The system of equations can have an infinite number of solutions when the equations are equivalent.
A system of equations can have infinitely many solutions when the equations are equivalent, meaning that the equations are identical when one is subtracted from the other. When this happens, the system of equations is said to have an infinite number of solutions. To solve a system of equations by elimination with infinitely many solutions, the equations must first be rearranged so that the same variable terms are on one side and the constant terms are on the other. Then, the coefficients of one variable must be made equal by multiplying one or both equations by a constant. After this, the equations can be added together or subtracted from one another and the variable terms will cancel out. This will result in an equation with only the constant terms, which is equivalent to 0=0. This equation is true for all values of the variables, so the system of equations has an infinite number of solutions.
The system of equations can have an infinite number of solutions when the equations are equivalent. To solve the system of equations by elimination with infinitely many solutions, the equations must first be rearranged, the coefficients of one variable must be made equal, and the equations can be added or subtracted so that the variable terms cancel out. This will result in an equation equivalent to 0=0, meaning that the system of equations has an infinite number of solutions.
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in convex quadrilateral wxyz, the degree measure of angle x is four times that of angle w. the measure of angle y is double that of angle x. lastly, the measure of angle z is 3 degrees larger than that of angle y. what is the degree measure of the largest angle in wxyz?
The measure of the largest angle in wxyz is 4 times the measure of angle w, plus double that measure, plus 3 degrees.
Angle w: x = 4w
Angle y: y = 2x = 8w
Angle z: z = y + 3 = 8w + 3
The largest angle in wxyz is z = 8w + 3.
In a convex quadrilateral wxyz, the degree measure of angle x is four times that of angle w. This means that the measure of angle x is four times the measure of angle w. The measure of angle y is double that of angle x. This means that the measure of angle y is twice the measure of angle x, or eight times the measure of angle w. Lastly, the measure of angle z is 3 degrees larger than that of angle y. This means that the measure of angle z is eight times the measure of angle w plus three degrees. Therefore, the measure of the largest angle in wxyz is 8w + 3.
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99/12 in long division please!
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.75, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
It is likely to randomly select a chocolate chip cookie from the batch.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
The probability of selecting the chocolate chip is given as 0.75.
Which is more than 50%
So, it is likely to randomly select a chocolate chip cookie from the batch.
Thus, It is likely to randomly select a chocolate chip cookie from the batch.
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Answer: B: Likely
Step-by-step explanation:
A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
Answer:
$12300
Step-by-step explanation:
You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.
InterestThe interest on an investment P at rate r for t years is ...
I = Prt
The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:
0.07x +0.17(19000 -x) = 2000
-0.10x +3230 = 2000 . . . simplify
1230 = 0.10x . . . . . . . . . . add 0.10x -2000
12300 = x . . . . . . . . . . . . divide by 0.10
The amount loaned at 7% was $12,300.
The question is in the picture
The value of x from the triangle is x = 30
What is the law of sines?The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.
Law of Sines :
a / sin A = b / sin B = c / sin C
Given data ,
Let the triangle be represented as ABC
Now , the length of the side b = x
The length of the side a = x + 2
The measure of sin A = 4/5
The measure of sin B = 3/4
So , to find the value of x , we use the law of sines
a / sin A = b / sin B
Substituting the values in the equation , we get
( x + 2 ) / ( 4/5 ) = x / ( 3/4 )
On simplifying the equation , we get
5 ( x + 2 ) / 4 = 4x / 3
Multiply by 3 on both sides of the equation , we get
15 ( x + 2 ) / 4 = 4x
Multiply by 4 on both sides of the equation , we get
15 ( x + 2 ) = 16x
15x + 30 = 16x
Subtracting 15x on both sides of the equation , we get
x = 30
Therefore , the value of x is 30
Hence , the value of x is 30
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Simplify: 1. Write the prime factorization of the radicand. 2. Apply the product property of square roots. Write the radicand as a product, forming as many perfect square roots as possible.
The prime factorization of the radicand 2 is 9√15.
A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.
As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.
Given that,
x= 3√135
Solving the equation further using the rule √A*B = √A*√B
x= 3√9*15
x= 3√9*√15
x=3*3*√15
x= 9√15
Therefore, the prime factorization of the radicand 2 is 9√15.
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The measure of angle JKL is 145°.
The measure of angle MKL is 60°.
The measure of angle JKM is x°.
Find the value of x.
X=
0
X
5
Xº
K
145°
M
60°
D
costs $14 per month plus $2 per movie watched. Plan B costs $20 per month plus $1
per movie watched. Let A represent the monthly cost of Plan A if Bo watches a per
month, and let B represent the monthly cost of Plan B if Bo watches x movies per
month. Graph each function and determine the number of monthly movies watched,
x, that would make the two plans have an equal monthly cost.
