Answer:
After substituting -4 for "a" and 16 for "b", the equation can be simplified and solved.
-The equation 2 (2x - 11) + 6 = -4x + 16
Expanding the equation on the left-hand side, we get:
4x - 22 + 6 = -4x + 16
Simplifying, we get:
10 = -10x + 32
Subtracting 32 from both sides, we get:
-22 = -10x
Dividing both sides by -10, we get:
x = 2.2
This means that there is exactly one solution, which is x = 2.2. So, statement 3 is true.
-The equation 4x - 8 (x - 2) = -4x + 16
Expanding the equation on the left-hand side, we get:
4x - 8x + 16 = -4x + 16
Combining like terms, we get:
-4x + 16 = -4x + 16
This equation is true for all values of x, so there are infinitely many solutions. So, statement 2 is true.
-The equation 10 + x + 2 - 6x = -4x + 16
Expanding the equation on the left-hand side, we get:
10 + x + 2 - 6x = -4x + 16
Combining like terms, we get:
-5x + 12 = -4x + 16
Adding 4x to both sides, we get:
-x + 12 = 16
Adding x to both sides, we get:
12 = 16
This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.
-The equation 9x +3 - 13x + 6 = -4x + 16
Expanding the equation on the left-hand side, we get:
9x + 3 - 13x + 6 = -4x + 16
Combining like terms, we get:
-4x + 9 = -4x + 16
Adding 4x to both sides, we get:
9 = 12
This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.
Therefore, the true statements are:
-The equation 2 (2x - 11) + 6 = ax + b has no solution.
-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.
-The equation -5 (4x-6) 14 = ax + b has exactly one solution.
Relative to a fixed origin O, the point A has position vector (2i + 3j - 4k), the point B has position vector (4i - 2j + 3k), and the point C has position vector (ai + 5j – 2k), where a is a constant and a < 0.
D is the point such that AB = BD.
(a) Find the position vector of D.
Given AC| = 4,
(b) find the value of a.
Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:
D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)
So, the position vector of point D is (3i + 0.5j - 0.5k).
(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).
The magnitude of this difference is given by:
|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4
So, we have:
√((a-2)^2 + 2^2 + 2^2) = 4
(a-2)^2 + 2^2 + 2^2 = 16
(a-2)^2 = 16 - 4 - 4
(a-2)^2 = 8
a-2 = ±2√2
Since a < 0, we have:
a = 2 - 2√2
So, the value of a is 2 - 2√2.
Step-by-step explanation:
what is the solution to 2j=16+4j
Answer: j = -8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
2j = 16 + 4j
collecting like terms, you would have
2j - 4j = 16
-2j = 16
divide both sides by 2
j = 16/(-2)
j = -8
The function machine at right
follows the equation h(x) = 5x + 2.
a. If the crank is turned backwards, what number should be pulled up into the machine in order to have a 4 come out of the top?
b. Keiko wants to build a new machine that will undo what h(x) does to an input. What must Keiko's machine do to 17 to undo it
and return a value of 3?
c. An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the
mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.
d. Choose a value for z. Then find a strategy to show that your equation, h¹(x), undoes the effects of the function machine h(x).
Answer: C
Step-by-step explanation: An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the
mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.
Which of the following equations has no solution?
A.m + 9 = 8
B.m - 3 = m + 3
C.m + 9 = 9 + m
D. All the choices
Answer:
B. m-3=m+3
Step-by-step explanation:
Because the others have a solution such as 0 and -1.
And That would eliminate D
2 + cscsecx/cscsecx = (sinx+cos)
Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg
Quanto é
78+34789+1+234+5678
the answer is 40780
I would show you my calculations but I don't know how to add pictures to your answer .sorry
I hope that helped
WILL GIVE BRAINLIEST, PLEASE HURRY
Which transformations take the graph of f(x)=6x to the graph of g(x)=6x−4+2?
Choose each correct answer.
Responses
The graph is translated to the right 4 units.
The graph is translated up 2 units.
The graph is translated down 4 units.
The graph is translated to the right 2 units.
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
What is Graph?
In mathematics, a graph is a collection of points, called vertices or nodes, and a collection of lines, called edges, that connect pairs of vertices. Graphs are used to represent relationships between objects, such as the connections between different parts of a network or the dependencies between different variables in a system. They are commonly used in fields such as computer science, operations research, and engineering to model and solve problems involving complex systems.
The correct transformations are:
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
The graph is translated up 2 units. This is because there is a constant term of +2 added to the function, which means the function has a vertical shift upwards by 2 units.
Therefore, the correct answers are:
The graph is translated to the right 2 units.
The graph is translated up 2 units.
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PLEASE HURRY
E
B
D
AC = 14 cm
EC = 84 cm
ED = 21 cm
C
Given the following segment lengths,
find the length of segment AB.
The length of the segment AB is 3.5 cm
What is a line segment ?
A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.
