for the linear equation in the slope-point form that is written above, we will get:
y = (1/2)*(x - 1) - 2
That is what we wanted to find.
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3 cups= fl.oz how ever knows it i need the hole probelem
3 cups is converted to 24 fl.oz.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity
We need to convert 3 cups to fl.oz.
A fluid ounce is a unit used in the measurement of the volume of liquids. It is commonly abbreviated as fl. oz. (or fl oz)
By the omni chart we have 1 cup=8 fl.oz.
As there are 3 cups we have to multiply 8 with 3
3 cups = 24 fl.oz
Hence, 3 cups is converted to 24 fl.oz.
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Marlene used the Distributive Property to find the product of 6 and 0.82. Which expression shows the Distributive Property?
The Distributive property on the expression gives a result of 4.9 and the distributed expression is (2 + 4) * 0.82
How to apply the Distributive property on the expression?From the question, we have the following parameters that can be used in our computation:
The expression is given as:
The product of 6 and 0.82
Mathematically, this expression can be represented as
6 * 0.82
To apply the distributive property,
We need to express 6 as the sum of two numbers
So, we have the following representation
6 * 0.82 = (2 + 4) * 0.82
Remove the brackets
6 * 0.82 = 2 * 0.82 + 4 * 0.82
Expand the terms of the expression
6 * 0.82 = 1.64 + 3.28
Evaluate the sum
6 * 0.82 = 4.92
Hence, the solution is 4.9
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Factor 100x² 140xy + 49y²
Answer:
100 times square times Y 49 gives= 14000
What is square root of -36 classified as
Answer:
undefined
Step-by-step explanation:
The square root of any negative number is undefined because there is no possible solution. - × - = + and + × + = +
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.
Please explain how you got the solution.
20 Points! Thanks!
Answer: One Real Solution
We can Identify the coefficients a, b, and c from your equation because as it says, it is in the format of the quadratic equation ( ax^2 + bx + c = 0 )
a=2,b=-4,c=2
Now we can use the discriminant to determine how many solutions this has using the equation b^2 - 4ac
Once we plug in our coefficients:
(-4)^2 - 4 x 2 x 2
Once we simplify, we get 0.
One real solution.
I hope this helps.
In this case, we first need to simplify the given quadratic equation 2x² - 4x = -2, and to do so, we perform the following simplification steps:
For a quadratic equation of the form ax² + bx + c = 0, the discriminant is calculated using the following formula:
Δ = b² - 4ac
In this case, we have that the equation that we must solve is 2x²-4=-2, which implies that the corresponding coefficients are:
a = 2b = -4c = 2By introducing these values into the formula we get:
Δ = b² - 4ac = (-4)² - 4·(2)·(2) = 0
Therefore, the discriminant for the given quadratic equation is Δ=0=0, which is zero, and indicates that the equation 2x²-4=-2 has only one real root.
We can say: It has a Real solution.angle PKW is 180 degrees if two additional rays were added, call them ray j and ray s respectively. how would you draw the diagram
The angle with 180° is a straight line, and the ray can be drawn in any way.
What is a ray?The definition of ray in maths, that it is a part of a line that has a fixed starting point but no endpoint.
Given that, angle PKW is 180 degrees and two additional rays were added,
The figure has been attached in answer.
We know when an angle measures 180° it makes a straight line and on it, we can draw as many ray as we want and in any way.
Hence, The angle with 180° is a straight line, and the ray can be drawn in any way.
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How do you find the genotype and phenotype ratio?
The genotypic ratio is the distribution pattern of the genes in the offspring obtained after a genetic cross.
The phenotypic ratio is the distributionn pattern of the physical characteristics in the offspring obtained after a genetic cross.
To find a phenotypic ratio, we look at the alleles of the parent organisms and estimate how often those genes will be exhibited by the offspring.
Phenotype is the constellation of observable traits; genotype is the genetic endownment of the individual.