We can see from the graph that Plan B is less expensive for the range [0, 4], however Plan A is superior if you watch 4 or more movies per month.
How are the cost equations obtained?We know that plan A costs $14 per month plus $2 per movie, so if you watch x movies, the cost is:
C₁(x) = $14 + $2*x
Plan B costs $20 per month plus $1 per movie, so if you watch x movies, the cost is:
C₂(x) = $20 + $1*x
You can see in the graph that the blue line is behind the green one between x = 0 and x = 4. Plan B is therefore less expensive in the range [0, 4].
The green line is underneath the blue one for x > 4, hence you should select plan A for x > 4.
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In the figure below, which term best describes point W?
A. Incenter
B. Centroid
C. Orthocenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?
" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
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what type of congruence transformation can you use to show that the figures are congruent to one another?
If a figure can be transformed into another figure by a sequence of translations, rotations, and reflections, and the size and shape remain the same, the figures are congruent.
A congruence transformation is a type of transformation that preserves the size and shape of a figure. The most common congruence transformations are translations, rotations, and reflections.
Translations involve moving a figure a certain distance in a certain direction without changing its size or orientation.
Rotations involve rotating a figure around a certain point without changing its size or shape.
Reflections involve flipping a figure over a certain line without changing its size or shape.
In order to show that two figures are congruent, you can use a combination of these congruence transformations to match one figure to the other. By using these transformation you can map each point of one figure to a corresponding point on the other figure and if the size and shape of figures remain the same, that means that the figures are congruent.
It's important to notice that Congruence is an equivalence relation and it's reflexive, symmetric, and transitive.
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you are interested in the number of english-speaking people on the planet who want to play a new kind of online video game. you asked 300 college students if they were interested in playing video games, 100 said yes, and of them 20 preferred your game to an existing game that is widely used. how many people were in the sample? select one: a. the number of english-speaking people on the planet who want to play a new kind of online video game. b. 300 c. 200 d. 100 e. 20
b. Total Sample = 300 college students
The question is asking how many people were in the sample of 300 college students that were asked if they were interested in playing video games. The answer is option B: 300.
To answer this question, we must first understand the context of the question. It is asking about the number of English-speaking people on the planet who want to play a new kind of online video game. To answer this, 300 college students were asked if they were interested in playing video games. Of those 300 students, 100 said yes, and 20 of those students preferred this new game to an existing game that is widely used. Therefore, the sample size was 300.
The sample size is 300 college students. From the 300 college students, 100 said yes to playing video games. Of these 100, 20 preferred the new game to an existing game. Therefore, the sample size is 300 college students.
Total Sample = 300
No. of Yes = 100
No. of Prefers new game = 20
So, Total Sample = 300 college students
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The octagon shown below eight congruent sides.What is the area,to the nearest square centimeter of the octagon?
The area of the octagon, to the nearest square centimeter, is 628 cm^2.
What is octagon?Octagon is a two-dimensional shape with eight sides and eight angles. It is a polygon with eight vertices, and it is one of the most widely recognized geometric shapes. It is often used in architecture, as well as in signage and logo designs. Octagons can also be found in nature, such as in the shape of honeycomb cells, some flower petals, and certain animal eyes.
To calculate the area of an octagon, we need to first calculate the length of the side. To do this we use the formula for the perimeter of an octagon: P = 8s, where s is the length of the side. Solving for s: s = P / 8.
The perimeter of the octagon is 80 cm. So the length of the side is 80 cm / 8 = 10 cm. Now we can use the formula for the area of an octagon: A = 2(1 + √2) s^2. Plugging in our value for s, we get: A = 2(1 + √2) (10 cm)^2 = 628.3 square cm. The area of the octagon, to the nearest square centimeter, is 628 cm^2.
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you are buying a flower arrangement. the florist has 9 types of flowers and 7 types of vases. if you can afford exactly 2 types of flowers and need only 1 vase, how many different arrangements can you buy?
The total number of different arrangements is 36 * 1 = 36
Permutation and Combination:
Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called a combination.
There are 9 types of flowers and you are choosing 2 of them, so the number of ways to choose the flowers is 9 choose 2 which is equal to (98)/(21)=36.
There is 1 vase and you are choosing 1 of them, so the number of ways to choose the vase is 1 choose 1 which is equal to 1.
The total number of different arrangements is 36 * 1 = 36.
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Scale is 1/4"=4'. What is the line's actual length?
Answer:
16x feet
Step-by-step explanation:
A scale of 1/4" = 4' means that every 1/4 inch on the drawing or map represents 4 feet in the actual measurement. To find the actual length of a line on the drawing or map, you need to multiply the length of the line in inches on the drawing by the denominator of the scale, and then divide by the numerator of the scale.
The formula is:
Actual length = (length on the drawing or map x scale denominator) / scale numerator.
In this case, the length on the drawing or map is x inches, and the scale is 1/4" = 4'.
So the actual length is: (x inches x 4') / 1/4" = 16x feet
Therefore, the actual length of the line on the drawing or map is 16x feet.
By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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so for this i just need to know how to find the area and perimeter
Answer:
Step-by-step explanation:
x=7
Answer: Area: 364 Perimeter: 80
Step-by-step explanation:
Since 2x=14, x=7. Then you plug 7 into 3x+5, so 3(7)+5=26. Then for area you do 14*26=364, and for perimeter you simply do (26+14)2=80
A cube with side length 5h^2 is sTacked on another cube with side length 3k . What is the total volume of the cubes in factored form?
(5h^2)^3 + (3k)^3
(5h^2 + 3k) + (25h^4 - 15 h^2k + 9k^2)
(5h^2 + 3k) + (25h^4 + 15 h^2k + 9k^2)
(5h^2 + 3k)^3
The correct option is Option A: (5h^2)^3 + (3k)^3
The total number of cubic units that the cube totally occupies is the definition of a cube's volume. A cube is a solid three-dimensional object with six square faces. Volume is simply the total amount of space an object takes up. A thing with a bigger volume would take up more room.
Total Volume = V₁ + V₂
V₁ = Volume of Cube 1
V₂ = Volume of Cube 2
Volume of Cube = (Side Length)³
V₁ = (5h²)³
V₂ = (3k)³
∴ Total Volume = (5h²)³ + (3k)³
And this cannot be simplified further.
Therefore, the correct option is Option A: (5h^2)^3 + (3k)^3
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Does the point (-3,2) lie inside, outside, or an a circle with center (4,0) and radius 5 units?
Answer:
The given point is outside of the circle---------------------------------------
Find the distance between the given point (-3, 2) and the center of circle (4, 0) using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]d=\sqrt{(4-(-3))^2+(0-2)^2} =\sqrt{7^2+(-2)^2} =\sqrt{49+4} > 7 > r=5[/tex]As we see the distance is greater than radius, hence it is outside circle.
write an equation that represents how many grams of flour we need (fff) for some number of grams of sugar (sss).
We need 600 grams of flour to make the recipe with 400 grams of sugar.
What is a ratio?
A ratio is a mathematical comparison of two or more values or quantities. It is represented as a fraction, with the numerator representing the first value or quantity and the denominator representing the second value or quantity.
An equation is a mathematical statement that asserts the equality of two expressions. In this case, the recipe uses 300 grams of flour for every 200 grams of sugar. To write an equation that represents this relationship, we can use the variable "f" to represent the number of grams of flour and "s" to represent the number of grams of sugar.
The equation that represents this relationship is f = (3/2)s. The coefficient of the "s" variable is 3/2, which represents the ratio of flour to sugar in the recipe (3 parts flour to 2 parts sugar). This equation states that the number of grams of flour, represented by f, is equal to 3/2 times the number of grams of sugar, represented by s.
So, in other words, if we know the number of grams of sugar we need, we can use this equation to find out how many grams of flour we need. For example, if we need 400 grams of sugar, we can substitute that into the equation:
f = (3/2)s
f = (3/2) * 400
f = 600
Hence, We need 600 grams of flour to make the recipe with 400 grams of sugar.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer: 2m+4
Step-by-step explanation:
To simplify, we need to combine "like terms", which means terms that are similar in that it is either just a number or a coefficient and variable. In this case, 3m and -m are like terms, and -6, 2, and 8 are like terms.
Now, we can combine.
-6 + 3m + 2 -m + 8
-4 + 3m - m + 8
4 + 3m - m
4 + 2m (also can be written as 2m + 4)
hope this helps!
Evaluate 8.5 x plus 7.9 y when x equals 7 and y equals 8
Answer:
=x^2+1 (Graph Example), 4x+2=2 (x+6) (Solve Example) Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples ». x+3=5. 1/3 +
Step-by-step explanation:
Answer:
y=x^2+1
Step-by-step explanation: 4x+2=2 (x+6)
b) p is directly proportional to the square of q. p is 3825 when q is 15. Work out p when q is 20.
Answer:
Step-by-step explanation:
What is a 4 regular graph?
A four-regular graph is a quartic graph.
A quartic graph is an example of a polynomial function with a degree of four. The formula denotes a quartic function's equation: f(x) = ax4 + bx3 + cx2 + dx + e, where a, b, c, d, and e are constants. A quartic function's graph is a straight line with up to four turning points or extrema. The roots of the polynomial are also referred to as the graph's x-intercepts or the answers to the equation f(x) = 0.
The values of the constants a, b, c, d, and e, as well as whether an is positive or negative, determine the shape of the quartic graph. The graph starts out with an upward slope if it is positive and a downward slope if an is negative. Factorization, the square-root approach, or numerical techniques like the bisection method or the Newton-Raphson method can all be used to solve quartic equations.
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The roots of the equation x^2+bx+c=0 are -4 and 2. Find c
Answer: -8
Step-by-step explanation:
How to find the answer
s= 7; 6s²
Answer:
294
Step-by-step explanation:
We will take our equation, and substitute in 7 for s, wherever we see it, so we have:
[tex]6 * 7^{2}[/tex]
Simplifying, we have:
[tex]6 * 49[/tex]
Which finally we multiply to:
6 * 49 = 294
So, your answer is 294.
Hope this helped!
Use the net to find the surface area of the prism.
HELP!!!!
360 in2
480 in2
432 in2
408 in2
The surface area of the prism shown in the figure is equal to 480 square inches. (Right choice: B)
How to find the surface area of the prismIn this problem we need to determine the surface area of a prism, that is, the sum of the areas of the five faces of the prism. There are three rectangles and two right triangles as faces of the prism, whose area formulas are described below:
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Where:
w - Width, in inchesl - Length, in inchesNow we proceed to determine the areas of all faces of the prism:
A = (8 in) · (9 in) + 2 · 0.5 · (15 in) · (8 in) + (9 in) · (15 in) + (17 in) · (9 in)
A = 480 in²
The prism shown in the figure has a surface area of 480 square inches.
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Factorise fully 9x + 18
Answer:
[tex] \sf \: 9(x + 2)[/tex]
Step-by-step explanation:
Given expression,
→ 9x + 18
Let's factorise the expression,
→ 9x + 18
→ (9 × x) + (9 × 2)
→ 9(x) + 9(2)
→ 9(x + 2)
Hence, the factor is 9(x + 2).
PLEASE HELP!!
I just can’t seem to get this at all.
The equation solved is 1+-2/x²=-x-1 is 2x²+x³-2=0
Find the value of p and q ?the value of p is p=-x-q/x²the value of q is q=-x³-px²Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axisThe coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.The point where the axes intersect is called the origin. Let's plot a point on the coordinate plane. The location of Point A is given as a horizontal component (x) and a vertical component (y) and written as (x,y). From the origin, to get to Point A, we would count two units to the right and three units upTo learn more about value of p and q refers to:
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Grace has a segment with endpoints A (3, 2) and B (6, 11) that is partitioned by a point C such that AC and BC form a 2:3 ratio. She knows the distance between the x coordinates is 3 units. Which of the following fractions will let her find the x coordinate for point C
Grace can use the fraction 3 / 5 of the distance from point A and 2 / 5 of the distance from point B to determine the x coordinate of point C.
How to determine the coordinates of a point that a line segment at a given ratio
Herein we find the case of a point partitioning a line segment by observing a given ratio. The equation that observes this fraction is shown below:
AC / BC = 2 / 3
AC / AB = 2 / 5
Vectorially speaking, this is equivalent to the following equation:
C(x, y) - A(x, y) = (2 / 5) · [B(x, y) - A(x, y)]
C(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)
If we know that A(x, y) = (3, 2) and B(x, y) = (6, 11), then the coordinates of point C are, respectively:
C(x, y) = (3 / 5) · (3, 2) + (2 / 5) · (6, 11)
C(x, y) = (9 / 5, 6 / 5) + (12 / 5, 22 / 5)
C(x, y) = (21 / 5, 28 / 5)
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Please help, i know you have to use pythagoras and the hypotenuse is 8.44 but i dont know how to get one of the sides
======================================================
Explanation:
Check out the diagram below.
I've defined the following points:
A = center of the circle, and center of the squareB, C, D, and E = vertices of the square that are on the circleF = midpoint of segment CDNow focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.
The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.
[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]
This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.
------------
We now know the hypotenuse of triangle ACF.
Use Pythagoras (aka Pythagorean Theorem) to have the following steps:
[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]
The final answer is 5.97With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.
Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.
In short, we're rounding to the nearest hundredth.
--------------------
Check:
x = 5.97 is the square's side length.
It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.
Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.
Use that radius to find the area of the circle.
A = pi*r^2
A = pi*(4.22142748)^2
A = 55.984594705958
A = 56.0
I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.