We have segments ratio as shown:
BC/AB = CD/ED
=> (AC - AB)/AB = (EC - ED)/ED
=> (14-AB)/AB = (84-21)/21 = 3
Let AB=x
=> (14-x)/x = 3
=> 14-x = 3x
=> 14 = 3x+x = 4x
=> 14/4 = x
=> x=3.5 cm
AB=x = 3.5 cm
The length of the segment AB is 3.5 cm
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The equations represent the elevations, y, of two hikers, in meters, after x hour. Wich ordered pair, (0, 0), (1, 7) or (2, 10), is a solution to the system? will the hikers ever be the same elevation? explain. Y = 6x + 1
y = 3x + 4
yes. the hikers will ever be the same elevation.6+1=7 the same elevation.
Y = 6x + 1
FIll the value of y in this equation
3x + 4= 6x + 1
3x=4-1
x=3/3=1
Y = 6x + 1
FIll the value of x in this equation
6+1=7. The height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface. Elevation should not be confused with the angular separation from the Earth's center. The summits of Mount Everest and Chimborazo have the highest elevation and greatest geocentric distance, respectively, because of the equatorial bulge.
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excel ran out of resources while attempting to calculate one or more formulas?
This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.
This can happen when a spreadsheet is extremely large, has many complex formulas or when a large number of calculations are performed simultaneously. To resolve the issue, you can try closing other programs and processes running on your computer, increasing the amount of memory allocated to Excel, breaking down a large spreadsheet into smaller spreadsheets, or simplifying the formulas in your spreadsheet. If these steps do not work, you may need to seek assistance from a technical support expert. This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.
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ratio of heights of 2 triangles is 3:4, area 4:3, ratio of their base?
Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.
It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3
We have to find the ratio of their base
The basic formula for the area of a triangle is equal to half the product of its base and height or [tex]\frac{1}{2} \times base \times height[/tex]
Let b₁ , b₂ are the base of two triangles respectively
So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]
So, ratio of the base of two triangles is 16:9
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Make a prediction about what might happen if you have ten birds.
Answers:
1.There is no relationship.
2.You'll have nine angry neighbors.
3.You'll have either five or six angry neighbors.
4.You'll have six angry neighbors.
5.You'll have either seven or eight angry neighbors.
The prediction about what might happen if you have ten birds will be 5. You'll have either seven or eight angry neighbors
What is a word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, it should be noted that as the number of birds increase, the number of angry neighbor increased too. Therefore, the prediction about what might happen if you have ten birds will be that you'll have either seven or eight angry neighbors.
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factoriser les expressions :
16x+4
Answer:
4(4x+1)
Step-by-step explanation:
16x+4
Factor out 4,
4(4x+1)
25 Points! Please help!!
Line l is a straight line. 2 line intersect line l to form 4 angles. From top left, clockwise, the angle are: x, y, z, w.
Which statements are true about the angles in the figure? Select two options.
Angle x and angle y are supplementary angles.
Angle W and angle Z are a linear pair.
Angle W and angle Y are adjacent angles.
Angle X and Angle Z are vertical angles.
The statements are A. ∠x and ∠y are supplementary angles, B. ∠w and ∠z are a linear pair.
Describe an angle and its types?Angle is the void between two surfaces or lines that meet. The angle is also expressed in degrees. The angle is 360 degrees for a full rotation.
Supplementary angle: When two angles add up to 180 degrees, they are considered to be supplementary angles.
Corresponding angle: The third line if two lines are parallel. Equal angles are formed by the matching angles.
Angles that are vertically opposed to one another are equal when two lines intersect.
Alternate angle: When two lines are parallel, a third line forms a z-angle, which is an equal angle to the parallel lines.
Complementary angle - When two angles add up to 90 degrees, they are considered to be complementary angles.
Angle x and angle y are supplementary angles. True.
Angle w and angle z are a linear pair. True.
Angle w and angle y are adjacent angles. False.
Angle x and Angle z are vertical angles. False.
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What is JL?
Right triangle J K L has K as its right angle. A segment connects K to M on side J L. Angle J M K is a right angle. K M equals 6 and J M equals 8.
JL =
Answer:
Step-by-step explanation:
To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.
Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:
JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)
KL = KM = 6
Finally, to find JL, we can use the Pythagorean theorem:
JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)
So, JL = 2√(13).
Jack Tupp, an auto parts dealer, earns 15% commission on his first $2,000 in
auto part sales, and 5% on the balance. Jack sold earned $5,975 worth of
auto parts last week. How much commission did Jack make?
Answer: Jack made $898.25 in commission
Step-by-step explanation:
Jack made $898.25 in commission. ($2,000 x 15%) + ($3,975 x 5%) = $898.25
[tex]5975-2000=3975[/tex] this is the amount jack earns 5% commission on
susan climbed 18 trees throughout each forest in her county. each forest is the same size. is this sample of the trees in the county likely to be representative?
Yes, this sample of the trees in the county likely to be representative if each forest is the same size.
What is representative sample?Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.