Phenotype = genotype + development (in a given environment).
The genotypic ratio and the phenotypic ratio may not necessarily be the same.
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What is 3/4 as a division problem?
After division, 0.75 is 3/4 as a division problem.
In the given question we have to find what is 3/4 as a division problem.
The given division problem is 3/4.
With the help of the division formula Dividend = (Divisor Quotient) + Remainder, we can confirm the quotient and the remainder of the division. If the remaining is 0, we can multiply our quotient by the divisor to see if it is accurate. The quotient is accurate if the product equals the dividend.
To solve this division problem we divide 3 by 4. The answer should come in the decimal form because 3 is less than 4. So we take decimal to solve this.
Now the solution of the given division problem is:
3/4 = 0.75
Hence, 0.75 is 3/4 as a division problem.
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Graph the system of inequality and shade the solution.
3x-2y<4
-2x-6y<-12
Answer: See attached.
Step-by-step explanation:
First, we will graph the two inequalities. We will graph as we would with normal linear equations.
However, they both use the < sign, so we will shade above a dashed line.
The solution to this system of inequalities is where the shaded parts overlap. You can see that in the attachment I have labeled it as such.
How do you prove ABCD is a rhombus?
A rhombus is a quadrilateral with four equal-length sides. The term equilateral quadrilateral refers to the fact that all of its sides are the same length.
What is a rhombus?A rhombus is a subset of a parallelogram. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles. A rhombus is also referred to as a diamond or rhombus diamond.
Show that a rhombus is formed when the diagonals of a quadrilateral intersect at right angles. We have a quadrilateral ABCD in which the diagonals AC and BD intersect at right angles at O. Their corresponding parts are all the same. As a result, the quadrilateral ABCD is a rhombus.
here know that
[tex]\angle A E D=\angle A E B & =\angle B E C \\[/tex]
[tex]& =\angle C E D=90^{\circ}[/tex]
in [tex]$\triangle A E B$[/tex]
[tex]\angle A E B+\angle E A B+\angle E B A=180^{\circ} \\[/tex]
Simplifying the above equation, then we get
[tex]90^{\circ}+\angle E A B+50^{\circ}=180^{\circ} \\[/tex]
[tex]\angle E A B=40^{\circ}[/tex]
[tex]$A B \mid C D$[/tex]
Hence,
[tex]\angle E A B & =\angle E C D=40^{\circ} \\[/tex]
[tex]8 \angle E D C & =\angle A B E=50^{\circ} \\[/tex]
[tex]\angle B C D & =\angle E C D+\angle E C B \\[/tex]
[tex]& \angle 40^{\circ}+50^{\circ} \\[/tex]
[tex]\angle B C D & \left.=90^{\circ}\right)[/tex]
Therefore, ∠ B C D is 90°
The complete question is:
In the given figure, A B C D is a rhombus. Diagonals A C and B D intersect each other at E. If ∠ 1=50° then ∠ B C D =
a) 100°
b) 90°
c) 80°
d) None of these
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Find the mode of this data set
Answer:
5, 4, 7
Step-by-step explanation:
Emy has 13 1/4 kilograms of sweet potatoes.She gave away 5 12 kilogramsof corn to her neighbors.how many kilograms of corn than potatoes did she gave away?
Answer:
2 1/4 kg
Step-by-step explanation:
Kason went to Bella's bakery and ordered 3 mango smoothies, 3 chocolate covered cherries, and 1 peanut butter cookie how much money did he spend ?
chocolate-covered cherry costs $ 0.75 mango smoothies costs $ 4.25 peanut butter cookie costs $ 1.25
Answer:
16.25
Step-by-step explanation:
3 x 0.75(chocolate covered cherries) = 2.25
3 x 4.25(mango smoothie) = 12.75
1 x 1.25( peanut butter cookie)= 1.25
12.75 + 2.25 + 1.25= 16.25
I hope this helps...
Answer:
Kaso spent $16.25 at Bella's bakery
Step-by-step explanation:
Each item costs a certain amount of money. What you have to do is multiply that amount by the number of each item. Then, add the sum.
Kason ordered 3 mango smoothies. Each smoothie costs $4.25. Therefore multiply 3(4.25)=12.75
Next, he ordered 3 chocolate covered cherries. Each cherry costs 0.75. Multiply 3(0.75)=2.25
Finally, Kason ordered 1 peanut butter cookie. Since each cookie costs 1.25, that is the amount he paid for the peanut butter cookie.
Add the 3 numbers together.
12.75+2.25+1.25=16.25
This is the amount of money he spent in total.
Is X 2 a factor of x³ 3x² 5x 6?
The factor theorem states that x+2 is a factor of x³+3x²+5x+6.
What are the factors?A factor is a number that completely divides another number.
To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
The numbers that can divide a number exactly are called factors.
There is therefore no residual after division.
The numbers you multiply together to obtain another number are called factors.
A factor is therefore another number's divisor.
So, the expression is: x³+3x²+5x+6
Check whether x+2 is the factor:
Then,(x = -2)
p(-2) = (-2)³+3(-2)²+5(-2)+6
p(-2) = - 8 + 12 - 10 + 6
p(-2) = 0
Therefore, the factor theorem states that x+2 is a factor of x³+3x²+5x+6.
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Correct question:
Examine whether x+2 is a factor of x³+3x²+5x+6
If x-10=22,then x is equal to
Answer:
Step-by-step explanation:
x = 32
x - 10 = 22
add 10 to both sides of the equation
-10 + 10 = 0
22+ 10 = 32
x = 32
Solve the system by substitution. y equals 2 x squared minus 3 x minus 1 y equals x minus 3
Laura has a deck of 10 cards numbered 1 through 10. She is playing a game of chance. This game is this: Laura chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an odd-numbered card is drawn. She loses $5 if an even-numbered card is drawn.
(a) Find the expected value of playing the game.
(b) What can Laura expect in the long run, after playing the game many times?
(She replaces the card in the deck each time.)
Laura can expect to gain money.
Laura can expect to lose money.
Laura can expect to break even (neither gain nor lose money).
We will observe that the anticipated value is $0, indicating that Laura should anticipate neither winning nor losing any money after a significant number of games.
What is the expected value?The predicted result of an experiment with N outcomes, each with a probability of p1, p2,..., pn, is:
EV = x₁*p₁ + ... + xₙ*pₙ
The results in this situation are:
x₁ = drawing an unlucky card = -$6
If there are five odd cards in a deck of ten cards, the probability is:
p₁ = 5/10 = 1/2.
x₂ = drawing a 2 = $2
There is only one 2 card on the deck, so the probability of drawing it is: p₂ = 1/10
x₃ = drawing a 4 = $4
p₃ = 1/10
x₄ = drawing a 6 = $6
p₄ = 1/10
x₅ = drawing a 8 = $8
p₅ = 1/10
x₆ = drawing a 10 = $10
p₆ = 1/10
So the expected value will be:
EV = (-$6)*(0.5) + ($2 + $4 + $6 + $8 + $10)*(1/10)
EV = 0
Thus, we will observe that the anticipated value is $0, indicating that Laura should anticipate neither winning nor losing any money after a significant number of games.
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The ratio of the measure of the sides of a triangle is 2:3:6, and the perimeter is 187cm. What is the measure of the largest side?
The measure of the largest side of the triangle is 102cm.
What is ratio?Ratio, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.
For example, 2:3:6 shows the ratio of the sides of a triangle. The perimeter which is the addition of the triangle is 187cm.
Therefore the measure of each side will be given as:
2/11×187= 34cm
3/11×187= 51cm
6/11×187= 102cm
This means that the measure of the three sides are 34cm, 52cm, and 102cm.
Therefore the measure of the largest side is 102cm
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