For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.
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Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (1, 9) and (8, 8).
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }[/tex]
Pls show your work thank you will mark the Brainliest
Answer D
Step-by-step explanation:
Two numbers are co-prime if they do not have any prime factors in common.
List all possible numbers that are co-primes with the following numbers that are < 50:
(a) 390
(b) 210
(c) 49335
On solving the provided question, we can say that Here, 21 and 22 only share a single element, which is 1. Since they are co-prime factor, their HCF equals 1.
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
21 and 22:
1, 3, 7, and 21 are the factors of 21.
1, 2, 11, and 22 are the factors of 22.
Here, 21 and 22 only share a single element, which is 1. Since they are co-prime, their HCF equals 1.
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Please help (will mark as brainlest)
Answer:
(9y + 4)(5x + 7)
Step-by-step explanation:
Sin (x-30)*cos (x/2) >0
Answer:
15
Step-by-step explanation:
Find the indicated side of the
triangle.
b
30°
12
a = -
Answer:
Find the indicated side of the
triangle.
b
30°
12
a = -
Step-by-step explanation:
A composite figure is shown.
Which of the following represents the total area of the figure?
A. 222 cm2
B. 240 cm2
C. 258 cm2
D. 294 cm2
The total area of the composite figure is 258 squared centimeters.
What is the area of the composite figure?The figure in the diagram is composed of two triangle and a rectangle?
The area of a triangle = 1/2 × base × height
Area of a rectangle = length × width
From the diagram;
Triangle 1
base = 4cmheight = 12cmTriangle 2
base = 12cmheight = 3cmRectangle
length = 18cmwidth = 12cmTo find the area of the composite figure, we find the area of the two triangle and rectangle and add.
Area = area of triangle 1 + area of triangle 2 + area of rectangle.
Area = ( 1/2 × base × height ) + ( 1/2 × base × height ) + ( length × width )
Area = ( 1/2 × 4 × 12 ) + ( 1/2 × 12 × 3 ) + ( 18 × 12 )
Area = ( 2 × 12 ) + ( 6 × 3 ) + ( 18 × 12 )
Area = 24 + 18 + 216
Area = 258cm²
Therefore, the area is 258 squared centimeters.
Option C) 258cm² is the correct answer.
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Answer:
258cm^2
Step-by-step explanation:
A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of multiplication problems to total problems?
Answer as a fraction in simplest form.
Answer: 1/3
Step-by-step explanation: The ratio of multiplication problems to total problems is 12:36, which can be simplified to 1:3.
Answer:
A
Step-by-step explanation:
Hi there.
We know this math exam has 12 multiplication and 24 division problems, making the overall exam questions 36 problems. (12+24=36)
The ratio is the fraction equivalent comparison between two variables. In this case, it's multiplication problems over total problems.
We know multiplication problems as 12, and we calculated the total, which is 36.
The answer would be 12/36; but it's divisible by 12 and can be further simplified to 1/3.
the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4. what are the coordinates of k?
Given that, the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4.
The coordinates of the point k are (9,10)
The concept of section formula asserts that if a line segment is divided into two pieces in a certain ratio, the coordinates at the point of division may be obtained using the formula:
(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = K
where (x1, y1) and (x2, y2) are the line segment's endpoint coordinates, and m:n is the provided ratio by which the line segment is divided.
The ends of the line segment IJ in this example are I(3,5) and J(17,19), and the ratio by which it is divided is 3:4, implying that IK:JK is 3:4.
As a result, m:n = 3:4, implying that m = 3 and n = 4.
When we enter these values into the formula, we get:
K = (3 x 17 + 4 x 3)/(3+4), (3 x 19 + 4 x 5)/(3+4)
When we simplify this expression, we get:
K = ( 51 + 12)/(7), (57 + 20)/(7)
K = (63)/(7),(77)/(7)
K = 9,10
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Select the correct answer.
What is the value of x in the triangle?
7√3
60°
OA. 21
OB. 10
O C.
C. 7
O D. 7√3
30%
Nathan was bored. He went outside to find something to do. His mother was planting flowers. Nathan offered to help her. They planted flowers from 2:40 p.m. until 5:10 p.m. They talked and had a good time together. How long did Nathan and his mother work together?
Answer: 2 hours and 30 minutes
Step-by-step explanation:
Your friend hides a dollar bill under one of three plastic cups. Under the other
two cups is a paper clip. You get to keep whatever is under the cup you
choose, but you don't know which contains the dollar bill. After you choose,
your friend lifts one of the other cups to reveal a paper clip and then gives you
the option of changing your choice.
Should you switch to the other cup?
A. No. The probability of winning the dollar is regardless of the cup
your choose.
B. Yes. If you switch cups, the probability of winning the dollar
increases from to 1/1.
OC. Yes. If you switch cups, the probability of winning the dollar is 3.
D. No. If you switch cups, the probability of winning the dollar is.
Answer: B
Step-by-step explanation:
